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New concepts for organic Rankine cycle power systems

I sistemi di conversione dell'energia termica basati sul concetto di Organic Rankine Cycle (ORC) si stanno diffondendo rapidamente vista la loro flessibilità in termini di taglia e temperature operative, che li pongono tra le opzioni più promettenti per lo sfruttamento di sorgenti di energia distribuite e con caratteristiche molto variabili come quelle rinnovabili. Questa tesi raccoglie alcuni contributi dell'autore nel campo della ricerca sui sistemi ORC, proponendo: (i) delle metodologie di progetto innovative a livello di componenti (e.g., il turboespansore), o di sistema (e.g., per considerare le prestazioni dinamiche del sistema fin dalle prime fasi del suo progetto); (ii) dei concetti originali; e alcuni studi di natura più fondamentale circa la fluidodinamica dei composti organici usati come fluidi di lavoro nei moderni impianti ORC.

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Tesi di Dottorato, Politecnico di Milano, Anno Accademico 2014

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New Concepts FOR Organic Rankine Cycle Power Systems Emiliano I.M. Casati 2014 New concepts for organic Rankine cycle power systems Proefschrift ter verkrijging van de graad van doctor aan de Technische Universiteit Delft, op gezag van de Rector Magnificus prof. ir. K. C. A. M. Luyben, voorzitter van het College voor Promoties, in het openbaar te verdedigen op maandag 29 september 2014 om 12.30 uur. door Emiliano I.M. CASATI Energy Engineer ''Politecnico di Milano geboren te Milano, Itali¨e Dit proefschrift is goedgekeurd door de promotoren: Prof. dr. P. Colonna Prof. dr. V. Dossena Samenstelling promotiecommissie: Rector Magnificus voorzitter Prof. dr. P. Colonna Technische Universiteit Delft, promotor Prof. dr. V. Dossena Politecnico di Milano, Itali¨e, promotor Prof. dr. F. Scarano Technische Universiteit Delft Prof. dr. H. Spliethoff Technische Universit¨at M ¨unchen, Duitsland Prof. dr. R. Martinez-Botas Imperial College London, Verenigd Koninkrijk Prof. dr. S.J. Song Seoul National University, Zuid-Korea Prof. dr. A. Guardone Politecnico di Milano, Itali¨e This research is supported by the Dutch Technology Foundation STW, Applied
Science Division of NWO, the Technology Program of the Dutch Ministry of
Economic Affairs (grant # 11143), and the Italian Ministry of Education, Univer-
sity, and Research. ISBN 978-94-6259-330-5 Copyright c 2014 by E.I.M. Casati 1 Front cover image from: The Direct Acting Solar Engine, F. Shuman, 1907 -
Review Publishing & Printing Company - Philadelphia. All rights reserved. No part of the material protected by this copyright notice
may be reproduced or utilized in any form or by any means, electronic or me-
chanical, including photocopying, recording or by any information storage and
retrieval system, without the prior permission of the author. 1Author e-mail address: e.i.m.casati@tudelft.nl and emilianocasati@gmail.com Dedicated to my beloved Alice we waited long enough for this book to be written . . . Table of Contents 1 Introduction 1 1.1 Energy Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 I Innovative Concepts 9 2 ORC Power Systems: from the Concept to Current Applications and an Outlook to the Future 11 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2 Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.3 State of the art . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.3.1 Technical options . . . . . . . . . . . . . . . . . . . . . . 28 2.3.2 Energy conversion applications . . . . . . . . . . . . . . 32 2.4 Future scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.4.1 Heat Recovery from Automotive Engines . . . . . . . . . 39 2.4.2 Domestic CHP . . . . . . . . . . . . . . . . . . . . . . . 41 2.4.3 Ocean Thermal Energy Conversion - OTEC . . . . . . . . 41 2.4.4 Concentrated Solar Power - CSP . . . . . . . . . . . . . . 42 2.4.5 Other applications . . . . . . . . . . . . . . . . . . . . . 42 2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3 Centrifugal Turbines for ORC Applications 57 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.2 Preliminary Design Method . . . . . . . . . . . . . . . . . . . . . 60 3.2.1 Mean-line Design Tool for ORC Turbines . . . . . . . . . 60 3.2.2 Optimization Procedure . . . . . . . . . . . . . . . . . . 61 i 3.3 Centrifugal Architecture for ORC applications . . . . . . . . . . . 62 3.4 Analysis of the Centrifugal Architecture . . . . . . . . . . . . . . 64 3.5 Design of Exemplary 1 MWe Machines . . . . . . . . . . . . . . 68
3.5.1 Design Assumptions . . . . . . . . . . . . . . . . . . . . 68 3.5.2 Design Methodology . . . . . . . . . . . . . . . . . . . . 69 3.5.3 Results: Transonic Turbine . . . . . . . . . . . . . . . . . 71 3.5.4 Results: Slightly Supersonic Turbine . . . . . . . . . . . 73 3.6 Design of Exemplary 10 kWe Machines . . . . . . . . . . . . . . 75
3.6.1 Design Assumptions . . . . . . . . . . . . . . . . . . . . 75 3.6.2 Design Methodology . . . . . . . . . . . . . . . . . . . . 77 3.6.3 Results: Transonic Turbine . . . . . . . . . . . . . . . . . 78 3.6.4 Results: Slightly Supersonic Turbine . . . . . . . . . . . 78 3.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4 Thermal Energy Storage for Solar Powered ORC Engines 89 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 4.2 Siloxanes: High-Temperature ORC Working Fluids . . . . . . . . 91 4.3 Concepts of TES Systems for Power Plants . . . . . . . . . . . . 93 4.4 Direct Storage of Working Fluid in Rankine Power Stations . . . . 95 4.4.1 Storage Methods . . . . . . . . . . . . . . . . . . . . . . 95 4.4.2 Discharge Methods . . . . . . . . . . . . . . . . . . . . . 96 4.4.3 Storage Systems . . . . . . . . . . . . . . . . . . . . . . 96 4.5 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 4.5.1 Working Principle . . . . . . . . . . . . . . . . . . . . . 98 4.5.2 Flashing Rankine Cycles with Organic Fluids . . . . . . . 100 4.5.3 Flashing the Organic Vapor Down to Saturated Conditions 101 4.5.4 Design Analysis Results . . . . . . . . . . . . . . . . . . 101 4.5.5 Dynamic Modelling . . . . . . . . . . . . . . . . . . . . 102 4.5.6 Control Strategy . . . . . . . . . . . . . . . . . . . . . . 102 4.5.7 Dynamic Analysis Results . . . . . . . . . . . . . . . . . 103 4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 A.1 Comparison Between Flashing and Evaporative Organic Rankine Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 A.2 Complete Flash Evaporation as a Working Condition for ORC Power Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 A.3 System Components Dynamic Modelling . . . . . . . . . . . . . 111
Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 ii 5 Design Methodology for Flexible Energy Conversion Systems Ac- counting for Dynamic Performance 121 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 5.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 5.2.1 Multi-Objective Design Optimization . . . . . . . . . . . 123 5.2.2 Assessment of Dynamic Performance . . . . . . . . . . . 124 5.3 Case of Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 5.4 System Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . 126 5.4.1 Preliminary ORC Power Plant Design . . . . . . . . . . . 126 5.4.2 Dynamic Modeling . . . . . . . . . . . . . . . . . . . . . 129 5.4.3 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . 133 5.4.4 The DYNDES Tool . . . . . . . . . . . . . . . . . . . . . 134 5.5 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . 139 5.5.1 Multi-objective Design Optimization . . . . . . . . . . . 139 5.5.2 Assessment of Dynamic Performance . . . . . . . . . . . 140 5.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 6 Design of CSP Plants with Optimally Operated Thermal Storage 149 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 6.2 Modeling Framework . . . . . . . . . . . . . . . . . . . . . . . . 153 6.3 Operation Strategy . . . . . . . . . . . . . . . . . . . . . . . . . 156 6.3.1 Reference Operation Strategy . . . . . . . . . . . . . . . 156 6.3.2 Optimal Control . . . . . . . . . . . . . . . . . . . . . . 156 6.4 Computational Infrastructure . . . . . . . . . . . . . . . . . . . . 157 6.5 Results & Discussion . . . . . . . . . . . . . . . . . . . . . . . . 157 6.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 6.7 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . 163 A.1 Solar Fields Design . . . . . . . . . . . . . . . . . . . . . . . . . 163 A.2 Financial Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 166 A.3 Modelica and Optimica listings . . . . . . . . . . . . . . . . . . . 168 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 iii II Fundamental Aspects 175 7 Flexible Asymmetric Shock Tube (FAST): Commissioning of a High Temperature Ludwieg Tube for Wave Propagation Measurements 177 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 7.2 Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 7.3 The FAST Set-Up . . . . . . . . . . . . . . . . . . . . . . . . . . 180
7.3.1 Working Principle . . . . . . . . . . . . . . . . . . . . . 181 7.3.2 Vapour Generator . . . . . . . . . . . . . . . . . . . . . . 182 7.3.3 Reference Tube . . . . . . . . . . . . . . . . . . . . . . . 184 7.3.4 Charge Tube . . . . . . . . . . . . . . . . . . . . . . . . 185 7.3.5 Fast Opening Valve . . . . . . . . . . . . . . . . . . . . . 185 7.3.6 Low Pressure Plenum . . . . . . . . . . . . . . . . . . . 185 7.3.7 Condenser and flow return pipe . . . . . . . . . . . . . . 187 7.4 Data Acquisition and Control system . . . . . . . . . . . . . . . . 187
7.4.1 Vapour generator control . . . . . . . . . . . . . . . . . . 187 7.4.2 Reference Tube control . . . . . . . . . . . . . . . . . . . 187 7.4.3 Charge Tube control . . . . . . . . . . . . . . . . . . . . 188 7.4.4 Low Pressure Plenum control . . . . . . . . . . . . . . . 188 7.4.5 Data Acquisition . . . . . . . . . . . . . . . . . . . . . . 188 7.5 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
7.5.1 Tightness characterization . . . . . . . . . . . . . . . . . 188 7.5.2 Valve Opening Sequence . . . . . . . . . . . . . . . . . . 189 7.5.3 Wave Speed Measurements . . . . . . . . . . . . . . . . . 193 7.6 Conclusions & Future Work . . . . . . . . . . . . . . . . . . . . 196 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 8 Nonclassical Gasdynamics of Vapour Mixtures 203 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 8.2 Admissibility Region for Rarefaction Shock Waves in Dense gas
Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206 8.3 Nonclassical Gasdynamics Behaviour of Dense Gas Mixtures . . . 212 8.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 A.1 iPRSV-WS Thermodynamic Model . . . . . . . . . . . . . . . . 219 9 Conclusions & Perspectives 229 iv Summary 235 Samenvatting 239 Acknowledgements 243 About the Author 245 List of publications 247 v 1 Introduction Chapter 1 1.1 Energy Scenario Energy provision is one of the major challenges for the Human Society, and it
is increasingly clear that the current production/consumption model is not sus-
tainable, due to the wake of consequences induced by the exhaustion of fossil
energy resources: global climate change, local pollution, and diffused geopoliti-
cal disorders. According to the Energy Technology Perspectives report published
by the International Energy Agency in 2012 (ETP-2012)1, global energy demand
has nearly doubled since 1980, driving up energy-related greenhouse gas (GHG)
emissions, which amount now to the 68% of the anthropogenic total. If current
trends will continue unabated, a further 85% rise is expected by 2050, leading
the world down the path towards a 6 oC rise in average global temperature during
the same period, with potentially devastating results regarding climate change,
long-term energy security, and, finally, our survival. The ETP-2012 introduced the so-called 2DS scenario, which identifies tech- nology options and policy pathways ensuring an 80% chance of limiting the global
temperature increase to 2 oC by 2050. According to the study, this figure is com-
patible with a sustainable future. Achieving the 2DS will require extensive transformation of the energy sys- tem, aiming at cutting energy-related GHG emissions in half by 2050 compared
to 2009. The message is clear: different energy systems deliver very different
futures. People and governments must choose what future they want, and start
building the appropriate energy system now if that future is to be realized. Furthermore, a collective effort is required in every aspect, since no single fuel, technology or sector can deliver a dominant proportion of the necessary
emissions reduction. Accordingly, the 2DS reflects a concerted effort to reduce
overall consumption and replace fossil fuels with a mix of renewable and nuclear
energy sources. It is discussed how substantial opportunity exists to increase en-
ergy savings, efficiency and know-how across sectors and technologies, such as
those between heat and electricity, or among transport and industry applications.
This sustainable energy system is foreseen to be smarter, more decentralised and
integrated. In the author''s opinion, energy conversion systems based on the organic Rank- ine thermodynamic cycle (ORC) have the potential to play a major role in this
envisaged framework. ORC power plants are one of the most proven solutions for
the exploitation of external 2 thermal sources in the power-output range from, say, 1Energy Technology Perspectives''ETP2012. Technical report, International Energy Agency, 2012. 2External with respect to the power system, as opposed to the internal combustion encountered 2 Introduction few kWE, up to tens of MWE. Furthermore, the cogeneration of thermal power
can usually be accomplished in a fairly straightforward way. In ORC power converters, a phase-changing organic compound is adopted as the evolving fluid which, following the working principle defining the Rankine
cycle, allows to exploit a given source in order to convert part of its energy content
into useful outputs, such as, e.g., mechanical, electrical, and thermal energy. The global diffusion of ORC power systems grew at a fast pace during the last 20 years, primarily thanks to the intense academic research effort which ac-
companied this idea since its early days. The possibility of tailoring the working
fluid and the operating thermodynamic conditions to the application at hand of-
fers important advantages. Higher conversion efficiency, lower cost and improved
compactness of the system can be attained by limiting the specific work in the
expansion process, and/or by reducing the irreversibility produced during thermal
power transfers. The ORC energy converters are extremely flexible in nature, and able to ex- ploit a virtually infinite variety of thermal sources. At the same time, this poses
great challenges from the design point of view. Innovative concepts can be de-
vised drawing from the fundamentals of the working fluid behavior, passing to the
component- and up to the system-level of detail, but the corresponding general-
ized design methodologies have to be concurrently developed and integrated. The
work documented in this thesis aims at contributing to these topics, by presenting
the original results of numerical and experimental research investigating the po-
tential of molecularly heavy and complex organic compounds as working fluids
for the ORC power systems of the future. 1.2 Thesis Outline This thesis is composed of two main parts, in turn constituted by self-contained
chapters, each addressing a specific sub-topic. The collected material forms the
basis of several publications on peer-reviewed international journals: five papers
are already published, one has been accepted for publication, and two are about
to be submitted for publication. The first part illustrates several advancements in the field of energy conversion
systems, with a focus on ORC turbo-generators. A more detailed description of in, e.g., gas turbines. 3 Chapter 1 the chapters follows. Chapter 2 presents an introductory review on ORC systems, with an overview of
their history, the description of the state-of-the-art from both the academic and the
industrial perspective, and an outlook to envisaged paths of development. The cumulative global capacity of ORC power systems is undergoing a rapid growth, which started a decade ago, in accordance with recent developments in
the energy conversion scenario. The potential for the conversion into electricity
of the thermal power coming from liquid-dominated geothermal reservoirs, waste
heat from primary engines or industrial processes, biomass combustion, and con-
centrated solar radiation is arguably very large. ORC power systems are one of the
most flexible conversion technologies, in terms of capacity and temperature levels,
for these energy sources, and are currently often the only applicable conversion
technology in many applications. In addition, they can co-generate heating and/or
cooling. Related research and development is therefore extremely lively. Firstly, basic elements on the thermodynamic cycle, working fluid, and design aspects are introduced, together with an evaluation of advantages and disadvan-
tages in comparison to competing power systems. An overview of the long history
of the development of ORC technology follows, in order to place the more recent
evolution into perspective. A compendium of the many aspects of the state of the
art is then illustrated by reviewing the engineering solutions currently adopted in
commercial power plants, the main-stream applications, together with information
about exemplary installations. An outlook on the many research and development
activities is provided, whereby information on new high-impact applications such
as automotive heat recovery is included. Possible directions of future develop-
ments are highlighted, ranging from efforts targeting volume-produced stationary
and mobile mini-ORC systems with a power output of few kWE, up to large base-
load ORC power plants. Chapter 3 documents the original research conducted in the field of ORC turbo-
expanders. As a matter of fact, these are the most critical components when effi-
cient ORC power systems have to be designed. The variety of possible working
fluids, the complex gas dynamics phenomena encountered, and the lack of sim-
plified design methods based on experience on similar machines, make the design
of efficient ORC turbines a complicated task. Relevant paths of development may thus be concerned with (i) the devel- opment of generalized design methodologies, and (ii) the assessment of non-
conventional machine architectures: the research presented in this chapter aims 4 Introduction at exploring both. The first critical evaluation of the centrifugal or radial-outflow
turbine (ROT) architecture as a candidate technology for ORC turbo-generators is
presented, together with a novel methodological framework for the design of these
machines. The developed tools can be of help for the designer of ROT machines,
for virtually any power-output. The first part of the chapter deals with the design of comparably large size turbines, i.e. in the MWE power output range, which is the power output typical
of present industrial applications. The second part of the chapter is devoted to the
assessment of the down-scaling potential of the ROT architecture, considering its
implementation in the promising field of mini-ORC turbo-generators, i.e., systems
with power output of the order of 10 kWE. The results show that the radial-outflow
turbine is a promising concept for future ORC power systems, since it allows for
the realization of efficient, compact, and reliable turbo-expanders in the investi-
gated power-output range. Chapter 4 deals with the assessment of a novel thermal storage system tailored
to high-temperature ORC systems for concentrating solar power (CSP) applica-
tions, stemming from the observation that the direct storage of the ORC working
fluids can be effective thanks to their favourable thermodynamic properties. The
feasibility of energy storage is of paramount importance for solar power systems,
to the point that it can be the technology enabler. The interest for highly effi-
cient and modular concentrated solar power plants of small to medium capacity
(5 kWE ''5 MWE) is growing: ORC power systems stand out in terms of efficiency, reliability and cost-effectiveness in such power-range. The concept of complete flashing cycle (CFC) is introduced as a mean of achieving an unmatched system layout simplification, while preserving conver-
sion efficiency. This is a new variant of the Rankine cycle, originally introduced
by the presented research, whereby the vapour is produced by throttling the or-
ganic working fluid from liquid to saturated vapour conditions. The discussion of a case study follows: a 100 kWE CFC turbo-generator with direct thermal energy storage, coupled with state-of-the-art parabolic trough col-
lectors. A dynamic model, developed for the complete system, is used to inves-
tigate the performance under extreme transient conditions. By adopting a rela-
tively simple and robust control strategy, the storage system is demonstrated to
be effective in decoupling the solar field and the ORC power block, which can
thus be operated close to nominal conditions notwithstanding the environmental
disturbances. The feasibility of remotely controlled operation is thus positively
assessed by means of this preliminary study. 5 Chapter 1 Chapter 5 presents a methodology conceived to help in the definition of the opti-
mal design of power generation systems. The innovative element is the integration
of requirements on dynamic performance into the procedure. Operational flexi-
bility is an increasingly important specification of power systems for base- and
part-load operation. Thus, it is crucial to discard, in an early phase of the design
process, plant configurations which feature unacceptable dynamic performance. The test case is the preliminary design of an off-grid power plant serving an off-shore platform, where one of the three installed gas turbines is combined with
an organic Rankine cycle turbo-generator in order to increase the overall energy
efficiency. At the top level of the procedure is a stationary model, capable of
performing the on-design thermodynamic cycle calculation, and the design of the
main components of the system. The results of these simulations are used within
the framework of a multi-objective optimization procedure to identify a number
of equally optimal system configurations. A dynamic model of each of these system designs is automatically parameter- ized, by inheriting its parameters values from the optimization results. Dynamic
simulations of selected reference transients allow then to discriminate among the
initial set of solutions, thus providing the designs that also comply with dynamic
requirements. Chapter 6 introduces a new methodology aimed at assessing the potential of
optimal control techniques in the context of thermal energy storage management
for concentrated solar power (CSP) plants. These systems present the possibility
of integrating a thermal energy storage able of sustaining several hours of full-
load operation in the absence of solar radiation. However, usually adopted design
software tools assume a short-sighted strategy for storage management. The novel
design method is applied to a test case, a state-of-the-art central receiver plant with
direct storage, using molten salts as working fluid, and operating in a context of
variable electricity prices. The system modelling and optimization problems are formulated and imple- mented using modern high-level modelling languages, thus demonstrating the po-
tential of the approach. Different operating strategies are compared based on a
detailed financial analysis. A wide system design space is considered, and the re-
sults are presented for all the foreseeable combinations of solar field size and stor-
age system capacity. The proposed method is an additional decision tool allowing
to treat the storage operation strategy as a new relevant variable in the design of
next generation energy systems. Notably, this could be of particular interest for 6 Introduction ORC-based CSP systems operating in the envisaged distributed generation sce-
nario, possibly cogenerating thermal power for heating or cooling purposes. The second part of this thesis presents the contribution regarding the experimental
and numerical investigation the non-classical gas dynamics behavior of dense va-
pors of single- and multi-component organic fluids. A more detailed description
of the chapters appearing in this part of the work follows. Chapter 7 describes the commissioning of the Flexible Asymmetric Shock Tube
(FAST) experimental setup designed and built at the Delft University of Technol-
ogy. The aim of this Ludwieg Tube facility is to measure the speed of propaga-
tion of pressure waves in organic vapors, with the final objective of providing the
first experimental evidence of the most exotic non-classical gas dynamics phe-
nomenon, i.e., the rarefaction shock wave (RSW) in the dense vapor region of
fluids formed by complex organic molecules. The facility operates at temperatures and pressures of the order of 400' C and 10 bar, respectively. A fast opening valve induces a rarefaction propagation in the
tube, which is sensed by using dynamic pressure transducers. The equipment and
measurement methodology are described in detail. The fast opening valve is char-
acterized in terms of its opening time, which is proven to be small enough to allow
for the detection of the RSW. The results regarding a shock wave forming in air
are presented, and used to demonstrate and validate the setup capabilities. Prelim-
inary expansion measurements in D6 siloxane are also presented, being of special
interest to the end of the envisaged non-classical gas dynamics experiments. Chapter 8 presents the first investigation about the non-classical gas dynam-
ics of binary mixtures of organic fluids in the vapour phase. Differently from
mixtures of ideal gases, thermodynamic properties of dense vapours of multicom-
ponent mixtures do not scale linearly with the mole fractions of each compound,
as molecular interaction among different molecules plays a major role. The fun-
damental derivative of gas dynamics ', being a derived thermodynamic property,
is also affected by non-ideal mixing effects. In addition, experiments on the ther-
mal stability of siloxane mixtures, and a deeper understanding on the chemistry
of thermal decomposition of these compounds, show that, at temperatures close
to the so-called temperature stability limit, a pure siloxane undergoes a rearrange-
ment transformation, whereby small quantities of other compounds of the same
family are formed. 7 Chapter 1 The composition of the mixture is therefore a new relevant variable in the study of BZT fluids, and, importantly, such mixtures are also considered as work-
ing fluids for ORC power systems, one of the possible applications of non-classical
gas dynamics. A predictive thermodynamic model is used to compute the relevant mixture properties, including its critical point coordinates and the local value of '. The
considered model is the improved Peng-Robinson Stryjek-Vera cubic equation of
state, complemented by the Wong-Sandler mixing rules. A finite thermodynamic
region is found where the non-linearity parameter ' is negative, and therefore non-
classical gas dynamics phenomena are admissible. A non-monotone dependence
of ' on the mixture composition is observed in the case of binary mixtures of
siloxane and perfluorocarbon fluids, with the minimum value of ' in the mixture
being always larger than that of its more complex component. The observed dependence indicates that non-ideal mixing has a strong influ- ence on the gas dynamics behaviour''either classical or non-classical''of the
mixture. Numerical experiments of the supersonic expansion of a mixture flow
around a sharp corner show the transition from the classical configuration, exhibit-
ing an isentropic rarefaction fan centred at the expansion corner, to non-classical
ones, including mixed expansion waves and rarefaction shock waves, if the mix-
ture composition is changed. 8 Part I Innovative Concepts 2 ORC Power Systems: from the Concept to Current Applications and an Outlook to the Future Part of the contents of this chapter will appear in: ''ORC Power Systems: from the Concept to Current Applications
and an Outlook to the Future'
P. Colonna, E. Casati, T. Mathijssen, C. Trapp, J. Larjola,
T. Turunen-Saaresti, & A. Uusitalo
J Eng Gas Turb Power, Submitted for Publication (2014) Chapter 2 Abstract The cumulative global capacity of Organic Rankine Cycle (ORC) power
systems for the conversion of renewable and waste thermal energy is undergoing
a rapid growth, which started a decade ago, in accordance with recent develop-
ments in the energy conversion scenario. It is estimated that the power capacity
of all these types of power plants currently adds up to at least 2, 000 MWE. The
potential for the conversion into electrical or mechanical power of the thermal
power coming from liquid-dominated geothermal reservoirs, waste heat from pri-
mary engines or industrial processes, biomass combustion, and concentrated so-
lar radiation is arguably very large. ORC power systems are one of the most flex-
ible conversion technologies in terms of capacity and temperature level of these
energy sources, and are currently often the only applicable conversion technology
for external thermal energy. In addition, they are suitable for the cogeneration of
heating and/or cooling, another advantage in the framework of distributed power
generation. Related research and development is therefore extremely lively. These
considerations motivated the effort documented in this chapter, aimed at providing
consistent information about the evolution, state, and likely future of this power
conversion system. Firstly, basic theoretical elements on the thermodynamic cy-
cle, working fluid, and design aspects are introduced, together with an evaluation
of advantages and disadvantages in comparison to competing technologies. An
overview of the long history of the development of ORC power systems follows, in
order to place the more recent evolution into perspective. A compendium of the
many aspects of the state of the art is then illustrated by reviewing the engineering
solutions currently adopted in commercial power plants, the main ''stream appli- cations, together with information about exemplary installations. An outlook on
the many research and development activities is provided, whereby information on
new high-impact applications such as automotive heat recovery is included. Pos-
sible directions of future developments are highlighted, ranging from efforts tar-
geting volume-produced stationary and mobile mini ''ORC systems with a power output of few kWE, up to large base ''load ORC power plants such as, e.g., for ocean thermal energy conversion '' OTEC. 2.1 Introduction The concept of an engine based on the Rankine thermodynamic cycle, whereby
the fluid is an organic compound instead of water (see fig. 2.1a''2.1b) originates
from two main observations [1''3]: ' if the selection of the working fluid is an additional degree of freedom for the design of the thermodynamic cycle, the fluid can be chosen such that it 12 ORC Power Systems: History, Status, Perspectives is optimal from both a thermodynamic and a technical point of view. The
properties of the fluid, e.g., the properties at the vapor-liquid critical point,
the saturation line, and the specific heat directly affect how well the tem-
perature profile of the thermal energy source and sink can be matched by
the corresponding cycle heating and cooling processes, see, e.g., figs. 2.1c''
2.1d. The conversion efficiency of the power system, aside from the ef-
ficiency of the expander, strongly depends on the exergy loss in both the
primary heat exchanger and the condenser. Furthermore, cycle configura-
tions that are not possible if water is the working fluid, can be contemplated:
the supercritical cycle configuration is possible even if the thermal energy
source is at low temperature. As for the advantages with respect to techni-
cal aspects, it is notable that: (i) the fluid pressure and density levels within
the system can be selected, to a certain extent, independently from the cycle
temperatures (for example, relatively low fluid temperature in the evapora-
tor can correspond to high pressure, and vice versa), (ii) effective thermal
energy regeneration can be realized by means of one single non-extractive
de-superheating process, (iii) for the majority of the organic Rankine cycle
(ORC) working fluids, the expansion process is completely dry, thus blade
erosion issues in turbines, and inherent expansion inefficiency due to con-
densation are avoided, (iv) several ORC working fluid are also suitable as a
lubricant for rotating machinery, thus further simplifyng the system. ' For low power output, from few kWE up to few MWE, the realization of an efficient, reliable, and cost-effective steam expander is challenging: the
volumetric flow is extremely small, the expansion ratio comparatively large,
and the specific work over the expansion is also very large, thus the design
of a simple axial or radial turbine is problematic and the efficiency bound to
be low. Steam volumetric expanders in turn must be complex, as challeng-
ing lubrication issues must be dealt with, and the net expansion efficiency
is heavily affected by blow-by and friction losses. Water cannot effectively
lubricate, therefore it must be mixed with a lubricant, which decreases ther-
modynamic efficiency, and can thermally decompose if it flows through the
evaporator. In addition, for several applications, the freezing temperature
of water is too high, and the very low pressure in the condenser can lead
to unfeasibly large dimensions of this component. If the working fluid is
organic, the much smaller enthalpy decrease of the expanding vapor allows
to design an expander, be it a turbine [2, 4, 5] or a positive displacement
machine (e.g., screw, scroll, vane, or piston expander) [6], featuring a lower
rotational speed and higher volumetric flow for a given power output. 13 Chapter 2 Summarizing, the selection of the working fluid affects at the same time the thermodynamic performance of the system, and the design of all its components.
For a detailed treatment, the reader is referred to Ref. [7]. For example, if the
thermal energy source features a relatively small potential and a rather high-
temperature (say 2 MWT, and Tsource > 300 oC), the selection of a fluid formed by complex molecules (large specific heat) yields to a slightly superheated and
regenerated cycle as the corresponding optimal cycle configuration. The rela-
tively large volume flow due to the small enthalpy drop over the expansion allows
for the design of an efficient and simple turbine, with sufficiently large flow pas-
sages. In particular, the small specific expansion work allows also to limit the
number of stages (e.g., 2 or 3), and the resulting rotational speed may be 10 '' 20 times smaller compared to a steam turbine for the same operating conditions. The
dominant need of reducing the number of stages, this increasing their pressure
ratios, together with the low values of the sound speed of the expanding organic
vapor, leads in most cases to the acceptance of highly supersonic flows, at least
in the first stator, which therefore requires special care in the fluid dynamic de-
sign. Depending on the condensing temperature, the volume flow at the outlet
of the turbine can be large, thus requiring a comparatively bulky regenerator and
condenser. As a consequence, cost issues related to the heat transfer equipment
might arise. Additional challenges ensue in case vacuum conditions have to be
managed. Conversely, the overall low maximum pressures in the system can be
beneficial as far as the cost of the evaporator and safety issues are concerned. It
is also notable that regeneration positively affects the thermal efficiency of the cy-
cle, but negatively affects the temperature at which the heat source can be cooled
(limited by the temperature of state 3 in figure 2.1a), thereby the amount of ther-
mal power that can be converted into mechanical power. Similar reasoning can
be applied to other applications, e.g., low- and medium-temperature geothermal
energy conversion, leading to different results. The working fluid is also subjected to a number of other constraints, which can be more or less stringent depending on the application, namely the fluid should be ' non-toxic, non-flammable, non-corrosive, and cost-effective, ' characterized by a low or zero Global Warming Potential (GWP) and Ozone Depletion Potential (ODP), ' thermally stable and compatible with all the containing and sealing materi- als up to the cycle maximum temperature, ' possibly a good lubricant, featuring also good heat transfer properties, 14 ORC Power Systems: History, Status, Perspectives ''0.6 ''0.4 ''0.2 0 0.2 0.4 0.6 0.8 50 100 150 200 250 300 T em p er a tu re [' C ] Entropy [kJ/kg K] Fluid saturation line ORC process Regeneration process 5 4 6 3 1,2 (a) (b) 0 500 1000 1500 2000 2500 3000 3500 50 100 150 200 250 300 T em p er a tu re [' C ] Thermal power [kW] Working fluid Heat source (c) 0 500 1000 1500 2000 2500 3000 50 100 150 200 250 300 T em p er a tu re [' C ] Thermal power [kW] Working fluid Heat source (d) Figure 2.1: The processes forming an exemplary superheated/regenerated Organic Rankine cycle
power plant in the T '' s thermodynamic plane of the working fluid 2.1a, together with the corre- sponding process flow diagram 2.1b. 2.1c: Q '' T diagram of the ORC evaporator, assuming that the energy source is flue gas at 300 oC, compared to the Q '' T diagram of the boiler of a simple steam power plant 2.1d having as energy input flue gas at the same conditions. 15 Chapter 2 ' if used for generator cooling, an electrical insulator and compatible with the adopted resin. With reference to high-temperature applications, one remarkable deficit of cur-
rently adopted working fluids (hydrocarbons, siloxanes, perfluorocarbons) is their
thermal stability in contact with typical containing materials, which sets the peak
cycle temperature threshold at around 350 oC, depending on the specific fluid,
and on additional technical, operational and cost-related constraints. These are
the frequency of fluid charge substitution, the level of fluid purity, the level of
plant sealing, and the dearation requirements in the low-pressure part of the plant.
Ideally, an organic fluid which would not thermally decompose (in contact with
stainless steel) at temperatures up to 500 '' 600 oC would substantially increase the conversion efficiency in some applications. So far the highest thermal stability
in realistic operating conditions was reported for a mixture of pentafluorobenzene
and hexafluorobenzene [8]. The fluid underwent dynamic thermal tests at temper-
atures up to 468 oC, and no decomposition was observed during the 532 hour test.
The fluid is claimed to feature low toxicity in case of acute and subacute expo-
sures, but products of thermal decompositions of perfluorocarbons are chemically
aggressive and possibly highly toxic [9]. These exemplary considerations show that the design of an optimal system is a complex problem, possibly leading to multiple technical solutions, with dif-
ferent equipment selection, each with its advantages and disadvantages. With
reference to the example previously illustrated, the selection of a working fluid
made of simpler molecules would result in a faster-rotating and smaller turbine,
possibly affected by lower efficiency, and requiring reduction or power electron-
ics for the coupling to the electrical generator. In turn, the adoption of such a
fluid could eliminate the need for a regenerator, and entail a more compact and
super-atmospheric condenser. One of the main and unique advantages of ORC power systems is that the technology is applicable to virtually any external thermal energy source,1 with
temperature differences between thermal source and sink ranging from approxi-
mately 30 to 500 oC [10]. ORC systems are therefore technically suitable for the
conversion of renewable or renewable-equivalent energy sources such as ' geothermal reservoirs (liquid-dominated or steam-dominated, whereby the steam is too contaminated to be directly expanded in a turbine), ' solar radiation, 1External with respect to the power system, as opposed to the internal combustion of reciprocat- ing engines or gas turbines. 16 ORC Power Systems: History, Status, Perspectives ' biomass combustion, ' industrial waste heat recovery, ' urban solid waste, and landfill gas combustion, ' heat recovery from other prime movers (reciprocating engines, gas turbines, fuel cells, etc.), ' ocean thermal gradient. Other advantages of ORC systems are: ' the overall simplicity of the plant configuration, ' the reliability and durability of slow-rotating expansion devices, ' the possibility of using common stainless steel (or in some cases aluminum) as construction material, thanks to the low peak system pressure and tem-
perature, and to the non-corrosive nature of the working fluids. This feature
can be compared, for instance, with materials required for high-temperature
water, gas turbines, or Stirling engines. The graph of figure 2.2 synthetically shows the current relation between the temperature of the energy source and the power capacity of ORC power systems
vs steam power plants. The graph refers either to systems that are commercially
available, or to those currently under development or studied. Notably, the state
of the art is quickly evolving, therefore figure 2.2 has been adapted here in order
to account for the fact that the boundary of ORC technology applications is ex-
panding toward the region of conventional steam power plant applications. This
chart might need to be updated in few years. If large-capacity high-temperature energy conversion systems are excluded from the comparison (primarily therefore steam power plants), competing tech-
nologies for the conversion of the mentioned energy sources are in principle the
Stirling engine, the Closed Brayton Cycle (CBC) power plant, and the externally-
fired gas turbine (EFGT). For low-temperature energy sources, e.g., geothermal
reservoirs or heat recovery, the Kalina cycle power plant [12] is also a potential
competitor, though power plants based on this concept are at a lower develop-
ment stage vs. ORC power systems, and face difficulties due to inherently higher
complexity [13]. Conventional Stirling engines can operate at a sufficient level of efficiency only if the thermal energy source is at high temperature (indicatively 700 ''1100 oC), 17 Chapter 2 W [kW e] T A V sour ce [ o C ] 10 1 10 2 10 3 10 4 10 5 0 100 200 300 400 500 Steam ORC-based OTEC M ic ro- O R C C H P sys te m s ORC fluid thermal stability limit Mainstream ORC systems Figure 2.2: Current and future fields of application of ORC vs Steam power systems in terms
of average temperature of the energy source, Tav.,source, and plant power capacity. Boundaries are
indicative, and evolving in time. Adapted from Ref. [11]. therefore they are developed mainly for high-temperature solar conversion [14,
15], biomass and biogas combustion [16], and domestic micro-cogeneration [17]
for a power range from 1 kWE up to several tens of kWE. The necessarily com-
plex kinematic mechanisms, and the challenging high-temperature sealing re-
quirements for the typically leak-prone working fluids (Helium, Hydrogen, Nitro-
gen, Air) have so far hampered the reliability of the systems being developed. Or-
ganic working fluids have been proposed for high-pressure/moderate-temperature
Stirling engines [18], but no actual development is known to the authors. High
power density, high net conversion efficiency (the world record is 31.25 % [19])
and possibly low cost, if large-series production is envisaged, are positive features
of Stirling engine technology. Developments of medium-capacity CBC power plants are related to systems employing carbon dioxide2 as working fluid [20], and they have been initially
proposed for next-generation nuclear power plants [21]. As previously illustrated,
CO2, being a simple molecule, is arguably unsuitable for the design of low power
output expanders. The development of medium-capacity (10 '' 50 MWE) super- critical CO2 CBC power plants is now actively pursued in combination with high- 2Note that Carbon Dioxide is an organic compound, as it contains carbon, therefore systems based on supercritical CO2 thermodynamic cycles entailing working fluid condensation, as it is the
case in some proposed configurations, qualify as supercritical Organic Rankine Cycle systems. 18 ORC Power Systems: History, Status, Perspectives temperature solar tower technology [22], and very high conversion efficiency at
moderate peak cycle temperature is possibly attainable (approximately 50 % at
750 oC). The EFGT concept is proposed for biomass combustion or gasification [23], and for high-temperature solar conversion [24], the main challenge being the high-
temperature at which the primary heat exchanger must operate. Prototypes so far
achieved limited efficiency, and issues of reliability still need to be solved. Fossil-fuel fired ORC systems compete with fuel cells, micro-gas turbines, Stirling and reciprocating engines for innovative applications, like micro-cogeneration
of heat and power (CHP) for apartments and houses [25]. Domestic cogeneration,
that is the use of small CHP systems in place of conventional gas or diesel boilers,
can be beneficial in terms of fuel utilization in countries with cold or moderate
climate. Research and development of ORC technology has been receiving an ever in- creasing impulse starting from the beginning of this century, together with a rapid
increase of the installed power capacity, and the number and diversity of applica-
tions. This work stems from the need for a reasoned synthesis about the evolution
of this technology (sec. 2.2), its state-of-the-art (sec. 2.3), and an outlook toward
the future (sec. 2.4), thus providing information on both commercial applications
and active research topics. 2.2 Evolution The idea of using a fluid different from water in a Rankine cycle for power con-
version is rather old. As early as 1826, Thomas Howard patented the concept
of an engine using ether as the working fluid [26]. Among the low-boiling pres-
sure fluids, several inorganic substances were considered and tested throughout
the years, with limited success. This short review is limited to Rankine engines
employing organic fluids. Probably the first organic working fluid used commer-
cially in Rankine cycle engines is naphtha. A patent of Franck W. Ofeldt [27]
is at the basis of several ORC engines adopting a reciprocating expander fed by
a naphtha vaporizer and powering launches, see Fig. 2.3a. Naphtha was used as
fuel, working fluid and lubricant, allowing to avoid the cost of the specialized op-
erator needed for steam engines, because of the much lower evaporation pressure
in the boiler. The Gas Engine & Power Company of New York claimed in 1890
to have sold five hundred ORC engines based on the Ofeldt design [28]. Simultaneously in Europe (1888), a British inventor by the name of Alfred Yarow also developed a naphtha-based ORC engine for launches [31]. One of 19 Chapter 2 (a) (b) Figure 2.3: Earliest ORC engines. 2.3a: engine of the Ofeldt naphta launch, 1897. Fuel is
pumped from the tank in the bows by air pressure, generated by a hand pump, and passes through a
coil boiler. Part of the vapour issuing from the boiler is fed to the burner that heats the boiler itself,
and the rest drives a three-cylinder engine. The long U-tube at the bottom is the condenser [29].
2.3b: Shuman''s solar ORC-based pumping system prototype installed in Philadelphia (US-PA),
1907. The the flat solar collector is also visible. It was called the hot box, with double glazing
containing the blackened pipes acting as the vapor generator [30]. these engines, built by the Swiss company Esher Wyss AG (later to become
Sulzer), reached a certain notoriety as it propelled the Mignon, the boat that Al-
fred Nobel launched in 1891 [32]. Even if the boiler was operated at a pressure
lower than that of steam engines, the early days of ORC engines were affected by
several accidents [33]. Frank Shuman, in 1907, was probably the first who had the idea of a solar ORC engine: he used a flat solar collector of about 110 m2 to boil ether at tem-
peratures around 120 oC and drive a 2.6 kWM engine, see also Fig. 2.3b [34]. Ro-
magnoli in 1923 used water at 55 oC to boil ethyl chloride and run a 1.5 kWM en-
gine [7, 35]. Professor Luigi D''Amelio (1893-1967), chair of thermal and hydraulic ma- chinery at the University of Naples, is possibly the father of modern ORC tech-
nology. In 1936, his work on a solar power plant for irrigation based on an ORC
engine using monochloroethane as working fluid [36] won him a prize of 10,000
Lire.3 A series of 3 cm-deep vessels full of water would receive solar radiation, 3The prize was awarded by the Libyan governatorate of Italy and the National Association of Combustion Control. Such solar ORC plant would have been used to pump water in the arid areas
of North Africa. 20 ORC Power Systems: History, Status, Perspectives Table 2.1: Specifications of the first solar ORC power plant proposed by Prof. L. D''Amelio in
1935, as reported in Ref. [36]. Working fluid C2H5Cl Surface of solar collectors 270 m2 Evaporation temperature 40 oC Evaporation pressure 2.7 bar Condensation temperature 23 oC Condensation pressure 1.3 bar Turbine isentropic efficiency 0.65 Net power output 4 kWM Net conversion efficiency 0.035 thus heating the water up to about 60 oC. The water is circulated to a shell and
tube evaporator where the working fluid is heated and evaporated in small pipes
at approximately 40 oC. The vapor is expanded in an impulse axial turbine stage,
and generates mechanical work. The monochloroethane vapor is condensed at
23 oC, and the liquid pumped back to the evaporator. The design specifications
of the plant are reported in table 2.1. The estimated thermal conversion efficiency
was about 3.5 %. The cited monograph outlines for the first time all the main
principles of ORC system and turbine design, notably including the selection of
the working fluid among several candidates, see also Refs. [37, 38]. In 1939, these
ideas were implemented in a 2.6 kWM prototype for the conversion of low-grade
geothermal energy which was commissioned and operated successfully in a labo-
ratory of the University of Naples [39]. The experience gained with the prototype
led to the realization of an 11 kWM geothermal ORC pilot power plant on the
island of Ischia in 1940. A second power plant of 250 kWM based on the same
technology was built in 1943 but was never operated [40]. After the second world
war, D''Amelio resumed his studies on the ORC concept, and his work presented
at the first conferences on solar energy received considerable attention [41, 42]. The first commercially operated geothermal ORC power plant, a so-called bi- nary power plant, was briefly operated at Kiabukwa, in the Democratic Republic
of Congo, in 1952 [43]. It featured a power capacity of 200 kWE, utilized geother-
mal water at 91 oC as heat source, and it supplied power to a mining company. The
second oldest geothermal ORC power plant was commissioned at Paratunka in
the Kamchatka peninsula in 1967 [43, 44]. It was a pilot plant exploiting geother- 21 Chapter 2 mal water at 85 oC, rated at 670 kWE, and using refrigerant R12 as the working
fluid [45]. It provided a small village with electricity and greenhouses with heat-
ing. Dr. Lucien Bronicki met Prof. D''Amelio during his PhD studies in the late 50''s in Paris4 and started to study the application of the ORC principle to small
solar power plants [46]. He and made an important contribution by outlining for
the first time the relation between the working fluid and the design of the expander
in an article published on an international journal [1]. In the 60''s, perfluorocar-
bons were studied by other authors as working fluids for mini-ORC turbines [47].
Several experimental solar ORC systems have also been reported. These adopted
static non-focusing collectors, thus achieving comparatively low maximum cycle
temperature (around 100 oC), and solar-to-electric efficiency (typically < 5 %).
Furthermore, also during the 60''s, few ORC-driven systems for the pumping of
water for irrigation or desalination purposes have been documented [34]. In these years, Dr. Bronicki and his group designed, built, and tested several small solar ORC units (2 ''10 kWE) with monochlorobenzene as the working fluid. These systems featured inlet fluid temperatures of the order of 150 oC. Some of
these plants have been reported as having run for 12 years without repairs [48].
In 1972, they realized a highly unconventional 0.4 kWE unit powered by a ra-
dioisotope, featuring a much higher TIT, and thus a cascaded cycle configuration
was adopted, employing different working fluid in the top and bottoming cycle
systems [49]. The group then succeeded in deploying the results of these studies
in the first commercial application of mini-ORC turbogenerators, i.e., the power-
ing of remote telecommunication stations and of the auxiliaries of gas pumping
stations [50]. The most important requirement was reliability in order to allow for
a very long operation without maintenance service, while conversion efficiency
was not so relevant (about 5 %). The first units of this type (3 kWE), using
monochlorobenzene as the working fluid, were operational in 1961. In the pe-
riod between 1961 and 1988, thousands of these small ORC turbogenerators were
installed. The power capacity ranges from 0.2 to 6 kWE, the working fluid is
commonly dichlorobenzene, or more rarely trichlorobenzene, due to the need of
high thermal stability, being the working fluid directly heated by combustion flue
gases. These systems pioneered the high-speed hermetic turbogenerator solution:
the radial-inflow turbine and the generator are directly coupled and enclosed in
a single sealed canister. Journal bearings support the shaft, using the working
fluid as a lubricant and coolant, without additives. The generator is a solid-rotor
brushless alternator: The three-phase output of the alternator is connected to the 4June 2013, personal communication. 22 ORC Power Systems: History, Status, Perspectives rectifier feeding the load. The electrical output terminals reach the outside of the
assembly thanks to ceramic feed-throughs. The high boiling point of the work-
ing fluid enables returning the condensate by gravity without the need for a feed
pump. The stainless steel evaporator is of the once-through type, and the con-
denser is naturally air-cooled in order to avoid moving parts. The recuperator is
tube-in-shell [46, 51]. In more recent years, photovoltaic panels substituted mini-
ORC turbogenerators for these applications. In 1975, Prigmore and Barber presented the first results of a research activ- ity aimed at coupling an array of solar flat-plate collectors, a 1 kWE ORC tur-
bogenerator using R113 as the working fluid, and a compression chiller for air
conditioning. The evaporation and condensation temperatures were equal to 93
and 35 oC, respectively, the efficiency of the ORC module was 7 %, and the sys-
tem overall COP approximately 0.5 [52]. The possibility of reaching maximum
cycle temperatures higher than 300 oC by adopting focusing collectors (mainly
linear), has been investigated in the late 70''s: a prototype was tested at Sandia
National Laboratories in New Mexico, in combination with parabolic trough col-
lectors to heat a thermal oil loop powering an ORC turbogenerator of 32 kWE, and
also supplying space heating and cooling with an absorption air conditioner [53]
. Also in the US, from 1976 to 1984, the Jet Propulsion Laboratory developed a
power system using parabolic dishes coupled with an ORC power module. The
cavity receiver was designed to heat toluene at approximately 400 oC and 42 bar.
The rotating parts (single-stage impulse turbine, centrifugal pump, and alternator)
were mounted on a single shaft rotating at 60,000 rpm. The same working fluid
was also used for bearing lubrication. A solar-to-electric conversion efficiency of
18 % was measured, with a power output of 16 kWE, thus lower than the design
value, due to test conditions [54]. ORC power systems have been adopted also in combination with solar ponds, whereby a temperature gradient is established in a water basin by an artificially in-
duced salinity-gradient. An experimental 5 MWE Solar Pond Power Plant (SPPP)
was operated from 1983 to 1990 in Beit Ha''aravah, Israel [55]. A 200 kWE SPPP
operated from 1986 to 2002 at temperatures as low as 65 oC in El Paso, Texas,
USA [56]. The first experimental geothermal cascading ORC power plant was called Magmamax, and it was located in East Mesa, Imperial valley, California [43].
Its initial design was very ambitious, as it was based on two interconnected ORC
power plants. The topping cycle utilized isobutane as the working fluid, while
the bottoming cycle adopted propane. The plant was commissioned in 1979, and
was rated at 12.5 MWE gross power (and 11 MWE net). Though it went through 23 Chapter 2 a number of operational problems and changes, it paved the way for the follow-
ing generations of geothermal power plants. After two other small experimental
geothermal ORC power plants [56], in 1984 the company founded by Dr. Bron-
icki commissioned its first commercial ORC power plant for the conversion of
geothermal energy in Wabuska, Nevada, featuring a capacity of 700 kWE [56]. As a consequence of the oil crisis of the late 70''s, many other units for geother- mal power plants manufactured by several companies followed, while also the
capacity of these plants gradually increased toward the multi-MWE range. The
working fluids were mainly light hydrocarbons, chlorobenzenes, and chloro-fluoro-
carbons (CFC). In this period, few ORC power plants were used also for the con-
version of other renewable energy sources, like industrial waste heat and engine
exhaust gases. The largest of these plants was built in Japan at Mitsui Engineer-
ing & Shipbuilding, featuring a power output of 15 MWE [57]. As a result of
rising concerns about air pollution, followed by rising fuel prices during the oil
crisis, investigations on the use of Rankine engines for automobiles started in the
70''s [58, 59]. Both steam and organic compounds were considered as working
fluids, with either a turbine or a piston expander. A 30 kWE prototype was suc-
cessfully tested as bottoming cycle on a long-haul truck [8, 60], but never made it
to the commercial market. In the 80''s, intense research and development activity
occurred also in East Germany, Finland, France, Japan, Israel, Italy, USSR. In
the US, notable developments were related to five 600 kWE units for industrial
heat recovery [61], and to a concept for electricity generation for the international
space station [62, 63]. Particularly relevant are the studies carried out in Italy during the 60''s and the 70''s by Prof. Gianfranco Angelino, one of the fathers of modern ORC power
systems technology, together with his colleagues at Politecnico di Milano, Prof.
Mario Gaia and Prof. Ennio Macchi. Their work was important also because it
helped laying the scientific and technical basis for research and development [2].
An example of the application of these investigations is documented in a study
presented by Bado and colleagues, a 35 kWE perfluorocarbon (C8F16) unit pro-
viding a net electric conversion efficiency of 19 % at condensing and collectors
cooling loop exit temperature equal to 40 and 300 oC, respectively [64]. Such unit
was subsequently built and tested, and a net efficiency of 17 % was recorded at a
turbine inlet temperature of approximately 270 oC [65, 66]. In these first proto-
types, axial turbines were directly coupled to an asynchronous generator rotating
at 3,000 rpm. Notable is the Borj Cedria 12 kWE solar power station in Tunisia,
which was commissioned in 1983. The working fluid was tetrachloroethylene, and
during field tests a net electrical efficiency of 11 % was recorded, with evaporation 24 ORC Power Systems: History, Status, Perspectives and condensation temperatures equal to 84 and 20 oC, respectively [67]. Based on
these studies, a company was established in 1980 by Gaia. The company was ini-
tially involved in the realization of experimental solar and geothermal ORC power
plants adopting various working fluids and single or multi-stage axial turbine [2].
Studies on the use of siloxanes as working fluids for high-temperature ORC power
systems were conducted in collaboration with Angelino and co-workers [63, 68].
The first biomass-fuelled turbogenerator, which was later to determine the com-
mercial success of the company, was commissioned in Bi`ere, Switzerland, in
1998 [11]. It was a skid-mounted 300 kWE genset, using siloxane MDM as the
working fluid, and featuring a 2-stage axial turbine. The plant was ordered by the
Swiss army in order to provide electricity and cogenerated heat to a barrack. In Finland, Prof. J. Larjola led the development of high-speed hermetic turbo- generators in the hundreds kWE range, in which the turbine, generator and pump
share the same shaft. One of the first applications of this type of ORC turbogener-
ator was the use as the charger of the batteries of a deep-see submersible [69]. The
hermetic turbogenerator configuration was similar to the early mini-ORC units for
remote power applications [70, 71]. The knowledge acquired with these develop-
ments was later utilized in commercial units that were marketed starting from the
early 2000''s [72]. Information concerning operational ORC power plants referred to the period before 1995 are collected in Ref. [3], containing also data from Ref. [73], which in
addition covers earlier years. During the 1980''s, however, fossil fuel prices were
relatively low: this led to most of the experimental plants being shut down because
economics were not attractive. The main data related to the majority of the plants
that have been commercially operated after 1995 are shown in Table 2.2. Fig. 2.4
presents a quantitative assessment of the the evolution of installed ORC power
plants in the same period, in terms of both cumulated power and number of units. 25 Chapter 2 Ins t. U ni ts [- ] Ins t. P ow er [M W e ] 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 0 5 10 15 20 25 0 200 400 600 800 1000 1200 1400 1600 Figure 2.4: Commercial ORC power plants commissioned between 1995 and the end of 2013,
based on the data reported in Tab. 2.2: number of units installed (solid line), and cumulated power
capacity (dashed line). 26 O R C
P o
w e r
S y
s t e m
s
: H
i s t o
r y
, S t a t u
s
, P e r
s p e c t i v
e s Manufacturer Country Output Out. cogen ''T Working Energy Turbine Turbine inlet N Year Ref kWE kWT '' o C Fluid source type/Nstgs Tmax, oC Pmax , bar units commiss. Atlas Copco (') CA 2100 '' R134a WH rad. in/1 na na 1 2012 TR 22500 '' n-Butane G rad. in/1 na na 2 2013 DE 3600 '' iso-Butane G rad. in/1 na na 1 2014 TR 22500 '' n-Butane G rad. in/1 na na 2 2015 Exergy (IT) TR 1000 '' FC B rad. out/na na na 2 2012 [74, 75] IT 1000 '' HC G,B na na 2 2013 IT,FR 100 '' 1000 '' RE,FC,SIL WH,B na na 4 2014 IT,TR 1200 '' 12000 '' HC WH,G rad. out+axial/na na na 7 2015 GE Energy (US) na 125 '' R245fa B rad. in/1 121 17.2 > 100 2009 '' 2011 [76] GE Oil & Gas (IT) CA 17000 '' Cyclo-pentane WH rad. in/2 250 1 2012 [77, 78] BN '' 1 2014 CN,TH '' 4 2015 Ormat (US) US,Vars. 400 '' 3500 '' n-Pentane G axial/1 '' 4 105 '' 170 na 67 1995 '' 1999 [79, 80] 2000 '' 15000 '' G,S 140 '' 180 na 144 2000 '' 2013 300 '' 6500 '' WH 110 '' 180 na 19 1999 '' 2013 Tri-O-Gen (NL) Vars. 80 '' 160 '' Toluene WH rad. in/1 325 32 21 2009 '' 2013 [72, 81] 135 '' 160 '' B 6 2012 '' 2013 Table 2.2: Overview of the main characteristics of commercial ORC power plants commissioned
after 1995, data from official companies'' websites and personal communications [TO BE COM-
PLETED - MISSING DATA]. For older data see, e.g., Refs. [3, 73]. Countries of installation are
indicated with ISO 3166 Codes. FC: (per)fluorocarbons, HC: hydrocarbons, RE: refrigerants, SIL:
siloxanes. Out. cogen ''T : thermal power cogenerated '' delivery temperature. Energy source: B = biomass, G = geothermal, S = Solar, and WH = waste heat. Nstgs: number of turbine stages. ''Vars''
stands for ''various'', and ''na'' for ''not available''. 2 7 Chapter 2 2.3 State of the art A brief description of the most commonly adopted technical options encountered
in commercially available systems is provided here. A sequential and iterative
design process is often carried out in the order in which these technical solutions
are presented. The design of one system component strongly depends on the oth-
ers, therefore a trend toward an increasingly integrated and automated approach
is pursued [82''84]. The number of possible combinations of the technical solu-
tions applicable at system and component level is very large, and it explains why,
even for similar specifications, the units that have reached commercial status can
differ considerably. As it was in other sectors of the power field, after a period
in which a relatively large variety of products compete for the market, evolution
may reduce this diversity in the future, at least for a given application. 2.3.1 Technical options The selection of the available solutions for the design of a system and its compo-
nents depends on the initial specifications, which most often are: ' Type of thermal energy source, average power capacity, and average tem- perature ' Available/usable cooling fluid (water or air) and its average temperature ORC modules can exhibit a certain level of standardization up to a power capacity of 2 '' 3 MWE, while larger power units, like those of larger geothermal power plants, are highly customized. Cycle configuration and working fluid As discussed in Sec. 2.1, the design decision about the cycle configuration and
the working fluid is closely coupled, and it has consequences on the choice of
the expander and its design [2]. Currently, saturated 5 and superheated cycle
configurations are common, while the supercritical cycle configuration has been
implemented only in few cases [74, 85]. Two and three pressure levels in the
evaporator have been adopted only in large geothermal power plants in order to
substantially reduce the average temperature difference between the geothermal 5In case the expander is a turbine, a small degree of superheating at the turbine inlet and through- out the expansion is needed in order to avoid droplets impact against the rotor. 28 ORC Power Systems: History, Status, Perspectives and the working fluid [86]. The supercritical cycle configuration might be opti-
mal from a purely thermodynamic point of view, but the power consumption of
the main feed pump becomes very large. Table 2.3 lists the working fluids that are
most commonly employed, together with their main properties. In general, fluids
formed by more complex molecules are suitable for high-temperature applications
(e.g. siloxanes, toluene), and small-medium power capacity, while those formed
by simpler molecules (e.g. refrigerants, alkanes) are adopted in low-temperature
applications, and are suitable also for large power output. Table 2.3: Main properties of the most diffused working fluids in current ORC plants, see
also Tab. 2.2. MW: molecular weight, Tboil: normal boiling temperature, pvap@80'C: vapour
pressure at 80 oC. MDM: octamethyltrisiloxane, MM: hexamethyldisiloxane, PP5: Perfluorode-
calin, PP2: perfluoro-methylcyclohexane, r245fa: 1,1,1,3,3-Pentafluoropropane, r134a: 1,1,1,2-
tetrafluoroethane. Data from Ref. [87]. Fluid Chemical MW TCR pCR ρCR Tboil pvap@80'C name formula [g mol''1] [oC] [bar] [kg m''3] [oC] [bar] toluene C7H8 92.1 318.6 41.26 278.8 110.6 0.389 cyclo-pentane C5H10 70.1 238.5 45.15 272.6 49.2 2.522 iso-pentane C5H12 72.1 187.2 33.78 215.7 27.8 4.575 iso-butane C4H10 58.1 134.7 36.29 224.6 -11.8 13.438 MDM C8H24Si3O2 236.5 290.9 14.15 302.9 152.5 0.091 MM C6H18OSi2 162.4 245.5 19.39 292.9 100.2 0.537 PP5 C10F18 462.0 291.9 17.88 565.0 140.7 0.133 PP2 C7F14 350.0 211.9 20.60 574.7 75.8 1.152 r245fa C3H3F5 134.0 154.0 36.51 489.3 15.1 7.893 r134a C2H2F4 102.0 101.1 40.59 545.6 -26.1 26.332 Rotating equipment In case of larger power plants, one of the advantages related to the selection of
an optimal organic working fluid is that it is possible to design an efficient tur-
bine for rotational speeds that allow for direct coupling to a synchronous gen-
erator (3,000/1,500 rpm if the grid frequency is 50 Hz, or 3,600/1,800 rpm if it
is 60 Hz). If this is not possible or wanted, reduction gears can then be used.
The shaft seal demands for special attention, especially if the working fluid is
used for lubrication, in order to avoid excessive leakage. Oil is often used in a
dedicated bearings system for the shaft, especially in slow-rotating turbines and
pumps, whereby mechanical seals are adopted for the shaft. The expander, elec-
trical generator, and feed pump can rotate independently from one another, or, in 29 Chapter 2 some cases and for systems rated at hundreds of kWE, they can share the same
shaft [72, 76, 81]. The so-called high-speed hermetic turbogenerator assembly
allows to enclose the rotating equipment into a single casing and use the working
fluid as bearings lubricant and generator coolant. In addition, thanks to the use
of an inverter, the rotational speed of the turbine can be varied in order to match
the machine optimum efficiency at the given operating condition. However, the
consequent high-rotational speed of the feed-pump leads to its highly sub-optimal
operation. Expander. ORC expanders are currently dynamic (turbines) in the vast ma- jority of the cases, while volumetric (screw, scroll) expanders are in the pre-
commercial or market-introduction phase. Turbo-expanders cover the power ca-
pacity (from about 100 kWM to several MWM), expansion ratio (approximately
from 5 to 100), and inlet temperature ( '' 120 to '' 350 oC) ranges typical of current commercial ORC power systems. Volumetric expanders derived from refrigerant
compressors are employed only in the low-temperature and low-capacity power
systems (1 to about 100 kWM) which are now being proposed to the market. An
exception are the 1 MWE screw expanders that have been recently installed in
a low-temperature geothermal power plant in New Mexico [88]. The maximum
volumetric expansion ratio of volumetric expanders currently prevents their use in
high temperature systems. These machines feature lower isentropic efficiency if
compared to turbo-expanders, which in turn are not yet available with a power out-
put of few kWE. Screw and scroll expanders can be cost-effective because they are
derived from volume-produced refrigerant compressors. A distinguishing techni-
cal feature is that they can tolerate a fraction of liquid working fluid. Ref. [89]
provides an overview on the main aspects of volumetric expanders for small ORC
power systems. ORC expanders are in general different from other common ma-
chines expanding steam, air or other gases, because dense vapor properties deviate
largely from ideal gas behavior, thus affecting the design, and because the speed
of sound is much lower than in light gases or steam [90''92]. Axial turbines are commonly adopted for medium to large power output ORC systems (several hundreds kWE to several MWE) in single or multi-stage arrange-
ment (currently up to four in large-capacity units). The isentropic efficiency in
nominal conditions typically goes from 80 % to less than 90 %. In case of smaller-
capacity systems (up to 200 kWE), the radial inflow configuration is preferred be-
cause it allows to achieve high efficiency with one single stage, even in case of
large expansion ratio/high TIT. The optimal rotational speed in these cases can be
of the order of several tens of thousands rpm. A two-stage radial inflow turbine
configuration has been recently implemented in a large ORC power plant [77]. 30 ORC Power Systems: History, Status, Perspectives Systems based on turbines adopting the multi-stage radial outflow configurations
have been recently successfully commercialized [75]. The first ORC scroll expanders proposed to the market are either semi-hermetic or hermetic, the power output varies from 1 to 10 kWE, the volumetric expansion
ratio is at maximum 4-5, while the rotational speed is between 1,500 and 6,000
rpm [93]. Screw expanders are in a slightly more advanced stage of development, and their power output reaches several hundreds kWE. They feature either the sigle-
screw or the double-screw configuration, and the maximum expansion ratio is
slightly larger than that of scroll machines (5-6) [89]. Their rotational speed can
be as high as 10-12,000 rpm in the smaller machines. Bearings. Conventional oil bearings are typically used in case the electrical generator is external to the turbine casing. If the working fluid has good lubri-
cant properties, especially designed bearings are adopted, thus simplifying the
turbine/generator assembly. These are often of the tilted pad type due to the high
rotordynamic stability they offer. The high-speed hermetic turbogenerator assem-
bly configuration also demands for special bearings, either magnetic, or lubricated
with pressurized working fluid [57, 76, 94]. Magnetic bearings are utilized in
some units that are in the initial commercialization phase with low turbine inlet
temperature. The implementation of this technology in higher-temperature sys-
tems requires additional study. Pump. The power consumption of an ORC pump is comparatively larger than that of the pump of a steam power plant, being the ratio of the specific pump work
to the specific turbine work larger. For this reason, even though standard centrifu-
gal water pumps are often adapted for the use in mainstream ORC systems, some-
times ad hoc pumps must be employed in order to achieve sufficient compression
efficiency. The cost and comparatively low efficiency of multi-stage pumps is one
of the main reasons why the supercritical cycle configuration is currently seldom
adopted [86]. Heat Exchangers Evaporator / Primary heater. The primary heat exchanger/evaporator can be of
the once through type [2, 72], or the shell and tube type, having the working fluid
typically in the shell side [95, 96]. Thermal energy can be transferred directly
from the heat source (flue gas, hot waste stream, geothermal reservoir, solar radi-
ation) to the working fluid, or indirectly via an intermediate thermal loop. Direct
heating allows for higher temperature and pressure in the evaporator, while indi-
rect heating demands for additional pumping power, thus direct heating implies 31 Chapter 2 higher net conversion efficiency. The choice among the two solutions depends
on many aspects: avoidance of hot spots that increase the risk of working fluid
decomposition, ease of control, safety regulations, and contractual issues. In case
of high-temperature applications, and if the working fluid is more expensive than
the diathermal oil, lowering the temperature of the working fluid is a way of de-
creasing the frequency of working fluid charge substitution, thereby lowering the
operating costs. Regenerator. The adoption of a regenerator depends on the working fluid, and optimal cycle configuration [83]. In some cases, the thermodynamic advantage
can be quite limited, but the adoption of the regenerator can help reducing the size
of the condenser, which is often a significant cost component. In smaller capacity
ORC power plants, the regenerator can be of the finned tube or plate type, thus
being very compact. In larger power plants, the regenerator is more often of the
shell and tube type. In any case, regenerators selection must account for a limited
pressure drop on the vapor side, which directly affects the turbine outlet pressure,
and thus its power output. This becomes a critical aspect if the condenser operates
at very low pressure. Condenser. Depending on the availability and regulations, water-cooled con- densers are preferred because of the higher achievable net efficiency of the power
plant. Wet cooling is also adopted if the ORC power plant cogenerates distric or
process thermal energy or if it powers an absorption chiller or refrigerator. De-
pending on the system capacity, compact heat exchangers are more commonly
adopted in low-power output systems, while shell and tube are adopted in larger
power plants. Direct air cooling is seldom adopted, because it considerably in-
creases the working fluid inventory, while air-coolers with an intermediate wa-
ter/glycol loop is the most frequently adopted technical solution. 2.3.2 Energy conversion applications The current applications of ORC power plants are listed here in order of rele-
vance in terms of presently installed power capacity. ORC power systems are
either the preferred or the only technology that can be adopted for the conver-
sion into electricity of several types of relevant thermal renewable energy sources.
For example, arguably most of the high temperature vapor-dominated geothermal
reservoirs are already exploited, while the potential of liquid-dominated ones is
still very large [43]. Similarly, in case of biomass combustion, the optimal plant
capacity is mainly limited by the cost of fuel gathering. In both cases, the flex-
ibility in terms of temperatures and scalability makes ORC power systems often
more attractive than steam power plants. This is testified by the steadily increasing 32 ORC Power Systems: History, Status, Perspectives number of ORC power plants being commissioned all over the world. Geothermal Reservoirs ORC power plants around the world are used mainly for the conversion of liquid-
dominated reservoirs at temperature of 120 '' 150 oC, though examples of op- erational plants fed by a mixture of steam and brine at higher temperature exist
(Zunil Guatemala - 20 MWE, Ribeira Grande I and II in San Miguel, Azores -
14 MWE, Olkaria III, Kenya - 13 MWE, and Oserian, Kenya - 1.8 MWE) [96].
The goethermal fluid usually contains also a substantial amount of incondensible
gases, which might form corrosive compounds. In case of two-phase geothermal
fluid, the steam and the brine are separated, and the steam is used to evaporate
the organic working fluid, while the brine is used for liquid working fluid preheat-
ing. The saturated cycle configuration with an alkane as a working fluid is the
most common. Sometimes the system includes a regenerator. In case of a steam-
dominated geothermal reservoir of large capacity, whereby a steam power plant is
used as the high-temperature conversion system, an ORC power plant as bottom-
ing cycle results into an efficient combined cycle configuration [97]. Exemplary
plants of this type are the Upper Mahiao, Philippines (125 MWE), the Mokai 1
and 2, New Zealand (100 MWE), and the Puna, Hawaii (30 MWE) [96]. Solid biomass or biogas combustion High-temperature ORC power plants in the MWE power range fuelled with vari-
ous types of solid biomass have been installed at increasing pace in Europe start-
ing from the early 2000''s, thanks also to favorable legislation. More than 200
ORC gensets of this type are in operation. Most often these plants are integrated
into wood-manufacturing sites, and feature the CHP arrangement, whereby the
heat discharged by the ORC unit, at temperatures typically below 100 oC, is used
for process purposes, or district heating. Many of these power systems adopt a
superheated and regenerated cycle configuration, indirect heating, two, or in few
cases, three-stage axial turbines, and MDM as the working fluid. The rated net
electrical efficiency is usually in the 15 '' 20 % range, while the total energy ef- ficiency can be as high as 90 %. Information on exemplary biomass CHP power
plants of this type can be found in Ref. [98] related to a 1 MWE power plant in
Lienz, Austria, in Ref. [99] for the 1.1 MWE power plant in Tirano, Italy, and in
Ref. [100] for that in Ostrow Wielkopolski, Poland, rated at 1.5 MWE. 33 Chapter 2 Flue Gas from Gas Turbines or Gas Engines Several examples of ORC turbogenerators used to recover waste heat from the
exhaust of gas engines already exists [77, 78], and the number of these instal-
lations is also increasing. In cases in which the reciprocating engine or the gas
turbine is fed with biogas, the addition of an ORC heat recovery system is often
economically viable because of the subsidized value of the generated electricity. Industrial Waste Heat Opportunity for heat recovery in the manufacturing and process industry are count-
less. The majority of the thermal energy is wasted at temperatures between 60 and
400 oC, with a capacity that monotonically increases toward vast quantities at low
temperature.
Only recently this enormous potential has attracted interest, and few ORC power
plants recovering various forms of thermal energy otherwise wasted are now op-
erational, while many feasibility studies are performed. First examples of industrial waste heat recovery ORC power plants can be found in the cement industry [101]. Throughout the production of cement, about
34 '' 40% of the process heat is wasted to the environment, mainly via the ex- haust gases from the rotary kiln, coming from the limestone preheaters and also
from the ambient air used for clinker cooling [102]. Depending on the cement
plant configuration, and the process efficiency, waste heat streams are available at
temperatures between 215 and 380 oC [103, 104]. The first ORC heat recovery
system (1.5 MWE) in a cement factory was commissioned in 1998 at the Hei-
delbergCement AG plant of Lengfurt, Germany. Other successfull examples are:
the 4 MWE ORC power plant at A.P. Cement Works in India (2007), and the
2 MWE Ait Baha, Morocco, plant of Italcementi (2010) [101]. Similar plants
are under construction or commissioning: a 4 MWE ORC plant in Alesd (Roma-
nia), a 5 MWE plant in Rohoznik (Slovakia), and a 1.9 MWE plant in Untervaz
(Switzerland). In comparison to the quite standardized cement production, steel manufactur- ing requires quite diverse processes. The potential for heat recovery in the steel
manufacturing industry by means of ORC power systems has been recently stud-
ied, and especially heat recovery from the exhaust gas of Electric Arc Furnaces
(EAF) and rolling mills has been found promising [105]. One of the implemented
arrangement features an intermediate loop, whereby saturated steam at tempera-
tures around 300 oC is used in order to transfer the thermal energy of the furnace
off-gas to the ORC working fluid [106]. Currently, a 3 MWE unit is under con- 34 ORC Power Systems: History, Status, Perspectives struction at the EAF of Elbe-Stahlwerke Feralpi in Riesa (Germany) as part of the
European H-REII Demo project (Heat Recovery in Energy Intensive Industries). The glass industry also offers vast opportunities for waste heat recovery by means of indirectly heated ORC power systems. An intermediate heat transfer
loop can collect thermal energy from the hot gas exiting the oven that melts
and refines the raw materials. The exhaust gas temperatures are relatively high
(400 '' 500) oC [101]. Since 2012 one such system (1.3 MWE) is in operation at the AGC floating glass production site in Cuneo, Italy. Other examples of suc-
cessful ORC power plant installations for industrial heat recovery are at the urban
solid waste incinerator plant in Roeselare, Belgium (3 MWE), and at the sintered
magnesite production site in Radenthein, Germany (1 MWE). The Roeselare plant
receives thermal energy at approximately 180 oC from a pressurized water loop
transferring heat from the incineration furnace, and is a retrofit, because initially
the plant was supposed to provide only district heating. The ORC system adopts a
saturated configuration, axial turbine, synchronous generator, and Solkatherm as
the working fluid. Concentrated Solar Radiation The design paradigm of concentrated solar power (CSP) plants based on ORC
engines is mainly related to the choice of the maximum plant temperature [107].
High temperature entails increased conversion efficiency, but calls for compara-
tively expensive solar collecting equipment and power block. The complementary
approach consists in selecting a low maximum plant temperature which allows to
adopt simpler technological solutions, but leads to lower conversion efficiency,
which in turn demands for a larger solar field surface for a given power output.
The STORES project, in the US, has investigated a new paradigm for the success-
ful deployment of thermal solar plants: economy of production can be achieved
by means of high-volume manufacturing of small-capacity standard and modular
systems, suitable for distributed energy conversion, instead of larger centralized
power plants. ORC turbogenerators have been identified as the optimal conversion
technology in this context, because of their performance and reliability [108, 109].
The main outcome of the study has been the construction of the first solar plant of
this kind in the Saguaro Desert, Arizona (US). The plant, entered in operation in
2006, uses pentane as the working fluid and features a nominal power of 1 MWE,
with no need for onsite staff. The cycle efficiency is 21 % with inlet-turbine and
condensation temperatures equal to 204 and 15 oC, respectively. The reported
average annual solar conversion efficiency is 12 % [110]. 35 Chapter 2 2.4 Future scenarios Research and development activities are very lively because, together with the
constant technological improvement related to current applications, new high-
potential ones in the field of renewable energy and waste eat recovery are consid-
ered and actively studied and developed. The growth of the scientific and technical
interest in ORC power systems is testified by the increase of scientific literature in
this field, see Fig. 2.5. The sudden increase of the number of publications related
to ORC technology in the 80''s and after 2000 can be correlated to the increase of
oil prices, though the more recent trend is continuing notwithstanding the decrease
and stabilization of oil prices of more recent years. It can be argued therefore that
policy and strategic considerations are driving these studies. N of publ . (nor m .) [- ] 1980 1984 1988 1992 1996 2000 2004 2008 2012 0 0.2 0.4 0.6 0.8 1 En. Eng.
En. Eng. + ORC 190975 127 Figure 2.5: Number of published journal articles or conference papers, since 1980, in English.
Results within the subject areas engineering and energy (dashed line) and, among these, works
dealing with ORC power systems, i.e., with the acronym ORC appearing in the article title, abstract
or among the keywords (solid line). The data series are normalized with respect to the maximum
value, which is explicitly indicated in the figure [111]. Nowadays, the application showing the highest growth potential is arguably heat recovery at largely different capacity and temperature levels. All the appli-
cations of ORC power systems described in Sec. 2.3.2 are undergoing a fast-pace
growth, which will continue in the coming years, given the global turn toward
renewable energy, which is also happening in various countries in Asia. Waste
heat recovery by means of ORC power systems is actively researched in case of 36 ORC Power Systems: History, Status, Perspectives automotive engines (from few up to 10 '' 15 kWE net power output) and larger stationary reciprocating engines, but also as bottoming units for medium-size in-
dustrial gas turbines (up to about 20 MWE), especially those used as mechanical
drive in gas compression stations, and for power generation in the chemical and
oil industry. With reference to fig. 2.2, new applications of ORC power systems are located at the boundaries in terms of temperature and power capacities highlighted in the
chart. At power levels of few kWE, the conversion efficiency of low-temperature
ORC systems (Tav.,source . 130 oC) is probably inherently too low for economic viability, though the system is feasible. A number of research efforts are ongoing aimed at developing Rankine cycle- based heat recovery systems for passenger vehicle applications, with a number of
studies identifying ORC turbogenerators among the most promising solutions [112''
114]. If the energy source is at high temperature, i.e., Tav.,source . 450 oC, in the power range starting from hundreds kWE, both steam and ORC power systems
are feasible and various economic and technical consideration drive the selection,
though ORC power systems are more often selected. It is only recently that, at this
temperature range, ORC power systems are being developed at multi-megawatt
capacity level, while for larger power capacity ORC power systems cannot com-
pete with steam power plants. At medium temperatures of the energy source,
Tav.,source . 300 oC, but large power capacity (> several hundreds MWE), ORC power plants are studied for the heat recovery from large processing units in the
oil and gas industry [105], and other sectors of the chemical industry are also in-
terested. At low temperature level of the heat source, currently the only very large
energy source that is driving some developments in the power sector is the ther-
mally stratified water of tropical and equatorial ocean regions, whereby Tav.,source
is actually extremely low (see sec. 2.4.3). As for the most relevant research topics, the supercritical cycle configuration is receiving attention because its thermodynamic merit needs careful evaluation,
together with implications on turbomachinery design, due to dense-gas effects,
and large expansion ratio [82, 83, 115]. The fluid dynamic design of unconven-
tional organic fluid pumps for high pressure levels, and large compression ratio,
whereby compressible effects might also play a role, should be considered, though
at the moment no study can be found in the literature. In analogy to steam power
plants, multiple pressure-level cycles and reheating of expanded vapor have been
considered in order to boost efficiency [10, 116]. However, the feasibility of these
solutions is challenged by the additional plant complexity they imply. The Lorentz
thermodynamic cycle is known to be thermodynamically the best option for the 37 Chapter 2 exploitation of sensible heat sources and, to this end, different solutions adopting
organic working fluids in so-called trilateral cycles have been proposed [117''
119]. Generally speaking, the criticality with such systems is related with the
fully wet expansion process, still posing technological concerns regarding the ex-
panding device, if this should be a turbine [120]. If very high electrical efficiency
is sought, the binary (or cascaded) cycle configuration can be attractive and its
evaluation has driven some interest, presenting several advantages if compared to
a single cycle with large pressure ratio [10, 43, 109, 121]. Research on new working fluids can have a large impact, especially because fluids for high temperature applications that satisfy all requirements do not exist.
However, fluid manufacturers are currently refraining from highly targeted devel-
opment of new working fluids because the dimension of the market would require
taking as a risk the large investments needed for R&D activities on new molecules,
new synthesis processes, and new production plants. The merit of using fluid mix-
tures has been addressed already many years ago [122], and still stimulates many
theoretical studies. An innovative idea that very recently sparked some interest is the integra- tion of the selection of the working fluid into the automated cycle optimization
procedure [123]. Furthermore, new developments due to the advancements of
simulation science promise to overhaul the traditional sequential and iterative de-
sign process. The new design paradigm can be termed virtual prototyping. The
physics involved in an ORC power system is relatively well understood and there-
fore it can be accurately modeled, The power of modern software and computers
are making it possible to develop and use a programming environment in which
the entire system and its components can be modeled and simulated to the level
of detail that is needed for preliminary design and optimization [124]. Dynamic
simulation capabilities allow considering requirements on transient operation and
control in this early design stage [84]. Applications that may feature critical con-
trol aspects are automotive heat recovery [114], and the conversion of concen-
trated solar radiation [125]. The fluid dynamic of expanders is often the aspect of an ORC system attract- ing more research effort. A sizable improvement of the expander performance
directly affects the power output and thus the return on investment, more often
without affecting the cost of each unit. On the contrary, improvement of the heat
exchanging equipment can often be obtained only by increasing the heat transfer
surface, therefore the cost of each unit. The fluid dynamics of turbo-expanders and
volumetric expanders is intensely studied [126], and the non-conventional features
of highly supersonic flows typical of high-temperature ORC turbines has driven 38 ORC Power Systems: History, Status, Perspectives even quite some fundamental studies [127, 128]. Recently, several research efforts
have been also devoted to investigate innovative turbine configurations, see, e.g.,
Ref. [129]. All types of volumetric expanders for mini-ORC power systems are currently studied theoretically and experimentally. Piston expanders would be suitable for
high-temperature applications, and they have recently been studied for truck en-
gine heat recovery systems [130], though the need for a lubricant, and the high
blow-by losses are difficult challenges to overcome. Predictive models for scroll
expanders are actively studied [131, 132], and also experimental activities are pur-
sued [93]. Models of single and twin-screw expanders [133] are also under strong
development. The literature reports very few articles dealing with heat exchangers specifi- cally designed for ORC power systems, see, e.g., Ref. [134] and [135]. However
the design of more compact and lighter heat exchanger plays a very important
role, particularly in the emerging field of mobile applications. To this end, several
heat transfer enhancement techniques are investigated, leading to new concepts
such as micro-channel [134, 136, 137] and porous [138, 139] heat exchangers.
The addition of nano-particles to the working fluid might be beneficial for ORC
power system for which ultra-high heat transfer to and from the working fluid is
relevant [140]. Polymeric materials heat exchangers might also be an option in
the future [141]. More detailed information on current and possibly future research and de- velopment activities is given in the following sections, depending on the specific
application. In this respect, one important factor that might influence the level and
amount of future research is the recent interest in ORC technology by large global
companies. This is testified either by the starting of R&D work devoted to new
applications, or by the acquisition of companies that developed ORC techology. 2.4.1 Heat Recovery from Automotive Engines The potential of recovering heat from the exhaust and the cooling system of auto-
motive engine cannot be understated. The development paradigm of this product
is radically different from that of stationary units, that now veers toward that of
economy of scale (larger, customized power plants). In case of mini-ORC power
systems the paradigm is rather oriented towards an economy of production (large
number of standardized units). If this industrial sector is successful, several new
large markets for mini-ORC power systems could open up, see, e.g., Sec. 2.4.2. Recently interest is being revived [142''146], and a considerable research and development effort by original equipment manufacturers (OEM) and tier-one sup- 39 Chapter 2 pliers has been focused especially on the waste heat recovery from long-haul truck
engines [130]. In this case, as opposed to car engines [147], the amount of thermal
power that can be recovered is arguably enough to allow for the design of an ORC
system that does not incur into the limitations inherent to very small expanders
and tight space constraints. In addition, the large number of operating hours at
cruising speed, plays an important role in the evaluation of the profitability of the
investment. Feasibility studies on heat recovery from car engines have unveiled
several limitations with current technological and economic conditions. The first units that will be marketed are likely to be add-ons for existing trucks and their engines, employing ethanol as the working fluid and high-speed tur-
bines. Because the system is designed to fit existing truck frames and engines,
strict requirements on the volume occupied by ORC components must be com-
plied with. Designers face the problem of the selection of the working fluid:
a simple-molecule compound, even water, allows for the design of a compara-
tively efficient simple-cycle system without internal regeneration, and compact
condenser, thanks to the relatively high pressure. On the other hand, if the ex-
pander is a turbine, the small flow passages and the high rotational speed pose
technological and efficiency issues. In turn, volumetric expanders likely require
a lubrication system, are kinetically complex, and subjected to vibrations. Regu-
lations and requirements on the working fluids for the automotive sector are also
quite stringent: aspects like toxicity, flammability, ODP and GWP are regulated.
Even though a rational approach would require that these aspects are considered in
relation to the corresponding indexes of the fuel, which is transported in quantities
that are at least an order of magnitude larger. Very importantly, the freezing point
of the working fluid must comply with the typical requirements of the automotive
sector, therefore operation of the ORC system should be guaranteed for engine
idle and startup temperatures as low as ''40 oC. Another notable difference with stationary applications is that the inherently dynamic operation of the unit [148]
demands for advanced control strategies [149], which in turn ask for appropriate
dynamic simulation capabilities [150]. An interesting concept that might be successful in the longer run, is the combined- cycle power train: in this case the primary engine and its integrated heat recovery
system are designed together in order to optimize all critical aspects: efficiency,
volume, weigth, reliability, etc. The potential for improvement with respect to the
add-on approach can be large, if one thinks to the similarity to the design method-
ology of combined-cycle power stations. In this case the gas and the steam tur-
bine systems are optimized in an integrated fashion, which often leads to a gas
turbine which is less efficient than what is achievable with a simple gas turbine 40 ORC Power Systems: History, Status, Perspectives cycle configuration, because the waste heat can be efficiently recovered, see, e.g.,
Ref. [151]. In a combined cycle powertrain, also the relatively large amount of
thermal energy dissipated by the engine cooling system could be recovered. Given
the radical changes with respect to current practice that such a system could im-
pose, it is likely that the whole cab and drivetrain should be designed around
the new combined-cycle powertrain. Another interesting possibility is that the
combined-cycle powertrain generates electricity to power electric in-wheel mo-
tors and batteries [152]. 2.4.2 Domestic CHP The potential advantages of finely distributed cogeneration have been studied [25],
especially in case of capillary natural-gas distribution, like in large parts of Eu-
rope. Besides the high utilization factor and total system efficiency, there might
be a strategic interest in promoting a new business model of distributed power
generation, due to the increasing difficulty to locate or refurbish power stations in
densely populated areas because of permitting and public acceptance. Among the technologies that are suitable for small-capacity electrical power conversion and cogeneration of heating, domestic ORC-based CHP units under-
went research and development activities [153, 154]. In comparison to Stirling
and micro-gas turbine generators, ORC systems display some potential advan-
tages. In case of recent developments, the power capacity is either very small
(1 kWE) [153] or small (10 '' 30 kWE) [154], and the need to keep the cost low, especially in the case of a new application promoted by small companies, resulted
in low-temperature cycles and the use of scroll expanders [155], whereby the elec-
tric efficiency is bound to be low (5 ''10 %). In any case, the total energy efficiency can reach values of the order of 90 %. The market for mini-ORC CHP units for
domestic use could be very large (e.g., several millions unit per year in Europe
only), but the higher investment cost compared to a traditional heater might be a
barrier to widespread market introduction. The introduction of mini-ORC power
systems for other applications, see Sec. 2.4.1, could boost the development of
derived products for this sector. 2.4.3 Ocean Thermal Energy Conversion - OTEC An ORC power plant could be suitable for the conversion of the energy deriving
from the temperature difference between surface and deep ocean water, which is
in the range 20 '' 25 oC in various parts of the tropical and equatorial belt. The OTEC concept has been studied for a long time, though no commercial applica- 41 Chapter 2 tion exists, the very low efficiency being the main technical and economic chal-
lenge [10]. Recently, experimental research has been resumed and pilot plants
have been built, utilizing mainly ammonia as the working fluid in a saturated
cycle configuration. ORC systems utilizing a refrigerant or a hydrocarbon as al-
ternative working fluid are being studied [156, 157]. Technical problems related
to deep-water pipes and pumps can now be solved thanks to advancements in
off-shore technology. Economic viability might be achieved in the future, de-
pending on energy value and policy, arguably only with large installations (many
tens to hundreds or more MWE). The co-production of other goods could also
positively influence the economic feasibility. An interesting overview of various
aspects related to OTEC power plants can be found in Ref. [10], together with the
illustration of a study on the hybridization of an OTEC power plant with the addi-
tion of solar concentrators, and the utilization of complex configuration (multiple
pressure level) for maximum efficiency. 2.4.4 Concentrated Solar Power - CSP The majority of the present research efforts are devoted to low-to-medium tem-
perature solar ORC systems, aiming at using comparatively inexpensive solar col-
lectors, and often cogenerating heat and cooling. In the authors'' opinion, also
considering the promising results achieved in the past [54, 66], the investigation
of higher temperature and thus high-efficiency systems is worth more attention.
The advantage of solar ORC power systems is arguably the possibility of locally
cogenerating heating and cooling power, and still achieving electric efficiency that
is competitive with photo-voltaic panels, at the cost of a more complex system,
possibly requiring more maintenance. The potential market of distributed solar
cogeneration is very large (medium and large building in the solar belt). In this
respect, innovative concepts aimed at including thermal storage, while simplify-
ing plant layout and operation, and preserving or improving performance might
be successful [120]. The combination of solar power conversion with other func-
tions has also been studied: examples are desalinized water, or combination with
cooling by means of absorption chillers [6, 158''161]. Also the hybridization
with other energy sources seems promising; this is the case of systems integrat-
ing concentrated solar input with biomass combustion [162], industrial waste heat
recovery, geothermal energy [163], or ocean thermal energy [10]. As anticipated,
the use of small-capacity solar or biomass-fueled ORC modules to power the elec-
trification of remote areas has been envisaged since the first studies on this tech-
nology [36, 46], and this research field is still actively investigated [121, 164]. 42 ORC Power Systems: History, Status, Perspectives 2.4.5 Other applications Other niche applications attracted some research efforts. An example is the heat
recovery from high-temperature fuel cells, which discharge flue gases at tempera-
tures exceeding 400 oC, and achieve extremely high electrical efficiency (50 % to
60 %, respectively). They have not reached widespread market introduction be-
cause of the very high cost per kWE and because of long-term reliability and main-
tenance issues. The first commercialized units are in the medium power range
(300 kWE to 3 MWE), and an ORC power system is the heat recovery system of
choice [165''168]. ORC turbogenerators are increasingly studied also as bottoming cycles in combined systems for advanced power conversion facilities. According to sev-
eral authors, this can be the solution of choice to recover power from the exhaust
of high efficiency small and medium-size gas turbines, in order to exceed 50%
efficiency at power levels as low as 5 MWE [169, 170]. Similar systems are being
considered also for CBC-based plants proposed for next generation nuclear and
CSP applications [171]. Another notable application that has been studied in the past and that might attract attention in the future is the conversion from solar radiation in space. At the
time of the initial activities aimed at the development of the International Space
Station, together with Stirling engine and Closed Brayton Cycle gas turbine, ORC
power systems were intensely studied, also experimentally [63, 172, 173]. It is
well possible that the increasing presence of devices orbiting around the earth and
further space exploration will drive the development of special solar or nuclear-
powered ORC systems, whereby the main advantage with respect to photovoltaic
panels could be the possibility of efficiently cogenerating the heat needed for
propulsion or for the thermal control of on-board equipment. 2.5 Conclusions The concept of the organic Rankine cycle (ORC) engine is almost coeval with
that of the steam engine and, similarly, the concept has been implemented into
actual power systems with an impressive growth of technological sophistication.
Arguably, the main cause of the recent success of ORC power systems is their
very high flexibility. It is a technology that can be used to convert external
sources of thermal energy at widely different temperature levels, and at an equally
wide range of capacities. This characteristic places ORC power systems in a
prominent position among the technologies that are suitable for renewable of 43 Chapter 2 renewable-equivalent thermal energy conversion (geothermal reservoirs, biomass
combustion, concentrated solar radiation, industrial waste-heat recovery, waste
heat recovery from reciprocating engines and gas turbines, ocean thermal gradi-
ent). ORC power systems can also cogenerate heat and cooling, thus are inher-
ently suitable for distributed energy conversion with unequaled efficiency. Technical solutions have been developed out of scientific and technical re- search, and some times quite fundamental investigation paved the way to highly
innovative improvements. This is the case, for instance, of the study on new fluids,
and their modeling, and the study of the complex gas dynamics of dense vapors
and supercritical fluid flows of organic substances. Equally important were tech-
nical inventions related to the various components of the system, and the hermetic
turbogenerator, or the recently re-descovered radial outflow turbine are good ex-
amples. Design problems are quite complex as fundamental aspects, like those
related to thermodynamic cycles, and fluid dynamics, cannot be studied without,
at the same time, taking into account realistic technical constraints. The develop-
ment of new technology benefits today from the application of the most advanced
engineering methods, like high-fidelity simulations of fluid flows, and complex
multi-physics system and component optimization. The cumulative installed capacity of ORC power plants have been growing at a sustained rate starting from the first years of the new millennium, as well as the
number of ORC power systems. The number of vendors is increasing, and large
manufactures of conventional power equipment are entering the market, together
with several new dynamic enterprises. The analysis of the available information
about commercial power plants shows that the range of power outputs of ORC
units that enter into operation is expanding towards both larger and smaller units,
if compared to few years ago. The application of ORC technology to geothermal
heat and biomass combustion conversion, the two applications that sparked the
growth of ORC installations, continues the trend, whereby the power output of
geothermal ORC power plants is increasing (the plants that were recently com-
missioned feature capacities from several tens of MWE up to the last one, which
reached almost 100 MWE). Biomass-fuelled ORC power plants are still spreading
in Europe, where policy is favorable, but the situation is not yet equally favorable
in other continents. Waste heat recovery from prime movers and industrial pro-
cesses by means of ORC power plants has also started to grow in recent years, and
it is the application with arguably the highest potential in the foreseeable future. Very recently, a considerable amount of research and development efforts are dedicated to the development of ORC systems for applications suitable for high-
volume production, and heat recovery from automotive engines stands out. The 44 ORC Power Systems: History, Status, Perspectives automotive industry is boldly committed to the initiative. Several solutions are
investigated, different above all with respect to the expander. Volumetric (piston,
screw, scroll) expanders are attractive, as much knowledge from small refrigera-
tion compressors is available, but limitations related to the maximum expansion
ratio and inlet temperature are difficult to overcome. High-speed turbines are
very promising given their ability to expand vapors from high temperature and to
handle large expansion ratio. In addition they potentially offer a high degree of re-
liability, given their simplicity, as it can be extrapolated from the experience with
turbo-chargers. The first models of mini-ORC turbogenerators for heat recovery
from the exhaust of truck engines will likely be commercialized in the next few
years. If successful, the production of a large number of standardized and cost-
effective units could promote the adoption of mini-ORC power systems in many
other high-volume applications. Examples are domestic CHP, distributed solar
power plants cogenerating heat and/or cooling with thermal storage, and capillary
waste heat recovery. The possibility that ORC power blocks will make OTEC
plants a viable solution for base-load energy conversion in the tropical oceans is
also interesting. As a final remark, it is worth noting that modern technological progress is often the outcome of strong collaboration between academia and industry. Aca-
demics shall continue to strive with their role of looking at high-risk high-reward
research, especially now that the technology grew further from its infancy. The
level of research and development should reach those of more mature energy con-
version technologies, like, e.g., gas turbines or reciprocating engines. The com-
panies that have been on the market since the beginning of the diffusion of ORC
power systems, and those that are now entering the market shall therefore maintain
or increase their attitude toward research and innovation, without which the solu-
tions needed in order to fulfill the high potential of current and future applications
cannot be identified. Nomenclature s, p = specific entropy [kJ kg''1 K''1], pressure [bar] T , ρ = temperature ['C], density [kg m''3] MW = molecular weight [g mol''1] W, Q = Electric power, thermal power [kW] Subscripts 45 Chapter 2 E, M = electrical, mechanical Acronyms ORC = Organic Rankine Cycle ROT = Radial Outflow Turbine OTEC = Ocean Thermal Energy Conversion CFC = Complete Flashing Cycle GWP = Global Warming Potential ODP = Ozone Depletion Potential CBC = Closed Brayton Cycle CHP = Combined Heat and Power EFGT = Externally Fired Gas Turbine SPPP = Solar Pond Power Plant EAF = Electric Arc Furnace CSP = Concentrated Solar Power 46 References [1] H. Tabor and L. Bronicki. Establishing criteria for fluids for small vapor turbine. SAE Technical Paper, (640823), 1964. [2] G. Angelino, M. Gaia, and E. Macchi. A review of Italian activity in the field of organic Rankine cycles. In VDI Berichte - Proceedings of the International VDI Seminar, volume
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J Eng Gas Turb Power, 135(4), pp. 042312 '' 1 '' 9 (2013) c ASME 2013 '' Reprinted with permission E. Casati, S. Vitale, M. Pini, G. Persico, & P. Colonna
J Eng Gas Turb Power, 136(12), pp. 122607 '' 1 '' 11 (2014) c ASME 2014 '' Reprinted with permission Chapter 3 Abstract A critical component in designing efficient ORC plants is the expander, which is typically a turbine. The variety of possible working fluids, the complex gas dynamic phenomena encountered,
and the lack of simplified design methods based on previous experience on similar machines make
the design of efficient ORC turbines a complicated task. Relevant paths of research may thus be
concerned with (i) the development of generalized design methodologies, and (ii) the assessment of
non-conventional machine architectures: this chapter explores both. In particular, the first critical
evaluation of the centrifugal or radial-outflow turbine (ROT) architecture as a candidate technology
for ORC turbo-generators is presented. In the first part of the chapter, starting from basic turbomachinery theory, all the special fea- tures involved in ROTs design are enlightened. The main findings being that, in order to design
efficient centrifugal turbines, particularly for low power output applications, it is needed that (i)
the blade discharge geometric angles, the radial chords, the stage expansion ratios, and the re-
action degrees are allowed to vary among each cascade, and (ii) the diameter and the speed of
revolution are included among the optimization variables. It is discussed how simplifying assump-
tions usually adopted in the axial turbines practice are typically not applicable. A novel design
methodology is derived and presented for the preliminary sizing of ROTs in the power size range
from several MWE down to few kWE, i.e., covering most of the applications foreseen today. An
original in-house mean-line code coupled to an external optimizer is developed, which allows to
determine the preliminary design of ORC turbines of various configurations and working with dif-
ferent fluids. This tool, named zTurbo, is adopted to verify the novel method by presenting several
exemplary design exercises. The second part of the chapter deals with the design of centrifugal machines with 1 MWE power output, handling expansion ratios of the order of 60, and rotating at 3000 rpm, thus representative
of present industrial applications. Several simplifications derived from the axial-turbines practice
are adopted in order to illustrate their consequences. The design of two different turbines is per-
formed with zTurbo, a transonic six-stage and a supersonic three-stage ones. It is confirmed that the
adopted simplifications lead to unwanted design features, such as converging meridional channels
and large flaring angles on the last stages. The predicted fluid-dynamic efficiency for the transonic
and the supersonic machine is around 86% and 81%, respectively. The third part of the chapter focuses on the assessment of the down-scaling potential of the ROT architecture, considering its implementation in the promising field of mini-ORC turbogenerators.
The novel design methodology is applied to the sizing of two 10 kWE ROTs, handling an expansion
ratio of 45: a 5 stages transonic, and a 3 stages slightly supersonic ones. The proposed design
procedure proves valuable in sizing machines with a meridional channel which monotonically di-
verges maintaining maximum flaring angles lower than 10'. The resulting turbines are projected
to exceed a fluid-dynamic efficiency of 79% and 77%, with speed of revolution around 124000 and
15400 rpm, respectively. The results show that the ROT architecture is a promising concept for future ORC power sys- tems, which allows for the realization of efficient, compact, and reliable expanders down to a power
output of few kWE. However, the design of these machines presents several criticality which are
unveiled here for the first time. 3.1 Introduction As anticipated in Ch. 2, ORC power systems have been demonstrated to be advantageous compared
to steam Rankine cycles for a number of applications: this is mainly a consequence of the increase
of specific cost of turbomachinery as the scale of the plant reduces. The use of organic fluids, char- 58 Centrifugal Turbines for ORC Applications acterized by high molecular weight, make available cost-effective solutions for the turbo-expander
[1''4]. The specific enthalpy drop along the turbine expansion line is inversely proportional to the
molecular weight of the fluid. This determines two main advantages in case of organic fluids: pri-
marily the relatively small specific work can be disposed in a low number of stages; secondarily,
for a target power output, a relatively large mass flow rate is required, resulting in an enlarged
size of small-capacity ORC turbines with respect to steam units [2]. On the other hand, the low
number of stages leads to high expansion ratios per stage; this, combined with the low speed of
sound, leads to the widespread application of transonic and supersonic turbines in ORC systems.
As a result, highly dissipative systems of shock waves are commonly found in these machines,
complicating their design and the performance of the whole system, particularly during part-load
operations [5, 6]. Moreover, part of the expansion process usually occurs in close proximity of the
saturated vapour curve, or even close to the critical point. In such thermodynamic conditions com-
plex equations of state are necessary to accurately describe the working fluid behaviour. This design
scenario is further complicated by the lack, in the open literature, of experimental data regarding
flows of organic fluids [7, 8], specially in the thermodynamic region of interest. The most successful commercial applications of ORC power plants have been deployed in the power size ranging from hundreds of kWE up to approximately 5 MWE, and these systems
represent now the state of the art of the ORC technology. Nonetheless, since the first examples
of implementation, the ORC technology proved suitable for the conversion of thermal energy into
electricity for very low power capacity, down to few kWE [1, 2, 9]. These small systems are often
referred to as mini-ORC (mORC) power plants, and many researchers are still investigating the
development of mORC modules, see e.g. Ref. [10] Furthermore, depending on the application,
i.e. mainly the temperature levels of the thermal source and of the rejection sink, different working
fluids are available in order to better suit the (often conflicting) design requirements [1''4]. Concluding, the potentially infinite variety of power-output and adopted working fluids, to- gether with the thermo- and fluid-dynamic operating conditions typically encountered, make the
design of efficient ORC turbines a challenging topic. Furthermore, simplified design methods based
on statistical information on similar existing machines are not yet available. Relevant paths of de-
velopment may be concerned with the development of generalized design methodologies, and the
assessment of non-conventional machine architectures: this chapter explores both. The original in-house mean-line code zTurbo, developed to perform the preliminary design of ORC
turbines, is described in §3.2. The concept of centrifugal turbine, and its application to ORC power modules are discussed in §3.3. An in-depth analysis of the specific features of centrifugal turbines is thus performed and, in §3.4, it is shown how the relation between the design assumptions and the resulting machine features differs from the axial arrangement. A novel and general methodological
framework is developed and presented, which may be of support to the designer of radial-outflow
turbines of any power output. The design of several exemplary centrifugal machines is thus pre-
sented. Comparably large size centrifugal machines, i.e. in the MWE power-output range, are dealth
with in §3.5, following the work on the same topic published in Ref. [11]. Similarly, §3.6 investi- gates in detail the down-scaling potential of the radial-outflow turbine architecture, considering its
implementation in the 10 kWE power-output range, following the work on the same topic published
in Ref. [12]. 59 Chapter 3 3.2 Preliminary Design Method The preliminary design of a turbine is the phase in which the fundamental machine features, such
as the number of stages, the velocity triangles, the speed of revolution, and the blading geometry,
are selected. As detailed in the seminal work of Macchi [5], this step is fundamental particularly if
no previous experience is available regarding the specific machine to be designed. In other words,
although advanced design methods based on computational fluid-dynamics constitute a precious
help for the designer, they can yield high turbine performance only if the boundary conditions es-
tablished in the preliminary design phase allow for it [5]. This is often obtained for conventional
turbines by making use of simple rules based on statistical information on existing similar machines
[13]. As anticipated, since this is generally not available when designing an expander for an ORC
power system, a more general approach must be followed. In particular, a simultaneous optimiza-
tion process accounting for all the main variables affecting the turbine efficiency is desirable: this is
typically achieved by resorting to so-called 0-D mean-line methods [14]. Several studies reported
a good agreement between the results of such calculations and measurements, if reliable loss and
flow angle correlations are applied [15''17]. The mean-line design code zTurbo, specifically conceived for ORC turbines and developed within
the present research, is described in §3.2.1. zTurbo has been thus introduced in an optimization pro- cedure, in order to automatically determine the optimal design features of the machines, depending
on the designer''s objective, as detailed in §3.2.2. 3.2.1 Mean-line Design Tool for ORC Turbines The main aim of this code, whose development has been directly contributed by the author, is to
provide a preliminary machine design without any limitation on the adopted working fluid, flow
regime, and architecture: axial, radial-inflow, and radial-outflow turbine arrangements can be de-
signed with zTurbo. The code is coupled with the FluidProp software library, allowing for an
accurate evaluation of the working fluid thermophysical properties [18]. The balance equations for
mass, energy, and momentum, alongside a loss model to evaluate entropy generation, are written
in a generalized formulation, and both subsonic and supersonic flows are properly treated in the
stationary and rotating frames of reference. The calculation scheme of a single turbine stage, as
performed by zTurbo, is briefly summarized in the following: 1. At the beginning, the total upstream thermodynamic conditions, the stage expansion ratio, and the mass flow rate are provided as external inputs (e.g. as outputs of the thermodynamic
cycle optimization). This is the case also for several geometric quantities related to manu-
facturing limits (e.g. trailing-edge thickness, hub/tip clearance, and stator/rotor gap). The
values of several design variables are thus initially assumed, among others: the rotational
speed, the reaction degree, the blades chords and outlet geometric angles, and the channel
minimum width (throat dimension). 2. By assigning the stage reaction degree, the stator outlet velocity and the corresponding isoentropic Mach number can be calculated. If the flow is supersonic, for instance, isen-
tropic expansion is assumed from the inlet section where total conditions are given (e.g.
pressure PT,in and temperature TT,in), up to the choked throat where sonic conditions are 60 Centrifugal Turbines for ORC Applications attained. The system of equations accordingly implemented is       
      s = s(pT,in, TT,in) hth = hT,in(pT,in, TT,in) '' 1
2 c(hth, s) 2 ' m = ρth(hth, s) · c(hth, s) · Ath , (3.1) where s is the specific entropy, and the subscript ''th'' indicates the (static) thermodynamic
conditions in the throat section. Solving the continuity equation appearing in system (3.1),
the throat flow passage area Ath can be evaluated and, if the throat width is assigned, the
blade height can be computed. On the contrary, if subsonic flow occurs at the outlet section,
the thermodynamic conditions are obtained by solving the balance equations for the mass
and the momentum in the tangential direction, between the geometric throat and the down-
stream non-bladed zone, as detailed in Ref. [17]. In both cases the flow angle is calculated
starting from the blade geometric angle (BDA) by applying a proper deviation correlation.
The blade number is evaluated by applying the Zweifel load criterion [19], which provides
the optimal solidity as a function of the flow deflection across the cascade. It should be
noted that a proper selection of solidity and blade loading would need a specific aerody-
namic optimization, which is beyond the intrinsic limitations of a mean-line approach. 3. The initial isentropic design represents the first guess for an iterative procedure to estimate the cascade losses. Several loss-prediction methods are available within zTurbo, such as
those proposed by Ainley & Mathieson [20], Craig & Cox [15], and Traupel [21]. Alter-
natively, user-defined loss coefficients can be specified. The estimation of losses allows to
correct the flow velocities and the blades height previously estimated (see point 2 above).
The choice of a suitable model is critical, since its accuracy becomes questionable for flow
conditions departing from the validity range of the method [22]. In the case at hand, the
situation is further complicated by i) the fact that the machine arrangement is not axial, ii)
the different fluids and thermodynamic operating conditions, iii) the onset of post-expanded
and supersonic flows, and vi) the possibly low scale dimensions of the machines, that may
induce a stronger interaction among different loss mechanisms (e.g., profile and tip-leakage
losses) which is unlikely to be properly captured by the models. 4. A similar methodology (i.e. points 1 to 4), implementing the conservation of rothalpy, is employed for the calculation across the rotor in the rotating frame of reference. The outputs of the procedure outlined above (relative to a single stage) are: i) the velocity diagrams,
ii) the meridional channel shape, and iii) the performance parameters (efficiency, loss coefficients,
etc.). For multi-stage turbines, such procedure is applied stage-by-stage, assuming a value for the
number of stages. The repartition of the expansion among the stages is a critical aspect, particularly
when dealing with turbines elaborating large expansion ratios with few stages [5]. 3.2.2 Optimization Procedure The methodology described in §3.2.1, once implemented in the framework of an optimization pro- cedure, allows to search for the optimal machine design [5, 23]. The optimization of a turbomachin-
ery is typically aimed at the maximization of its fluid-dynamic efficiency, which may be formulated
in general terms as: ηT' = f (Ψ, ', M, Re, sh, ') = ''w ''hTS '' ' C2 out
2 , (3.2) 61 Chapter 3 The subscript ''T''' clarifies that the ideal total-to-static enthalpy drop used to calculate the efficiency
is reduced by a fraction (in the range 0 < ' < 1) of the discharge kinetic energy, supposing this can
be recovered downstream of the last stage. In other words, ηT' = ηTT if ' = 1, and ηT' = ηTS if ' =
0; the choice of a value for ' has a deep influence on the turbine design, as shown in Ref. [5]. The
functional dependence of η from the work and flow coefficients Ψ and ', and the Mach and Reynolds
numbers M and Re, is expressed by the first equality in Eq. (3.2). This dependence includes also the
term sh, synthetically indicating the turbine shape and accounting for the influence of geometrical
parameters such as the solidity, the blade angles, the ratio of the trailing-edge thickness and of the
tip clearances with respect to the blade chord, etc. From a mathematical point of view, several
main aspects have to be taken into account: i) the definition of a suitable objective function to be
maximized or minimized, ii) the independent variables and their range of variation within the design
space, iii) the geometrical and fluid-dynamics constraints bounding the space of solutions, and iv)
the algorithm to be used to search the design space for the optimal solution. In this chapter the efficiency defined in Eq. (3.2) is chosen as the objective function, with ' = 0.5. This assumption implies that a diffuser is used downstream of the last rotor, and is able
to recover half of the kinetic energy of the exiting flow. Concerning the optimization strategy, a
flexible and non-intrusive approach is desirable in order to leave to the user the choice of the in-
dependent variables, the constraints, and the search algorithm. Therefore, zTurbo is coupled to a
well known open source external optimization software Dakota [24]. An evolutionary optimization
strategy, based on a single-objective genetic algorithm, is adopted in the present analysis. For a
single objective optimization, the application of a gradient-based algorithm would require a lower
computational effort. However, due to the possibly highly non-regular behavior of the fitness func-
tion, local optima may be found during the search. Genetic algorithms span the whole design space,
and have therefore the advantage of being more robust under this respect, proceeding towards the
global optimum [25]. In particular, the adopted optimization method is the single objective version of the multi- objective elitist genetic algorithm proposed in [26] and implemented in [24], based on binary en-
coding and dynamic memory allocation. 3.3 Centrifugal Architecture for ORC applications Some critical challenges encountered in the design of efficient vapour turbines are a consequence
of the large variation of the volumetric flow rate over the expansion. The low speed of sound
characterizing ORC working fluids further complicates the design of the expander, leading to su-
personic regime within the flow passages [5]. In the centrifugal architecture, the fluid enters the
machine close to the rotational axis, and flows outward in the radial direction (see fig. 3.1). This
is advantageous primarily because it provides a natural increase of the passage area along the flow
path. Another major advantage is the possibility of implementing multi-stage arrangements in a
comparatively easy way [27, 28]. The counter-rotating centrifugal steam turbine was proposed by
Lj¨ungstrom in the early 20th Century and widely adopted until the Sixties [29]. The limits of the
Lj¨ungstrom turbine emerged for large-capacity machines, resulting in a maximum power capacity
of about 65 MWE per unit. This is mainly due to the difficulty, for larger output, of elaborating
the corresponding volumetric flow rates in a single-casing arrangement. Eventually, the require-
ment of two counter-rotating electrical generators determined the success of the axial-flow concept
[29]. Notably, none of these issues applies in the ORC context and, as such, several studies have
discussed the potential merits of these machines in this field [5, 30, 31]. These characteristics have
recently driven also the industrial interest towards centrifugal ORC turbines, which have been thus 62 Centrifugal Turbines for ORC Applications successfully introduced in the market. Summarizing: 3 2 1 STATOR
and CASE
(THRUST BALANCING) ROTOR VAPOR INLET VAPOR INLET VAPOR OUTLET 2 1 3 Figure 3.1: Centrifugal turbine schematic, adapted from [32] 1. The low specific expansion work typical of ORC fluids allows to i) adopt the stator-rotor ar- rangement (radial sequence of stators and rotors), and ii) maintain a relatively low peripheral
speed, which is typically well below the mechanical stress limit. 2. The peripheral speed of the blades does not change along the blade span, and no radial equilibrium establishes in the span-wise direction [16]. This results in a design and man-
ufacturing simplification, since the velocity diagrams can be chosen such that the reaction
degree and work coefficient at midspan are optimal. These conditions are maintained all
along the span of the (untwisted) blades. Notably, a mean-line method is thus expected to
yield more accurate predictions in this case. 3. The relatively small temperature variation across an ORC turbine, typically of the order of 100 oC), makes the thermal gradient acting on adjacent blade rows far less critical than in
steam machines; as a result, all blade rows can be installed as well as machined on the same
disk. 4. Full admission inlet stages can be adopted: the first rows, characterized by a low volumetric flow rate, can be placed where the rotor diameter is smaller, thus allowing for comparatively
larger blade height. The simplicity of the multi-stage assembly allows to maintain tight
clearance between moving parts, thus reducing leakages. In addition, disc-friction losses
are comparatively low. Notably, these last aspects regard loss mechanisms which are particularly severe for small turbines[2,
9, 27]. 3.4 Analysis of the Centrifugal Architecture An in-depth analysis of the specific features of centrifugal turbines is performed here, following Ref.
[12]. The aim of the treatment is, starting from the design procedures proposed in the literature, 63 Chapter 3 to derive a novel methodological framework which may be of support to the designer. It is in
fact shown how, in the general case, the relation between the design assumptions and the resulting
machine features differs from the axial arrangement case. This, in turn, makes the development of
design procedures specific for the radial-outflow turbine architecture necessary, in particular as the
machine power output is reduced. Most of the available works on the subject of radial-outflow centrifugal turbines (ROTs) deal with the design of large power output machines and, usually, simplified procedures are borrowed
from the vast literature available in the field of axial turbines, lacking specific treatments. A typical
assumption is therefore that all the rows feature the same geometrical blade discharge angles (BDA)
[11, 27, 28, 32]. Referring to Fig. 3.2, this implies that, for all the N stages of the machine, the Figure 3.2: Schematic of the two-dimensional flow through a turbine stage of the repeating type.
All the rows feature the same geometrical angles (BDA). The peripheral velocity is assumed to be constant along the machine, i.e., U2 N = U3. The stage reaction degree is 0.5, and the velocity triangles are thus symmetrical. The sign convention for the flow angles is also reported, adapted
from [22] following holds α1 N = ''β2, and α2 N = ''β3. (3.3) Usually also the blade chords are kept equal, i.e. bst N = brot. (3.4) Other simplifying assumptions are commonly introduced regarding the distribution of the total ex-
pansion among the stages, and among stator and rotor in each stage (i.e. the stage degree of reaction
R). For instance, these quantities can be kept constant among the stages, i.e., p out pin ! stg N = p out pin !1/N total , (3.5) R N = a, with (0 < a < 1). (3.6) Eq. 3.5 indicates that the total load is divided such that each stage features the same expansion ratio.
Similarly, Eq. 3.6 bounds the value of the stage reaction to be the same for all the stages. A typical
design choice in the case of axial turbine stages is to impose that the reaction degrees is around
50% (a = 0.5 in Eq. 3.6), i.e., a value ensuring close-to-optimal stage efficiency [17], Eq. 3.3.
By assuming that the variation of the mean-line peripheral velocity is negligible and that the axial 64 Centrifugal Turbines for ORC Applications velocity component conserves throughout the expansion, the so-called repeating-stage arrangement
is obtained, see, e.g., Fig. 3.2. Repeating stages are usually characterized by similar stator and rotor
blades, namely α3 N = α1, W3 N = C2, W2 N = C3. (3.7) Notably, these conclusions rest on assumptions that can only be partly realized in radial machines,
since the peripheral speed varies in the stream-wise direction. Proper design rules are therefore to
be established if centrifugal turbine arrangements are of interest. Even if the constraints imposed
by the repeating stage approach are neglected, radial outflow machines dimensioned on the basis
of common axial turbine design criteria, i.e., fulfilling Eq. 3.3, 3.4, 3.5, and 3.6, may show i)
different velocity triangles per-stage, notwithstanding the geometrical similarity of the stages, and
ii) a characteristic meridional channel shape, which tends to be convergent in the first stages while
becoming divergent in the last stages, see, e.g., § and Refs. [11, 32]. A converging-diverging meridional shape of the flow channel is typically an undesirable fea- ture, particularly in case of mini-ORC turbines, since i) the blade height might already be insuf-
ficient at the inlet (a full-admission first stage is preferable as far as efficiency is concerned), and
ii) large variations of the meridional channel lead to span-wise velocity components which, even
though not captured by a mean-line analysis, deteriorate the performance of the turbine. In a radial turbine, contrary to what happens in axial turbines, the stage chord has an influ- ence on the distribution of the stage diameters along the machine, and thus on the work extraction
process. This is in turn governed by the variation of peripheral speed, being Dout = Din + b, (3.8) w ' U 2 = '2 D2 out. (3.9) This feature has an impact also on the variation of the volumetric flow rate, and consequently of
the flow passage area Aout needed to accommodate the flow along the expansion. For instance, by
applying the continuity equation to the outlet section of the bladed region of a subsonic row, see,
e.g., Fig. 3.2, such area may be expressed as Aout = Hout o = ' m ρout Vout Nblds ǫ , (3.10) where Hout and o are the blade height and the channel outlet section width (normal to the flow) at the
outlet of the channel, respectively, and Vout is the corresponding flow velocity magnitude. Nblds is
the number of blades, while ǫ accounts for possible correction factors (e.g., that for blocking effects
due to the boundary layer or the blade section). Assuming a rectilinear suction blade end-side, the
relation among the outlet section width o and the blade geometric discharge angle BDA is expressed
as o = S cos(BDA), (3.11) where the blade pitch S is evaluated according to the equation S = ' Dout N'' 1 blds. (3.12) Finally, in order to express the blade height Hout, Eq. 3.10 may be rearranged into Hout = ' m ρout Vout cos(BDA) Dout ' ǫ . (3.13) 65 Chapter 3 This last variable greatly affects the meridional channel shape, which may be characterized by the
so-called flaring angle δ, i.e., the ratio between the blade height at the outlet and at the inlet of a
given row. Assuming a constant span among subsequent rows, the blade height at every row inlet
may be specified as equal to that at the outlet of the previous row, i.e., for every row ''i'' apart for the
first stator (for which i=1), the equality Hi in = Hi-1 out holds. This leads to the following expression for the flaring angle of the ith row δ i '' Hout Hin i ' ρi-1 out ρi out |{z} A · Vi-1 out Vi out |{z} B · cos  BDAi-1  cos BDAi  | {z } C · Din Din + b !i | {z } D . (3.14) Terms A and B in Eq. (3.14) are determined by the expansion process across the machine, i.e.,
by the distribution among the stages of the loading and of the reaction degree R. If simplifying
assumptions are adopted, by assigning, for instance, common values to every stage as in Eqs. 3.6
and 3.5, both A and B may be considered approximately the same for all the stages. Referring to
Fig. 3.2, and using V to indicate the velocity magnitude of the flow discharged by a generic row,
it can be noted that Vi out = C i
out and V i-1 out = W i-1 out if the i th row is a stator. Conversely, Vi out = W i out and Vi-1 out = C i-1
out if the i th row is a rotor. This implies that, if the reaction degree in around 0.5, B '' 1, being C i
out = W i-1 out for a stator, and W i out = C i-1
out for a rotor. Hence, the influence of term B on δ vanishes. In radial-outflow turbines B tends to be lower than one as a consequence of the increasing peripheral speed that, in turn, increases also the rotor outlet velocity. This fact can be
handily explained by resorting to the energy balance in the relative frame of reference, which states
the conservation of rothalpy rt across the rotating cascade, i.e. referring to Fig. 3.2 rt = h2 + W2 2 2 '' U2 2 2 = h3 + W3 2 2 '' U3 2 2 , (3.15) which leads to W3 = W i out = V i out = s 2(rt '' h3 + U3 2 2 ). (3.16) Compared to an axial stage having the same features, i.e., the same stator outlet velocity Vi-1 out, inlet rothalpy and expansion ratio (which leads to a similar value of static outlet enthalpy h3), a
centrifugal stage is affected by a greater W3 due to the larger kinetic term U 2 3 /2, In these conditions B has an adverse effect on the flaring angle, and this can be compensated only by acting on the other terms of Eq. (3.14). Regarding term C, assuming that all the blades have the same value of BDA according to Eq. 3.3, the equality C = 1 is obtained. The meridional channel shape becomes therefore primarily a
function of terms A and D. The quantity represented by term D, i.e., the row diameters ratio, is plotted against the row inlet diameter in Fig. 3.3, considering different values of the radial chord. It can thus be seen how, for
radial stages placed at progressively larger diameters, D tends to unity, i.e., its potential influence on
δ vanishes. In other words, as expected, centrifugal stages characterized by small values of the ratio
b/Din tend to behave like axial stages, with the chord size having little influence in determining the
meridional channel shape, which is rather determined by the expansion process, i.e., by term A in
Eq. (3.14). This is the case of the ROTs described in Ref. [28], and proposed for Rankine cycle
power systems working with potassium and ranging in size from 20 up to 200 MWM. In the case
small of ROT''s, however, the low mass flow rate leads to comparatively large b/Din ratios, due pri-
marily to the need of obtaining acceptable blade height at the turbine inlet. The design is therefore 66 Centrifugal Turbines for ORC Applications D in, row [m] ( D in /D out ) row [- ] 0 0.2 0.4 0.6 0.8 1 0.6 0.7 0.8 0.9 1 b [m] = 0.01
b [m] = 0.02
b [m] = 0.03 Figure 3.3: Diameters ratio for a centrifugal row (Din/Dout) row, i.e. term D in Eq. (3.14), as a function of the row diameter Din, row and of the radial chord b. likely to include rows characterized by a (Din/Dout)row value smaller than unity, i.e., D < 1, see Fig.
3.3. For this condition, if the simplifying design assumptions previously described are adopted,
a convergent meridional channel is likely to be obtained since A, B '' const. and C '' 1. This is the case of the preliminary fluid dynamic designs presented in §3.5, and of the 240 MWM ROT described in Ref. [32]. As anticipated, however, this is not a suitable solution, specially for small
power-output machines. The present treatment demonstrates therefore that, although useful in re-
ducing the complexity of the preliminary design, the simplifying assumptions usually adopted, e.g.
Eqs. 3.3-3.6, are not applicable in general in the ROT field. A novel design methodology is thus
necessary, following two main guidelines, i.e. 1. the blade discharge geometric angles, the radial chords, the stage expansion ratio, and the reaction degrees are allowed to vary among each cascade, 2. the diameter and the speed of revolution are included among the optimization variables. In particular, this last choice stems from the difficulty of providing an a priori estimation for the design quantities at hand, e.g. based on statistical information regarding existing machinery, as done
in the turbomachinery practice [13, 33]. As a consequence, all the afore-mentioned quantities add
to the independent variables involved in the optimization problem. This will be discussed further,
with the help of several examples, in the next sections. 3.5 Design of Exemplary 1 MWe Machines The purpose of this section is to clarify the procedure presented in §3.4, by performing the design of two exemplary centrifugal turbines in the MWE power-output range. The tool adopted for the
preliminary design is the in-house software zTurbo, presented in §3.2.1. The treatment follows the 67 Chapter 3 work documented in Ref. [11], which constitutes also the first published investigation of the use of
the ROT architecture in the ORC field. The main design assumptions adopted are detailed in §3.5.1. 3.5.1 Design Assumptions The results of the thermodynamic cycle analysis provide the needed inputs to the turbine prelimi-
nary design procedure. Operating conditions typical of an industrial high-temperature ORC turbo-
generator are considered here. The main characteristics of this cycle, resumed in Tab. 3.1, are
common to all the machines designed in the present section. The working fluid is siloxane MDM,
whose T ''s diagram is represented in Fig. 3.4. The outlet pressure corresponds to a condensation
temperature of about 95 oC, which frequently occurs in ORC power plants co-generating electricity
and thermal power to be used, e.g., for district heating. The mass flow rate value is imposed in order
to obtain a power-output close to the target one of about 1.2 MWM. It can be noted that the first Fluid MDM ' mflow [kg s'' 1] 22 TT,in [ oC] 274 pT,in [bar] 10 zin 0.61 pout [bar] 0.17 pT,in pout 59 ' Vout ' Vin s 85 Table 3.1: Thermodynamic cycle parameters assumed for the preliminary design of the turbines
presented in this section, after [11]. The last two terms indicate the pressure and the isoentropic
volumetric flow rate ratios across the turbine expansion. The working fluid is siloxane MDM (oc-
tamethyltrisiloxane, C8H24O2Si3): MW = 236.53 [g mol'' 1], TCR = 290.9 [oC], pCR = 14.15 [bar], ρCR = 302.9 [kg m'' 3]. part of the expansion takes place in the so-called dense gas region, where the compressibility factor
is significantly lower than unity, i.e. zin < 1. In these conditions relevant real gas effects occur, and
accurate thermodynamic models must be adopted in order to obtain a meaningful turbine design
[6]. As anticipated, the software library presented in Ref. [18] is adopted to this end. As a common feature of comparatively low-output power generating systems, ORC turbo- generators are likely to work in off-design conditions for a large part of their operative life-time.
Thus, preserving a reasonably good turbine efficiency in a wide operating range is of paramount
importance. This can be better accomplished by using transonic or slightly supersonic machines, i.e.
with maximum flow Mach numbers lower than approximately 1.4. Additionally, the condition of
subsonic flow at the rotors inlet (in the relative frame of reference) is imposed. These configurations,
where the stages can be constituted of converging-only blades, are able to handle load variations by
adapting to the new conditions through post-expansion phenomena. If the load change produces a
post-expanded flow with Mach number not exceeding about 1.4, the induced efficiency losses are
comparatively limited [17]. On the contrary, if Mach numbers larger than 1.4 are attained already in
design conditions, the onset of dissipative shock patterns is expected to strongly affect the turbine 68 Centrifugal Turbines for ORC Applications s [kJkg -1 oC-1] T [ o C ] -0.4 -0.2 0 0.2 0.4 0.6 0.8 100 150 200 250 300 CR IN p out = 0.17 bar p T,in = 10 bar Figure 3.4: Saturation curve of siloxane MDM in a T -s diagram, showing the thermodynamic
boundary conditions for the turbine design, i.e. the inlet total conditions, point IN, and the discharge
pressure. Point CR indicates the liquid-vapour critical point of the fluid. efficiency, in particular during off-design operations [6, 17]. However, the choice of dealing with
highly supersonic flows is typically justified by the opportunity of minimizing the number of stages
[9]. As mentioned in §3.3, however, the adoption of the centrifugal architecture allows to increase the number of stages with relative ease, thus relaxing this constraint. Therefore, all the machines whose design is proposed in the following belong to one of these general classes, i.e., they are either transonic or slightly supersonic ones. To this end, it is possible
to tentatively vary the number of stages, or to include also this among the optimization variables.
In the present case, the designs of a subsonic six-stage turbine, and of a three-stage transonic one
featuring supersonic post-expanding flows are presented. The losses-estimation method proposed by Craig & Cox is adopted here [15], see §3.2.1, and the only losses modelled are the profile, and the secondary ones. 3.5.2 Design Methodology The variables and parameters involved in the design are collected in Tab. 3.2, see also §3.2.1. Primarily, the rotational speed ' is constrained to the value of 3000 rpm, in order to directly couple
the turbine and the electrical generator. This, in fact, adds an important economic benefit to the
resulting machine, in that electronic converters are not required. Both the tip clearance tcl and the
trailing-edge thickness te are set to minimum values, related to mechanical resistance or manufac-
turing limits, and common to all the rows [5, 23]. The radial clearance cl, i.e. the gap between the
cascades, is also assigned a fixed value, since a proper optimization of this parameter is outside the
capabilities of a generalized mean-line approach. However, considering its strong impact on the
performance of axial turbines [34], an even larger influence may be expected in radial machines. In
centrifugal turbines, in fact, the radial gap directly affects the variation of the radial coordinate and, 69 Chapter 3 Common parameters ' [rpm] 3000 tcl [mm] 0.1 te [mm] 0.1 cl [mm] 1 Hmin [mm] 10 δmax ['] ±30 6-stage Machine Design Variables LB UB Din [mm] (x 1) 200 '' (pT,in/pS,out)stg (x 1) 1.97 1.97 R (x 1) 0.4 0.6 BDA ['] (x 1) 65 75 b [mm] (x 1) 25 40 3-stage Machine Design Variables LB UB Din [mm] (x 1) 150 '' (pT,in/pS,out)stg (x 3) 3.5 5 R (x 3) 0.1 0.6 BDA ['] (x 6) 60 75 b [mm] (x 6) 25 60 Table 3.2: Design variables, with relative lower (LB) and upper (UB) bounds, and parameters
involved in the proposed design methodology as applied to a N-stages centrifugal turbine. 70 Centrifugal Turbines for ORC Applications hence, may induce a diffusion effect due to the increase of passage area in the flow direction. The
minimum blade height Hmin constitutes a critical parameter as the size of the machine is reduced
and, in the present case, it is assigned a value of 10 mm. The flaring angle δ, i.e. the angle between
the end-wall contour and the radial direction, is constrained in the typical range adopted for axial
machines of ±30 ' [5, 23]. The lower constraint on the inlet diameter Din may be tentatively de- termined in order to be compatible with the minimum blade height, keeping however in mind that,
owing to the possibility of a converging meridional channel, this does not necessarily occur in the
first stage, see §3.4. Regarding the 6-stage machine, the design assumption of repeating stages ( §3.4) is adopted in order to illustrate its consequences on the result. Coherently, the main variables of the problem, i.e. the
pressure drops, the degrees of reaction, the radial chords, and the blades outlet geometric angles, are
assumed to be the same for all the stages. In particular, the blades angles, which are given values
typical for turbine cascades, are opposite in sign between stators and rotors. The global total-to-
static pressure ratio is evenly distributed among the stages, i.e. (pT,in/pS,out)stg = (pT,in/pS,out) 1/Nstgs . The reaction degree is left to vary between 0.4 and 0.6, in a region of high stage-performance. This
allows also to split almost equally the expansion ratio between the stator and the rotor, thus limit-
ing the maximum Mach number within the stage. The constraints imposed on the radial chord are
selected in order to preserve acceptable blade aspect ratios and to limit the turbine dimension, i.e.
its maximum diameter. In the 3-stage machine, due to the increased stage-loading, all the preceding simplifications are
removed in order to limit the maximum Mach number to 1.4 and to respect the constraint on the
maximum flaring angle. In particular, the pressure drops, the degrees of reaction, the radial chords,
and the blades outlet geometric angles are allowed to assume values differing among the stages,
according to the novel design procedure introduced at the end of §3.4. 3.5.3 Results: Transonic Turbine The main features of the optimized 6-stage turbine are shown in Tab. 3.3. The optimal velocity
triangles are shown in Fig. 3.5a and, as expected ( §3.4), there is no similarity among them, notwith- standing the design assumption of repeating-stages. Another expected feature of the machine is
the shape of the meridional channel, see Fig. 3.5b, which appears to be slightly convergent in the
first stages, while in the last one the flaring angle reaches the prescribed upper limit of 30 '. This
trend is strictly combined to the other quantities of the problem, and more insight may be gained by
considering again Eq. (3.14). An increase in the flow passage area is required along the stream-wise direction, in order to accommodate for the considerable growth of the volumetric flow rate as the expansion process
proceeds. Being the blades angle and the radial chord values constrained to be the same in this
case, the only free variable that can be exploited to this end is the flaring angle. In the first stages,
where the increase in passage area determined by the diameter increase is comparatively large, the
meridional channel tends to be convergent. On the contrary, an increasing divergence is needed in
the subsequent stages. The adoption of a comparably large number of stages reduces the blade aerodynamic load- ing, which is an interesting quantity for underlying differences and analogies with respect to the
axial architecture. In axial machines, this quantity is normally proportional to the stage specific
work w. Conversely, for radial outflow configurations, the reduction of the the aerodynamic load- 71 Chapter 3 Pm [MW] 1.27 δmax ['] 30 Din [m] 0.2 Dout [m] 0.98 Hmin [mm] 8.2 Hmax [mm] 147 R 0.47 BDA ['] 66 b [mm] 30 ηT'=0.5 0.87 Mmax 1.16 ηT'=0.5,CFD 0.86 Mmax,CFD 0.99 Table 3.3: Main results for the 6-stage 1 MWM transonic turbine. 6 th rot 2 nd rot 3 rd rot 4 th rot 1 st rot M U3= 0.44 M W3= 0.93 M C3= 0.56 0.92 M W2= 0.58 M U2= 0.40 M C2= 0.93 0.94 0.40 0.51 0.56 0.49 0.52 0.92 0.91 0.42 0.70 0.95 0.65 0.79 0.90 0.36 0.89 0.85 1.00 0.94 0.95 0.40 0.38 5 th rot 1.16 1.10 0.91 0.48 0.45 0.90 0.36 (a) ROT radius [mm] H [m m ] 0 200 400 -200 -100 0 100 200 Rotational
axis 3 2 nd rot 6 th rot 1 st rot 2 3 rd rot 4 th rot 5 th rot (b) Figure 3.5: Design results for the 6-stage transonic 1 MWM turbine, following the repeating-
stage assumption, adopting the boundary conditions reported in Tab. 3.1, and the Craig & Cox loss
estimation method [15]. Fig. 3.5a shows the velocity triangles, in black those referring to the rotor
inlet section, in grey to the rotor outlet. The Mach numbers corresponding to the different velocity
components are also detailed. The meridional section is depicted in Fig. 3.5b. ing, expressed by the work coefficient Ψ, does not imply a direct decrease of w, as shown in Fig. 3.6a. In fact, by assuming the definition typical of axial turbines, i.e. Ψ = wstg/2U 2 , with U = (Uin + Uout)stg/2, can be noted how Ψ can lower throughout the expander, notwithstanding the
fact that ''hTT, stg, i.e. the specific work extracted, increases. This results in the initial stages be-
ing characterized by a lower specific work, but larger blade deflections and aerodynamic loadings,
which cause the profile losses to increase. The trend is thus strictly correlated to the constraints
imposed on the geometry. The loss-estimation method of Craig & Cox [15] predicts a significant variation of the losses 72 Centrifugal Turbines for ORC Applications N row w [kJ /kg] 2 4 6 8 10 12 0.5 1 1.5 2 2.5 3 6 8 10 w Ψ Ψ (a) N row [% ] 1 2 3 4 5 6 7 8 9 10 11 12 2 4 6 8 p s ζ ζ ζ (b) Figure 3.6: Design results for the 6-stage transonic 1 MWM turbine of Fig. 3.5. 3.6a: evolution of
the load distribution among the stages, in terms of the aerodynamic loading expressed by Ψ (solid
line), and of the stage specific work w (dashed line). 3.6b: row-by-row evolution of the kinetic
energy loss coefficients ζp (solid line), and ζs (dashed line) accounting for profile-, and secondary-
losses. The presented results are obtained with the Craig & Cox model [15]. throughout the machine, as shown in Fig. 3.6b. This is a direct consequence of the turbine config-
uration, featuring stages characterized by very different geometrical quantities (e.g. solidity, aspect
ratio etc.). In particular, end-wall loss coefficients are found to be more influential in the first stages,
characterized by lower blades aspect-ratios. The same trend characterizes also the profile losses,
which assume larger values in the high deflection blades of the first stages. As a result, the stage
efficiency increases along the machine, passing from about 75% in the first stage to about 95% in
the last one. 3.5.4 Results: Slightly Supersonic Turbine The main features of the optimized 3-stage turbine are shown in Tab. 3.4. The increased aero-
dynamic loading lead to an efficiency penalty with respect to the 6-stage machine. The optimal
velocity triangles are shown in Fig. 3.7a and, as expected ( §3.4), the optimized blades geometrical angles vary along the machine in this case. It can be noted that the application of the design procedure proposed in §3.4 allows to avoid any converging part in the meridional channel, as shown in Fig. 3.7b. At the same time, the con-
straint on the maximum flaring angle is respected notwithstanding the fact that the same expansion
is performed with three stages only. This is achieved by an increase of the chords in the last stages,
accompanied by a reduction of the deflection and a consequent increase of the radial velocity com-
ponent. 73 Chapter 3 Pm [MW] 1.22 Mmax 1.36 δmax ['] 30 Din [m] 0.29 Dout [m] 0.85 Hmin [mm] 7.1 Hmax [mm] 153 ηT'=0.5 0.84 Mmax 1.36 ηT'=0.5,CFD 0.81 Mmax,CFD 1.40 Stage 1st 2nd 3rd (pT,in/pS,out)stg 3.7 4.7 4.8 R 0.23 0.35 0.40 Table 3.4: Main results for the 3-stage supersonic turbine. 2 nd rot 3 rd rot 1 st rot M U3= 0.56 M W3= 1.14 M C3= 0.64 M W2= 0.81 M U2= 0.51 M C2= 1.28 0.75 1.29 0.63 0.65 1.33 0.87 0.73 0.62 1.01 1.36 1.20 0.43 (a) ROT radius [mm] H [m m ] 0 100 200 300 400 -200 -100 0 100 200 Rotational
axis 3 2 nd rot 3 rd rot 1 st rot 2 (b) Figure 3.7: Design results for the 3-stage supersonic 1 MWM turbine, following the repeating-
stage assumption, adopting the boundary conditions reported in Tab. 3.1, and the Craig & Cox loss
estimation method [15]. Fig. 3.7a shows the velocity triangles, in black those referring to the rotor
inlet section, in grey to the rotor outlet. The Mach numbers corresponding to the different velocity
components are also detailed. The meridional section is depicted in Fig. 3.7b. 3.6 Design of Exemplary 10 kWe Machines The purpose of this section is to further clarify the procedure presented in §3.4 by presenting the design of two exemplary centrifugal turbines in the 10 kWE power-output range. The tool adopted
for the preliminary design is the in-house software zTurbo, presented in §3.2.1. The treatment 74 Centrifugal Turbines for ORC Applications N row w [kJ /kg] 2 4 6 1 1.5 2 2.5 3 3.5 12 14 16 18 20 22 24 w Ψ Ψ (a) N row [% ] 1 2 3 4 5 6 2 4 6 8 10 p s ζ ζ ζ (b) Figure 3.8: Design results for the 3-stage supersonic 1 MWM turbine of Fig. 3.7. 3.8a: evolution
of the load distribution among the stages, in terms of the aerodynamic loading expressed by the
work coefficient Ψ (solid line), and of the stage specific work w. 3.8b: row-by-row evolution of
the kinetic energy loss coefficients ζp (solid line), and ζs (dashed line) accounting for profile-, and
secondary-losses. The presented results are obtained with the Craig & Cox loss model [15]. follows the work documented in Ref. [12], which constitutes also the first assessment of the down-
scaling potential of the ROT architecture, considering its implementation in the field of low power-
output mini-ORC turbo-generators. The modelling framework resembles closely the one presented
in §3.5.1, and is discussed in §3.6.1. 3.6.1 Design Assumptions The results of the thermodynamic cycle analysis provide the needed inputs to the turbine prelimi-
nary design procedure. The solution presented by Lang [35] for an ORC turbo-generator recovering
thermal power from the exhaust of an heavy-duty truck engine is adopted here. The main charac-
teristics of this cycle, resumed in Tab. 3.5, are common to all the machines designed in the present
section. The working fluid is siloxane D4, whose T ''s diagram is represented in Fig. 3.9. The
outlet pressure corresponds to a condensation temperature of about 100 oC. The mass flow rate
value is imposed in order to obtain a power-output close to the target one of about 10 kWM. Also
in this case the first part of the expansion takes place in the so-called dense gas region, where the
compressibility factor is lower than unity, see also Tab. 3.5. Relevant real gas effects are therefore
expected, and accurate thermodynamic models are needed [6, 18]. For the reasons detailed in §3.5.1, two machine configurations are presented: a five-stage tran- sonic turbine, and a three-stage one, which is slightly supersonic. The loss estimation method adopted is the one proposed by Traupel [21]. However, as already mentioned, the predictive capability of these models is expected to decrease as the flow Mach
numbers increase, and as the size of the machine is reduced. Thus, a comparison among different
models is presented for the three-stage expander, by re-designing the same machine using the Craig 75 Chapter 3 Fluid D4 ' mflow [kg s'' 1] 0.266 TT,in [ oC] 242.5 pT,in [bar] 3.9 zin 0.80 pS,out [bar] 0.087 pT,in pS,out 45 ' Vout ' Vin s 53 Table 3.5: Thermodynamic cycle parameters assumed for the preliminary design of the turbines
presented in this section, after [35]. The last two terms indicate the pressure and the isoentropic
volumetric flow rate ratios across the turbine expansion, respectively. The working fluid is siloxane
D4 (octamethylcyclotetrasiloxane, C8H24O4Si4): MW = 296.62 [g mol'' 1], TCR = 313.3 [oC], pCR = 13.32 [bar], ρCR = 301.3 [kg m'' 3]. s [kJkg -1 oC-1] T [ o C ] -0.4 -0.2 0 0.2 0.4 0.6 100 150 200 250 300 CR IN p out = 0.09 bar p T,in = 3.92 bar Figure 3.9: Saturation curve of siloxane D4 in a T -s diagram, showing the thermodynamic bound-
ary conditions for the turbine design, i.e. the inlet total conditions, point IN, and the discharge
pressure. Point CR indicates the liquid-vapour critical point of the fluid. & Cox model [15]. Beside the estimation of profile and secondary losses, also those due to tip-
leakage are considered in this case, being an increasingly significant contribution for comparatively
small machines. The modeled physical phenomena account for the reduction of the useful mass
flow rate, and for a larger flow angle deviation downstream of the cascade [36]. In particular, tip-
leakage losses are assumed to be null across the stator, owing to the possibility of using an almost
hermetic sealing on the turbine shaft [5]. On the contrary, unshrouded rotor crowns are assumed, 76 Centrifugal Turbines for ORC Applications and the associated tip leakage losses estimated. Shrouded rows are generally preferred in small
turbines in order to reduce tip-leakages [37] but, in the present chapter, greater importance has been
attributed to easy the machine realization, see e.g. §3.3. 3.6.2 Design Methodology The design of the machines considered here, given their comparatively low power-output, is per-
formed following the novel design procedure purposely introduced at the end of §3.4. In particular, the pressure drops, the degrees of reaction, the radial chords, and the blades outlet geometric angles
are allowed to assume different values among the stages. The variables and the geometric param-
eters needed to perform the turbine design, see e.g. §3.2.1, are collected in Tab. 3.6. The design framework is similar to the one described in §3.5.4, and all the quantities are described therein. As anticipated, both the inlet diameter Din and the speed of revolution ' appear in this case among
the variables to be optimized, see e.g. §3.4. For the blade height H, which is a critical quantity given the low power-output, the minimal value compatible with mechanical resistance and manu-
facturing limits is assigned as the lower bound [5, 23]. Further analysis conducted on the machines
presented in §3.5 by means of CFD tools highlighted that, for centrifugal turbines, is beneficial for the machine performance to adopt maximum flaring angles lower than those suggested from the
axial turbines practice [11]. Following this results, the range of variation of the flaring angle δ is
now reduced to ±12'. Common parameters tcl [mm] 0.1 te [mm] 0.1 cl [mm] 1 Hmin [mm] 2 δmax ['] ±12 Design Variables LB UB Din [mm] (x 1) 20 100 ' [krpm] (x 1) 5 20 (pT,in/pS,out)stg (x Nstgs) 2 5 R (x Nstgs) 0.1 0.6 BDA ['] (x Nrows) 55 75 b [mm] (x Nrows) 2 12 Table 3.6: Design variables, with relative lower (LB) and upper (UB) bounds, and parameters
involved in the proposed design methodology as applied to a N-stages centrifugal turbine. 3.6.3 Results: Transonic Turbine The main features of the optimized 5-stage mROT are shown in Table 3.7. Is to be noted that the
optimal angular velocity, i.e. 12400 rpm, is considerably lower than the values encountered for
traditional axial or centripetal machines designed for a comparable application and power output,
see e.g. [35]. The optimal velocity triangles are shown in Fig. 3.10a and, as expected, the blades 77 Chapter 3 Pm [kW] 10.6 ηT'=0.5 0.79 Mmax 0.98 ' [rpm] 12400 Din [mm] 53 Dout [mm] 180 Hin [mm] 2 Hout [mm] 15 δmax ['] 9.0 Stage 1st 2nd 3rd 4th 5th (pT,in/pS,out)stg 2.2 2.5 2.6 2.4 2.3 R 0.31 0.36 0.39 0.40 0.40 Table 3.7: Main results for the 5-stage 10 kWM transonic turbine. geometrical angles vary along the machine, suggesting that customized geometry configurations are
needed in order to achieve highly efficient mROTs. As already observed in §3.5.4, the proposed design procedure proves successful in obtaining a smooth increase of the blade heights along the machine, with the concurrent increase of the radial
chords. The resulting meridional contour is depicted in Fig. 3.10b. The maximum flaring angles,
of the order of 9' are, are located on the last stage. The relation between the stages aerodynamic loading, the imposed deflections, and the corre- sponding profile losses, is similar to what already observed and discussed in the previous sections.
In particular, the specific work elaborated by the stages decreases along the machine, while the de-
flections and consequently the losses tend to follow an opposite trend, as shown in Fig. 3.11. As a
result, also in this case the stage efficiency increases along the machine, passing from about 72% in
the first stage to about 88% in the last one. As expected, tip leakages heavily affect the performance,
and the associated loss coefficient reaches maximum values in the first two rotors, characterized by
larger tip clearance/blade-height ratios. Notably, tip-leakage losses are comparable in magnitude
with profile and secondary ones. 3.6.4 Results: Slightly Supersonic Turbine The main features of the slightly supersonic 3-stage design are shown in Table 3.8. As anticipated,
the design is performed adopting two different loss-estimation methods, i.e. the Craig & Cox [15],
and the Traupel one [21]. The comparison among the predictions of such models is included in
all the figures presenting the outcome of the design. It can be concluded that the obtained turbine
design is scarcely dependent from the adopted loss prediction method. Coherently with the similarity theory [13], stating that the smaller the machine, the higher the speed of revolution needed to achieve better performance, the three-stage turbine rotates at
15400 rpm. The optimal velocity triangles are shown in Fig. 3.12a and, also in this case, the
blades geometrical angles vary along the machine. The meridional channel of the optimal design is
depicted in Fig. 3.12b, and its appearance is similar to that of the 5-stage machine. With respect to the transonic machine, the use of only three stages increases the blade aero- dynamic loading, as shown in Fig. 3.13a, thus lowering the overall turbine efficiency. The main
sources of loss are reported in Fig. 3.13b, from where it can be noted that the major differences 78 Centrifugal Turbines for ORC Applications 5 th rot 2 nd rot 3 rd rot 4 th rot 1 st rot M U3= 0.40 M W3= 0.88 M C3= 0.53 0.45 M W2= 0.61 M U2= 0.37 M C2= 0.95 0.99 0.48 0.61 0.97 0.58 0.43 0.98 0.81 0.52 0.61 0.99 0.53 0.96 0.71 0.39 0.38 0.97 0.97 0.93 0.91 1.00 0.45 0.41 (a) ROT radius [mm] H [m m ] 0 20 40 60 80 100 -40 -20 0 20 40 Rotational
axis 3 5 th rot 2 nd rot 3 rd rot 4 th rot 1 st rot 2 (b) Figure 3.10: Results for the design of the 5-stage transonic 10 kWM turbine designed following
the novel methodology presented in this chapter, adopting the boundary conditions reported in
Tab. 3.7, and the Traupel loss estimation method [21]. Fig. 3.10a shows the velocity triangles,
in black those referring to the rotor inlet section, in grey to the rotor outlet. The Mach numbers
corresponding to the different velocity components are also detailed. The meridional section is
depicted in Fig. 3.10b. among the two models are found in the predictions of the secondary loss coefficient in the first
stages, characterized by aspect ratios close to one. From this perspective, the Craig & Cox model
resulted to be somehow more conservative. 3.7 Conclusions The first critical evaluation of the centrifugal or radial-outflow turbine (ROT) architecture as a can-
didate technology for ORC turbo-generators is presented. All the special features involved in ROTs
design are enlightened, the main findings being that, in order to design efficient centrifugal turbines
it is needed that i) the blade discharge geometric angles, the radial chords, the stage expansion ra-
tios, and the reaction degrees are allowed to vary among each cascade, and ii) the diameter and the
speed of revolution are included among the optimization variables. It is discussed how simplifying assumptions usually adopted in the axial turbines practice are typically not applicable. A novel design methodology is derived and presented for the preliminary
sizing of ROTs in the power size range from several MWE down to few kWE. The in-house mean-
line optimization code zTurbo, which allows to determine the preliminary design of ORC turbines
of various configurations and working with different fluids, is presented and adopted to verify the
novel method by presenting several exemplary design exercises. First, the design of two 1 MWE centrifugal turbines is presented, a transonic six-stage and a supersonic three-stage machines. These expanders handle an expansion ratio of 60, and rotate at
3000 rpm. Simplifications derived from the axial-turbines practice are adopted in order to illustrate 79 Chapter 3 N row w [kJ /kg] 2 4 6 8 10 0 0.5 1 1.5 2 2.5 3 3.5 5 6 7 8 9 10 w Ψ Ψ (a) N row [% ] 1 2 3 4 5 6 7 8 9 10 0 5 10 p s l ζ ζ ζ ζ (b) Figure 3.11: Design results for the 5-stage transonic 10 kWM turbine of Fig. 3.10. 3.11a: evo-
lution of the load distribution among the stages, in terms of the aerodynamic loading expressed by
the work coefficient Ψ, and of the stage specific work w. 3.11b: row-by-row evolution of the kinetic
energy loss coefficients ζp (solid lines), ζs (dash dotted lines), and ζl (dashed lines) accounting for
profile-, secondary- and tip leakage-losses. The presented results are obtained with the Traupel loss
estimation model [21]. their consequences. The results of the design exercises, carried out with zTurbo, confirm that the
adopted assumptions lead to unwanted design features, such as converging meridional channels and
large flaring angles on the last stages. The predicted fluid-dynamic efficiency for the transonic and
the supersonic machine is around 86% and 81%, respectively. Thus, the down-scaling potential of the centrifugal architecture is assessed, by applying the novel design methodology to the sizing of two 10 kWE ROTs, handling an expansion ratio of 45.
The design of a 5 stages transonic turbine, and of a 3 stages slightly supersonic one is presented. The
proposed design procedure proves valuable in overcoming the criticality previously highlighted. In
particular, the resulting meridional channel monotonically diverges maintaining maximum flaring
angles lower than 10'. The resulting turbines are projected to exceed a fluid-dynamic efficiency of
79% and 77%, with speed of revolution around 124000 and 15400 rpm, respectively. This research therefore demonstrates that the ROT architecture is a promising concept for fu- ture ORC power systems, capable of preserving its features and performance when downscaled, for
both transonic and slightly supersonic configurations. In particular, transonic machines are expected
to outperform the supersonic one during partial load operations, thus contributing to significantly
enhance the average efficiency of the ORC turbo-generator which, in the typical case, is called to
work within a wide range of operating conditions. The detailed part-load modeling tool necessary to
assess and quantify this last point will be developed as one of the next steps of the present research.
Finally, CFD-based tools have a demonstrated their strong potential in deepening the results of the
mean-line analyses presented here, and they will be therefore further developed in the future. Nomenclature 80 Centrifugal Turbines for ORC Applications Pm [kW] 10.3 ηT'=0.5 0.77 Mmax 1.33 ' [rpm] 15400 Din [mm] 57 Dout [mm] 162 Hin [mm] 2 Hout [mm] 18 δmax ['] 11.8 Stage 1st 2nd 3rd (pT,in/pS,out)stg 3.6 4.1 4.5 R 0.25 0.37 0.42 Table 3.8: Main results for the 3-stage 10 kWM supersonic turbine. 2 nd rot 3 rd rot 1 st rot M U3= 0.58 M W3= 1.06 M C3= 0.52 M W2= 0.76 M U2= 0.50 M C2= 1.23 0.62 1.16 0.58 1.20 0.66 0.93 0.73 0.59 1.12 1.31 1.21 0.49 (a) ROT radius [mm] H [m m ] 0 20 40 60 80 100 -40 -20 0 20 40 Rotational
axis 3 2 nd rot 3 rd rot 1 st rot 2 (b) Figure 3.12: Results for the design of the 3-stage supersonic 10 kWM turbine designed following
the novel methodology presented in this chapter, adopting the boundary conditions reported in Tab.
3.5. Fig. 3.12a shows the velocity triangles, in black those referring to the rotor inlet section, in
grey to the rotor outlet. The Mach numbers corresponding to the different velocity components are
also detailed. The solid lines represent the results obtained with the Traupel model [21], while the
dashed ones those pertaining to the Craig & Cox one [15]. The corresponding meridional section is
depicted in Fig. 3.12b. In this case, the results of the two models are not distinguishable. s, p = specific entropy [kJ kg''1 K''1], pressure [bar] T , h = temperature ['C], specific enthalpy [kJ kg''1] ρ, c = density [kg m''3], speed of sound [m s''1] MW, z = molecular weight [g mol''1] , compressibility factor 81 Chapter 3 A, ' m = flow passage area [m2], mass flow rate [kg s''1] ' V = volumetric flow rate [m3 s''1] R = ''hSS,rot/''hTS,stg = stage reaction degree Re, M = Reynolds and Mach numbers Sh, rt = shape factor, rothalpy [kJ kg''1] w, P = specific work [kJ kg''1], power [kW] C, W, U = absolute, relative, and rotational speed [m s''1] U = (Uin + Uout)stg/2 = average stage peripheral velocity [m s''1] BDA = blade geometric discharge angle ['] V = mean flow velocity magnitude [m s''1] D, S = cascade diameter [m] and pitch [m] H, b = blade height and chord [m] cl, tcl = inter-row radial and tip clearance [m] o, te = throat width and trailing-edge thickness [m] Nx = cardinality of quantity x Greek symbols ' = recovery fraction of discharged kinetic energy η = efficiency Ψ, Φ = work and flow coefficients α, β = absolute and relative flow angles ['] ''x = finite difference for quantity x ' = angular speed of revolution [rpm] δ = row flaring angle ['] ǫ = correction factor for blocking effects ζ = ''hS,loss V2 out /2 = loss coefficient (''hS,loss is the static enthalpy drop due to the considered loss, velocity V = C for the
stators, and V = W for the rotors) Subscripts E, M = electrical, mechanical min, max = minimum, maximum value CR = critical thermodynamic conditions (liquid-vapour) T, S = total and static thermodynamic conditions th, in, out = sonic throat, inlet, and outlet sections r = radial direction st, rot, row, stg(s), bld(s) = stator, rotor, row, stage(s), blade(s) Acronyms ORC = Organic Rankine Cycle ROT = Radial Outflow Turbine 82 Centrifugal Turbines for ORC Applications N row w [kJ /kg] 2 4 6 0 0.5 1 1.5 2 2.5 3 3.5 10 12 14 16 Ψ (a) N row [% ] 1 2 3 4 5 6 0 5 10 15 ζ (b) Figure 3.13: Design results for the 3-stage supersonic 10 kWM turbine of Fig. 3.12. 3.13a: evo-
lution of the load distribution among the stages, in terms of the aerodynamic loading expressed by
the work coefficient Ψ, and of the stage specific work w. 3.13b: row-by-row evolution of the kinetic
energy loss coefficients ζp (solid lines), ζs (dash dotted lines), and ζl (dashed lines) accounting for
profile-, secondary- and tip leakage-losses. The black lines represent the results obtained with the
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1986. ACS, Washington-DC, USA. 87 4 Thermal Energy Storage for Solar Powered ORC Engines Part of the contents of this chapter appeared in: E. Casati, A. Galli, & P. Colonna
Solar Energy 96(0), 205-219 (2013) c Elsevier 2013 '' Reprinted with permission E. Casati, A. Desideri, F. Casella, & P. Colonna
Proceedings of the 18th IEA SolarPACES Conference, Marrakech - MA (2012) c SolarPACES 2012 '' Reprinted with permission Chapter 4 Abstract The feasibility of energy storage is of paramount importance for solar power systems, to the point that it can be the technology enabler. Regarding concentrated solar power (CSP) sys-
tems, the implementation of thermal energy storage (TES) is arguably a key advantage over systems
based on photovoltaic (PV) technologies. The interest for highly efficient and modular CSP plants
of small to medium capacity (5 kWE''5 MWE) is growing: organic Rankine cycle (ORC) power
systems stand out in terms of efficiency, reliability and cost-effectiveness in such power-range. In this chapter, a thorough investigation on thermal storage systems tailored to high-temperature ORC power plants is addressed first, stemming from the observation that the direct storage of the
ORC working fluid is effective thanks to its favorable thermodynamic properties. The concept of
complete flashing cycle (CFC) is then introduced as a mean of achieving an unmatched system
layout simplification, while preserving conversion efficiency. This is a new variant of the Rankine
cycle, originally introduced by the presented research, whereby the vapor is produced by throttling
the organic working fluid from liquid to saturated vapor conditions. The presentation and discussion of a case study follows: a 100 kWE CFC system with direct thermal energy storage, coupled with state-of-the-art parabolic trough collectors. The proposed
turbogenerator achieves an estimated 25% efficiency, which corresponds to a value of 18% in de-
sign conditions for the complete system. With siloxanes as working fluids, the estimated values of
storage density are around 10 kWhE m'' 3 ST, without considering additional filling materials. A dynamic model, developed and for the complete system, is used to investigate the perfor- mance under extreme transient conditions. By adopting a relatively simple and robust control strat-
egy, the storage system is demonstrated to be effective in decoupling the solar field and the ORC
power block, which can thus be operated close to nominal conditions notwithstanding the environ-
mental disturbances. The feasibility of remotely controlled operation is thus positively assessed by
means of this preliminary study. 4.1 Introduction The debate over the advantages and disadvantages of various solar technologies is lively [1, 2].
Peters and colleagues compared PV- and CSP-based systems for large-scale solar power plants (>
50 MWE), and concluded that the cost and efficiency of storing energy can turn the competitiveness
in favor of CSP systems [3]. Another potentially important benefit of CSP systems integrating TES,
along with dispatchability, is their ability to provide grid flexibility: this feature might enable higher
overall penetration of other variable-generation technologies such as those based on PV cells and
wind turbines [4]. Recent studies have underlined the techno- and socio-economic opportunity of shifting toward a global energy system which is more integrated and complex than presently, and which heavily
relies on distributed generation [5]. Within the same context, also small-size CSP power plants
in the 100 kWE''5 MWE power range have been investigated [6, 7]. It has therefore been argued
that the new development paradigm of ''getting bigger by going smaller' could provide a path to
viability for CSP technologies in general, through modularity and economy of production, thus
overcoming the bankability issue which is negatively affecting the sector [8]. Another notable advantage of thermal CSP plants for distributed generation is the possibility of co-generating electricity and useful thermal output for maximum energy utilization and flexibility.
The thermal energy discharge from the primary mover can either be used for industrial or domestic
purposes on-site, or/and drive an absorption chiller for air-conditioning or process cooling [9, 10]. Among the technologies suitable for high-efficiency conversion of thermal power into electric- ity and heat in this range of capacity, ORC turbogenerators stand out in terms of reliability and 90 Thermal Energy Storage for Solar Powered ORC Engines cost-effectiveness, see, e.g., Ref. [11]. ORC power plants are steadily adopted for the increasing
exploitation of geothermal reservoirs, while the growth of the number of ORC power systems for
the thermal conversion of biomass fuel and industrial waste heat is remarkable [12]. ORC-based
CSP plants have been widely studied, and prototypes were put into operation already several years
ago [13, 14]; commercial power plants went recently on-line [15], and new ones are planned or are
currently under construction. To the knowledge of the author, however, no research has been published on TES systems specifically conceived to be integrated into ORC power plants. The study documented here stems
from the need of a thorough investigation on thermal storage systems tailored to ORC power plants,
and from the observation that the direct storage of high-temperature ORC working fluids is effective
thanks to its high heat capacity and other favorable thermodynamic properties. The chapter is structured as follows: in §4.2 the organic fluids of the class of siloxanes are briefly introduced; these compounds are widely used as working media for high temperature ORC
power systems. Is to be noted that the addition of storage filling materials other than the working
fluids itself is not considered at this stage of the research. In §4.3 a brief overview of TES-systems integration in power stations is reported. §4.4 deals in detail with the proposed technical solutions for the direct thermal storage of working fluid, discussing their applicability to ORC systems. A
case study illustrating the application of one of the proposed storage systems is treated in §4.5. §4.6 summarizes the conclusions and the foreseen developments. 4.2 Siloxanes: High-Temperature ORC Working Fluids The ORC working fluids considered in this study belong to the family of siloxanes, see table 4.1.
These light silicon oils are already employed in commercial high-temperature ORC applications
since they are non-toxic, environmentally friendly, low-flammable, bulk-produced and highly ther-
mally stable; mixtures of siloxanes are widely employed as heat transfer fluids (HTF) in multiple
fields, comprising the CSP industry [16, 17]. Multiparameter equations of state, employing the Table 4.1: Main properties of the fluids considered in this work. MW: molecular weight, Tboil:
normal boiling temperature, pvap@80'C: vapour pressure at 80 'C. Fluid MW TCR pCR ρCR Tboil pvap@80'C [g mol''1] ['C] [bar] [kg m''3] ['C] [bar] Water 18.0 373.9 220.64 322.4 100.0 0.474 D6 444.9 372.7 9.61 246.8 245.0 0.002 D4 296.6 313.3 13.32 301.3 175.3 0.035 MDM 236.5 290.9 14.15 302.9 152.5 0.091 Span-Wagner functional form [18], have been recently developed for these fluids [19, 20]. These
thermodynamics models, implemented in a software library, are adopted throughout this work
[21, 22]. The specific thermophysical properties of the working fluids heavily affect the design
of the most critical components, namely the turbine and the heat exchangers. Other fluids may be
preferred for the same application, based upon multiple considerations, see e.g. Refs. [11, 23]. 91 Chapter 4 Figure 4.1 illustrates the thermodynamic features of interest in this case for siloxane D4 and water
using the T ''s state diagram. A typical analysis of thermodynamic cycles is presented here, whereby
the cycle minimum and maximum temperature are fixed, and different working fluids are evaluated
in terms of obtainable conversion efficiency and other technological aspects. Note that fixing the s [kJKg -1 oC-1] T [ o C ] -0.4 -0.2 0 0.2 0.4 0.6 0.8 100 150 200 250 300 350 400 CR h g c'' c d f p min= 0.09 bar T min p max= 4.92 bar T flash d ls d vs s=s c a a'' e'' b b'' T max e h=h c '' '' '' (a) Siloxane D4 s [kJKg -1 oC-1] T [ o C ] 2 4 6 8 100 150 200 250 300 350 400 CR 4 3 6 1 5 p min= 1.01 bar T min p max= 39.76 bar T flash 3 ls 3 vs h=h 2 2 T max (b) Water Figure 4.1: Comparison between the T ''s thermodynamic diagram of D4 and that of water: the
highlighted temperature levels, resulting from the studied application and thus common to both
fluids, are Tmin = 100'C, Tmax = 250'C, and Tflash = 220'C (dash-dotted black lines). CR: liquid''
vapour critical point, solid-black line: saturation line enclosing the VLE region, solid-grey: isobaric
lines, dashed-black: iso-enthalpy lines. Note that the scale of the specific entropy in diagram (a) is
different from that in diagram (b). minimum and maximum cycle temperature results also in the specification of the minimum and
maximum cycle (saturation) pressure for the considered fluid. The expansion ratio available for
work extraction is thus also fixed. From these preliminary considerations, the comparison of the thermodynamic features of molec- ularly complex fluids with those of water along expansions yields interesting conclusions: I A consequence of the large complexity of the fluid molecular structure, thus of the high value of the specific heat capacity, is the so-called retrograde shape (positive slope) of the
bubble line in the T ''s diagram of the fluid, which helps visualizing how the expansion of the
saturated vapor is inherently dry, see, e.g., Ref. [24]. This thermodynamic feature implies,
contrary to what can be observed for a simple-molecule fluid like water, that for a complex
organic fluid (a) Starting from saturated liquid conditions, see state c in fig. 4.1a, an isenthalpic pressure-reduction representative of a flashing process can result in the fluid being
in a saturated''vapor state (process c '' d, whereby qd = 1). If the pressure is further reduced, also superheated-vapour states are attainable. (b) The previous observation, applies also to an isentropic pressure-reduction process (c '' e'). 92 Thermal Energy Storage for Solar Powered ORC Engines (c) An isentropic expansion starting from saturated vapour conditions always evolves towards superheated''vapour states (dvs '' e). (d) Furthermore, the temperature of the superheated vapor at the end of the expansion may be so high that internal heat-regeneration is mandatory if high cycle efficiency
is required [25]. II Mainly as a consequence of the higher molecular weight, a lower specific enthalpy drop is associated with the given expansion. Thus, the working fluid mass-flow through the ex-
pander must be larger for the same power output. In combination, the low specific enthalpy
drop and the higher mass-flow rate allow for the realization of comparatively simple and
efficient turbines even for low or very low power outputs [14, 23]. III The saturation pressure corresponding to the maximum cycle temperature is lower (e.g., 4.9 bar for D4 versus 39.8 bar for water): this is a major advantage if TES is of interest.
Conversely, very low condensation pressure (e.g., 0.09 bar for D4 versus 1.01 bar for water)
entails technological challenges for other components (e.g., turbines and condenser), see
Refs. [11, 26]. 4.3 Concepts of TES Systems for Power Plants The basic principle of storage system integration into power plants is the so-called flow-storage,
whereby the TES gets its charge according to several main concepts, corresponding to the plant
configurations summarized in fig. 4.2a. In solar power plants, storage systems deal with secondary
energy since, as opposed to fuelled thermal plants, storage on the primary energy side (fuel storage)
is not possible. Fuel control would be feasible (defocusing of heliostats or collectors) but it is
avoided because of the energy loss. Energy storage integrated into the primary heat transfer loop,  a b c d 1 2 3 4 (a) Basic schemes for secondary energy storage in
Rankine power plants: 1) primary energy, 2) sec-
ondary energy, 3) mechanical energy, 4) electrical
energy. The tags a, b, c and d help identifying sev-
eral so-called flow-storage options, adapted from
[27]. Solar field
(Oil) TES system
(Oil/Salt) Heat exc.
(Oil/H20) Power block (H20) (b) State of the art: simplified process flow
diagram of the Andasol solar power plant,
adapted from [28]. Figure 4.2: Thermal energy storage in Rankine-cycle power plants. 93 Chapter 4 see case a of fig. 4.2a, is the most adopted concept in commercial CSP plants. In this case, sensible
heat is accumulated into a liquid, which can be thermal oil and/or molten salt [29]; in so-called
direct systems the heat transfer fluid serves also as storage medium, while in indirect systems a
separated system is used to store thermal energy, see fig. 4.2b. The Spanish Andasol solar power plants, which are in operation since 2009, are representative of the state-of-the-art for technology based on parabolic troughs [30]. They adopt an indirect ther-
mal storage system whereby thermal oil transfers the energy collected from the solar field to molten
salt contained in two tanks, see fig. 4.2b; such layout, involving multiple subsystems with different
working fluids, is arguably unfeasible for small-scale solar power plants due to complexity and cost. Other concepts, see cases b, c, and d in fig. 4.2a, are based on the storage of energy in the working fluid itself, and have been implemented in steam power plants. Thermal storage can be used
to make pre-heated feed water available to the steam generator (b), mainly for peaking purposes,
in power plants with regenerative feed-water heating [31]. The storage vessel can also supply the
turbine with steam in saturated or superheated state, at both live-steam (c) or medium/low pressure
(d) conditions. Also in these cases both indirect and direct system concepts can be implemented. Indirect systems for working fluid storage are extensively investigated as TES for direct steam generation (DSG) power plants [28]. Direct systems have been successfully used for decades, and
also recently built CSP plants adopt this TES configuration. A direct system for the accumulation
of working fluid is often called steam accumulator [27, 29]. The main advantage of steam accumu-
lators is that they are simpler than indirect systems, in that no intermediate fluid loop and the related
heat exchangers are needed; §4.4 treats in detail these concepts. The evaluation of the profitability of energy systems is a complicated task, involving a number of considerations from different domains. Among the main elements of the evaluation one needs to
consider the projected investment cost and efficiency of the complete system, possible environmen-
tal hazards, operation strategy, O&M cost, and the local regulatory framework, i.e., tariffs and/or
incentives [32]. In particular, when newly proposed concepts are considered, the uncertainty related
to equipment costs has a large impact on the reliability of such evaluation [33]. Also for this rea-
son, an exhaustive economic evaluation is beyond the scope of the present work, which in turn is
aimed at the thermodynamic and technical assessment of a new concept for thermal energy storage
suitable for small solar-powered ORC plants. The analysis identifies and discusses the factors af-
fecting the performance and the projected costs of the considered systems, such as their efficiency,
the temperature and pressure levels in the storage system, the volumetric expansion ratio across the
turbine, and the pressure level in the condenser. The typical thermodynamic performance parameters for a TES system integrated into a thermal power plant are 1. the storage density ρex [kWhM m'' 3 ST], which is useful to evaluate the size of the storage unit and, thus, to give a first estimate of its cost. Since thermal energy is stored for subsequent
conversion into work, density of available energy (exergy) has to be considered [34]. The
parameter EEED (Equivalent Electrical Energy Density [kWhE m'' 3 ST ]), accounting for the subsequent conversion into electricity, is also introduced here. This value quantifies the
equivalent electrical energy stored as thermal energy into one cubic meter of liquid at the
storage conditions. For a given size of the storage in terms of equivalent hours of storage
heq,st, the value of the EEED of a certain TES concept allows for a preliminary estimation of
the storage volume and of the required mass of fluid. 2. The turnaround efficiency ξturn, which accounts for exergy losses along the entire charge- standstill-discharge cycle, and depends both on design and on operational parameters. ξturn
is typically chosen as the objective variable for the thermodynamic optimization of a storage 94 Thermal Energy Storage for Solar Powered ORC Engines system [35]. Systems implementing the direct storage of the working fluid attain the highest
levels of ξturn, namely up to 95%, mainly as a consequence of the absence of any heat
exchange process external to the storage vessel [27]. 4.4 Direct Storage of Working Fluid in Rankine Power
Stations
The concepts originally proposed and adopted in steam power plants are introduced here, and their
extension to ORC systems is discussed. Being direct storage systems highly integrated into the
power plant, both the storage concept and its discharge mode have to be considered in order to
properly characterize the system. Three main storage concepts and three discharge methods have
been introduced in the past [27]: these are described in §4.4.1 and §4.4.2 respectively. §4.4.3 treats their combination to form several possible storage systems, refer to figure 4.3. 4.4.1 Storage Methods The working fluid is typically stored in the liquid phase, in order to exploit its greater storage
density. A STORAGE AT CONSTANT PRESSURE It entails the storage of sensible heat in liquids, usually at atmospheric pressure. Two-tank
arrangements, as well as single-tank systems exploiting the thermocline effect (displacement
storage) are feasible [36, 37]. Silicon oils have been already adopted as the storage fluid in
these systems [38]. If the direct-storage configuration is adopted, pressurization is needed
in order to prevent boiling, and an external pressurizer may be needed in this case. Hot
pressurized fluid can thus be extracted from the storage vessel at constant pressure, and this
is the main advantage in power generation applications. B EXPANSION STORAGE AT ALMOST CONSTANT PRESSURE In this case liquid and vapour working fluid are stored in thermodynamic equilibrium at
the saturation temperature. A ''vapour cushion' is present at all times in the upper part of
the storage tank. Hot saturated liquid is extracted from the bottom of the vessel, causing
the vapour volume to increase. Additional vapour is produced by evaporation of a small
part of the liquid volume, thus causing the pressure to decrease slightly. The drains coming
back from the working fluid loop have to be collected and stored in a separate cold-storage
vessel, which, being at lower temperature and pressure, is also relatively inexpensive. With
respect to the displacement storage solution (A), the complications related to pressurization
and thermocline promotion can be avoided and the vessel does not have to withstand severe
thermal gradients during the charge-discharge phases. C SLIDING PRESSURE STORAGE (RUTHS ACCUMULATOR) In analogy with method B, liquid-vapour equilibrium is maintained in the storage vessel. In
this case, however, not the liquid but the vapour forming the cushion is extracted during the
discharge phase. The wide pressure swing during the discharge phase, a characteristic of
this method, is a major drawback as far as power production is concerned [39]. The main
advantage of this storage method is the fast reaction time, allowing for high discharge-rates
of saturated steam. 95 Chapter 4 4.4.2 Discharge Methods 1. VAPOR GENERATION BY FLASH EVAPORATION Internal flashing in the vessel pertains to the sliding pressure method of storage. In external
flash processes the liquid is extracted from the storage tank, and thus throttled; processes
featuring multiple flashing steps are also conceivable. The obtained vapour stream can be
sent directly to a turbine.
In case water is the working fluid, flashing systems require the adoption of so-called wet-
turbines, which imply well-known technical challenges and rather low efficiency [40]. How-
ever, in case the working fluid is an organic compound, the flashed saturated vapour can be
directly fed to a high efficiency ''dry' turbine (see Sec. 4.2, point Ic). The so-called ret-
rograde characteristic of the working fluid allows also for the complete evaporation of the
liquid stream by throttling (see Sec. 4.2, Ia). The phase-separator and the relative liquid-
drain circuit are therefore, in principle, unnecessary. 2. FEED WATER STORAGE In case of conventional thermal power stations, thermal storage upstream of the steam gen-
erator is a proven solution for peak-load generation. With such a method, peak-load can
be sustained to an extent limited by the amount of power to be gained by cutting-off all the
regenerative bleeds, and by the overload capacity of the main turbine generator set [27]. In
the case of ORC power systems, extractive regeneration is never employed, therefore the
peaking potential would be due exclusively to the overload capacity.
This discharge method is not applicable to solar steam power plants as the only storage sys-
tem; in periods with low solar radiation, feeding the turbine only with steam can become
impossible [41]. 3. CASCADING STORAGE A combination of method 1 and method 2 provides more flexibility for the complete system. In case the working fluid is formed by complex molecules, a fourth discharge method can
be identified, namely 4. DIRECT LIQUID EXPANSION The liquid extracted from the pressurized storage vessel can be directly fed to an expander. If
the working fluid is a complex organic molecule, the so-called wet-to-dry expansion process
becomes possible (see Sec. 4.2, Ib). Wet-to-dry expanders have been proposed and tested
with promising results [40, 42]. However, since none of them has reached technological
maturity, wet-to-dry expansion has not been considered in this study, despite its notable
potential. 4.4.3 Storage Systems Figure 4.3 shows the main possible system configurations obtained by combining the storage meth-
ods described in Sec. 4.4.1 (A, B, and C), and the discharge methods treated in Sec 4.4.2 (1, 2, and
3), see Ref. [27]. The configurations C2 and C3 are not realizable, while configuration B and C may
be combined: vapor may be taken from an expansion storage vessel in addition to liquid (shown by
the lines for configurations B2/C1 and B3/C1). The A1 scheme has been proposed for nuclear power plants [27], while the B2/C1 scheme for CSP plants [41]. The A3 scheme gained acceptance in the late 1920s: the displacement storage
plant of the coal-fired power station in Mannheim, Germany, is well known [39]. The C1 scheme
(pure sliding pressure) found wider application, mainly as a solution for buffer-storage. Within 96 Thermal Energy Storage for Solar Powered ORC Engines METHOD OF STORAGE (A) DISPLACEMENT (B) EXPANSION (C) SLIDING PRESSURE M O D E O F D IS C H A R G E (1 ) V A P O R ( F L A S H E D ) (2 ) F E E D R E P L A C E M E N T (3 ) C A S C A D IN G A1 A2 A3 B1 C1 B2 B2/C1 B3 B3/C1 Figure 4.3: Main configurations of direct storage systems for steam power plants, as a com-
bination of storage methods and discharge modes. Labels correspond to those adopted for the
description in §4.4.1 and §4.4.2. For the sake of simplicity, only single-stage flash ORC systems are considered, without internal regeneration. Adapted from [27]. the island grid of Berlin, the 50 MWE Charlottenburg plant - built in 1929 - has been operated with
steam accumulators of 67 MWhE storage-capacity for more than 60 years. Sliding-pressure systems
have recently been realized [43], and this concept has been proposed as a solution to supply DSG
plants with buffer-storage capabilities [44]. Two-phase refrigerant accumulators working according
to this principle are key components in automotive air conditioning systems [45]. It can thus be concluded that all the above mentioned concepts are applicable in principle to ORC power systems. However, applying the very same concepts for thermal energy storage to ORC
power plants leads to EEED levels (see Sec. 4.3) which are lower than those of direct water-steam
systems, and also of state-of-the-art indirect systems (see Sec. 4.5). In case the working fluid is a
siloxane, for a given power output, the same thermal storage capacity requires a larger vessel, if
compared to a steam power plant. It is worth noting that the problems related to fluid containment at concurrently high-pressure and high-temperature levels, which have ultimately hindered the diffusion of water-steam storage
systems, are reduced in case working fluid is an organic compound (sec. 4.2, III). Beside the
vessel volume and the pressurization level, also the cost of the fluid largely contributes to the total
investment cost of the storage system. At present, siloxanes are approximately two times more
expensive than synthetic oils (typically mixtures of diphenyl-diphenyl ether), in terms of cost per
unit of thermal energy delivered [32]. However, contrary to synthetic oils, siloxanes are classified
as non-hazardous materials. Such classification is expected to play an important role if the proposed
technology will be applied, particularly if the distributed energy scenario is considered. 97 Chapter 4 The cost of the storage system is however only a fraction of the final investment for a power plant. The case study presented in §4.5 shows that the direct-storage configuration allows for a substantial simplification of the overall layout of the plant, with a beneficial effect on its initial cost. 4.5 Case Study In order to evaluate the proposed integrated TES system for small-scale solar ORC power plant, the
system of figure 4.4a ( ' Wnet=100 kWE) has been studied. The ORC working fluid is circulated and heated in the SF, which is composed of parabolic trough
collectors with evacuated absorber tubes: the feasibility of such concept has been preliminarily
assessed in a recent study [46]. The main novelty is the adoption of one of the TES systems intro-
duced in sec. 4.4: the working fluid serves also as the storage medium, making the configuration
completely of the direct type. The selected TES system is based on a displacement-type storage,
with vapour generation through external flashing (type A1 in fig. 4.3). The concept is aimed at maximizing the simplicity of the plant layout, since lowering of initial cost and maintenance requirements, as well as ease and safety of remotely controlled operation, are
considered as key aspects for distributed power applications. The design data adopted here are reported in table 4.2: the general specifications are common to all the ORC plants modelled in this study (see also A.1 and A.2). A relatively high value of
the condensing temperature Tcond is chosen, since avoiding excessively low vacuum levels in the
condenser is mandatory in high temperature applications, because the presence of air due to inward
leaking accelerates the thermal degradation of the working fluid. The data specific to the proposed exemplary system in terms of fluid and operating conditions, have been determined based on the treatment described in A.1 and A.2, where the main trade-off
existing between system efficiency, plant simplification, and components design are discussed in
detail. Realistic assumptions regarding both the design of the dry air-cooled condenser and of the
plates-regenerator are considered. This information has been obtained from the preliminary design
of these components, performed with a commercial package for heat exchanger design [51]. 4.5.1 Working Principle In nominal conditions, the temperatures at the outlet of the solar field Tout,SF, and in the hot region
of the storage vessel TST,hot (which, in turn, equals that of the fluid fed to the ORC system), are con-
sidered to be both equal to Tc. For modelling purposes this is chosen as the main operating variable
(see A.1 and A.2), while pc is supposed to be maintained at a level higher than the corresponding
vapour pressure, by an external pressurizer (1 bar in design conditions). Cold fluid is extracted from the vessel (b) and pumped through the SF: under normal operating conditions the mass flow is controlled by acting on the pump in order to maintain a set outlet
temperature Tc. Also in this case the temperature at the outlet of the regenerator TORC,out, and that
of the stored cold fluid TST,cold, are assumed to be equal to Tb. The hot fluid extracted from the
storage vessel (c) is externally flashed to saturated vapour conditions, before being fed to the ORC
turbogenerator (d, with qd = 1, see Sec. Ia). The superheated vapour leaving the turbine enters the
regenerator (e), and then the condenser ( f ). The fluid, in saturated liquid conditions (a), is then
pumped back, through the regenerator, to the bottom part of the storage vessel (b). The mass flow circulating in the SF is determined by the available irradiation together with the area of the collectors which, in turn, is related to the chosen solar multiple (SM). Optimal combi- 98 Thermal Energy Storage for Solar Powered ORC Engines b  c c b d(q d=1 ) a e f 2 1 PI Ta m b , Vw ind ,  in c DN I T c Solar field (SF) TES system ORC plant (a) s [kJKg -1 oC-1] T [ o C ] -0.4 -0.2 0 0.2 0.4 0.6 0.8 100 150 200 250 300 350 CR c d(q d=1) f h=h(c) a e b (b) Figure 4.4: (a) simplified plant layout of a CSP ORC power plant working according to the single-
stage flash process, integrating a direct TES system based of the displacement-storage type, from
[47]. (b) cycle state points in the T ''s thermodynamic diagram of D4 (black points and solid-black
lines). CR: liquid''vapour critical point, solid-gray line: contour of the vapor-liquid equilibrium
region, dashed: iso-enthalpy line. nations of SM and storage-vessel size can be determined only through detailed techno-economic 99 Chapter 4 Solar field design data HCE Schott PTR-70 SCA ET-150 ηopt,p 0.75 DNIdes [W m -2] 850 θinc ['] 0 Tamb [ oC] 25 Vwind [m s -1] 0 ''pb'c' [bar] 1 SM 1 Main design data for the ORC plants ' Wnet [kWE] 100 heq,st [hours] 4 Tcond [ oC] 80 ''pp,cond [ oC] 15 ǫreg 0.85 ηs,turb 0.85 ηs,pumps''fans 0.75 ηM''E 0.97 ''pef [%pcond] 50 ''pfa [%pcond] 10 ''pa'b [bar] 0 ''pfan [Pa] 50 Design data for the exemplary system Fluid D4 pcond [bar] 0.035 TR,c = TR,st 0.998 Tc = TST [ oC] 312.6 pc = pST [bar] 14.2 Calculated design performance of the exemplary system ' mfluid [kg s -1] 1.81 ' mair [kg s -1] 8.61 ηORC 0.251 ηSF,glob 0.71 ηSYS,glob 0.18 Amirrors [m 2] 704 VRturb 246 EEED [kWhE m -3
ST] 6.2 VST [m 3] 65 mfluid,st [kg] 3E4 Table 4.2: Design data for steady-state modelling, common to all the simulated systems (see
also A.1 and A.2). For a detailed description of the adopted HCE and SCA technologies, see
Refs. [48, 49]. ''pb'c' : pressure drop in the SF, ''pp,cond: pinch point temperature difference in the
condenser, ǫreg: regenerator effectiveness [50], ηM''E: electro-mechanical efficiency of the generator
and of all the electrical motors. ''pef, ''pfa, ''pa'b, and ''pFan : pressure drops in the regenerator
(vapour side), in the condenser (process side), in the regenerator (liquid side), and in the condenser
(static, air side) respectively. optimization [41, 52]. The values adopted here have therefore to be considered as indicative. 4.5.2 Flashing Rankine Cycles with Organic Fluids The main implication of the working principle presented in Sec. 4.5.1 is that the plant always
operates according to a thermodynamic cycle which includes a flashing evaporation process while, 100 Thermal Energy Storage for Solar Powered ORC Engines usually, the flash process is adopted only when the storage is being discharged [27]. Referring to
figure 4.1, the ''flashing cycle' (FC) of the working fluid in the temperature-entropy diagram is
identified by the state points a, b, c, d (with qd = 1), e, f (1, 2, 3, 3vs, 4 for water). When evaluated
for the exploitation of thermal energy sources whose thermal capacity can be assumed as infinite,
such power cycles feature an inherently lower efficiency compared to the corresponding evaporative
cycle operating between the same maximum and minimum temperature (state points a, b, c, g, h, f , and 1, 2, 5, 6 for water) [40]. However, if the working fluids is an organic compound, it can be shown that the efficiency penalty affecting the flashing cycle may be comparatively low. A detailed
treatment is reported in A.1. Flashing ORC power systems for waste-heat recovery applications
have been recently investigated by Ho and colleagues [53]. The flashing cycle boasts notable benefits in case of a solar ORC power system with thermal storage: i) it avoids phase transition in the SF, with major advantages [46, 54, 55]; ii) it decouples
the SF and the ORC power block by means of a suitable direct thermal storage system, see figure
4.4a. A minor efficiency reduction can thus be accepted, in view of the substantial simplification it
allows for, both in terms of plant layout and operation. 4.5.3 Flashing the Organic Vapor Down to Saturated Conditions A further simplification of the plant configuration derives from the possibility of reaching complete
vaporization of the working fluid by flashing (see sec. 4.2, point Ia). In this way several components
become redundant, namely the flashing vessel and the liquid drain circuit. More details are provided
in A.2. To the authors'' knowledge, ORC power systems working according to the flashing cycle
principle, whereby the working fluid is throttled down to saturated vapour conditions before entering
the turbine, refer to figure 4.4b, have not been considered before, thus this concept is named here
complete flashing cycle (CFC). 4.5.4 Design Analysis Results The steady state modeling of the system is performed with an in-house code implemented in a well
known computer language for technical computing [56], coupled with an in-house library for the
accurate estimation of the thermophysical properties of the fluids [21]. The calculated performance
is reported in table 4.2, while table 4.3 shows the thermodynamic properties of the state points of
the thermodynamic cycle. Notwithstanding the selected high design value for Tcond, the calculated
efficiency of the ORC power system exceeds 25% which, combined with the efficiency of the SF,
yields a global efficiency in design conditions close to 18%. This value can be compared to the
measured values of recently-built state-of-the-art CSP plants. These steam power plants are much
larger, and adopt an indirect storage system with synthetic oil as HTF, and their efficiency is of the
order of 22% [57]. Even if no index of annual performance has been estimated yet, ORC power systems are char- acterized by excellent off-design performance. This characteristic can partially overcome the lower
design efficiency in a highly dynamic application such as CSP [46]. The calculated values of equivalent electrical energy density (EEED) storage are lower than those characterizing traditional TES solutions, and this holds for all the considered working fluids
(see fig. 8). The proposed system approaches, for the EEED, the limiting value of 6.2 [kWhE m -3
ST], see table 4.2, assuming that the storage vessel delivers its full energy content without any variation
in the discharged fluid properties (conditions corresponding to state c). Thermal losses, as well as
exergy losses due to deterioration of the stratification [58] are thus neglected: such simplifications 101 Chapter 4 Table 4.3: Thermodynamic properties of the state points of the ORC system. State labels refers
to the layout of fig. 4.4a and to the T ''s diagram of figure 4.1a. States 1 and 2 refer to the cooling
air stream. state T p v h s q [oC] [bar] [m3 kg-1] [kJ kg-1] [kJ kg-1 k-1] [kgsv kg -1 tot] a 80.0 0.04 0.001 -172.6 -0.43 0 b 205.6 14.20 0.001 59.1 0.12 - c 312.7 14.20 0.002 291.8 0.56 - d 283.2 8.49 0.011 291.8 0.57 1 e 234.9 0.06 2.489 233.6 0.59 - f 87.6 0.04 2.551 4.5 0.07 - 1 30.0 1.01 0.880 0.0 - - 2 67.0 1.01 1.052 37.2 - - are typically justified for daily charge-discharge cycles (relatively short standstill times). A recently
designed displacement storage system using synthetic oil as HTF, and proposed as an add-on to the
APS Saguaro ORC-based CSP plant [15], reaches the value of approximately 15 [kWhE m -3
ST] [59]. The lower value calculated for the proposed system is mainly due to the low specific work extracted
from the turbine, which causes the fluid to be injected back in the storage vessel at high temperature
(Tb ' TORC,out). 4.5.5 Dynamic Modelling In order to study the dynamic performance of the plant and its control system, a modular dynamic
model has been developed using the Modelica object-oriented modelling language [60]. The mod-
els of the ORC plant components have been taken from the recently developed ORC library [61],
which is in turn based on the ThermoPower library [62, 63], while the models for the TES system
and for the solar field were developed specifically for this work, possibly in combination with ex-
isting library models (as in the case of the solar collectors). The momentum equation is always
implemented in the stationary form, being the propagation of pressure disturbances much faster
than the process of mass and energy transport. Pressure and specific enthalpy are selected as state
variables, and all closure equations (pressure loss, heat transfer models, and fluid properties) are ex-
pressed as a function of (p, h). All the needed fluid properties (and their derivatives) are computed
with the ExternalMedia library [64] coupled to Fluidprop [21]. The dynamic models of the system
components, as shown in figure 4.4a, are shortly described in A.3. 4.5.6 Control Strategy As mentioned in §4.5.5, the models of a few components in the system implicitly account for ideal control of some local quantity by appropriate means, as detailed in A.3. The solar field pump model
incorporates an ideal mass flow controller (e.g., by acting on the pump rotational speed or on a
throttling valve), while the component modelling the flashing valve an ideal controller of the outlet 102 Thermal Energy Storage for Solar Powered ORC Engines steam quality. Both the model of the dry condenser and of the stratified storage tank embed an ideal
pressure controller, i.e. able of maintaining always the imposed pressure value without any dynamic
characteristic. This is appropriate for the level of detail of the present study, where the main focus
is on the dynamics of the temperatures in the solar field and in the storage tank. The control strategy selected in this preliminary study aims at keeping the temperature at the outlet of the SF (Tout,SF) close to the nominal value under transient conditions. This ensures that
the storage tank is always loaded from the top with fluid at the design temperature, thus avoiding
as much as possible mixing phenomena that could reduce the efficiency of the downstream ORC
system. The open-loop dynamic response of Tout,SF to variations of the pump flow rate strongly de- pends on the value of DNI: at low irradiation, the flow rate must be reduced to keep the outlet
temperature constant, so the system dynamics become slower. However, the analysis of a linearized
simplified model of this system (which is beyond the scope of this chapter) shows that its frequency
response does not change much with DNI in a frequency range slightly above '-1, where ' is the
residence time of the fluid in the solar field at nominal DNI. This allows to tune a fixed-parameters
proportional-integral (PI) controller with a crossover frequency 'c = 2''' 1 in that particular fre- quency range. In order to further improve the control performance, feed-forward compensation of the effects of DNI has been added to the controller output. The computation follows the assumption of negligi-
ble heat losses from the SF to the ambient; this of course relies on the possibility that DNI readings
from an accurate pyrheliometer are available to the control system. Finally, a lower saturation limit has been applied to the controller output, in order to prevent the flow rate from becoming too small for very low DNI, which could be dangerous in case of abrupt
solar irradiance increases such as, e.g., when a cloud leaves the field. For the present study, the low
limit is set at 1.0 kg s''1, with the nominal value being 2.7 kg s''1 and the maximum value being 4.5
kg s''1. 4.5.7 Dynamic Analysis Results The complete model introduced in sec. 4.5.5, and controlled according to the scheme described in
sec. 4.5.6, is used to study the dynamic performance of the case-study plant working as outlined in
sec. 4.5.1. As anticipated, the main goal is to assess if the whole system can be safely and efficiently
operated through automatic control procedures. From the point of view of safe operation, the main concern regards the possibility of thermal decomposition of the working fluid to occur: for D4 the limit is close to 400'C =Tmax [16].
Due to the favourable properties of silicon oils, the corresponding heat transfer coefficient is large
enough to prevent, under all the foreseeable operating conditions, the wall temperature to exceed
Tmax [46].
However, as a consequence of the adopted control strategy, a drop in the mass flow circulating in
the SF follows a reduction of the solar input: a subsequent sharp increase in the DNI may thus cause
the limit of Tmax to be exceeded somewhere along the absorber, on the internal wall surface (Twall). From the efficiency point of view, keeping the outlet temperature from the SF Tout,SF close to the nominal value allows to preserve the stratification in the storage vessel: the turnaround efficiency of
the TES system is consequently increased, and the power block can be operated in conditions close
to the design ones for a larger number of hours. The virtual plant is thus tested under a situation representative of extreme working conditions [65], whereby a series of clouds (3 in this example) causes the solar input to periodically drop, 103 Chapter 4 and than sharply return to the nominal value. This effect is modelled by applying a signal with
subsequent ramps to the DNI input of the solar field model (see fig. 4.5): the DNI is supposed to
drop down to 10% of its nominal value, perturbing the initial steady state condition (design point,
storage fully charged). The monitored quantities are the electrical power ' WE,net, the mass flow circulating in the SF ' mSF, the temperatures Tout,SF and TST,hot, and the maximum wall temperature along the absorber Twall,max. t [s] D N I ; S F [- ] T w al l, m ax [ o C ] 0 1000 2000 3000 4000 0 0.2 0.4 0.6 0.8 1 1.2 280 300 320 340 T wall, max DNI T wall, max 'm (a) t [s] D N I ; E , ne t [- ] T S T , hot ; T S F , out [ o C ] 0 1000 2000 3000 4000 0 0.2 0.4 0.6 0.8 1 280 300 320 340 E, net DNI T ST, hot T SF, out ' W ' W (b) Figure 4.5: Dynamic simulations results, for the virtual solar ORC plant, under time-varying
solar input. The black dotted line represents the non dimensional DNI (with respect to its nominal
value): it drops to 10% its nominal value in 5 s, remains constant for 240 s, then returns to its
nominal value in 5 s; the interval between two subsequent drops is approximately 230 s. 4.5a black
solid line: ' mSF; red dash-dotted line: Twall,max. 4.5b black solid line: ' WE,net; red solid line: Tout,SF; red dashed line: TST,hot. From the results reported in figure 4.5, it appears that the virtual plant is characterized by time constants which are large enough to lead to an overlapping effect of the disturbances, as already
noted in previous works [65]. The variation of the controlled variable ' mSF is shown in figure 4.5a. The ability of the simu- lated control system to maintain Tout,SF close to its nominal value is proved: the maximum predicted
range of oscillation around the design value is 25 'C (fig. 4.5b).
Also the temperature Twall,max, which occurs in the last segment of the discretized collector for all
the simulated conditions, remains within safe values and, in particular, it is always lower than its
design value, see fig. 4.5a.
The effectiveness of the TES system in decoupling the ORC power block from the SF is assessed
(fig. 4.5b): the oscillations in TST,hot (corresponding to the turbine inlet temperature) are substan-
tially damped with respect to those in Tout,SF: a maximum difference of about 10 'C is predicted. As
a consequence, the maximum drop in the delivered power ' WE,net is approximately 20%. 104 Thermal Energy Storage for Solar Powered ORC Engines 4.6 Conclusions This chapter documents a study about extending direct flow-storage methods applicable to steam
power plants to ORC power systems. So-called direct thermal storage systems are feasible, whereby
the same fluid is circulated in the heat source, serves as thermal storage medium, and is also the
working fluid of the ORC turbogenerator. A case study regarding a 100 kWE solar plant imple-
menting such concept is presented: the proposed system features a constant-pressure thermocline
storage system, with vapour generation through external flashing of the liquid extracted from the
storage vessel. The thermal storage system can be integrated into the plant, thus decoupling the thermal energy source from the ORC power block: the system can be classified as constant-parameters storage,
whereby the fluid enters and leaves the vessel (in principle) in the same thermodynamic condition,
see states c and b in fig. 4.4a. Apart from a substantial simplifications in terms of both plant
layout and operational strategy, this configuration ensures high exergetic performance of the thermal
charge and discharge processes [27]. The power cycle operates according to a newly conceived variant of the Rankine cycle, whereby a flashing evaporation process precedes the power-generating expansion. The properties of the
adopted complex-molecule working fluids are such that flashing can lead to saturated or superheated
vapor conditions. This characteristic implies further simplifications of the system if compared to
conventional steam power plant system with thermal storage. The efficiency of an ORC power
plant working according to the newly introduced complete flashing cycle (CFC) may be, under the
described assumptions, comparable to that of a conventional evaporative ORC power system. A design value of the solar-to-electric efficiency of 18% is calculated for the exemplary 100 kWE solar ORC power system with direct thermal storage and the flashing cycle configuration. The
storage density values obtained with siloxanes as the working fluids are of the order of 10 kWhE per
m3 storage, i.e. around half of what is typically achieved with the storage of diathermic oils. The
advantages in terms of simplification of the plant layout could overcome the relatively low values of
storage densities, the need of pressurization, and the specific cost of the fluids. To be noted also that
the addition of storage filling materials, not considered in this work, is expected to be advantageous
under these aspects. A dynamic model, developed for the complete system, is used to investigate the performance under extreme transient conditions: the reaction to the passage of subsequent clouds, causing the
solar input to drop to 10% of its nominal value, is simulated. A relatively simple and robust control
strategy allows to maintain the working fluid temperature at the outlet of the solar field approxi-
mately constant, without risking thermal decomposition of the fluid itself. The storage system is
demonstrated to be effective in decoupling the solar field and the ORC power block, which can
thus be operated close to nominal conditions notwithstanding the environmental disturbances. The
feasibility of remotely controlled operation is thus positively assessed by means of this preliminary
study. A detailed techno-economic analysis of the proposed system aimed at clarifying these open questions will be developed as the next step of the project. In order to improve system performance,
particularly in terms of storage density, it might be worth investigating the binary cycle configura-
tion, whereby direct thermal storage is implemented in the topping cycle. 105 Chapter 4 A.1 Comparison Between Flashing and Evaporative Or-
ganic Rankine Cycles
This section presents the thermodynamic evaluation of the steady-state evaporative (EC) and flash-
ing (FC) cycle configurations, as introduced in sec. 4.5. The effect of different working fluids is also
addressed. The general design data, common to all the modeled ORC systems, are those reported in
table 4.2, and figure 6 shows the conceptual plant layouts of the considered systems. The working
principle is the same described in sec. 4.5, whereby the ORC power block shown in fig. 4.4a has
been lumped here into a single component, and no storage system is considered. The thermody- P S F b '' g b ' m Solar field (SF) ORC plant (a) EC P S F b '' c b d v s d ls d'' ls d ' mliq ' mvap Solar field (SF) Flash system ORC plant Pflash (b) FC Figure 6: (a) simplified plant layouts of ORC power systems working according to the conven-
tional evaporative cycle, and (b) single-stage flash cycle. State points correspond to those in the
T ''s chart of fig. 4.1a. namic evaluation is carried on by varying the maximum temperature of the cycle, which is kept the
same, i.e., Tmax ' Tc = Tg. It is further assumed that: 1. In the EC the working fluid exits from the thermal energy source (the solar field) as saturated vapor at Tmax, i.e., state point g in fig. 6a; 2. In the FC the working fluid exits from the thermal source (c) in the state of saturated liquid at Tmax, and then undergoes the flashing process. It is assumed here that the flash evapo-
ration leads to saturated vapor conditions at the outlet of the flashing subsystem (process
c '' d, where qd = 1): a critical assessment of this assumption is presented in A.2. As a consequence, no liquid drains from the flash vessel have to be recirculated ( ' mliq = 0). From these assumptions follows that, for each value of Tmax, all the state points defining the two
thermodynamic cycles can be determined for a given working fluid. Note that the condensation
temperature Tcond is fixed and specified. The results of the steady state simulations, performed
with an in-house code implemented in a well-known language for technical computing [56], are
presented in figures 7 and 8. The main term of comparison is the global system efficiency ηSYS,glob, i.e. the solar-to-electric efficiency, defined as ηSYS,glob ' ηORC · ηSF,glob, (1) 106 Thermal Energy Storage for Solar Powered ORC Engines where ηORC ' ' Wnet/ ' QORC,in (2) is the thermal efficiency of the ORC system. ' Wnet = ' Wturb '' ' Waux is the electrical power output of the plant, decreased of the power consumption for auxiliaries; ' Wnet is constrained to be the same for all the simulated cases. ' Waux is obtained by summing the power consumption of all the pumps (subscripts P in eq. 3) and the fans in the system and it is therefore evaluated as ' Waux = ' WP ORC '' ' WP SF '' ' WP flash '' ' WFan. (3) ' WP flash in eq. 3 is zero for both the EC and the FC systems (in this last case by virtue of assumption 2), since no liquid drains from the flash are present. ' QORC,in is the thermal power supplied to the ORC system and, for the FC, it reads ' QORC''FC,in = 'mvap · (hc '' hb' ) + 'mliq · (hc '' hd' ls ). (4) Here the 2nd term in the right-hand side vanishes because of assumption (2). In the EC case, equation
4 becomes ' QORC''EC,in = 'm · (hg '' hb' ). (5) The global efficiency of the solar field is ηSF,glob = ' QORC,in/ ' Qav, (6) and it accounts for the optical and thermal efficiency. The thermal power made available by the
direct radiation of the sun at the given design point is given by ' Qav = DNIdes · ASF. (7) The area of the solar field ASF can be evaluated as ASF = ' Wnet/[ηORC( 'qabs '' 'qhl '' 'qpiping)] (8) All the terms of the denominator in eq. 8 represent thermal power specific to the m2 of SF aperture
area. 'qabs = DNIdes · ηopt is the thermal power absorbed by the collectors. Having assumed a null incidence angle for design calculations, the optical efficiency ηopt is equal to the peak value ηopt,p
[66]. 'qpiping accounts for thermal losses in the piping subsystem of the SF, and a value of 10 W/m 2 is assumed here [67]. ' qhl = F (Tin,SF, Tout,SF, θinc, Vwind) accounts for the thermal efficiency of the solar absorbers, and is evaluated according to the detailed procedure presented in Ref. [49]1. Figure 7a shows ηSYS,glob (eq. 1) as a function of Tmax. In order to better compare different working fluids, reduced temperatures are used (TR,max). As a consequence of the critical temperature
increase with molecular weight (table 4.1), and being the condensing temperature the same for all
the simulated cycles, more complex fluids attain higher efficiencies for a given TR,max. As expected,
being throttling a purely dissipative process, the FC efficiency for a given TR,max is always lower than
that of the corresponding EC for the same working fluid. For all the fluids this penalty decreases
for increasingly higher TR,max, and tends to vanish with larger molecular complexity of the fluid. It can thus be concluded that, if siloxanes are adopted as high temperature working fluids, and if the maximum cycle temperature is close to the fluid''s critical temperature, the flash cycle
configuration does not imply severe efficiency losses with respect to the traditional evaporative
cycle solution. 1The coefficients adopted in the correlation proposed in the reference have been slightly modi- fied, as a consequence of the different fluids and flow regimes, as discussed in Ref. [46]. 107 Chapter 4 T c,R [-] gl ob, S Y S [- ] 0.7 0.75 0.8 0.85 0.9 0.95 1 0.05 0.1 0.15 0.2 D 6-EC D 6-FC D 4-EC D 4-FC MDM-EC
MDM-FC η (a) Global system efficiency ηSYS,glob as a func-
tion of TR,max. T c,R [-] V R tur bi ne [- ] 0.7 0.75 0.8 0.85 0.9 0.95 1 10 0 10 1 10 2 10 3 10 4 D 6-EC D 6-FC D 4-EC D 4-FC MDM-EC
MDM-FC (b) Turbine volumetric expansion ratio VRturb as
a function of TR,max. Figure 7: Elements for comparison between corresponding evaporative and flashing ORC systems
for different working fluids. In case of flash cycles, throttling down to saturated vapor conditions is
assumed. The quantity ηSYS,glob can be considered as the key merit parameter in the comparison, since it is directly related with the area of the solar field and, thus, to the main cost-driver of any CSP installa-
tion [68]. However, also considerations about other critical components, such as the turboexpander
and the storage system, should be accounted for in order to better define a suitable working fluid
and the operating conditions for the given application. In particular the specific cost of the turbine,
for small-scale ORC systems, strongly influences the cost of the power block. Figure 7b shows the
turbine volumetric expansion ratio (VRturb = ( ' Vin/ ' Vout)turb) as a function of maximum cycle reduced temperature TR,max. The volumetric expansion ratio strongly influences the design/complexity of the
expander and therefore its cost [69]. For a given fluid and TR,max, the expansion due to the throttling
process causes the enthalpy drop across the expander and VRturb to be significantly lower in the
FC than in the EC case. Smaller expansion specific work and smaller volumetric expansion ratio
allow for the design of a more efficient turbine in the FC case than in the EC case, if the level of
technology (therefore cost) is to be the same. Note that if higher turbine efficiency for the FC case is
accounted for, the differences in ηSYS,glob shown in figure 7a between the FC and EC configurations
would be further reduced. In case flashing is considered as the discharge method of an hypothetical storage system (see sec. 4.4.2), state c can be regarded as the state of the fluid extracted from the storage vessel, such
that Tmax ' Tc = TST. This holds for the case-study presented in §4.5, whose storage density EEED (see sec. 4.3) can be evaluated as EEED = ' Wnet ' mvap + ' mliq · ρls 3600 [kWhE m'' 3 ST ] (9) In this case, ' mliq becomes zero because of assumption 2. This simplified approach assumes that the storage, initially fully charged with fluid in conditions corresponding to state c, delivers its full
energy content without any variation in fluid properties. Thermal losses, as well as exergy losses 108 Thermal Energy Storage for Solar Powered ORC Engines due to deterioration of the stratification [58] are thus neglected. Such simplifications are typically
justified for daily charge-discharge cycles, that is for relatively short standstill times. The EEED T c,R=Tst,R [-] E E E D [kW h E m -3 st or ed ] 0.7 0.75 0.8 0.85 0.9 0.95 1 2 4 6 8 10 D 6 D 4 MDM Properties at EEED=EEED MAX Fluid T c,R[-] Tc[ oC] p c[bar] D 6 0.895 333.5 6.3 D 4 0.938 293.8 11.0 MDM 0.895 276.2 12.3 Figure 8: Comparison between flashing organic Rankine cycles for different working fluids.
Throttling down to saturated vapour conditions is assumed. Equivalent electric energy density
EEED as a function of maximum cycle reduced temperature TR,max. reaches a maximum value for all the working fluids considered here. This maximum value does
not correspond to the maximum storage temperature; furthermore, the EEED line is quite flat in the
region where the maximum is reached. The differences among fluids are comparatively large, as
well as the conditions of the stored fluid in terms of pressure and temperature. In absolute terms,
the reached values of EEED, of the order of 10 kWhE m'' 3 ST, are around half of what is typically achieved with the storage of diathermic oils [32, 59] but, as anticipated, no additional filling material
is considered in this study. In order to summarize these results, table 4 reports the main values obtained with the simula- tions that are needed to select the working fluid, if D6 and D4 are considered. Only these fluids are
evaluated here since they allow for higher ηSYS,glob values. The comparison is then carried on, aim-
ing at the same value of ηSYS,glob, which is taken equal to the maximum value reached in case D4 is
the working fluid. Storing D6 at higher temperature is not considered here given the corresponding
extremely high values of VRturb, though it allows for the higher values of ηSYS,glob (up to 0.185). As expected, the two working fluids allow attaining the same efficiency at almost the same value of Tc, which however corresponds to a storage pressure pc 2.2 times larger in case D4 is the
working fluid. On the other hand, the condensing pressure in case D6 is the working fluid is 16
times lower. Its very low value constitutes a design criticality for the condenser and the turbine.
The volumetric expansion ratio of the turbine, for instance, is almost 4 times larger in case D6 is the
working fluid, whereby the inlet volumetric flows are similar.
The value of EEED is nonetheless 25% lower if D4 is the working fluid, and the corresponding
specific mass of fluid is 12% larger: these effects, combined with the higher pressure needed, would
make D6 the preferred working fluid if only the benefits for the thermal storage are considered. 109 Chapter 4 Fluid D6 D4 ηSYS,glob 0.178 0.178 TR,c 0.895 0.998 Tc [ oC] 333.6 312.7 pc [bar] 6.3 14.2 pcond [bar] 0.002 0.035 VRturb 954 246 EEED [kWhE m'' 3 ST] 8.2 6.2 mfluid [kg kWh'' 1 E ] 66 74 Table 4: Main information needed to compare solar ORC power systems with thermal storage
operating according to the flashing cycle, in case siloxane D6 and D4 are considered as the working
fluids. A.2 Complete Flash Evaporation as a Working Condi-
tion for ORC Power Systems
The analysis of the performance of a flashing ORC, see fig. 6b, as a function of the flashing con-
ditions is presented in this section. Only the results for working fluid D4 are reported, since they
are representative of all the other investigated systems featuring siloxanes as working fluid. The
system performance is evaluated according to the procedure and the parameters defined in A.1; in
this case, however, no simplifying assumption based on the absence of liquid drains can be applied
(see eq. 3 and 4): the liquid drains from the flashing vessel have to be compressed and circulated
back to the heat source, see figure 6b. This stream is supposed to merge with the main one in the
solar field, such that temperature equality between the flows is ensured, while the vapor is delivered
to the ORC turbogenerator. Figure 9a and 9b show the trends of the quantities of interest as a function of the flashing tem- perature Tflash = Td, and the corresponding vapour pressure pflash = pd. Each curve corresponds to a
given maximum temperature which, as discussed in A.1, can also be seen as the storage temperature
Tmax ' Tc = TST; the storage pressure is assigned a value of 1 bar higher than the corresponding vapor pressure (pmax ' pc = pST). For each value of Tmax, the value of Td whereby complete flash- ing evaporation is reached (Td for which qd = 1) is also plotted (flash evaporation is considered as
an isenthalpic process). Figure 9a shows how, for each maximum temperature Tmax , the system efficiency ηSYS,glob initially grows for decreasing Td until it reaches a relative maximum (ηSYS,glob,max): this is a conse-
quence of the total mass flow which need to be circulated, see fig. 9b, and the corresponding power
consumption of the auxiliary components. As it is characteristic of CSP power systems, the thermal efficiency of the solar field ηSF,glob is a decreasing function of the temperature of the fluid flowing in the collector. Since the value of
ηSYS,glob includes this effect, lower storage temperature (and pressure) levels lead to comparatively
higher values of ηSF,glob; such an effect, however, does not counterbalance the concurrent decrease
of ηORC. 110 Thermal Energy Storage for Solar Powered ORC Engines T flash=Td [ oC] p flash= pd [bar] gl ob, S Y S [- ] A S F [m 2 ] 100 150 200 250 300 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 500 600 700 800 900 7.47 4.92 3.09 1.83 1.00 0.50 0.09 p CR 0.22 N line Tmax,R Tmax p max T d@ qd=1 1 0.808 253.1 6.19 192.1 2 0.888 278.2 8.86 228.0 3 0.949 297.3 11.50 257.5 4 0.998 312.7 14.20 288.2 1 4 3 2 10.9 η (a) Solid black lines: global system efficiency.
Dashed black lines: area of the solar field. T flash=Td [ oC] p flash= pd [bar] E E E D [kW h E /m 3 st ] out -s t [kg/ s] 100 150 200 250 300 0 5 10 15 20 0 1 2 3 4 p CR 7.47 4.92 3.09 1.83 1.00 0.50 0.09 10.9 0.22 N line Tmax,R T max p max Td@ qd=1 1 0.808 253.1 6.19 192.1 2 0.888 278.2 8.86 228.0 3 0.949 297.3 11.50 257.5
4 0.998 312.7 14.20 288.2 1 4 3 2 'm (b) Solid black lines: equivalent electrical energy
density. Dashed black lines: total mass flow en-
tering the flashing subsytem (i.e., extracted from
the storage vessel) Figure 9: Detailed analysis of the performance of a flashing-cycle ORC system, in case D4 is
the working fluid. For different maximum temperature levels (Tmax ' Tc = TST), the quantities of interest are plotted as a function of the flashing temperature (Tflash = Td); The corresponding
vapor pressure is also indicated. For each value of Tmax, the value of Td whereby complete flashing
evaporation is reached (Td for which qd = 1) is plotted as a solid grey line. For increasingly higher Tmax, the corresponding ηSYS,glob values tend to become constant in the region where ηSYS,glob,max occurs. This implies that, for higher values of Tmax, extending the
throttling down to saturated vapour conditions leads to a comparatively low efficiency decrease with
respect to ηSYS,glob,max. Figure 9a shows the variation of the SF area ASF, which, having imposed the
system net power output, is directly related with ηSYS,glob. If EEED (eq. 9) is considered, figure 9b shows how strongly this quantity is dependent upon Td. The figure displays that a relative maximum of the EEED corresponds to the situation whereby
the working fluid is flashed down to saturated vapor conditions. The locus of such maxima, for
varying Tmax, corresponds to the line for D4 of fig. 8. Since this operating condition allows for
important advantages (such as maximum storage density for the given Tmax, and simplification of
the flashing system layout), without implying noteworthy efficiency penalties, it can be considered
as a reasonable working condition for a system implementing the FC configuration, especially when
storage temperatures close to the critical temperature of the working fluid are considered. A.3 System Components Dynamic Modelling The dynamic models of the system components, as shown in figure 4.4a, are described in this sec-
tion, following the treatment presented in Ref. [47]. SOLAR FIELD 111 Chapter 4 The solar field is modelled as a single loop of parabolic collectors connected in series: the large ratio
between length and diameter allows a one-dimensional (1D) discretization of the absorber tube. The
finite-volume approach with an upwind scheme for mass flow and specific enthalpy is used [65].
The model is implemented connecting 2 sub ''components: the Flow1D model available from the ThermoPower library [62], and the newly developed SolAbs model , which interacts through a
distributed thermal connector [63]. Flow1D models the working fluid flow through the absorber, or heat collecting element (HCE), accounting for friction losses. The flow regime in the HCE is always turbulent, and the fluid-
wall convective heat transfer coefficient U [kWT m'' 2 'C''1] is modelled, in off-design condition, according to the relation U = Udes · ( 'mfluid/ 'mfluid,des) 0.65. SolAbs models the dynamic 1D thermal energy balance on a HCE cross section. It accounts for conduction and storage in the metal pipe, convection and radiation in the vacuum chamber between
the glass envelope and the metal pipe, conduction and storage in the glass envelope, convection
and radiation transfers with the ambient air [67]. SolAbs implements the relations between the
environmental parameters (DNI, θinc, Tamb, and Vwind), and the axial temperature distribution along
the absorber. Both the thermal power lost to the environment 'qhl (see A.1), and the power transferred
to the fluid can thus be evaluated. The pump circulating the fluid through the solar field is modelled by prescribing the flow rate passing through the machine (see also sec. 4.5.6), and by neglecting the specific enthalpy change
across it. This follows the assumption that the dynamics of the recirculation pump is negligible
compared to that of the solar collector, and that local flow controllers will be used in the solar field.
The complete solar collector model has been validated with reference data from [67]. STORAGE SYSTEM
The thermocline storage is modelled following a 1D, finite volumes approach: the tank, supposed
cylindrical, is discretized along its axis [70]. As anticipated, constant pressure is prescribed in the
tank, thus implicitly accounting for an ideal pressurization system. The model evaluates changes
in the volume of fluid, as a consequence of thermal expansion and mass balance. The implemented
dynamic mass and energy balance equations account for the conductive heat transfer in the fluid
and in the metal wall (along the vessel height), and the heat transfer between the wall and the
fluid. Thermal energy storage in the metal wall is neglected, and three constant overall heat transfer
coefficients are defined to model the thermal power lost to the environment from the top roof, the
foundation, and the lateral walls of the tank. The four connecting flanges have a fixed position: the
first volume to the top is linked to the outlet of the SF and to the inlet of the flashing valve, and the
last volume to the bottom is connected to the outlet of the regenerator and to the inlet of the solar
field pump. The turbulence mixing effects due to the introduction of the fluid on the stratification in
the tank are neglected. Due to the numerical diffusion of the finite volume method, it is necessary
to employ a fairly high number of nodes (at least N = 30) in order to model the thermocline
that develops in the tank. Also note that the delay between the temperature changes at the top
inlet and the corresponding changes at the top outlet is represented in the model as the dynamics
of a well-stirred volume having (1/N)th of the total volume, and is thus typically underestimated
for such large values of N. This represents a worst-case scenario in terms of the burden imposed
on the ORC system controllers by the fast variations of the SF outlet temperature. Since it is
very hard to represent this dynamics accurately (detailed 3D CFD models would be required), this
approximation is arguably the safest for a system-level dynamic model. The thermocline storage
model has been validated based on experimental data from the open literature [70]. The valve performing the flashing process is modelled assuming ideal control of the thermo- 112 Thermal Energy Storage for Solar Powered ORC Engines dynamic conditions at the outlet. More specifically, the pressure loss across the valve is implicitly
determined by the following equation in the model: hvs(pd) = hc, i.e., by assuming an isoenthalpic
transformation such that the outlet conditions correspond to saturated steam (hvs(p) is the dew-point
specific enthalpy as a function of pressure). ORC POWER BLOCK
The turbogenerator model is implemented connecting the ChockTurb model [71], and the ElecGen
model from ThermoPower. ChockTurb models a supersonic turbine as a de Laval nozzle, assumed
to be chocked in all operating conditions. The result of the design calculation is the critical nozzle
area (where sonic conditions occur) and, for off-design conditions, the relation between mass flow
and inlet pressure is implemented (considering the expansion as isentropic). ElecGen only models
the electrical generator, without accounting for any dynamics. Both the turbine isentropic efficiency,
and the generator electro-mechanical efficiency, are considered constant. The PlateHXC component models a counter ''current plate heat exchanger: it is implemented connecting different sub ''models from [62]: two Flow1D components, representing the fluid flow in the two sides of the exchanger, two ConvHT components modelling the convective heat transfer
between the two streams and the interposed metal wall, and a MetalWall component modelling the
heat conduction and the storage of energy in the metal parts. The DryCond component models a condenser with ideal pressure control and negligible sub- cooling. This prescribes both the pressure and temperature on the main pump side, and the pressure
at the regenerator side. The pump of the ORC power block is equivalent to that of the solar field, previously described. In this case however, the circulating mass flow rate imposed to the pump is determined by the
ChockTurb model. The complete dynamic model of the ORC power block has been validated by comparison to transient data collected during a recent experimental campaign [61]. Nomenclature s, p = spec. entropy [kJ kg''1 K''1], pressure [bar] T , h = temperature ['C], spec. enthalpy [kJ kg''1] u, ρ = spec. int. energy [kJ kg''1], density [kg m''3] v, q = spec.volume [m3 kg''1], vapour quality [kgsv kg'' 1 tot ] V, m = volume [m3], mass [kg] heq,st = equivalent hours of storage Greek symbols θinc = incidence angle ['] ξturn = TES turnaround efficiency ηopt,p = peak opt. efficiency ηs = isoentropic efficiency ηSF,glob = global solar field efficiency ηSYS,glob = global (i.e. solar-to-electric) system efficiency 'c = crossover frequency 113 Chapter 4 Subscripts E, T = electric, thermal M, des = mechanical, design conditions CR = critical thermodynamic conditions (liquid-vapour) R = Reduced (w/r to critical value) amb = ambient conditions sv, sl = saturated vapour, saturated liquid turb, cond = turbine, condenser Acronyms TES = Thermal Energy Storage CSP = Concentrated Solar Power ORC = Organic Rankine Cycle PV = Photovoltaic HTF = Heat Transfer Fluid DSG = Direct Steam Generation O&M = Operations and Maintenance VLE = Vapour Liquid Equilibrium SF = Solar Field ST = STorage SYS = System SM = Solar Multiple HCE = Heat Collecting Element SCA = Solar Collector Assembly DNI = Direct Normal Irradiation [W m-2] EEED = Equiv. Elec. En. Density[kWhE m'' 3 ST] VR = turbine Volumetric expansion Ratio EC = Evaporative Cycle FC = Flashing Cycle CFC = Complete Flashing Cycle CFD = Computational Fluid Dynamics 114 References [1] V. Fthenakis, J.E. Mason, and K. Zweibel. The technical, geographical, and economic feasi- bility for solar energy to supply the energy needs of the US. Energy Policy, 37(2):387''399,
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Energy 68, 667-679 (2014) c Elsevier 2014 '' Reprinted with permission Chapter 5 Abstract This chapter presents a methodology to help in the definition of the optimal design of power generation systems. The innovative element is the integration of requirements on dynamic
performance into the system design procedure. Operational flexibility is an increasingly important
specification of power systems for base- and part-load operation. Thus, it is crucial to discard,
in an early phase of the design process, plant configurations which feature unacceptable dynamic
performance. The test case is the preliminary design of an off-grid power plant serving an off-shore
platform where one of the three gas turbines is combined with an organic Rankine cycle turbo-
generator to increase the overall energy efficiency. At the core of the procedure is a stationary
model, capable of performing the on-design thermodynamic cycle calculation, and the design of the
components of the system. The results of these simulations are used within the framework of a multi-
objective optimization procedure to identify a number of equally optimal system configurations. A
dynamic model of each of these systems is automatically parameterized, by inheriting its parameters
values from the design model. Dynamic simulations allow then to discriminate among the initial set
of solutions, thus providing the designs that also comply with dynamic requirements. 5.1 Introduction The recent liberalization of the electricity markets, along with the rapid expansion of the utiliza-
tion of non-dispatchable renewable energy sources, such as wind and solar radiation, is stressing
the necessity-opportunity of improving the flexibility of power generation systems [1]. New power
technologies play therefore a significant role in providing such flexibility, and the electricity indus-
try has acknowledged that this need will increase in the near future [2]. In the case of base-load
power plants, changes to the scheduling procedures are leading to the latest combined-cycle gas
turbine units being designed to operate efficiently and reliably under a wide range of rapidly vary-
ing conditions. Furthermore, both new coal and nuclear power plants are conceived with increased
capability of operating under fast-load variations. In addition, older power stations are retrofitted
in order to increase dynamic operation performance [3]. Operational flexibility is mandatory for
off-grid power systems, and often preserving high energy conversion efficiency is also demanded.
The electrification of remote areas is widely studied [4], together with the powering of industrial
installations with systems operating in island [5]. In this context, system dynamic modeling and simulation is becoming a powerful design tool, especially if the level of detail of system and component models can be tuned to the design needs.
In a recent work, Garcia and colleagues investigated options to increase the robustness of energy
networks, by simulating energy flow scenarios in which multiple forms of energy commodities,
such as electricity and chemical products, may be exchanged [6]. They studied the interactions
between the grid and such advanced hybrid energy systems, by using dynamic models of various
units and simulating their operation. Concerning the detailed study of advanced power systems,
Zhu and colleagues analyzed distributed combined cycle plants based on micro gas turbines and
fuel cells, with the aim of reducing the costs related to ancillary services in a deregulated market
[7]. A detailed model of a complete combined cycle, based on a steam Rankine unit cascaded to a
gas turbine, developed in order to study and optimize its start-up procedure is presented in Ref. [8].
Model-based control techniques for the same type of power plant are dealt with in Ref. [9].
Notwithstanding the mentioned advancements, to the knowledge of the author the integration of
dynamic performance analysis into the design process has not been considered yet. Discarding plant configurations featuring unacceptable dynamic performance (e.g., ramp-up and -down time) at a very early design phase can be very valuable. A traditional design approach,
mainly aimed at increasing steady-state efficiency, might lead to systems that cannot comply with 122 Energy Systems Design Accounting for Dynamic Performance dynamic requirements, even if aggressive control strategies are pursued. This chapter is aimed at the development of an automated preliminary design methodology in which system transient performance can be seamlessly evaluated together with other typical design
requirements. In order to test the automated design tool, a relevant test case has been selected,
namely the power plant of an off-shore oil and gas platform in the North Sea, operating off-grid.
The problem consists in evaluating if it is possible to increase the efficiency of the three gas turbines
(GTs) by installing an organic Rankine cycle (ORC) turbo-generator powered by the exhaust gases
of one of the GTs, and still comply with stringent dynamic requirements. This chapter is structured as follows: the novel design methodology is outlined in §5.2, while §5.3 deals with the description of the case study. A detailed description of the models is presented
in §5.4. The results are thus reported and discussed in §5.5. Concluding remarks are given in §5.6. 5.2 Methodology The objective of this study is to develop and demonstrate a methodology for the preliminary de-
sign of power generation systems that integrates the fulfilling of dynamic requirements into the
automated procedure. This goal is attained by performing two main steps. In the first step, N performance metrics are selected (e.g., the thermal efficiency, the overall system volume, the net present value), and a multi-objective optimization problem is solved in
order to find a set of preliminary system designs which lead to optimal performance of the system
at the rated operating point. The outcome is an N-dimensional Pareto front of system designs,
which are optimal with respect to different objectives. In the second step, the dynamic performance
of the system is assessed by simulating critical transients for each design on the Pareto front, and by
verifying whether requirements and constraints involving dynamic variables are met or not. System
designs which do not meet the dynamic requirements are discarded. The end-result of the procedure is a reduced set of optimal system designs complying with the trade-offs between different objectives, while ensuring proper system operation during critical
transients. Based on this result, properly informed decisions about the final system design can be
taken, thus avoiding the risk of discovering criticalities of transient operation at later project stages,
i.e., during detailed design, or even commissioning, when corrective action might be very expensive
or impossible. 5.2.1 Multi-Objective Design Optimization The design methodology utilized in the present chapter is described in detail in Ref. [10], where it is
applied to the exemplary case of an ORC power system. The design algorithm is implemented using
the Matlab language; several new features were added in the present thesis to the previous version
of the program. The design procedure is briefly summarized here for the sake of completeness. First of all, boundary conditions, which hold for all designs, are defined. For example, in the case of an ORC heat recovery system, these are the mass flow rate, temperature and composition
of the flue gas source, the selection of the working fluid, and the choice of the components, such as
once-through boiler, shell and tube recuperator, and condenser. The thermodynamic states at the in-
let and outlet of each component can thus be identified by applying basic energy and mass balances.
Subsequently, the design of the plant equipment, e.g., the number, length, and diameter of tubes in
the heat exchangers, or the turbine flow coefficient, is carried out automatically, ultimately leading
to the evaluation of the chosen performance metrics. An iterative procedure then explores the de- 123 Chapter 5 sign space, looking for optimal design configurations. The multi-objective optimization approach
based on a genetic algorithm (GA) is adopted in this case. Such design procedure takes care of the typical trade-offs, such as, for example, the one ex- isting between the improvement of turbine performance, i.e., by reducing pressure losses in the
recuperator (counter-pressure at the turbine discharge), and the reduction of thermodynamic irre-
versibility in the heat exchangers. The first goal might be obtained by reducing the heat transfer
surface without altering the flow velocity. However, such surface reduction would lead to a deterio-
ration of the heat exchange (larger irreversibility), due to the larger temperature difference between
the hot and the cold stream. 5.2.2 Assessment of Dynamic Performance The set-up of the second step of the design procedure requires to identify critical scenarios involving
system transients, e.g. sudden load changes, load rejections, or unit trips. Requirements on critical
variables are formulated, such as rise time, settling time, damping, maximum deviation, maximum
or minimum allowed value during the transient, etc. A nonlinear dynamic model of the plant based on first principles is needed, in such a way that it can be parameterized starting from the detailed design data obtained from the first step of
the procedure. An effective way to build such model is to use the fully modular approach of the
equation-based, object-oriented modeling language Modelica [11]. On the one hand, this allows
to carry out the modeling task reliably and in a short time, by leveraging on existing and well-
tested libraries of reusable component models. On the other hand, the equation-based approach of
the language makes it possible to easily customize the models for the specific requirements of the
design problem at hand. In most cases, the system dynamics is the result of the interaction between the inherent plant dynamics and the control system action, with the controller often playing a crucial role. The defi-
nition of the design parameters cannot be complete without the values of the controller parameters.
It is then necessary to define control system tuning criteria leading to desirable or optimal perfor-
mance, which can be applied automatically given the specific values of the design parameters. The
assessment of dynamic performance can then be carried out automatically for each design point on
the Pareto front, by first running the simulation code generated from the Modelica model with the
specific choice of parameters and then checking if all the requirements on critical variables are met. 5.3 Case of Study Off-shore oil and gas platforms are a proper case of study to incorporate the dynamics of the power
generation system directly in the design phase, as they are typically equipped with stand-alone
(island) power generation systems. Moreover, in off-shore applications, preventing a failure of the
power generation system is crucial as it may cause a loss of oil and gas production and a drop of the
economic revenue. The case of study is the power generation system installed on the Draugen oil and gas off- shore platform, located 150 km off-shore from Kristiansund, in the Norwegian Sea. The platform,
operated by A/S Norske Shell, produces natural gas, exported to Kårstø (Norway) via the 'sgard gas
pipeline, and oil, which is first stored in tanks at the bottom of the sea and then exported via a shuttle
tanker once every 1-2 weeks. Three Siemens SGT-500 gas turbines are installed on the platform,
supplying an electrical base load of 19 MWE. The power demand is increased up to 25 MWE (peak
load) during oil export. In order to guarantee a high reliability of the power generation system, two 124 Energy Systems Design Accounting for Dynamic Performance TUR water GENA2 condenser recuperator pump natural gas exhaust gases air LPC HPC HPT LPT PT CC GENA1 natural gas exhaust gases air LPC HPC HPT LPT PT CC GENB natural gas exhaust gases air LPC HPC HPT LPT PT CC GENC OTB GAS TURBINE B GAS TURBINE C GAS TURBINE A 1 2 3 6 7 8 11 10 Figure 5.1: Simplified layout of the power generation system on the Draugen off-shore oil and
gas platform. The organic Rankine cycle module is added to recover part of the thermal power
released with the exhausts of turbine A. turbines are kept in operation at all times, each covering 50% of the load, while the third is kept
on stand-by, allowing for maintenance work. Despite the low energy conversion efficiency, this
strategy ensures the necessary reserve power for peak loads, and the safe operation of the engines. The design point specifications for the Siemens SGT-500 gas turbine are listed in Table 5.1 as provided by the manufacturer. The twin-spool engine employs two coaxial shafts coupling the low
pressure compressor (LPC) with the low pressure turbine (LPT) and the high pressure compressor
(HPC) with the high pressure turbine (HPT). The power turbine (PT) transfers mechanical power
through a dedicated shaft to the electric generator (GEN). Table 5.1: Design point specifications for the Siemens SGT-500 industrial twin spool gas turbine
installed on the Draugen off-shore oil and gas platform. Turbine inlet temperature [oC] 850 Exhaust gas temperature [oC] 379.2 Exhaust gas mass flow [kg s''1] 91.5 Electric power output [MWE] 16.5 Thermal efficiency [%] 31.3 Fuel Natural gas The performance of the power generation system may be enhanced by harvesting part of the ex- haust thermal power from one or more engines, by means of an ORC unit [10]. Figure 5.1 shows the
layout of the power generation system considered in this chapter. Preliminary calculations suggest
that incrementing the installed power by adding two or three ORC units (one for each gas turbine)
is not economically feasible. In fact, the utilization factor of the whole plant decreases in this case, 125 Chapter 5 if compared to the layout given in Fig. 5.1. Therefore, only one ORC unit is considered as the bot-
toming unit for gas turbine A. Due to the relatively low temperature of the gas turbine exhaust (see
Tab. 5.1), its thermal energy can be transferred directly to the ORC unit through the once-through
boiler (OTB), without the need of an intermediate oil loop. Thus, the working fluid is first expanded
in the ORC turbine (TUR), and subsequently cooled down in the recuperator. In this way the inlet
temperature in the OTB may be increased by recovering energy from the superheated vapor exiting
the turbine. The ORC fluid is then condensed and pumped up to the highest pressure level through
the recuperator, thus closing the cycle. Based on the analysis performed in Ref. [10], the selected
ORC working fluid is cyclopentane. This compound is already adopted for operating ORC systems
in this range of temperature, see Ref. [12]. For the steady state calculations, thermodynamic and
transport properties of cyclopentane are calculated according to the model implemented in a well-
known program [13]. The same thermodynamic library is linked to the dynamic modeling tool by
means of a specific interface for the Modelica language [14], and to the general interface to fluid
property libraries Fluidprop [15]. It is assumed that in the new power generation system the base-load power demand (19 MWE) is shared between the combined cycle (gas turbine A and ORC) and one gas turbine, while the
other engine is on stand-by. As a net power output up to 6.4 MWE can be harvested by the ORC
turbo-generator, the load is split so that the combined cycle provides 13 MWE and the remaining
6 MWE are supplied by gas turbine B [10]. Note that the combined cycle alone could potentially
cover the entire base-load power demand with a higher efficiency; however, this option is discarded
since the necessary reserve power for peak loads would not be immediately available during normal
operation, as it would require the ignition of one of the gas turbines. Moreover, the proposed
configuration allows to stop the combined cycle for maintenance by running gas turbine B and C,
each supplying 50% of the load. 5.4 System Modeling 5.4.1 Preliminary ORC Power Plant Design As described in §5.2.1, the design procedure starts with the calculation of the thermodynamic states of the working fluid at the inlet/outlet of each component, see Fig. 5.1, by solving mass and energy
balances, complemented by constitutive equations; the details of the non-linear system of equations
can be found in Ref. [10]. At this stage, the gas turbine is modeled as a lumped thermal source,
whose output constitutes the main input for the ORC turbo-generator design optimization. The
characteristics assumed for the gas turbine exhaust stream are reported in Tab. 5.1. Figure 5.2
illustrates the T ''s diagrams of two ORC power unit candidates obtained via the multi-objective
optimization approach described in §5.5.1, while the results of the thermodynamic states calculation are listed, for one such candidate designs, in table 5.2. HEAT EXCHANGERS
The heat exchange equipment is designed following the well-established standard procedure de-
tailed in Ref. [16]. Compared to the work carried out in the previous work by Pierobon and
colleagues [10], a new model of a once-through boiler has been developed and implemented. More-
over, since finned tubes have been foreseen in order to enhance the heat transfer process, specific
correlations are utilized to evaluate the heat transfer coefficients and the pressure drops outside the
tubes. 126 Energy Systems Design Accounting for Dynamic Performance s [kJkg -1 oC-1] T [ o C ] 0 0.5 1 1.5 50 100 150 200 250 V=126 m 3 V=45 m 3 CR p = 3831 kPa 1 2 1'' 2'' 4 3'' 3 6 4'' 5'' 5 6'' 7 9 9'' 7 8 8'' p = 104 kPa p = 2416 kPa '' '' '' '' '' Figure 5.2: Saturation curve (black line) and cycle state points represented in the T '' s diagram
of the working fluid cyclopentane (C5H10): MW = 70.1 [g mol'' 1], TCR = 238.5 [oC], PCR = 4515 [kPa], ρCR = 272.6 [kg m'' 3]. The states relative to two exemplary ORC systems are reported, characterized by a volume of 126 m3 (filled dots) and 45 m3 (empty dots). The gray lines represent
selected isobars. Table 5.2: Results of the thermodynamic states calculation for one exemplary ORC system char-
acterized by a volume of 45 m3. state T P h s ρ q [oC] [kPa] [kJ kg-1] [kJ kg-1 k-1] [kg m-3] [kgsv kg -1 tot] 1 50.0 104.0 1.4 0.004 714.9 0 2 51.4 2416.0 5.9 0.008 716.2 - 3 104.9 2416.0 117.5 0.326 657.3 - 4 193.9 2416.0 348.4 0.871 511.4 0 5 193.9 2416.0 567.2 1.340 67.7 1 6 229.7 2416.0 659.8 1.531 53.4 - 7 143.0 104.0 535.4 1.600 2.1 - 8 74.1 104.0 423.8 1.308 2.6 - 9 50.0 104.0 390.0 1.207 2.8 1 127 Chapter 5 The basic design procedure of heat exchangers requires determining the surface area by evalu- ating, through an iterative procedure, the overall heat transfer coefficient Uout defined as 1 Uout = 1 hout + 1 hout,f + Dout log Dout Din 2λtubes + Dout Din 1 hin + Dout Din 1 hin,f , (5.1) where h is the convective heat transfer coefficient, and D is the tube diameter. λtubes is the thermal
conductivity of the tubes material, while ''f' refers to the fouling factor. Regarding the once-through boiler, due to the high thermal resistance of the exhaust gases flowing outside the tubes, finned tubes are selected in order to enhance hout. This is modelled by
replacing the heat transfer and the fouling coefficients outside the tubes in Eq. (5.1) with a term
involving the fins area and their effectiveness. Since the heat transfer occurs in both the single-
and the two-phase region, specific equations must be adopted. In case of subcooled liquid and
superheated vapor, the heat transfer coefficient inside the tubes is evaluated with the correlations
proposed by Gnielinski [17]. The pressure drops related to single-phase flow are estimated using
the method described in Ref. [16]. The heat transfer coefficient in the two-phase region is evaluated
by discretizing the tubes into finite segments (typically 50) and thus applying the method proposed
by Shah [18]. The gas-side heat transfer coefficient is evaluated through the approach proposed in
Ref. [19], and the correlation derived therein for the air-side Nusselt number in a finned-tubes heat
exchanger reads Nu = 0.22 Re 0.6 Pr1/3 (A/A tubes) ''0.15 , (5.2) where A is total heat transfer area and Atubes is the outside tubes surface area including the fins. The recuperator is considered to be of the shell-and-tube type, and modelled accordingly, by following Ref. [16]. The tubes are equipped with external fins, in order to enhance the heat transfer
coefficient on the shell side, where the fluid is in the superheated vapour state. The corresponding
Nusselt number is evaluated as Nu = 0.134 Re 0.681 Pr1/3 ((p fin '' tfin)/lfin) 0.2 (p fin/tfin) 0.1134 , (5.3) where pfin, tfin, and lfin are the fin pitch, thickness, and length, respectively. The pressure drops on
both sides for the single-phase regions within the tubes are estimated according to Ref. [16]. The total pressure drops occurring in the two-phase flow are estimated by dividing them into three contributions: the static one, vanishing for the proposed configuration (horizontal tubes), the
kinematic one, and the one due to viscous friction. The last two terms are evaluated according to the
methods proposed in Refs. [20, 21]. For the pressure drops outside the finned tubes the correlation
presented in Ref. [22] is adopted. The equation is valid for banks of tubes in cross flow configura-
tion, with plain transverse fins, and it can be used for both staggered and in-line arrangement. SUPERSONIC TURBINE
The modeled expander is a turbine, which is usually the choice for ORC plants of the considered
power capacity. These are usually one- or two-stage axial machines, leading to large pressure ratios
across each stage; as a consequence, the flow is usually supersonic at the outlet of the first stator.
The expander is therefore modeled as an equivalent choked de Laval nozzle, whose throat flow
passage area is the sum of the throat areas of the nozzles constituting the first stator row. Isoentropic expansion is assumed from the inlet section, where total conditions (i.e. total pres- sure PT,6 and total temperature TT,6) are assumed to be known by virtue of the thermodynamic state
calculation, to the throat, where sonic conditions are attained, i.e., the flow speed equals the speed 128 Energy Systems Design Accounting for Dynamic Performance of sound c. The corresponding equations are:       
      s6 = s(PT,6, TT,6) hth = hT,6(PT,6, TT,6) '' 1
2 c(hth , s6) 2 ' m = ρth(hth, s6) · c(hth, s6) · Ath , (5.4) where s6 is the specific entropy at the turbine inlet, and the subscript ''th' indicates the sonic throat
section. The continuity equation relates the mass flow rate through the nozzle ' m to the density ρth and the flow passage area Ath in the throat section. By solving system (5.4) for given design
conditions in terms of thermodynamic state and mass flow rate at the turbine inlet, the total nozzle
throat area Ath can be evaluated. 5.4.2 Dynamic Modeling The dynamic model of the combined cycle system is developed by using components from exist-
ing Modelica libraries. The gas turbine sub-system model is built by utilizing basic components
included in the ThermoPower library [23], while the ORC system model adopts component models
from the Modelica ORC library [24], with suitable adaptations regarding the heat transfer coeffi-
cients in the 1D once-through boiler model. Figure 5.3: Object diagram of the gas engine sub-system. Figure 5.3 shows the Modelica object diagram of the GT sub-system, which has fluid con- nectors for air intake, fuel inlet, and exhaust gas, and one mechanical connector for the power
turbine shaft. Figure 5.4 shows the Modelica object diagram of the entire combined cycle system.
Note that, according to object-oriented modeling principles, a-causal physical connections belong-
ing to different domains (mechanical, thermo-hydraulic, electrical) are made between the different
objects; input-output connections are only used for the control systems, which are inherently causal. GAS TURBINE ENGINE
The low and high pressure compressors are described by quasi-static models, employing the maps 129 Chapter 5 Figure 5.4: Object diagram of the entire combined cycle system. of axial compressors provided with a commercial software [25]. The compressor maps used here
are those originally presented in Ref. [26]. These maps are represented by tables reporting values
for reduced flow, pressure ratio, isoentropic efficiency and speed of revolution for the complete
operating range of the component. Following the methodology proposed in Ref. [27], the maps
are scaled so that they can represent the part-load characteristic of the axial compressors of the
SGT-500 gas turbine. For all the turbines, which have many stages, the Stodola equation is used to
express the relation between inlet and outlet pressure, the mass flow rate and the inlet temperature
in off-design operating conditions [28]. In order to predict the turbines off-design efficiency, the
correlation relating the isoentropic efficiency and the non-dimensional flow coefficient proposed
in Ref. [29] is utilized. The part-load performance of the electric generator is modeled using the
equation proposed by Haglind [30]. The model of the combustion chamber assumes that the mixing and the combustion processes take place inside a constant volume. The mass and the internal energy of the volume are calculated
using the thermodynamic properties of the combustion products exiting the combustion chamber.
Mass and energy dynamic balances are formulated, by assuming complete combustion and no heat
loss to the environment (adiabatic process). The pressure drops are lumped at the outlet of the
combustion chamber and are estimated by assuming a quadratic dependency with respect to the
volumetric flow. The Modelica mechanical connections between the compressors, shaft inertias,
turbines, and generator connector allow to compute the variation of the angular speed of the low
pressure, high pressure and power turbine shaft. The values of the inertia of the rotating masses
(shaft, blades, generator) and the volume of the combustion chamber are set according to data pro-
vided by the gas turbine manufacturer. ORC SYSTEM
The once-through boiler, which is one of the components of the object diagram of Fig. 5.4, is 130 Energy Systems Design Accounting for Dynamic Performance implemented by combining basic ThermoPower modules, see Fig. 5.5: 1D flow models for the
gas side (top) and fluid side (bottom of the figure), and the 1D thermal model for the tube bundle
(middle). The exchange of thermal power is modeled with so-called 1D thermal ports (in orange
in the figure); the counter-current model establishes the topological correspondence between the
control volumes on the tube walls, and the control volumes on the gas flow model. Figure 5.5: Modelica object diagram of the once-through heat exchanger model The tube metal wall is modeled by a 1D dynamic heat balance equation, discretized by finite volumes. The flow models contain one-dimensional dynamic mass and energy balance equations,
discretized by the finite volume method, assuming a uniform pressure distribution; the relatively
small friction losses are lumped in an external component model. Here, the pressure drops in off-
design conditions are estimated assuming a quadratic dependency from the volumetric flow, with
the design point value set from the results of the detailed design step described in §5.4.1. Since the focus of the dynamic analysis is to evaluate the plant performance during critic tran- sients, the models for the convective heat transfer are simplified in comparison to the ones adopted
for the heat exchangers design (see §5.4.1). Due to their relatively small contributions, the thermal resistance in the radial direction and thermal diffusion in the axial direction are thus neglected in the
dynamic models. The heat transfer coefficient between the gas and the outer pipe surface is much
lower than the one between the inner pipe surface and the ORC working fluid flow. Therefore,
the overall heat transfer is essentially dependent on the flue gas side only, and the working fluid
temperature is always close to the inner surface temperature of the pipe. The heat transfer coefficient at the interface between the flue gas and the metal wall, in off- design conditions, is evaluated with the relation presented in Ref. [31], i.e. ǫ = ǫdes ' m ' mdes !n , (5.5) where ǫ is the heat transfer coefficient, ' m the mass flow rate, and the exponent n takes the value 0.6. The thermal interaction between the wall and the working fluid is described by specifying a
sufficiently high constant heat transfer coefficient, so that the fluid temperature is close to the wall
temperature, and the overall result is dominated by the gas side heat transfer. The model of the ORC turbine is the same as that employed in the design procedure (see Equations (5.4)). In this case, the throat passage area Ath is a fixed parameter obtained from the 131 Chapter 5 design calculation. Hence, Equation (5.4) states the relation between mass flow rate and turbine
inlet conditions, during off-design operation. The off-design isoentropic efficiency is expressed as
a function of the flow coefficient Φ = '/ '' 2''hs, with ' being the speed of revolution, and ''hs the isoentropic enthalpy drop across the expansion [29]. The recuperator is modeled by the counter-current connection of 1D ThermoPower modules, much as the once-through boiler, see Fig. 5.5. The heat transfer on the vapor side dominates,
therefore the overall heat transfer coefficient is taken equal to that at the interface between the
working fluid and the metal wall. Both the overall heat transfer and the pressure drops, in off-design
conditions, are modelled as already detailed for the once-through boiler. The condenser is trivially modeled as a fixed pressure component. This is justified considering the large availability of cooling sea-water, which allows the cooling circuit to be controlled in such
a way that the condenser pressure is nearly constant. For simplicity, the condensate is assumed to
leave the component in saturated conditions (no subcooling) with no pressure losses. The pump model is based on a head-volume flow curve derived by fitting the data of an existing centrifugal pump designed for similar volumetric flows and heads. The curve is given as a function
of α = ' m ' m''1 des · ρdes ρ ''1, and can be expressed as H = Hdes · (b1 + b2 e α) · ' 'des !2 , (5.6) where H is the head and, in the present case, the coefficients assume the values b1 = 2.462 and
b2 = ''0.538. The monotonic exponential functional form increases the model robustness compared to typically adopted polynomial expressions. The isoentropic efficiency of the pump is expressed
as a function of ' = α · 'des ''' 1, following Ref. [32]. The off-design electric efficiency of the ORC generator is calculated as for the case of the gas turbine generator, while the electro-mechanic efficiency of the pump motor is evaluated by assum-
ing a quadratic dependency on the ratio between the actual the nominal load value. CONTROL SYSTEMS
As explained in §5.3, the system under consideration operates off-grid. The alternating current (AC) grid-system of the off-shore platform is powered by the two synchronous generators connected to
the gas and ORC turbines, which can be assumed to rotate at the same speed, as the electrical con-
nections are very short. The gas turbine features the fastest load response, so it is used to control the
network frequency (or, equivalently, the shaft rotational speed). As the low pressure and high pres-
sure compressor are not equipped with variable inlet guide vanes, the load can only be controlled by
opening or closing the fuel valve. The feedback controller included in the gas turbine sub-system
(see Fig. 5.3) replicates the functional model provided by the gas turbine manufacturer, including
the controller transfer function, and a simplified model of the fuel-system dynamic response, also
given as a transfer function. Note that this controller is embedded in the GT unit and its parameters
cannot be changed by the end-user, so the controller parameters are taken as they are in the context
of this study. The goal of the ORC control system is to target the maximum possible heat recovery from the GT exhaust, while ensuring that no acid condensation takes place, which might be particularly
dangerous since also heavy fuels can be fed to the turbine combustor. This goal is attained by using
the feed pump speed to control the temperature of the exhaust gases exiting the OTB at the design
point value, which is as low as possible, yet high enough to avoid condensation. During stationary
operation, the design of the heat exchanger is such that the highest temperature of the organic
fluid, at the turbine inlet, is lower by a safety margin with respect to the thermal decomposition 132 Energy Systems Design Accounting for Dynamic Performance temperature of the working fluid. In addition, the control system must ensure that this temperature
does not exceed the safety limit anywhere in the high-temperature part of the ORC power plant
during system transients. The most critical operational transient from this point of view is the trip of gas turbine B: when this happens, the network frequency drops, so the GT controller reacts by opening the fuel valve to
regain the set-point frequency. Consequently, the GT exhaust flow rate and temperature increase,
leading to an increase of the OTB exhaust gases temperature, which is then counteracted by the
ORC controller by increasing the feed flow to the OTB and thus, eventually, also the share of the
load generated by the ORC system. Preliminary simulations carried out with different designs of the system showed that, as ex- pected, the dynamic response of the ORC system is much slower than the response of the GT
system, even for aggressive designs of the temperature controller. This leads to significant and po-
tentially unacceptable overshoot of the pump speed during the transient. This means that the peak
value of the turbine inlet temperature (which is one of the critical variables of the process) is almost
insensitive to the tuning of the ORC system controller. Such peak is quickly reached due to the
fast response of the GT compared to the ORC system. In particular, the response time of the ORC
power system is comparatively long since the flow rate through the turbine, and thus the generated
power, change very slowly with the OTB pressure. This means that the contribution of the ORC
controller to the limitation of the frequency undershoot is marginal. Based on these considerations, the ORC Proportional-Integral (PI) controller was tuned in order to obtain the minimum possible settling time of the controlled variable, while avoiding the overshoot
of the pump speed during the trip response transient and obtaining well-damped responses for all
involved variables. The simulations showed that this is possible by setting the proportional gain
to a value that is proportional to the heat exchanger volume, thus accounting for the process gain
variability with the design parameters, while keeping the integral time at a suitable constant value. 5.4.3 Validation The shell and tube heat exchanger design model, described in §5.4.1, was validated using an exam- ple proposed in Ref. [16]. The differences between the simulation results and the data reported in
the reference are within 1% in terms of both overall heat transfer coefficient and pressure drops. For
the once-through boiler it is verified that the heat transfer coefficients and the pressure drops related
to both singe- and two-phase flow are within the range of values specified in Ref. [33]. The off-design, steady-state simulation results of the gas turbine model presented in §5.4.2 were compared to the partial load characteristics given by the gas turbine manufacturer in the 10%-
100% range. Exhaust gas mass flow rate and temperature, fuel mass flow rate, and pressure in the
combustion chamber were checked. The quantity showing the larger mismatch is the fuel mass
flow: the relative error is about 3% for loads larger than 60%, and increases up to about 15% if the
load decreases down to 10%. The dynamic model of the gas turbine was validated by comparison with simulation results of the reference model provided by the gas turbine manufacturer, which is based on proprietary
experimental data. The validation scenario assumes that the three GT units initially share a total
load of 24 MWE, delivering 8 MWE each. At some point in time, one unit trips, so the other
two ramp up their load in order to match the total power demand, with a transient reduction of
the network frequency. The result of the simulations are compared in Fig. 5.6, which shows the
normalized network frequency and the load of unit B. At time t = 50 seconds, one of the gas
turbines trips; subsequently, the reference model predicts a minimum normalized frequency drop of 133 Chapter 5 time [s] fr eq. [- ] 40 50 60 70 80 0.97 0.98 0.99 1 1.01 Reference model
This work Figure 5.6: Dynamic validation results, normalized frequency vs time. Comparison between the
reference model provided by the gas turbine manufacturer and the model developed in the present
chapter. 0.0206 and a rise time of 5.5 s, while the model presented here gives a normalized frequency drop
of 0.0202 and a rise time of 6.0 s. Based on this results, it is possible to conclude that the gas turbine
dynamic model developed in the present chapter is able to reproduce both the steady-state and the
dynamics of the gas turbine with reasonable accuracy, over the entire range of loads encountered
during real operation. The model of the ORC system is composed of software objects taken from a library that was developed in order to model a 150 kW ORC system using toluene as the working fluid, and suc-
cessfully validated for transient operation against experimental data [24]. The developed models
are therefore deemed reliable, considering the similarity of the application at hand with the one
presented in the cited reference. Furthermore, it has been verified that the on-design and off-design
steady-state operating points predicted by the ORC system model are consistent with those com-
puted by the design tool described in §5.4.1. 5.4.4 The DYNDES Tool The DYNDES computer tool couples steady state and the dynamic software models in order to provide an integrated program for the optimal design of power generation systems, including dy-
namic criteria. The two computer programs are interfaced by means of shared files and command
scripts. More in detail, the results of the multi-objective design optimization is saved in an ap-
propriate file, then the dynamic simulation program is run in command-line mode to: i) extract
information from the design results file (e.g. the optimal design data relative to the geometry of the
once-through boiler), ii) convert such data into parameters and inputs for the dynamic models, iii)
run the simulations, and iv) save quantities of interest for further post-processing. Figure 5.7 shows
the flowchart of the DYNDES tool. 134 Energy Systems Design Accounting for Dynamic Performance Start multi-objective optimization ORC system simulation Set pressure drop=0 Pressure drop=0 ' YES NO YES NO Evaluate objective functions Check on results OK ' Convergence Achieved ' NO YES Multi-objective design optimization Shell & tube
recuperator
Once-through boiler COMPONENTS DESIGN Simulation dynamic tests Dynamic model simulation (predefined tests ) Post-processing Parameters & variables INTERFACE (via Modelica script) Store solutions Parametrize dynamic model Store solutions Turbine DYNDES Figure 5.7: Architecture of the DYNDES design tool. The results of the multi-objective design
optimization are utilized as inputs for the dynamic simulations of the power generation system. The
software integrates the steady state and the dynamic model via a scripting command. 135 Chapter 5 Starting from the same computing environment that is used for the steady-state model, the available multi-objective optimizer runs by first acquiring the array of the parameters and of the
upper and lower bounds for the vector of the optimization variables ¯ X, which in the case at hand reads ¯ X = [P6, ''Trec, ''TOTB, T11, DOTB,in, tOTB, lOTB, uexh, Drec,in, trec, lrec, prec, lrec,b], (5.7) where P6 is the turbine inlet pressure, ''Trec = T8 '' T2 the minimum temperature difference in the recuperator, and ''TOTB the temperature difference between the two streams in the once-through
boiler, at the location where the ORC fluid is in saturated liquid condition. Note that this does
not necessarily correspond to the so-called pinch-point of the heat exchanger, since the minimum
temperature difference between the two streams in the OTB might also be located at its inlet. T11
is the lower temperature reached by the exhaust, see Fig. 5.1. The variables uexh, DOTB,in, tOTB and
lOTB are the velocity of the exhaust gases, the inner diameter, the thickness and the length of the
tubes of the once-through boiler. Similarly, Drec,in, trec, and lrec refer to the same quantities in the
recuperator, while prec is the tubes pitch. The variable lrec,b indicates the baffle spacing given as a
percentage of the shell diameter. The objective functions chosen in the present analysis are collected in the array ¯ J, i.e. ¯ J = [ '' ' Wnet,ORC, VOTB + Vrec], (5.8) where ' Wnet,ORC is the net power output of the ORC power unit, and the second metric accounts for the total ORC module volume which is determined by the more bulky components, i.e. the heat
exchangers. The first term is selected in order to maximize the power output of the combined cycle
plant while the latter term is added to the objective function since compactness represents a crucial
design requirement in the considered application. The integration of dynamic simulations into the
the automated design procedure allows to discard unfeasible designs. Since the dynamics of the
condenser can be neglected for the reasons explained in §5.4.2, the volume of the condenser is not included in the second term of the objective function, see Equation 5.8. The multi-objective optimization uses a controlled elitist genetic algorithm (GA) to search for solutions which minimize simultaneously the two objective functions [34]. Compared to gradient-
based methods, a GA is less prone to converge to local minima of the problem. This typically
comes at the cost of an increased computational cost, due to the large number of evaluations of
the objective functions [34]. The GA parameters are specified as follows: population size equal to
200, generation size equal to 100, crossover fraction equal to 0.8, and migration fraction equal to
0.2. These numerical values are selected in order to ensure the repeatability of the solution when
different simulations are performed, and are selected as suggested in Ref. [34]. Table 5.3 lists the upper and lower bounds utilized for the optimization variables, according to the limits reported in Ref. [16]. As the SGT-500 engine can operate on a wide range of both
liquid and gas fuels, the limit temperature of the flue gas at the outlet of the OTB is set to 140 'C,
in order to prevent the condensation of corrosive compounds. Supercritical cycle configurations are
not considered here, and the upper bound for the turbine inlet pressure is thus set equal to 90% of
the critical pressure of cyclopentane. Table 5.4 lists the parameters which are kept constant during the multi-objective optimization. The fin profile and the configuration of the once-through boiler and of the recuperator are retrieved
from Refs. [16, 33]. The condensing pressure of the working fluid is fixed to 1 bar, corresponding
to a temperature of 50 'C, in order to avoid inward air leakage into the condenser. Referring to Fig. 5.7, the calculation loop regarding the ORC module determines the ther- modynamic states at the inlet and at the outlet of each component, as detailed in Ref. [10]. The
pressure drops in the heat exchangers are initially set to zero. At this point the design procedure 136 Energy Systems Design Accounting for Dynamic Performance Table 5.3: Design variables involved in the multi-objective optimization, with relative upper (UB)
and lower (LB) bounds. The bounds relative to the tubes inlet diameter Din, length l, and thickness
t are assumed equal for the design of the once-through boiler and of the recuperator. Variable LB UB Turbine inlet pressure P6 [bar] 5 41.1 Pinch point recuperator ''Trec [ oC] 10 40 Temperature difference OTB ''TOTB [ oC] 10 80 Exhaust gas temperature T11 [ oC] 140 180 Inlet diameter of the tubes Din [mm] 16 50 Length of the tubes l [m] 1.83 7.32 Thickness of the tubes t [mm] 1.6 3.2 Tube pitch prec [-] 1.1 1.3 Baffle spacing lrec,b [%] 20 100 Gas velocity uexh [m s -1] 10 70 of the once-through boiler and of the recuperator (see §5.4.1) is started, obtaining as outputs both the pressure drops and the design parameters of the components, which are then stored. The model
of the ORC system is thus run again, but in this case the pressure losses in the OTB and in the re-
cuperator are included in the computation. The results are then checked with respect to the second
principle of Thermodynamics. It is also verified that the velocity in the tubes and on the shell side
of the recuperator lies within the ranges specified in [16]. The process is repeated until the average
change in the spread of the Pareto front is lower than the specified tolerance, which is assumed here
equal to 10''3. When the multi-objective optimization terminates, the inputs of the dynamic models
are stored in a file that is then used by the dynamic simulator as previously explained. The dynamic models are parametrized using the data for the heat exchangers and the turbine corresponding to the optimal ORC modules, as determined by the multi-objective optimization pro-
cedure. These models are then used to predict the dynamics of the complete system in a predefined
transient scenario. Note that the number of dynamic simulations to be performed is equal to the
number of points of the Pareto front. The dynamic test, conceived to assess the dynamics of the complete system, consists in the simulation of the failure of a gas turbine unit. This has been defined according to the specifications
of the platform owner, and represents the worst scenario the power system can possibly undergo
without compromising the platform functionality. The same dynamic test is thus applied to all the
design candidates previously defined. It is assumed that the combined cycle (gas turbine A and ORC) and the gas turbine B are providing the normal load (13 and 6 MWE each) while at time t0 gas turbine B trips. Hence, the
combined cycle undergoes a load increment of '' 1.2 MWE s'' 1 (e.g. 6 MWE in 5 s, see Figs. 5.8b and 5.10a) and must take over the entire power demand, until gas turbine C is ignited. The
process ends by storing the desired outputs of the dynamic analysis (e.g., the maximum undershoot
of the electrical network frequency) for each choice of system design. Finally, post-processing is
performed within the software environment for scientific computing. 137 Chapter 5 Table 5.4: Parameters assumed for the multi-objective optimization. Parameter Value Organic Rankine cycle Working fluid cyclopentane Pump isoentropic efficiency [%] 72 ORC turbine isoentropic efficiency [%] 80 Electric efficiency of the generator [%] 98 Condensing pressure [bar] 1.04 Once-through boiler Layout in-line [16] Material stainless steel Longitudinal pitch [mm] 83 Transversal pitch [mm] 83 Fin pitch [mm] 1.5 Fin thickness [mm] 1 Fin height [mm] 24 Fin efficiency [%] 95 Recuperator Layout triangular pitch [16] Material cupro-nickel Fin pitch [mm] 2 Fin thickness [mm] 1 Fin height [mm] 12 Fin efficiency [%] 95 138 Energy Systems Design Accounting for Dynamic Performance 5.5 Results and Discussion 5.5.1 Multi-objective Design Optimization Table 5.5 lists the results of the multi-objective optimization procedure applied to the test case.
The arithmetic mean average (AMA), the percentage relative standard deviation (RSD), and the
minimum and maximum values of the optimized variables are reported. A low RSD means that
the variable does not change significantly with the optimal configurations of the ORC unit. The
pinch point, the tube diameter and the tube pitch of the recuperator present the lowest RSDs. As a
practical implication, table 5.5 provides the designer with the optimal geometry of the heat transfer
equipment; the closest available standardized values can then be selected for the design of the actual
equipment. Figure 5.8a shows the two-dimensional Pareto front which relates the net power output of the ORC module with the sum of the volumes of the once-through boiler and of the recuperator. The
Pareto front is formed by 70 optimal solutions, ranging from a net ORC power of 3.9 MWE up to
5.8 MWE. The trend of the volume vs. the net power output is approximately hyperbolic. The total
net power output and the thermal efficiency of the combined cycle unit range from 20.4 MWE to
22.3 MWE and from 38.7% to 42.2%. Due to space constraints on the Draugen platform, design
points with a volume higher than 100 m3 are discarded from the Pareto front (triangular dots in Fig.
5.8a). Table 5.5: Results of the multi-objective optimization. Maximum, minimum, arithmetic mean
average, and relative standard deviation of the optimized variables. The values are relative to the 70
points of the Pareto front. Variable Max Min AMA RSD [%] P6 [bar] 38.3 24.1 34.3 15.0 ''Trec [ oC] 23.0 22.1 22.6 1.0 ''TOTB [ oC] 58.7 43.0 52.0 12.6 T11 [ oC] 158.6 142.7 148.1 4.2 DOTB,in [mm] 47.0 23.5 29.9 18.8 tOTB [mm] 3.0 1.9 2.2 11.6 lOTB [m] 6.8 5.7 6.4 5.6 uexh [m s -1] 64.2 55.6 62.5 3.5 Drec,in [mm] 18.7 16.6 17.9 1.7 trec [mm] 3.0 2.2 2.5 7.7 lrec [m] 4.3 3.8 4.0 3.8 prec [-] 1.29 1.19 1.27 2.1 lrec,b [%] 80.1 68.1 76.9 4.6 139 Chapter 5 5.5.2 Assessment of Dynamic Performance As far as the results of the analysis of the system dynamics are concerned, Fig. 5.8b illustrates
the transient response of the system for two points of the Pareto front (i.e., those corresponding to
the designs with the largest and the smallest volume). The influence of the ORC power module
design on the network frequency transient is clearly visible: the lower the volume, the larger the
undershoot and the overshooting of the frequency. On the contrary, large values of the volume limit
the frequency drop, by increasing the thermal inertia of the system. Figure 5.9a relates the volume to the minimum frequency reached during the transient, for each point of the Pareto front. The curve presents a highly non-linear trend, with the magnitude of the
frequency variations increasing more sharply for decreasing volume. According to the standards for
power quality adopted by the platform owner, the frequency undershoot must not exceed 4% of the
nominal value. Thus, as results from the dynamic analysis, ORC power modules characterized by
overall volume VORC lower than 50 m 3 violate this constraint. These designs are therefore identified as unfeasible, and marked with the hollow square ( ) symbol in Figs. 5.8a and 5.9a. Figure 5.9b reports the rise time as a function of volume. The rise time is defined here as the time required
for the frequency to return back to 99% of the value at steady state. The trend of the curve is also
non-linear with a minimum of approximately 14 s at 65 m3. P NET,ORC [MWE] V O R C [m 3 ] 3.5 4 4.5 5 5.5 6 40 60 80 100 120 140 (a) time [s] fr eq. [- ] loa d [M W ] 1200 1250 1300 1350 0.96 0.98 1 1.02 0 5 10 15 20 V ORC=45 m 3 V ORC=126 m 3 load (b) Figure 5.8: 5.8a multi-objective optimization results, Pareto front showing the relation between
the objective functions, e.g. the ORC system net power and the volume of the heat transfer equip-
ment VORC. The designs identified by the  symbol are discarded due to the unacceptable frequency
undershoot, while those marked with ' due to volume limitations. The other designs (filled circles) are deemed acceptable. 5.8b results of the dynamic test, the grey line represents the correspond-
ing load variation. Normalized frequency and combined cycle load vs time for the two designs
characterized by the maximum and minimum values of VORC. Figure 5.10a shows the time evolution of the temperature at the inlet of the ORC turbine T6, together with that of the exhaust gases exiting the gas turbine T10 for three points of the Pareto
front. As the load of the gas turbine undergoes a sharp variation, the temperature and the mass flow
of the exhaust gases entering the OTB rise. As anticipated in §5.4.2, the dynamics of T6 is much slower than that of T10. The two major contributions to the delay are the inertia of the metal walls 140 Energy Systems Design Accounting for Dynamic Performance V ORC [m 3] fr eq. unde rs hoot ing [% N O M ] 40 60 80 100 120 140 3.0 3.5 4.0 4.5 5.0 (a) V ORC [m 3] ri se ti m e [s ] 40 60 80 100 120 140 14.0 14.5 15.0 15.5 16.0 16.5 17.0 17.5 18.0 (b) Figure 5.9: Results of the dynamic test. 5.9a frequency undershoot vs volume VORC, all the points
of the Pareto front are reported. The designs identified by the  symbol are discarded due to the unacceptable frequency undershoot (> 4%). 5.9b rise time vs VORC, all the points of the Pareto front
are reported. time [s] T 6 , T 10 [ o C ] loa d [M W ] 1150 1200 1250 1300 1350 1400 1450 200 250 300 350 400 0 5 10 15 20 25 30 V ORC=45 m 3 V ORC=76 m 3 V ORC=126 m 3 load T 6 T 10 (a) V ORC [m 3] T 6 [ o C ] 40 60 80 100 120 140 250 255 260 265 (b) Figure 5.10: Results of the dynamic test, the grey line represents the corresponding load varia-
tion. 5.10a turbine inlet temperature T6, and exhaust gases temperature at the once-through boiler
inlet T10 vs time for three selected designs corresponding to points of the Pareto front (the two
designs characterized by the maximum and minimum volume of the heat exchanging equipment
VORC, together with an intermediate value). 5.10b maximum turbine inlet temperature vs VORC, all
the points of the Pareto front are reported. 141 Chapter 5 and of the working fluid in liquid phase contained in the heat exchangers. Note that, while the mass
of the exhaust gases is negligible, that of the liquid cyclopentane contained in the OTB and in the
recuperator is approximately 15 times larger than its mass in the vapor phase. The peak of T6 is reported as a function of volume in Figure 5.10b. This value is of paramount importance, being closely related to the maximum temperature reached by the ORC working fluid.
This is eventually encountered in the fluid layer close to the metal wall in the boiler (OTB) but,
as a consequence of the approximations introduced in §5.4.2, the accurate evaluation of its value is presently beyond the capability of the developed models. As a rough estimation, design point calcu-
lations using the methodology outlined in §5.4.1 indicate that the wall temperature of cyclopentane in the hotter part of the OTB is expected to be 10-30 'C higher than the corresponding bulk value.
As the thermal stability of the working fluid is a major concern in the design of ORC systems,
the minimum risk of decomposition should be ensured. In a recent work, Ginosar and colleagues
identified 300 'C as the upper temperature limit for safe operations of an ORC system working
with cyclopentane [35]. Therefore, a maximum temperature at the turbine inlet of 270 'C can be
accepted, which is also in agreement with other published information, see e.g. Ref. [12]. The dynamic analysis allows to identify a clear minimum for T6 which, for the considered case, lies at around 250 'C, with a volume of 65 m3. Values close to 265 'C are achieved for both
smaller and larger volumes. Even though the estimated safety limit is not exceeded, the designs
characterized by values of volume ranging from 60 to 80 m3 may be deemed preferable in the light
of the present analysis, as they are located in vicinity of the minimum T6. 5.6 Conclusions The design of innovative energy conversion systems conceived for flexible operation needs to take
into account dynamic requirements on critical transient scenarios as early as possible in the design
cycle, in order to avoid costly design changes in later phases, or sub-optimal system performance.
The methodology and tools presented in this chapter constitute a first step in this direction. The design tool DYNDES presented here demonstrates the potential of this preliminary auto- mated design method, if the main design objectives are aspects such as system performance, com-
pactness and flexibility. The software utilizes the multi-objective optimization approach to search
for optimal designs with potentially conflicting objectives, which the user can select based on the
specific requirements of the system under investigation. As the routine optimizes the geometry of
the heat transfer equipment, such a procedure bridges the gap between the mere optimization of
the thermodynamic cycle and the preliminary design of system components that constitutes the first
step towards the realization of power systems. The system response during transients becomes one
of the crucial design criteria, leading to the exclusion from the optimal solutions of several designs
which do not satisfy dynamic requirements, e.g., the tolerance on network frequency variations. The proposed methodology has been applied to the case study of an ORC-based combined cycle power plant for an off-grid oil platform. The test cases demonstrates how dynamic analysis
enables to exclude those system configurations which, although potentially more efficient or com-
pact, may lead to unacceptable frequency fluctuations, or increase the risk of decomposition of the
working fluid. The proposed methodology and tools are readily applicable to other systems combining gas turbines and ORC power modules, and it can also be extended to cover other cases of advanced en-
ergy conversion systems with demanding dynamic requirements, such as off-grid energy conversion
systems, heat recovery in automotive engines, solar thermal plants, etc. 142 Energy Systems Design Accounting for Dynamic Performance Acknowledgments The funding from the Norwegian Research Council through Petromaks with project number 203404/E30
is acknowledged. We also acknowledge the kind support from Siemens Industrial Turbomachinery
AB, Finspång, Sweden for providing the dynamic model of the SGT-500 gas turbines and the nec-
essary technical documentation. Nomenclature s, P = specific entropy [kJ kg''1 K''1], pressure [kPa] T , h = temperature ['C], specific enthalpy [kJ kg''1] c, MW = speed of sound [m s''1], molecular weight [g mol''1] A, ' m = area [m2], mass flow rate [kg s''1] u, V = velocity [m s-1], volume [m3] Re, Pr, Nu = Reynolds, Prandtl, and Nusselt numbers D, p, l, t = diameter [mm], pitch [mm], length [m], and thickness [mm] ', ' W = speed of revolution [RPM], power Φ = '/ '' 2''hs = turbine flow coefficient Greek letters ρ = density [kg m''3] ''x = finite difference for quantity x λ = thermal conductivity [W m-1 K-1] ǫ = heat transfer coefficient [W m-2 K-1] Subscripts E, M = electrical, mechanical des, s = design, isoentropic process exh = exhaust gases fin, b = fin, baffle f, rec = fouling, recuperator min, max = minimum, maximum value CR = critical thermodynamic conditions (liquid-vapour) T, S = total and static thermodynamic conditions th, in, out = sonic throat, inlet, and outlet tot, sv = total, saturated vapour conditions Acronyms AC = Alternating Current AMA = Arithmetic Mean Average CC = Combustion Chamber LPC = Low Pressure Compressor LPT = Low Pressure Turbine 143 Chapter 5 GA = Genetic Algorithm GEN = Electric Generator GT = Gas Turbine HPC = High Pressure Compressor HPT = High Pressure Turbine ORC = Organic Rankine Cycle OTB = Once Through Boiler PI = Proportional Integral PT = Pressure Turbine RSD = Relative Standard Deviation TUR = Turbine 144 References [1] Wietze Lise, Jeroen van der Laan, Frans Nieuwenhout, and Koen Rademaekers. Assessment of the required share for a stable EU electricity supply until 2050. Energy Policy, 59(0):904 ''
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with Optimally Operated Thermal Storage'
E. Casati, F. Casella, & P. Colonna
Solar Energy, Accepted for Publication (2014) Chapter 6 Abstract Concentrated solar power plants are increasingly considered worldwide, in order to meet
the demand for renewable power generation. A distinctive feature of these plants is the possibility of
integrating thermal energy storage such that full-load operation can be sustained for several hours
in the absence of solar radiation. A number of design software tools are available for sizing the
plant and evaluating the return on investment. These usually assume a short-sighted strategy for
storage management. This work presents a new methodology aimed at assessing the potential of
optimal control techniques when applied to the operation of energy storage systems in general. The
design method is applied to a test case, a state-of-the-art central receiver plant with direct storage,
using molten salts as working fluid, and operating in a context of variable electricity prices. The
system modelling and optimization problems are formulated and implemented using modern high-
level modelling languages, thus demonstrating the potential of the approach. Different operating
strategies are compared based on a detailed financial analysis. A wide system design space is
considered, and the results are presented for all the foreseeable combinations of solar field size
and storage system capacity. A potential increase of the order of 5% in terms of yearly revenue is
estimated, in case improved control strategies are adopted. This figure translates into an increase of
more than 10% of the investment profitability by considering over-life financial figures. It is further
shown how, in case of state-of-the-art systems, it is always profitable to adopt optimal control to
the end of increasing electricity production. However, the potential of these techniques is discussed
also under the point of view of investment cost reduction, since the same yearly revenue can be
harvested with smaller energy storage, if optimally operated. This aspect, unveiled here for the first
time, might become significant in case technologies with different cost structure are of interest, i.e.,
in case the storage cost constitutes a comparatively large part of the total investment. The novel
method is thus an additional decision tool allowing to treat the storage operation strategy as a new
relevant design variable for next generation energy systems. 6.1 Introduction Evolving towards a society not depending on fossil fuels is becoming a matter of the greatest inter-
est, as it is increasingly clear that the current energy consumption and generation trend is not sustain-
able, due to the exhaustion of fossil fuel resources and its effects on climate change [1, 2]. Devices
to convert concentrated solar energy into useful work have been designed for over a century [3''5].
The oil crisis triggered substantial R&D on solar energy conversion, and pilot plants were built
during the 1980s. In recent years, renewed interest in concentrated solar power (CSP) plants has
sparked a new surge in investments; in 2011 the power capacity of the CSP plants that were op-
erational worldwide totalled 1.3 GWE, that of plants under construction amounted to 2.3 GWE,
while that of planned plants added up to 31.7 GWE [6]. A very relevant advantage of CSP power
plants compared to other renewable energy conversion options is that the installation can integrate
a comparatively inexpensive thermal energy storage system (TES), enabling power to be generated
when the sun is not shining, and contributing to their distinctive ability to provide dispatchable
electricity. Recent research aimed at quantifying the added values of CSP dispatchability, the key
findings being: i) the dispatchability of CSP adds quantifiable economic benefits, ii) the flexibility
of CSP can aid the integration in the grid of other renewable energy technologies, such as solar
photovoltaics [7]. Of all CSP technologies available today, that of central receiver systems (CR, also known as solar towers) is moving to the forefront, and it might become the technology of choice. The
interested reader is referred to Ref. [8] for a thorough review of the history of this technology, the
state of the art, and the ongoing R&D efforts. State-of-the-art CR systems use molten salts as the 150 Design of CSP Plants with Optimally Operated Thermal Storage Receiver on Tower Dry Condenser DNI Power Block Cold TES tank Steam Gen. Hot TES tank Q REC, inc Heliostats Field T REC, in T TES-C, in= TTES-C, out= TREC, in = 290 oC T TES-C, in T TES-C, out T TES-H, out T TES-H, in T REC, out T REC, out =TTES-H, in=TTES-H, out= 565 oC Figure 6.1: Schematic layout of the Gemasolar 20 MWE solar tower plant, capable of 15 hours of
full-load off-sun operation thanks to the storage system, adapted from [11]. The main simplification
adopted in the model presented here, i.e., the neglection of thermal losses in all the subsystems apart
from the receiver (see §6.2), is also made explicit. working fluid in both the solar receiver and the storage subsytems, i.e., they implement the so-
called direct TES concept [9], which may be sized such that it provides several hours of nominal
operation without solar radiation [10]. The schematic layout of the first commercial plant of this
type, operating in Spain since 2011, is shown in Fig. 6.1. The storage unit completely decouples the power block from the variable solar energy source, which is beneficial for both plant efficiency and reliability: in order to achieve better overall per-
formance during the day, the control techniques for CSP systems usually aim at maintaining the
solar receiver outlet temperature close to its nominal value, by varying the heat transfer fluid (HTF)
mass flow rate. However, in the absence of significant energy storage, the operating point of the
power block needs to follow the variations of the solar radiation, as discussed in Refs. [12, 13]. On
the contrary, the integraton of a direct TES system into the power plant allows to use an additional
control variable, i.e., the mass flow rate from the storage tank to the primary heat exchanger (steam
generator). Thus, the receiver outlet temperature and the power delivered to the conversion cycle
can be controlled independently. This makes it possible to sustain constant power output during
short transients (e.g., clouds passage), or to shift the production to better meet variable-price tariffs. In the present work, according to a scheme currently adopted mainly in the USA, the produced electricity is supposed to be sold to a utility company at the previously negotiated power purchase
agreement (PPA) bid price, multiplied by time-of-day (TOD) factors pre-defined by the applicable
tariff, which account for the higher value that the produced power has during peak hours. The PPA
price is thus negotiated by the producer in order to balance the investment and operational costs,
and hopefully make a profit. For a detailed description of the PPA approach and how this allows
to overcome the shortcomings of the other commonly adopted metric, i.e., the levelized cost of
electricity (LCOE), the interested reader is referred to the works of Ref. [14] and [15]. The availability of a TES system coupled with variable energy prices demands for an opti- mized operation of the plant, maximizing the revenues by exploiting the TES ability to shift the
production to higher priced time slots. This problem has been considered by many authors in recent
times, see, e.g., [16''18]. With reference to real-time operation, Ref. [19] discusses the potential
of weather forecast-based operation of CSP plants, stressing the importance of forecast quality.
In Refs. [20, 21], a methodology to maximize the revenues for a plant operating in a free energy 151 Chapter 6 market is presented; the CSP plant is run with a price-driven strategy and, based on electricity pric-
ing and weather forecasting, an economically optimized bidding strategy for the day-ahead energy
market is determined. The authors identify a period comprising the next one or two trading days
as a reasonable optimization horizon, considering the trade-off between profit gain and forecast
quality. More recently, the authors of Ref. [22] assessed the potential of a solar-thermal generation
system in a fluctuating electricity prices context, by considering the innovative CSP technology
proposed in Ref. [23]. Ref. [24] investigated the influence of the operation strategy, focusing on the
charge/discharge process for a thermocline storage, on the yearly production of a parabolic trough
CSP plant. The research work documented here stems from the need of generalizing the analysis on opti- mized dispatching strategies for CSP plants, by considering the whole design-space of present-days
systems, e.g., in terms of storage capacity and solar multiple. Furthermore, a novel assessment
of how different control procedures can influence the design of the plant and the financial perfor-
mance of the project is presented. When a new CSP plant is being considered for construction at
a specific location, models and tools are needed to assess the potential of eneregy production, and
thus eventually compute the PPA price level that can repay for the investment within the specified
time. A widely adopted, publicly available software tool for this purpose is the System Advisory
Model (SAM) [10, 25, 26], which is assumed as a reference in this work. The TES control strategy
assumed by SAM is such that, for each hourly interval of operation, the controller tries to use all the
available thermal power from the solar field and from the TES to drive the power block at the max-
imum possible load. This strategy is clearly sub-optimal when the TOD factor shows significant
variations during peak hours, so it can be safely assumed that the plant being evaluated will eventu-
ally be operated using some kind of optimal control that will try to maximize the economic revenue
by exploiting the available storage instead of the strategy assumed by SAM. In order to make correct
decisions in terms of plant sizing and design would be therefore advantageous to include optimal
control even at this very early stage. To this end, the method presented here is based on a dynamic model of the plant, replicating the basic modelling assumptions of the SAM software, which is then employed to formulate and solve
a dynamic optimization problem in order to give a credible estimation of the potential of a future
CSP plant, assuming optimal control is used for its operation. Since the full details of the real-
time implementation of the optimal controller cannot be available at this very early design stage,
it is reasonable to consider an idealized set-up of the control problem, assuming perfect matching
between the model and the plant dynamics, and perfect knowledge of the future solar irradiation.
The attained performance represents therefore the theoretical limit of the operation of a real-time
optimal controller, which in reality will have to face modelling errors, unmodelled disturbances,
and uncertain weather forecasts. Although the obtained results will be slightly optimistic, they
will represent controlled plant operation in a much more credible way than those obtained with the
short-sighted control policy usually assumed. Modern object-oriented languages and simulation
tools are used in order to concisely formulate and solve the optimal control problem with minimal
implementation effort. The main goal of the work is to show that, by means of these techniques and tools, the note- worthy advantages offered by optimal operation procedures can be easily unveiled and taken into
account during the earliest design stages. The chapter is structured as follows. The CSP plant model,
replicating the main features of the SAM model, is introduced in §6.2. The reference control strat- egy and the optimal control problem are formulated in §6.3. The computational infrastructure is discussed in §6.4, while the main results are presented and discussed in §6.5. §6.6 illustrates the main conclusions and an outlook to future work. 152 Design of CSP Plants with Optimally Operated Thermal Storage 6.2 Modeling Framework The CSP plant selected as a test case is a state-of-the-art 100 MWE molten salts plant with direct
storage, whose schematic layout is shown in Fig. 6.1. The general modelling framework closely
follows the one used by SAM, as described in [26], therefore the following main simplifying as-
sumptions hold: 1. the HTF temperature at the receiver outlet is assumed to be always kept at its nominal value TREC, out. Also the temperature of the HTF exiting the steam generator, i.e., TTES-C, in,
is assumed to be constant within the considered operating range. The heat losses in the
piping are neglected, leading to the equalities TREC, out = TTES-H, in and TREC, in = TTES-C, out.
Furthermore, also the storage tanks are supposed to be adiabatic, that is, perfectly thermally
insulated, such that TTES-H, in = TTES-H, out, and TTES-C, in = TTES-C, out. As a consequence, only
two temperature levels are present in the system model, as indicated in Fig. 6.1. 2. Parasitic losses introduced to account for energy storage in the semi-steady framework of the SAM program have not been modelled: this is the case of the energy consumptions and
time delays associated with the start-up and shut down of all the subsystems [26]; 3. energy storage is explicitly modelled only in the TES tanks, since the (controlled) dynamics of the receiver system and power block is much faster; 4. the temperature dependency of the thermodynamic properties of the HTF, i.e., density and specific heat, is neglected; 5. perfect knowledge of future solar irradiation values is assumed, based on customarily adopted weather data files such as those described in [27]. As shown in the following, these assumptions can enormously reduce the complexity of the design
problem, while preserving the consistency of the results with respect to a corresponding omni-
comprehensive SAM model. For simplicity and numerical robustness, all the power variables are normalized with respect to the nominal power block thermal power, all the mass flow rate variables to the corresponding mass
flow rate, and the TES tank level to its nominal height. Notably, following the above mentioned
assumptions and simplifications, the equalities mPB = QPB and mHTF = QHTF hold, relating the
circulating mass flow rate of HTF through the power block and the receiver to the thermal power
transferred within the same subsystems. The general design data considered, i.e., the variables
which are fixed in this work, are collected in Tab. 6.1. The operating limits regarding the receiver
and the power block are expressed in terms of minimum/maximum fractions (i.e., f min/ f max) of the
relative design values for the incident radiative power QREC,inc, and for the mass flow rate fed to
the steam generator mPB. Similarly, the maximum storage level is equal to the nominal tank height,
while the minimum value is given an absolute value.
Based on all the above mentioned assumptions, the system model contains a single dynamic equa-
tion, describing the state of charge of the TES, and several algebraic equations, describing the power
block and the TES operation set points. The solar input can be defined in terms of the power avail-
able to the receiver QREC,inc,av (i.e., the total radiative flux which may reach the receiver if the solar
field is fully focused) as QREC,inc,av = DNI(t, loc) ASF ηopt(t, loc, SF) ǫavail ǫrefl . (6.1) In Eq. 6.1, the functional dependence of DNI and of the field optical efficiency ηopt from the time-
varying weather conditions (t), and from the plant location (loc), is made explicit. As anticipated, 153 Chapter 6 Table 6.1: General design data adopted for the 100 MWE (nominal) solar tower system consid-
ered here, after Refs. [10, 25, 26]. The plant is assumed to be located in Daggett (CA), latitude
34.9o, longitude ''116.8 o, average direct normal irradiation (annual) 2791 kWh m''2. ηPB is the power block thermal efficiency, ηREC,th and αREC the receiver thermal efficiency and absorptivity,
respectively. ǫavail and ǫrefl refer to the heliostats availability and reflectivity, both values accounting
for the average field performance. Wel, gross [MWE] 115 ηPB [%] 40 αREC [%] 94 ηREC,th [%] 88 ǫavail [ ''] 0.99 ǫrefl [ ''] 0.90 f min QREC,inc [''] 0.25 f max QREC,inc [''] 1.2 f min mPB [''] 0.25 f max mPB [''] 1 xTES,min [m] 1 f max xTES [''] 1 weather data in the TMY3 format, containing data for various locations with an hourly sampling, are considered in this work. The value of ηopt is evaluated hourly as a function of the solar position
but, as shown in Eq. 6.1, it is also dependent on the solar field characteristics (SF). The same is
obviously true for the total reflective area ASF. The dimension of the solar field can be better expressed in terms of the solar multiple (SM) value, that is, the ratio of the receiver design thermal output to the power block design thermal input.
As the solar field size is increased, there will be a growing number of hours throughout the year
whereby the available solar power exceeds the power block design power. In these conditions, the
TES system is used to harvest (part of) the exceeding energy, until defocusing (part of) the heliostats
migh become necessary. Thus, a techno-economic optimal combination of the solar field size and
of the storage capacity has to be determined for the given plant and location [28]. In particular,
the solar power harvesting system constituted by the solar field, the tower, and the receiver, is the
most capital intensive part of any solar energy project, and its optimization is therefore critical for
the minimization of the overall costs [8, 10, 29]. The SM is thus used as the key parameter in the
following analysis, and four solar fields characterized by SM = 1.5, 2, 2.5, and 3.5 are designed
for the same hypothetical plant, i.e., starting from the specfications reported in Tab. 6.1. Apart for the nominal characteristic indicated by the SM, however, the detailed design of the components involved is necessary in order to define both ASF and the ηopt(t, loc, SF) relation ap-
pearing in Eq. 6.1. In the present work, the PTGen program available within SAM [25, 26], and
based on the DELSOL3 code [30, 31], is adopted to this end. Solar fields with a surround radially-
staggered layout are considered. Even though several other geometries have been proposed in the
literature [8], this arrangement is chosen here for the sake of simplicity. The solar field modelling
assumptions adopted in this study, together with the resulting designs, are reported in A.1. Summarizing, since all the computations involved by Eq. 6.1 can be carried out off-line once the solar field has been designed, QREC,inc,av is eventually computed as a known, time-varying input
for the plant model. Also the price of the produced electricity P depends on known hourly TOD factors, in turn deter-
mined by the selected tariff, on the hour of the day, on the day of the week, and on the season, 154 Design of CSP Plants with Optimally Operated Thermal Storage according to P = TOD(t) PPA. (6.2) The power actually reaching the receiver QREC,inc may then be calculated as QREC,inc = QREC,inc,av '' Qdef , (6.3) where Qdef is the power dumped by defocusing heliostats, which is a control variable of the problem.
The following (normalized) equations QREC,abs = QREC,inc αREC , (6.4) QHTF = QREC,abs ηREC,th , (6.5) mHTF = QHTF , (6.6) WPB = mPB ηPB , (6.7) hTES dxTES dt = mHTF '' mPB , (6.8) xTES(0) = xTES,0 , (6.9) complete the model. Eq. (6.4) gives the thermal power absorbed in the receiver QREC,abs and
Eq. (6.5) the power QHTF transferred to the HTF. Eq. (6.6) relates the mass flow rate of HTF
through the receiver mHTF to QHTF, while Eq. (6.7) establishes the relation between WPB, mPB, and
the power block efficiency ηPB, which is assumed to be linear in this work. Finally, the differential
equation (6.8) describes the dynamics of the TES system, where hTES is the capacity of the stor-
age tank in terms of hours of operation at nominal power block load. The corresponding initial
conditions for the state variable are explicitly defined by Eq. (6.9). Several constraints need to be enforced in order to ensure feasible operation, namely QREC,inc ' f max QREC,inc , (6.10) 0 ' Qdef ' QREC,inc,av , (6.11) 0 ' mPB ' 1 , (6.12) xTES,min ' xTES ' f max xTES . (6.13) The first inequality states the maximum power that can be handled by the receiver, calling for a
partial defocusing of the heliostat field if the available power QREC,inc,av becomes too high; the
defocused power Qdef (second inequality) is non-negative and less than the available power. The
normalized flow rate of HTF to the power block is comprised between 0 and 1 per unit (third
inequality), while the storage tank state of charge xTES is limited between a lower and an upper
bound. Furthermore, both the solar field thermal power QREC,inc and the power block HTF flow mPB
have a minimum operating load, and need to be turned off if the desired load level is lower than
that. The first constraint is enforced by substituting QREC,inc,av = 0 whenever QREC,inc,av ' f min QREC,inc , which is done as a pre-processing task. The second constraint is handled by introducing extra terms
in the optimization problem, see §6.3.2. The resulting model has two known, time-varying inputs QREC,inc,av(t) and fTOD(t), and two control variables mPB(t) and Qdef(t). The model is readily encoded using the equation-based, object-
oriented language Modelica [32], see also §6.4 and listing 1 in A.3. 155 Chapter 6 6.3 Operation Strategy 6.3.1 Reference Operation Strategy The model described in §6.2 can be used to predict the performance of the considered solar tower plant when the reference operation strategy, defined following Refs. [25, 26] is applied. This ap-
proach aims at satisfying the nominal power cycle demand, by making use of the available re-
sources, namely of the solar field (SF) and the TES system, in a prioritized order. A sequence of
logical statements is used to determine whether the power cycle demand can be met with only the
SF, or with the SF and the TES, always in this order, while ensuring that the operative constraints
(Eqs. 6.10-6.13) are satisfied. In other words, the algorithm aims at running the power block at the
maximum possible load for every time step, defocusing the solar field when its output QREC,inc,av ex-
ceeds the sum of the nominal thermal power input of the power block and of the maximum storage
charging rate that fulfills the capacity limits over a one-hour horizon. In this way, the values of the
decision variables mPB and Qdef are determined disregarding any information about the electricity
price and of future availability of solar irradiation. The SAM software approximates the differential-algebraic equations of the model by assuming that all variables are constant within each hour of operation, i.e., by using the forward Euler''s
method. As there is no feedback from xTES to any other variable of the model, the forward and
backward Euler''s methods give the same results in this case, only shifted by one time step, which is
irrelevant when determining yearly revenues. 6.3.2 Optimal Control The model described in §6.2 can be adopted to assess the potential of an optimized operation strat- egy for the considered plant, aimed at maximizing the revenue deriving from the sold electricity.
The control objective is an integral cost to be minimized over the integration interval from time tin
to tfin, i.e., min Z tfin tin ''WPB P + c du dt !2 + g s (u '' f min mPB ) dt . (6.14) The first term in the integral accounts for the normalized instantaneous revenue from the sale of
electricity. The second term, with c > 0, is introduced to penalize fast changes and oscillations of
the control variable, as well as repeated re-starts of the plant during the same day. This provision,
which aims at avoiding stressful operating regimes for the power block, is implemented in order to
coherently follow the approach programmed into SAM. The third term, with g > 0, is introduced to
avoid power block operation below the minimum load, along with the additional constraints u = mPB + s , (6.15) 0 ' s ' u . (6.16) The free control variable u, which is the output of the dynamic optimization problem together with
Qdef, is the unconstrained normalized value of the HTF flow to the power block, while s is a slack
variable. If u > f min mPB , the term is minimized by taking the lowest possible value of s (s = 0), so that mPB = u. Conversely, if u < f min mPB , the term is minimized by taking the highest possible value of s (s = u), so that mPB = 0. The values of c and g are empirically chosen to be the smallest possible,
which actually succeeds at avoiding control oscillation, restarting of the power block in the same
day, and operation below the minimum load, while perturbing as little as possible the optimization
of the first term, i.e., the economic revenue of the plant. An additional constraint might be added to 156 Design of CSP Plants with Optimally Operated Thermal Storage obtain a specific value of the storage at the end of the operational period; this can be instrumental
in comparing the performance of the optimal control to that of the original control strategy on equal
grounds. The above-described optimal control problem can be readily encoded using the Optimica
language [33], an extension of Modelica that also allows to specify the control objective and the
constraint equations, see also §6.4 and listing 2 in A.3. 6.4 Computational Infrastructure Traditional codes for plant design and optimization are written from scratch in programming lan-
guages such as Fortran or C++, which is tedious and error-prone. The approach proposed in this
work leverages on modern, high-level modelling languages for the problem formulation, and on
software tools that automatically transform this description of the problem into low-level code that
can be coupled with state-of-the-art numerical solvers. The model is encoded using the Modelica language [32, 34], which is a high-level, non- proprietary, equation-based language for the modelling of systems described by differential-algebraic
equations, while the optimization problem is encoded using the Optimica extension to the Modelica
language [35]. The Modelica/Optimica language is supported by different tools, each implementing
alternative strategies for the solution of the dynamic optimization problem [36, 37]. The tool described in [36] was used in the work described here. A collocation method was adopted in order to solve the problem [38, 39]: the time-varying variables of the problem are ap-
proximated by Lagrange polynomials, that define the values of the variable in the optimization
interval tin ' t ' tfin as a direct function of the values at a finite set of nodal points, which become the unknowns of the problem. In this way, the infinite-dimensional optimal control problem stated
in §6.3.2 is transcribed into a large, finite-dimensional nonlinear programming (NLP) problem, which is then solved by an open-source NLP solver [40]. In order to directly compare the results with those obtained by the SAM program, which solves the differential equation by Euler''s method, 0-order polynomials (i.e., piecewise constant functions)
were used, with one-hour time intervals. It is worth pointing out that the proposed approach easily
allows to use more accurate interpolations, simply by changing the set-up of the problem tran-
scription. It is also easy to experiment with alternative solution strategies (e.g., multiple-shooting
instead of collocation), as well as with different techniques to reduce the size of the NLP by means
of symbolic manipulation, in order get the best performance in terms of convergence robustness and
CPU time. In all these cases, the high-level formulation of the problem remains the same, only the
choice of the tool and its configuration need to change, thus avoiding problem-specific low-level
programming. Last, but not least, the computational framework used to obtain the results presented in this chapter has been entirely built using open-source software and open standards. It is then possible to
use it as the foundation of extensions to publicly available tools such as the SAM program, without
any issue that might arise from the use of commercial software. 6.5 Results & Discussion The first analysis aims at assessing the performance of the model developed in this work, see §6.2, by comparing its predictions to the yearly simulation results yielded by a reference SAM model
(i.e., with all the main settings keeping their default values). The simulation is performed with
a control algorithm emulating the SAM control strategy, see §6.3. The results are shown in Fig. 157 Chapter 6 6.2a, whereby the yearly revenue (Rev) is shown as a function of the TES system capacity hTES, for
several SM values. As expected, the revenue increases for larger SM values (larger solar fields) and, h TES [eq. hours] R ev. [M $] 5 10 15 20 60 80 100 SM = 3.5
SM = 2.5
SM = 2.0
SM = 1.5 (a) h TES [eq. hours] R ev. [% ] 5 10 15 20 0 2 4 6 SM = 3.5
SM = 2.5
SM = 2.0
SM = 1.5 '' (b) Figure 6.2: Yearly simulation results in terms of revenue from electricity placement on the market
(i.e., Rev, ordinates axis). The results are shown as a function of the TES system capacity (i.e.
hTES, abscissae axis). The symbols refer to the SM values. 6.2a comparison between the reference
SAM model (dashed lines) and the Modelica model documented in this work (solid lines). 6.2b
percentage differences between the two models predictions. for a given SM value, tends to grow as the size of the storage is increased, that is, as the amount of
energy which needs to be dumped through defocusing is reduced. On the other hand, a maximum
revenue is reached for each SM value, beyond which an increase of hTES does not influence further
the revenue. As reported in Fig. 6.2b, the predictions of the two models are in close agreement. Further- more, the larger deviations, of the order of 5%, are encountered for plant layouts of negligible
practical interest, i.e., those characterized by large solar fields and comparatively small storage ca-
pacity. It is therefore proved that the adopted assumptions allow to develop a comparatively simple
model, able of accurately predict the yearly system performance. This simplified model is thus used to carry on the comparison between the reference and the op-
timized operation strategy, see §6.3. In order to provide the first insight, the results regarding a 10-days summer period are presented in Fig. 6.3. The considered tariff was adopted by the utility
company Pacific Gas and Electric in 2011, as defined in SAM [26]. The observed system is char-
acterized by a comparatively small storage capacity with respect to the field size. The time period
starts with a week-end, which has a different fTOD schedule. In order to perform the comparison on
a fair basis, the initial and final state of the TES in the optimization problem are constrained to be
the same as they are in the simulation using the SAM control. First of all, it can be noted from Fig. 6.3a that the use of optimal control allowed to increase the revenue of the period of about 7%, from 2.92 to 3.13 M$. The defocusing operation, envisaged
in both cases, is managed differently, affecting the mass flow rate through the receiver, see, e.g.,
Fig. 6.3b. The same graph shows how the power block operation varies as a consequence of the 158 Design of CSP Plants with Optimally Operated Thermal Storage t [d] Q [- ] R ev. [M $] 0 2 4 6 8 10 0 0.5 1 1.5 2 0 1 2 3 Q REC,inc,av Q def Q def OPT Rev.
Rev. OPT (a) t [d] m [- ] 0 2 4 6 8 10 0 0.5 1 1.5 m REC OPT m REC m PB m PB OPT (b) t [d] x T E S [- ] T O D [- ] 0 2 4 6 8 10 0 0.5 1 1.5 2 -4 -2 0 2 4 x TES x TES OPT TOD (c) Figure 6.3: Comparison between reference and optimized solar tower plant operation during a
10-days period, from July the 7th to July the 16th. The considered system features solar multiple
SM = 1.5 and storage capacity hTES = 3 eq. hours. different control strategy. The effects of the optimized control strategy can be clearly understood
by considering also Fig. 6.3c, whereby both the storage level and the TOD factor are shown. Being
the storage capacity comparatively small, the optimal controller can not manipulate large amounts
of energy, and the plant load profile is therefore similar in the two cases. However, the production
tends to be shifted towards the afternoon hours of working days (when the TOD factor is highest),
by reducing the load during off-peak hours, i.e., by limiting mPB to a value sufficient to prevent
storage overloading while avoiding the need of defocusing. Note that the hourly values of mPB,
represented by the red dots, never fall in the forbidden region between zero and the minimum load,
as expected from the problem formulation. 159 Chapter 6 h TES [eq. hours] R ev. [M $] 5 10 15 20 50 60 70 80 90 100 SM = 3.5
SM = 2.5
SM = 2.0
SM = 1.5 (a) h TES [eq. hours] h T E S ( at = R ev. ) [% ] R ev. ( at = h T E S ) [% ] 5 10 15 20 -50 -40 -30 -20 -10 0 10 20 -2 0 2 4 SM = 3.5
SM = 2.5
SM = 2.0
SM = 1.5 '' '' (b) Figure 6.4: Yearly results for the comparison between reference and optimized solar tower plant
operation. The results are shown as a function of the TES system capacity hTES. The symbols refer
to the SM values. 6.4a results in terms of harvested revenue Rev, black lines: optimized operation,
gray lines: reference operation (these lines correspond to the solid black lines reported in Fig. 6.2a).
6.4b percentage differences among the results shown in Fig. 6.4a; red lines (and red ordinates axis):
iso-abscissae comparison (i.e., possible increase in revenue for a given hTES), black lines (and black
ordinates axis): iso-ordinates comparison (i.e., possible decrease of hTES for a given revenue). In order to present a thorough analysis, however, the yearly system performance must be considered.
The solution strategy is the same, and the optimal control result has been obtained by separately op-
timizing each month of operation, and then by summing the resulting monthly revenues. Since the
adopted approach assumes perfect knowledge of the weather forecast within the analysis interval,
considering monthly intervals may seem inappropriate. However, as discussed in Ref. [20], expand-
ing the forecasting horizon to more than 2 '' 3 days has only a minor effect on the yearly revenue, since the storage capacity limitation constrains the amount of energy that the optimizer can shift.
The plant yearly revenue as a function of the storage capacity, with and without optimal control and
for several SM values, is shown in Fig. 6.4a. Fig. 6.4b sheds some more light on these results. It can be seen that, for any storage capacity, the optimal operation strategy allows for a positive gain in terms of revenue, ranging approximately
from 2% up to 5% (see red lines, and red ordinates axis). Notably, a complementary perspective
can be considered, i.e., the operating strategies can be compared for equal revenue yields, thus eval-
uating the potential reduction in TES system size they allow for, or, in other words, their impact
on the system design. Also in this case, the gain achievable thanks to the optimized operation is
considerable (see black lines, and black ordinates axis). To put these conclusions in the right perspective, that is, in order to properly discriminate among
an increase in the yearly revenue and a decrease of the capital cost, a financial analysis considering
the whole plant life-time is necessary. A detailed financial model has been developed to this end,
based on the framework implemented in SAM [26]; the adopted methodology is detailed in A.2. All 160 Design of CSP Plants with Optimally Operated Thermal Storage h TES [eq. hours] N P V . [M $ ] 0 5 10 15 20 -40 -20 0 20 40 60 80 100 120 140 SM = 3.5 SM = 2.5 SM = 1.5 SM = 2.0 Figure 6.5: Financial comparison between reference and optimized solar tower plant operation
strategy: net present value (NPV) as a function of TES system capacity hTES, for several SM values
(corresponding to different line formats). Grey lines: reference control strategy; red lines: optimized
strategy exploited to increase yearly revenue (see Fig. 6.4b, red lines); black lines: optimized
strategy exploited to decrease the investment (see Fig. 6.4b, black lines). The black-dotted line
(SM = 1.5) is not shown, being undistinguishable from the corresponding grey-dotted one. the considered plants are assumed to sell electricity at the same PPA price. The Net Present Value
(NPV) of the project is adopted as the financial figure of merit, with the purpose of examining costs
and revenues together, in order to evaluate mutually exclusive investment features and decisions
[41]. The results of the analysis are summarized in Fig. 6.5, where the NPV is shown as a function of the TES system capacity, for several SM values. It can be noted that all the gray curves, referring
to the base case, i.e., to the reference control strategy, reach a maximum NPV value (NPVmax) for a
given storage capacity value hTES. Referring again to Fig. 6.2a, such hTES value is the one allowing
to reach the maximum revenue for the given SM value. In other words, this analysis allows to
properly penalize solutions yielding the same revenue with an increasingly large investment. The red curves show the impact of the optimal operating strategy on the project NPV, ac- counting for the revenue increase it allows for (see, e.g., Fig. 6.4b, red lines). It can be seen that the
location of NPVmax in terms of hTES is not varied with respect to the base case, as expected after Fig.
6.4a. In all cases, the financial advantage resulting from a complete analysis is larger if compared to
only the yearly revenue. The SM = 1.5 case can be considered as an example: NPVmax = 91.5 M$
for hTES = 5 eq. hours is obtained for the base-case, i.e., the gray-dotted line in Fig. 6.5. For the
same system (SM = 1.5, hTES = 5 eq. hours), adopting the optimized control strategy allows for
an yearly revenue increase of '' 4%, as shown in Fig. 6.4b. Notably, this figure is coherent with 161 Chapter 6 previously published results [20]. However, this induces a gain of '' 11% in terms of NPV, with NPVmax = 103 M$, as shown by the red-dotted line in Fig. 6.5. The black curves account for the impact of the optimal operating strategy on the project NPV as well but, in this case, what is being evaluated is the reduction in the investment it enables (see,
e.g., Fig. 6.4b, black lines). As expected, the NPV is in general larger than the one characterizing
the base-case, and this gain grows for larger TES system capacity. However, the gain results always
lower than in the previous case, approaching the same value in the SM = 3.5 case. The factor
determining this situation is the comparatively low specific cost of the storage system which, for a
state-of-the-art system with SM = 2.5 and hTES = 15 eq. hours, accounts for approximately 10% of
the total installed cost. Even though these conclusions are strongly influenced by the parameters adopted in the fi- nancial analysis, their validity is expected to hold under all the foreseeable realistic scenarios for
state-of-the-art systems. 6.6 Conclusions Concentrated solar power plants with thermal storage are a promising technology, increasingly
considered as an option for widespread conversion of renewable energy. In a context of time-varying
tariffs, the storage system can be used to shift the production to the most profitable hours, exploiting
the dispatchability capabilities of this technology. The aim of the work presented here was to
assess the potential of optimal control techniques, applied to the storage operation, to increase
the profitability of the plant. To this end, the model of a state-of-the-art central receiver plant
has been developed using high-level modelling languages, based on data available in the literature
and in the SAM reference software. Optimal control problems have then been formulated and
solved. The different operating strategies are compared based on a detailed financial analysis over
the project life-time. A wide system design space is considered, and the results are presented for all
the foreseeable combinations of solar field size and storage system capacity. A novel methodology is introduced, which allows to properly assess the potential of optimal control in terms of both the increased revenue and the reduced investment cost it allows for. In other
words, it becomes possible to evaluate the influence of the operating strategy on the system design.
It is demonstrated that optimal control should be taken into account when estimating the potential
plant revenue since its design and sizing phase. This constitutes a new tool in the designer''s hands
who, depending on the specific project characteristics and financial framework, may be keen on
favouring a larger electricity production or a comparatively lower investment cost. In summary, the
main findings of the work are: ' For state-of-the art systems operating in a context of time-varying tariffs, it seems profitable to exploit optimal control to the end of increasing electricity production. This is mainly due
to the comparatively low impact of the storage system cost on the investment. On a yearly
basis, an average gain in the revenue of the order of 5% is obtained with respect to usually
adopted short-sighted strategies. However, this figure is amplified to more than 10% in
terms of net present value of the investment when applying the complete financial analysis
presented here. Notably however, the storage capacity for which maximum profitability
occurs seems to be independent from the considered operating strategy. ' The potential of optimal control in terms of investment cost reduction has been unveiled for the first time. For the case-study technology considered, this follows the possibility
of harvesting the same revenue with a smaller storage capacity. Even if this solution is 162 Design of CSP Plants with Optimally Operated Thermal Storage suboptimal for current CSP practice, it might assume practical significance in evaluating
plants with different cost structure, e.g., featuring larger storage relative cost, as is case of
PV/batteries installations. ' The results have been obtained with open-source software, and a total of about 50 code lines. A future step of this research might involve the implementation of the proposed methodology as an
extension of reference design models, such as the model implemented into the SAM program. 6.7 Acknowledgements This work has been carried out during E. Casati''s research period at Politecnico di Milano, Dipar-
timento di Elettronica, Informazione e Bioingegneria, supported by the Dutch Technology Foun-
dation STW, Applied Science Division of NWO and the Technology Program of the Ministry of
Economic Affairs, grant # 11143. The authors thankfully acknowledge the precious suggestions
about JModelica.org from their colleagues at the University of Lund, Sweden: F. Magnusson, J.
'kesson, and C. Andersson. The help received by the NREL staff working on the SAM support
forum, in particular by P. Gilman, has also been invaluable. A.1 Solar Fields Design This section details the procedure adopted in order to obtain the design of the solar fields considered
here. It shows how the field reflective surface ASF and its time-varying optical efficiency ηopt are
defined, see Eq. 6.1. As described in §6.2, several solar fields characterized by different SM values are designed for the same hypothetical plant power output, location, and so forth, using the data
reported in Tab. 2. For a given SM value, the adopted algorithm, based on the DELSOL3 code
[30, 31], searches for a system design capable of yielding the highest financial returns, accounting
for capital and other costs against the projected electricity production. The main objective of the
tool is to optimize the geometric relationships among the main components of the solar power
harvesting system, i.e., the solar field, the tower, and the receiver [25]. It is worth noting that all
the designed fields share the design boundaries defined by the data in Tab. 2, aiming at reducing
the complexity of the treatment and at facilitating the reproducibility of the results. The ranges of
variation for the design variables, in particular, have been selected such that reasonable layouts can
be obtained regardless of the considered SM value. The modelled receiver is of the tubular type, with constant absorptivity αREC and emissivity ǫcoating. The main constraint regarding the design of this component is the maximum admissible
heat flux on its surface (see ''rec. max flux'). Regarding the solar field, a general layout constraint
is expressed in terms of the maximum/minimum distance of the farther/closer heliostats row from
the tower (see ''helio.-tow. distance/HTOW'). The modelled technology relies on square heliostats
with a 12 m side (reflective part), whose main optical properties are also reported in Tab. 2. As
anticipated in §6.5, these are arranged in a radially staggered, surround field which, for the sake of the layout optimization, is discretized in radial and azimuthal zones (see ''N rad. zones' and ''N
azim. zones'). In order to solve the SF design problem, an optimal number of heliostats has to be
allocated within each zone. The program evaluates discrete combinations of values for the main
design variables, i.e. the diameter of the receiver DREC and its height-over-diameter ratio (H/D)REC,
and the tower height HTOW, with a grid-spacing based on the search interval and on the number of 163 Chapter 6 Common parameters Location Daggett - CA Longitude -116.8 Latitude [o] 34.9 Wel, gross [MWE] 115 ηPB [%] 40 αREC [%] 94 ǫcoating [ ''] 88 rec. max flux [kWT m'' 2] 1000 (helio. - tow. distance/HTOW )min [ ''] 0.75 (helio. - tow. distance/HTOW )max [ ''] 12 Ahelio [m 2] 144 image error [mrad] 1.53 N rad. zones [ ''] 12 N azim. zones [ ''] 12 non SF land area [m2] 182109 SF land area multiplier [ ''] 1.3 N opt. levels 10 (DREC, (H/D)REC, HTOW) [ ''] Design Variable LB UB DREC [m] 8 30 (H/D)REC [m] 0.5 2.5 HTOW [m] 100 300 Table 2: Design parameters and variables used within the radially-staggered solar field layout
optimization, with relative lower (LB) and upper (UB) bounds. Several quantities appeared in Tab.
6.1, and are reported here for the sake of clarity. For all the three design variables, the defined range
of variation is discretized into 10 points. These data are common to all the solar fields designed in
this work. optimization levels (see ''N opt. levels').
The most critical step is the evaluation of the flux distribution on the receiver surface as a function
of solar position, which DELSOL3 calculates based on sophisticated aiming techniques. This infor-
mation allows to iterate on the system design, accounting for the maximum flux levels the receiver
can withstand, until an optimum layout is determined. The results regarding the geometry of the
solar power harvesting system are reported in Tab. 3. The radial step indicates the distance among
two subsequent heliostats rows, and it is assumed constant within each field. It can be noted that the
relation between the area ASF and the SM value is not linear, reflecting the decrease of the optical
performance as the solar field size grows. As detailed in [25], DELSOL3 outputs also a 2D matrix
reporting the field optical efficiency appearing in Eq. 6.1, and defined as ηopt(t, loc, SF) = ( FREC AREC) (DNI Ahelio Nhelio)'' 1 , (17) where FREC [kWT m'' 2] is the average flux incident on the receiver at the given time, and AREC [m2] is the receiver surface. In other words, the total radiation incident on the receiver is divided by the total
radiation incident on the heliostat field mirrors for a given solar position. This last bit of information
is fully specified in terms of Azimuth and Zenith angles which, in turn, can be calculated for the
given time of the year (t) and the plant location (loc) by means of standard methods, see, e.g., [28].
The values of ηopt, calculated for the fields whose geometry is defined by the data in Tab. 3, are
reported in Tab. 4. 164 Design of CSP Plants with Optimally Operated Thermal Storage Solar Multiple (SM) 1.5 2.0 2.5 3.5 Nhelio [ ''] 6435 8012 10979 16058 ASF [m 2] 926640 1153728 1580976 2312352 total land area [km2] 7.12 6.85 11.65 20.13 DREC [m] 10.5 13 13 15.5 HREC [m] 24.0 23.5 29.5 35.0 AREC [m 2] 792 960 1205 1704 HTOW [m] 144 189 189 211 min dist. from tow. [m] 108 142 142 158 radial step [m] 135 177 177 198 max dist. from tow. [m] 1597 1558 2089 2534 Table 3: Design results for the optimized solar power harvesting system. The adopted parameters
and variables are listed in Tab. 2. Z. SM A. [o] [o] 0 30 60 90 120 150 180 210 240 270 300 330 0.5 1.5 .680 .680 .680 .680 .680 .680 .680 .680 .680 .680 .680 .680 2.0 .720 .720 .720 .720 .719 .719 .719 .719 .719 .720 .720 .720 2.5 .667 .667 .667 .667 .667 .667 .667 .667 .667 .667 .667 .667 3.5 .640 .640 .640 .640 .640 .640 .640 .640 .640 .640 .640 .640 7 1.5 .680 .680 .679 .678 .678 .677 .677 .677 .678 .678 .679 .680 2.0 .720 .720 .719 .716 .715 .714 .713 .714 .715 .716 .719 .720 2.5 .669 .667 .666 .664 .664 .663 .663 .663 .664 .664 .666 .667 3.5 .638 .638 .638 .637 .637 .637 .636 .637 .637 .637 .638 .638 15 1.5 .674 .673 .672 .669 .668 .666 .666 .666 .668 .669 .672 .673 2.0 .714 .714 .710 .706 .703 .700 .699 .700 .703 .706 .710 .714 2.5 .659 .659 .658 .656 .654 .653 .652 .653 .654 .656 .658 .659 3.5 .632 .631 .631 .630 .629 .627 .627 .627 .629 .630 .631 .631 30 1.5 .659 .659 .656 .652 .647 .645 .643 .645 .647 .652 .656 .659 2.0 .704 .702 .697 .688 .680 .674 .672 .674 .680 .688 .697 .702 2.5 .646 .645 .642 .638 .635 .631 .631 .631 .635 .638 .642 .645 3.5 .617 .616 .615 .612 .611 .609 .609 .609 .611 .612 .615 .616 45 1.5 .642 .641 .636 .630 .624 .619 .617 .619 .624 .630 .636 .641 2.0 0.690 .687 .678 .666 .653 .646 .643 .646 .654 .666 .678 .687 2.5 .627 .626 .622 .616 .610 .606 .605 .606 .611 .616 .622 .626 3.5 .599 .598 .595 .591 .589 .586 .585 .586 .589 .593 .595 .598 60 1.5 .603 .600 .594 .585 .577 .570 .569 .572 .578 .585 .594 .600 2.0 .646 .641 .630 .614 .599 .589 .585 .589 .600 .615 .631 .642 2.5 .588 .585 .579 .572 .564 .558 .557 .559 .564 .573 .580 .586 3.5 .560 .559 .556 .551 .546 .543 .543 .543 .547 .551 .556 .559 75 1.5 .480 .476 .469 .460 .448 .440 .440 .442 .450 .462 .470 .478 2.0 .499 .494 .483 .464 .447 .432 .431 .434 .449 .466 .485 .496 2.5 .464 .461 .454 .447 .436 .429 .428 .431 .437 .448 .457 .464 3.5 .447 .445 .442 .436 .431 .426 .426 .428 .432 .438 .443 .448 85 1.5 .313 .308 .301 .294 .283 .275 .280 .278 .286 .299 .304 .311 2.0 .296 .291 .282 .265 .255 .242 .244 .245 .257 .268 .286 .294 2.5 .297 .294 .288 .281 .271 .265 .266 .267 .273 .283 .291 .297 3.5 .292 .292 .290 .283 .278 .273 .275 .276 .281 .286 .292 .294 Table 4: Design results for the optimized solar fields. Field optical efficiency ηopt (see Eq. 17),
calculated for the fields whose geometry is defined by the data in Tab. 3. The results are reported,
for the four solar multiples considered, as a function of Azimuth (A.) and Zenith (Z.) angles, which
define the solar position. 165 Chapter 6 General N 25 dr 8.2 iinfl 2.5 Nloan 20 [year] [% year''1] [% year''1] [years] fdebt 50 rloan 8 rinc. tax 40 rITC 30 [%] [% year''1] [% year''1] [% DC+IC] Direct and Indirect Costs (Eqs. 21, 22 ) SIcoeff 15 SFcoeff 180 BOPcoeff 350 PBcoeff 1200 [$ m''2] [$ m''2] [$ kW''1 E ] [$ kW''1 E ] TEScoeff 27 TOWfixed 3 TOWscaling 0.0113 RECref 110 [$ kWh''1 T ] [M$] [ ''] [M$] AREC, ref 1571 RECscaling 0.7 contin. 7 rEPC 11 [m''2] [ ''] [%] [% DC] rland 2.47 rsales tax 5 basesales tax 80 [$ m''2] [%] [% DC] Operating Income (Eq. 23) O&Mcap,coeff 65 O&Mgen,coeff 4 rinsurance 0.5 rPPA, escalation 1 [$ kW''1 E ] [$ MWh''1 E ] [% DC+IC] [% year''1 ] rperf. degr. 0.5 [% year''1] Table 5: Data adopted in the financial analysis. The meaning of the reported quantities is discussed
in the body of the appendix. A.2 Financial Analysis The financial model presented here has been developed following the SAM framework [26] and the
work of [41]. The parameters for the analysis, reported in Tab. 5, are assigned typically encountered
values, see, e.g., [10]. The selected figure of merit is the Net Present Value (NPV) of the solar power
project, i.e., the sum of the actualized net cash flows along the project life [41], which reads NPV = N X n=0 Fn (1 + d)n = F0 + F1 (1 + d)1 + F2 (1 + d)2 + · · · + FN (1 + d)N . (18) N is the analysis period (i.e., the project life), and d the nominal discount rate d = ((1 + dr/100) (1 + i/100) '' 1) · 100 , (19) where dr is the real discount rate, and i is the inflation rate. The Fn terms represent the net after-tax
cash flows in the n years: a negative value represents a net outflow, a positive value a net inflow.
They are evaluated as Fn =      
     ''(1 '' fdebt/100) (DC+IC) if n = 0 (20a) op. inc.(n) '' inc. tax(n) + tax sav.(n) + ... (20b) ... '' debt repaym.(n) '' debt int. paym.(n) if 0 < n ' N (20c) For the first year of the analysis, i.e. conventionally the 0th year, the financial balance accounts for
the debt portion of the investment only, expressed as a fraction fdebt of the total installed costs, i.e., 166 Design of CSP Plants with Optimally Operated Thermal Storage as shown in Eq. 20a, the sum of direct-costs (DC) and indirect ones (IC), respectively defined as DC = (SI + SF + BOP + PB + TES + TOW + REC) (1 + contin. 100 ) , (21) IC = EPC + LC + Stax . (22) The first two terms in Eq. 21 account for the solar field costs, in terms of site improvement SI and of heliostats cost SF, as SI = ASF SIcoeff and SF = ASF SFcoeff, respectively. Similarly, BOP and
PB account for the cost of the Balance Of Plant and of the power block, as BOP = Wel, gross BOPcoeff
and PB = Wel,gross PBcoeff. TES relates the storage system cost to its capacity in terms of thermal
energy, i.e TES = Wel,gross TEScoeff. The tower cost is evaluated by multiplying a fixed cost compo-
nent to an exponential function of the tower height, i.e., TOW = EXP (TOWscaling HTOW) TOWfixed.
The receiver cost is found by multiplying the cost of a reference component (i.e., RECref) by the
corresponding surface ratio, i.e., REC = RECref (AREC/AREC, ref) RECscaling . A contingency factor (i.e. ''contin'.) is also considered. As shown in Eq. 22, the indirect costs account for the Engineering-Procurement-Construction Costs (EPC), calculated as a percentage rEPC of the direct costs. The land cost term LC is eval-
uated by applying the unit cost coefficient rland to the total land area needed (see Tab. 3). The
sales tax Stax is a one-time tax included in the project total installed cost, and therefore in the
depreciable basis (see in the following), and is calculated on a fraction of the direct costs as
Stax = DC (basesales tax/100) (rsales tax/100). Regarding the financing scheme, a fraction fdebt of the total installed cost is assumed to be borrowed. This initial debt is payed back through annual amounts (i.e. ''debt repaym.'), calculated
by using the levelized mortgage payment methodology, i.e., by assuming constant payments on
principal amount over the loan term Nloan at the rate rloan. The payment of interests is evaluated by
applying the same rate on the remaining debt, through annual amounts (i.e. ''debt int. paym.'). For the calculation of the cash flows for the following years of the analysis, i.e., when 0 < n ' N, Eq. 20c applies (the dependency from n, common to all terms, is not explicitly indicated in the
following in order to improve readability). The first term accounts for the operating income the
project generates in the nth year, i.e., op. inc. = Rev '' (O&Mcap + O&Mgen + insurance) . (23) Rev indicates the yearly revenue from sold electricity, i.e., for the 1st year, the performance indicator
used throughout §6.5. Thus, an annual average value for the energy price PE can be defined as PE = E/Rev, with E being the sold energy. These values are used as the basis for the analysis and, for the
following years (i.e., for 1 < n ' N), the plant revenue is calculated as Rev = Ecorr/PE,corr, whereby Ecorr corrects E accounting, year after year, for the degradation of performance rperf. degr., and PE, corr
applies the annual PPA price escalation rate rPPA, escalation to PE. Furthermore, both quantities are
yearly inflated by considering the iinfl rate. The O&Mcap and O&Mgen terms in Eq. 23 refer to the operating and maintenance costs related to the plant nameplate power capacity and the generated energy E, and are evaluated by multiplying
these quantities by the corresponding coefficients O&Mcap,coeff and O&Mgen,coeff. Also the annual
insurance cost is considered as an operating expense (therefore reducing the taxable income, see the
following), and is calculated as a percentage rinsurance of the total installed costs (i.e., DC+iC) . For
the years of the analysis following the first, all the quantities appearing between brackets in Eq. 23
are recalculated accounting for inflation. The second term in Eq. 20c refers to a global annual income tax, which applies to a percentage 167 Chapter 6 rinc. tax of the taxable income, and reads inc. tax = (rinc. tax/100) (op. inc. '' debt int. paym. '' depreciation) . (24) The depreciation term represents the decrease in value of project assets over the analysis period,
and it reduces the taxable income. In the present work, the so-called Modified Accelerated Cost
Recovery System depreciation schedule offered by the US Federal government using a five-year
life and half-year convention is used, commonly referred to as 5-yr MACRS [41]. The depreciation
is expressed as a percentage of the depreciable basis, corresponding to the total installed costs in
this analysis, and it applies to the first five years of the project life as follows: 20%, 32%, 19.2%,
11.52%, 11.52%, and 5.76%. The third term in Eq. 20c refers to tax savings deriving from tax credits or incentives. In the present analysis, only an Investment Tax Credit equal to a fraction rITC of the initial investment (i.e.
of the total installed costs) is considered. This applies on the first year of the analysis, i.e. for n = 1
only. A.3 Modelica and Optimica listings Listing 1: Plant model in Modelica. model CSP_tower input Real Q_rec_inc_av ;
input Real m_PB ;
input Real Q_def ;
output Real x_TES ;
Real m_rec_HTF ;
Real Q_rec_inc ;
Real Q_rec_abs , Q_rec_HTF , Q_rec_HTF , Q_lost , W_PB ;
parameter Real alpha_rec = 0 .94 ;
parameter Real eta_rec_th = 0 .88 ;
parameter Real eta_des = 1;
parameter Real f_max_Q_rec_inc = 1 .2 ;
parameter Real T_TES ;
parameter Real x_TES_0 = 0 .05 ;
equation
Q_rec_inc = Q_rec_inc_av - Q_def ; Q_rec_HTF = Q_rec_abs * (1 - eta_rec_th ); m_rec_HTF = Q_rec_HTF ;
W_PB = m_PB * eta_des ; T_TES * der ( x_TES ) = m_rec_HTF - m_PB ; initial equation x_TES = x_TES_0 ; end CSP_tower ; Listing 2: Optimization problem in Optimica. 168 Design of CSP Plants with Optimally Operated Thermal Storage optimization optim ( objectiveIntegrand = - plant.W_PB * f_TOD + c* du_dt '2 + g*s*(u- plant.f_min_m_PB ),
startTime = 0, finalTime = 7* 24 * 3600 ); CSP_tower plant ( T_TES = 15 * 3600 );
parameter Real g = 1;
parameter Real c = 2250000;
// Known inputs
input Real Q_rec_inc_av ;
input Real f_TOD ;
// Unknown control variables
input Real f( min =0, free = true );
input Real du_dt ( free = true , nominal = 4e -5);
// Other extra variables
Real s( free = true );
Real u( min =0, max =1 .0 ); equation Q_rec_inc_av = plant.Q_rec_inc_av ; TOD = plant.TOD ; u = plant.m_PB + s; der (u) = du_dt ; f = plant.Q_def ; initial equation plant.m_pb = 0; constraint s >= 0; s <= u;
m_PB >= 0; m_PB <= 1;
Q_def >= 0;
x_TES >= 0 .05 ; x_TES <= 1;
Q_rec_inc >= 0; Q_rec_inc <= f_max_Q_rec_inc ;
f >= 0; f <= plant.Q_rec_inc_av ;
plant.x_st ( finalTime ) = 0 .05 ; end optim ; Nomenclature Q, W = thermal and electrical power [various units] m, P = mass flow rate [kg s''1], electricity price [$ kWh''1 el ] t, Rev = time [various units], plant yearly revenue [M$ year''1] T , x = temperature ['C], storage level [ ''] η, α = efficiency and absorptivity [ ''] ǫavail, ǫrefl = average heliostats availability and reflectivity [ ''] A, H = surface [m2], height [m] D, hTES = diameter [m], storage capacity [eq. full-load hours] loc = plant location [-] Subscripts & superscripts 169 Chapter 6 E, T = electric, thermal REC, TOW = receiver, tower TES-C, TES-H = cold and hot tanks in the TES system in, out = inlet and outlet conditions of a given HTF stream opt, inc, av = optical, incident (radiative flux), available min, max = minimum and maximum in, fin = initial and final Acronyms R&D = Research & Development CSP = Concentrated Solar Power TES = Thermal Energy Storage CR = Central Receiver (i.e. solar tower) HTF = Heat Transfer Fluid PPA = power purchase agreement TOD = Time Of Day LCOE = Levelized Cost Of Electricity SAM = System Advisory Model DNI = Direct Normal Irradiation [W m-2] NLP = Non-Linear Programming PB = Power Block SF = Solar Field SM = Solar Multiple O&M = Operations and Maintenance NPV = Net Present Value 170 References [1] M. Mediavilla, C. de Castro, I. Capell´an, L. J. Miguel, I. Arto, and F. Frechoso. The tran- sition towards renewable energies: Physical limits and temporal conditions. Energy Policy,
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Renewable Energy Laboratory, U.S. Department of Energy, 1995. 173 Part II Fundamental Aspects 7 Flexible Asymmetric Shock Tube (FAST): Commissioning of a High Temperature Ludwieg Tube for Wave Propagation Measurements Part of the contents of this chapter will appear in: T. Mathijssen, E. Casati, M. Gallo, N.R. Nannan, C. Zamfirescu,
A. Guardone, & P. Colonna
Meas Sci Technol, To be submitted for publication (2014) Chapter 7 Abstract This chapter describes the commissioning of the Flexible Asymmetric Shock Tube (FAST) setup, designed and built at the Delft University of Technology. The aim of this Ludwieg Tube facility
is to measure wave propagation speed in the high pressure side of the tube, with the final objective
of providing the first experimental evidence of the rarefaction shock waves in the dense vapor region
of fluids formed by complex organic molecules. Measurements can be performed for a variety of
fluids, and up to temperature and pressure conditions equal to 400' C and 20 bar, respectively. A
fast opening valve induces a pressure disturbance propagating in the tube, which is thus sensed
through 4 dynamic pressure transducers. The FAST components and the measurement methodology
are described in detail. The fast opening valve is characterized in terms of its opening time. The
results regarding a shock wave forming in air are presented, and used to demonstrate and validate
the setup capabilities. Preliminary expansion measurements in D6 siloxane are also presented,
being of special interest to the end of the envisaged non-classical gas dynamics experiments. 7.1 Introduction The branch of gas dynamics investigating exotic specimens such as rarefaction shock waves, and
mixed or split waves, is called non-classical [1, 2]. However, the existence of non-classical gas
dynamic phenomena in the single-phase vapour region is still an open question in fluid mechanics.
Nsotwithstanding a certain number of attempts, experimental evidences are lacking. The empirical verification of the voluminous theoretical body forming non-classical gas dy- namics, contributed by a number of scientists worldwide since the first decades of the 20th century,
would constitute a big advancement for science. Furthermore, a comparatively close at hand indus-
trial application already exists in the field of organic Rankine cycle (ORC) turbogenerators [3, 4],
a technology for the conversion of thermal energy into electricity presently growing at a fast pace
[5]. This work documents the design, construction, and commissioning phases of the flexible asym- metric shock tube (FAST) set-up. This is a dense gas Ludwieg tube conceived and installed at the
Delft University of Technology, The Netherlands, with the aim of providing the first experimental
proof of the most fascinating and evanescent non-classical gas dynamics effect, namely the rarefac-
tion shock wave (RSW). The theoretical framework surrounding this research is summarized in §7.2, together with a literature review regarding past experiences in the field of experimental non-classical gas dynamics.
A conceptual description of the FAST set-up and of its working principle, and the detailed descrip-
tion of the main components are provided in §7.3. The data acquisition and control infrastructures are presented in §7.4. The results of the preliminary experiments conducted in order to validate the functioning of the FAST are reported and discussed in §7.5, while the conclusions of the work and an putlook to the future are presented in §7.6. 7.2 Fundamentals The first studies in the field of non-classical gas dynamics were conducted by Nobel-laureate Hans
Bethe, in 1942 [6]. An early contribution is also due to Zeldovich [7] and Weyl [8]. Though, it
was Thompson who first provided a systematic treatment in its seminal works [1, 9, 10]. A recent
review can be found in Ref. [11]. A necessary condition for non-classical behaviour to be physically 178 Commissioning of the FAST setup '=0 Vapour
phase Liquid
phase Critical
point BZT
region S at ur at ion cur ve Two-phase region v r P r 0.5 1 1.5 2 2.5 0.8 0.9 1.0 Figure 7.1: Saturation and ' = 0 curves in the vR '' PR plane of reduced specific volume and
pressure, as computed by the SW thermodynamic model [19], for siloxane D6 (dodecamethylcy-
clohexasiloxane, C12H36O6Si6): MW = 444.9 [g mol'' 1], TCR = 372.7 [oC], PCR = 9.61 [bar], ρCR = 246.8 [kg m'' 3]. Reduced thermodynamic variables are made dimensionless by their critical point values. The non-classical region (BZT region) is bounded by the saturation curve and the
' = 0 curve. admissible is that the fundamental derivative of gas dynamics ' ' 1 + ρ c ''c ''ρ ! s = v3 2c2 ''2P ''v2 ! s , (7.1) a thermodynamic property of the fluid first introduced by Hayes [12], is negative in part of the
covered domain. In definition (8.1), ρ is the density, s is the entropy, P is the pressure, v = 1/ρ is the
specific volume, and c is the zero-frequency speed of sound c ' (''P/''ρ)s. If ' is negative in a finite thermodynamic region, RSWs are admissible, among other so-called non-classical waves [9]. From
basic gas dynamics theory [9, 12], an expansion perturbation entirely embedded in the ' < 0 region
necessarily evolves as a discontinuity, namely as a non-classical rarefaction shock wave, whereas
a compression disturbance disintegrates into an isentropic non-classical compression wave. After
the names of the above mentioned scientists, substances characterized by thermodynamic states
featuring negative values of ' in the dense vapour phase are called Bethe-Zel''dovich-Thompson
(BZT) fluids. Much attention has recently been devoted to the computation of the negative-' region, and to the identification of BZT compounds among both pure fluids, see Ref. [13] for a review, and binary
mixtures [14]. Currently, there are three classes of substances predicted to be BZT by the most
accurate thermodynamic models available, namely hydrocarbons [15], perfluorocarbons [15''17],
and siloxanes [18]. Figure 7.1 shows the saturation curve and the non-classical (' < 0) region of
the cyclic siloxane D6.
Experimental evidence of non-classical gas dynamics is available only for flows displaying liq-
uidvapour phase transition, see Refs. [20''22], or in allotropic phase changes in solid-solid sys-
tems [23]. In the single-phase vapour region, only classical gas dynamics phenomena have been 179 Chapter 7 observed so far. Compared to the amount of theoretical and numerical studies on non-classical
gas dynamics, a comparatively limited amount of effort has been devoted to experimental assess-
ments, mainly due to the technical difficulties related to the observation of these fleeting waves, as
discussed in Refs. [24, 25]. A first attempt has been carried out in the former USSR by Borisov and colleagues in 1983 [26, 27] who claimed to have measured a RSW in Freon-13 (trifluorochloromethane, CCl3F). Fer-
gason et al. [24, 28] and others [22, 29] refute that this could have been a RSW in the single phase
region and provide alternative interpretations of that experiment by pointing towards critical point
phenomena and two-phase effects. Recent studies show that the fundamental derivative of gas dy-
namics indeed is negative in the two-phase critical point region [30] and that rarefaction shockwaves
are possible in close-to-critical conditions [31]. In the early 2000''s, a shock-tube experiment has been pursued at the University of Colorado at Boulder, with the aim of producing a RSW in perfluorocarbon fluid PP10 (Perfluorofluorene,
C13F22), see Ref. [24]. The experiment eventually failed because the working fluid underwent
thermal decomposition due to the extremely high operating temperature. This put into evidence
one of the major obstacles, namely that the BZT thermodynamic region is very close to the thermal
decomposition temperature of suitable organic fluids, which is in the range 350''400 oC. In addition,
the repeatable rupture of the shock-tube diaphragm proved unattainable due to the relatively small
pressure difference and the large acoustic impedance of the fluid [32, 33]. 7.3 The FAST Set-Up Building on the experience acquired during the Boulder experiment, the novel FAST set-up for
the generation of RSWs has been conceived, designed and constructed at the Delft University of
Technology, The Netherlands, with the participation of an international consortium of academic
and industrial partners, as documented in Ref. [25]. Siloxanes have been selected as the working fluid class for the available knowledge regarding their thermal stability [34, 35], thermodynamic properties [19, 36''38], and their use as working
fluids in thermal energy conversion systems [39''41]. Moreover, the products of thermal decom-
position of siloxanes are non-toxic polymers, whereas thermal decomposition of perfluorocarbons
may result in highly corrosive hydrofluoric acid (HF) and possibly other very toxic compounds.
Furthermore, the flammability of siloxanes is far lower than that of hydrocarbons. Few of the compounds of the siloxane family are candidate BZT fluids [18]. Initially, D6 is chosen as working fluid as the result of a trade-off between the size of the predicted BZT region and
the thermal stability of the fluid. The design of the RSW experiment drove studies aimed at better identifying the thermody- namic region within which non-classical phenomena are admissible, see, e.g., Ref [42]. Given that
the experimental conditions are difficult to realize and that the rarefaction shock wave is expected
to be weak, therefore more challenging to measure, several authors proposed methods aimed at
relaxing the experimental constraints by producing comparatively stronger phenomena [28]. In particular, Guardone et al. [43] presented an analytical procedure to identify the thermo- dynamic states resulting in the RSW exhibiting the maximum pressure difference, the RSW with
maximum Mach number, and the RSW with the largest strength, over the entire dense-vapour ther-
modynamic region of a given BZT fluid. Uncertainty quantification applied to flow simulations has
been preliminarily used, as an aid in determining the optimal experimental conditions [44]. 180 Commissioning of the FAST setup State B State A Low
Pressure
Plenum PT1 PT2 PT4 PT3 Charge Tube FOV nozzle RSW Figure 7.2: Conceptual layout of the FAST dense gas Ludwieg tube setup, representative of
a time instance after the opening of the FOV separating the charge tube (CT) from the reservoir
(LPP). A rarefaction shock wave (RSW) propagates into the charge tube at supersonic speed W.
Past the RSW, the fluid is accelerated from rest conditions A to post-shock conditions B and flows
into the reservoir through the nozzle. At the nozzle throat, sonic conditions S are attained. 7.3.1 Working Principle The working principle of the FAST setup is depicted schematically in Fig. 7.2. The Ludwieg-
tube facility is composed of a high-pressure charge tube connected to a low pressure plenum. The
charge tube and the reservoir are separated by a fast opening valve. The fluid is initially at rest
and the temperature is kept uniform by a suitable thermal control system. The experiment starts
when the FOV is opened, thus connecting the charge tube to the reservoir. Depending on the
pressure, compression or rarefaction waves will propagate into the charge tube. In case of suitable
initial states A (charge tube) and R (reservoir) in a BZT fluid, the rarefaction waves are expected to
coalesce forming a RSW. The fluid is accelerated from rest conditions A to condition B, and thus
flows into the LPP through a nozzle integrated in the FOV. The nozzle is designed to work in choked
conditions in the RSW experiment, in order to prevent disturbances to propagate from the plenum
into the charge tube. Fast response absolute dynamic pressure transducers are flush-mounted along
the charge tube in order to measure the incident wave. A time-of-flight (TOF) method can be adopted to determine the speed of the waves travelling in the CT as discussed in Ref. [25]. The wave arrival time is measured at four consecutive stations,
i.e. pressure probes PT1 '' PT4 in Fig. 7.2. Since the distance between the stations is known, the wave speed can be easily calculated. This procedure can be first adopted to estimate the speed of sound in the unperturbed state, namely by inducing a weak (acoustic) disturbance propagating through the charge tube. This mea-
surement is expected to be more accurate than the prediction obtained by means of the thermody-
namic models available for siloxanes [19]. Stronger pressure waves can be generated in the same way (e.g., by varying the initial pressure levels in the setup) and their speed of propagation measured according to the same principle. In
case a RSW is formed, its speed must be greater than the local speed of sound just determined. In
other words, by measuring the difference in wave speed between to subsequent experiments, it is
possible to detect if a wave is moving at supersonic speed, thus proving that it is indeed a RSW. Fig. 7.3 shows the RSW and the expansion up to the nozzle throat in the reduced volume- pressure plane, and the flow Mach number profile along the charge tube at time t = tI, i.e. the
instant in which the shock is predicted to be fully formed [25]. 181 Chapter 7 v r P r 1.0 2.0 3.0 4.0 0.5 0.6 0.7 0.8 0.9 1.0 Two-phase region '=0 RSW B A Ise nt ropi c expa ns ion (noz zle ) S x/L M 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Solution at time t = t I Nozzle throat (sonic) Isentropic
expansion through the nozzle State A Rarefaction
shockwave State B Figure 7.3: Left: Expansion in the charge tube up to the nozzle throat in the vr-Pr plane. Right:
Mach profile at time t = tI for a fully formed RSW. The entire setup is constructed out of stainless steel AISI 316Ti, and all connections are sealed
using graphite gaskets, making the facility an hermetically closed system, whose schematic layout
is shown in Fig. 7.4. In order to attain the desired conditions in the CT, the working fluid is heated
and vaporised in the vapour generator (HFT). Once the target pressure is obtained, a valve is opened
connecting the HFT with the reference tube (RT), a component used for the thermal control of the
charge tube (CT), and the CT itself, where the desired super-heating is thus induced by heating the
vapor. Once all temperatures have stabilized, the test can begin. The valve between the HFT and
the RT is closed just before the FOV opening to avoid flashing of the liquid in the vapour generator.
Most of the fluid in the CT flows to the LPP and condenser (COND) after the FOV is opened,
where it condenses and is stored in the return line (RL). For the subsequent experiments, the FOV
is closed again and the valve between HFT and RT is opened in order to fill with vapor this last
volume together with the CT. This procedure can be repeated until the liquid level in the HFT lies
within acceptable limits. 7.3.2 Vapour Generator The vapour generator, or HFT, is a 5.9 liter vessel designed to bring the working fluid up to the
desired thermodynamic conditions, see Fig. 7.5. During normal operation, the HFT contains a
liquid-vapour mixture of the working fluid, in conditions of thermodynamic equilibrium (i.e. satu-
ration). A connecting pipe leads to a burst disc that breaks at 27 bar followed by an overpressure
valve as safety precaution. At the bottom of the vessel, the liquid can be extracted through a manual
valve (connected to flange 1 in Fig. 7.5). The connection to the reference tube is done through
flange 7, which can be closed off by similar valve. Another connection leads to the flow return pipe
through flange 3, and can be closed off by a pneumatic valve. The flanged connection 8 is used to
fill the HFT with liquid. Several other flanges accommodate the required instruments. A PT-100
temperature sensor is installed at flange 2 (TE1.0 in Fig. 7.4), a static pressure transducer with stain-
less steel membrane at flange 5 (P1.0), and a radar liquid level meter at flange 6 (LL). The vessel 182 Commissioning of the FAST setup RT LPP COND RL CT PIT2 HFT TE4.0 TE1.0 LL P1.0 PIT4 PIT1 PIT3 TE2.0 TE3.0 Figure 7.4: Schematic overview of the FAST setup. 183 Chapter 7        Figure 7.5: Drawing of the vapour generator (HFT). Numbers corresponding to flanged connec-
tions: 1. liquid drain, 2. PT-100 T sensor (TE1.0 in Fig. 7.4), 3. to return line (RL), 4. to burst disc,
5. static pressure transducer (P1.0), 6. liquid level meter (LL), 7. reference tube (RT) is equipped with a 1.5 kW ceramic band heater on the bottom section. To ensure good conducting
contact between the band heaters and the wall, a 2 mm graphite layer is inserted between the band
heater and the metal wall. Under normal operation conditions, the liquid level is high enough to
cover the wall in contact with this heater, which is used as the main supply of thermal energy. Preliminary tests have highlighted that condensation occurs in the unheated sections, after which the condensate accumulates and cools below saturation conditions. This subcooled liquid
periodically flows back in the bulk liquid, temporarily ceasing boiling with a pressure drop as a
consequence. This induces a periodic instability, which prevents to maintain the desired stable ther-
modynamic conditions. In order to overcome this problem, all the walls of the HFT are heated.
However, since saturation conditions must be guaranteed in the vessel, the walls are kept at a tem-
perature below the saturation value, such that no super-heating of the vapour occurs. In the middle
section of the vessel a 2.8 kW ceramic band heater is used, again with an interposed graphite layer.
The pipe leading to the burst disc (flange 4), the pipe leading to the reference tube (flange 7), and
the top of the vessel are equipped each with a 6 m long 1 kW heating wire. The entire HFT is
covered with a layer of minimum of 50 mm rockwool insulation. 7.3.3 Reference Tube The reference tube, or RT, is a component used for the thermal control of the charge tube. For this
purpose it has the same geometry of a section of the charge tube except for its length, which is 500
mm. It has an internal diameter of 40 mm and 15 mm thick walls. On one end, a PT-100 is mounted
to accurately measure the fluid temperature (TE2.0 in Fig. 7.4). Two lines connect the RT tube to 184 Commissioning of the FAST setup the rest of the setup: one leads to the HFT, while the other leads to the charge tube. The thermal
input is provided by a 335 W glass silk heating jacked, which includes a 25 mm glass silk insulation
layer. 7.3.4 Charge Tube The charge tube, or CT, is the long pipe through which pressure waves propagates. The inside
diameter is equal to 40 mm, and the inner surface is rectified and electrolytically polished in order
to reduce friction effects which cause attenuation in the propagating waves. The 15 mm thick walls
enhance an even distribution of the thermal power. It is built up of six elements of 1520 mm length
each, joined through custom made male-to-female connections with copper seals. The entire pipe
measures 9 m in total, and is placed on sliding supports which allow for thermal expansion. Each
section is heated by a 950 W glass silk heating jacket, which includes a 25 mm thick insulation layer.
One end of the pipe connects to the fast opening valve which is inserted into the LPP, while at the
other end a PT-100 temperature sensor is mounted (TE3.0 in Fig. 7.4). The pressure measurement
stations are created by flush-mounting four high frequency pressure transducers along the CT at a
distance of 4, 4.3, 8.4 and 8.7 m from the FOV (PIT1 ''PIT4). The instruments are placed in pairs in order to perform speed of flight measurements at two different locations in the tube. In the case
of a RSW in D6, a RSW is expected to form between the first and second measurement pair [25]. 7.3.5 Fast Opening Valve The most complex piece of equipment of the setup is the fast opening valve, or FOV, contained in the
LPP and shown in Fig. 7.6. This custom designed component is able to operate up to 400'C without
lubrication, in order to avoid contamination of the working fluid. When the FOV is in the opened
position, the working fluid can flow through the venting holes present in the inner and outer body.
In the closed position, a sliding cylinder is interposed between these two bodies, obstructing the
venting holes. The sliding cylinder is pressed into a perfluoroelastomer compound sealing pad on
the flange to ensure the first sealing point. The second sealing is performed by a perfluoroelastomer
O-ring placed between the sliding cylinder and the inner body. A high temperature spring built with
austenitic nickel-chromium steel is compressed while closing the FOV, and three radial clamps are
used to prevent it from being released. To open the FOV, the clamps are actuated, allowing the
spring to push the sliding cylinder away, thus leaving the venting holes open. A movable nozzle
insert allows to fine-tune the throat section, i.e. the minimum flow passage area, in the range
420 '' 600 mm 2. A peculiarity of this valve is that the nozzle is located on the high pressure side of the sealing, as opposite to typical solutions adopted in Ludwieg tube facilities [45, 46]. 7.3.6 Low Pressure Plenum After the FOV has been opened, the fluid flows into a 113 liter low pressure plenum (LPP), contain-
ing the FOV itself. The LPP has an outer diameter of 406.4 mm and 9.53 mm thick stainless steel
walls. The electric motor triggering the FOV and the manual nozzle positioning gear are mounted
on the LPP with sealed feedthrough shaft connections. At the bottom, the vessel is connected to the
condenser. A lid with a 648 mm diameter flange gives access to the vessel interior for installation
of the FOV, sealed by a graphite gasket compressed by 20 Mx50 bolts. The thermal input to the
vessel is supplied by four heating jackets with a nominal power of 1450, 425, 960 and 490 W. 185 Chapter 7 LPP 7 1 2 3 1 11 4 5 6 1 CT 8 9 10 Figure 7.6: Cross-section of the Fast Opening Valve (FOV) at the aperture instance. 1. venting
holes (closed), 2. spring (still almost completely compressed, but releasing its force), 3. outer body,
4. sliding cylinder (SC) (obstructing the venting holes, and pushed towards the right by the spring),
5. inner body, 6. nozzle with adjustable throat section, 7. nozzle actuating system, 8. one of the
three radial clamps '' open position (not engaging the SC, which is thus free to move under the spring force), 9. flanged connection to CT, 10. first sealing element (static pad) '' not engaged by the SL (not sealing), 11. second sealing element (dynamic O-ring) '' engaged position (compressed between the SL and the inner body, where it is grooved). 186 Commissioning of the FAST setup 7.3.7 Condenser and flow return pipe A pneumatic valve connects the LPP to the condenser (COND). The condenser is a cylindrical
vessel with outer diameter of 168.28 mm, 7.11 mm thick walls, and welded cooling ribs. The
condensed liquid flows from the bottom of the condenser into the flow return line (RL). This pipe
is connected through another pneumatic valve to the HFT. 7.4 Data Acquisition and Control system In the following, the control strategy necessary to reach and maintain the desired thermodynamic
conditions in the CT is illustrated. A major challenge is the avoidance of hot-spots, which pose a
serious danger in terms of decomposition of the working fluid. 7.4.1 Vapour generator control As anticipated, saturation conditions are enforced during normal operation, and controlled by mon-
itoring the presence of liquid through the level meter measurement (i.e. LL in Fig. 7.4). To this
end, the quantity of working fluid initially loaded in the HFT has to be carefully measured. As a
consequence, a single thermodynamic quantity is enough to characterize the state of the fluid in
the HFT: the pressure and temperature sensors available, i.e. TE1.0 (accuracy 0.1 % of its 400 'C
range) and P1.0 (accuracy 0.1 % of its 10 bar range), are used for this scope (with redundancy).
The fluid in the HFT can be brought to a different saturation point by increasing/decreasing the
thermal input to the HFT, by acting on the heaters (the involved transformation is isochoric). To
be noted that the pressure level thus established in the HFT, during normal operation, is common
to the RT and the CT (with all the valves opened). Furthermore, the saturation temperature is also
estimated from the pressure reading through the equation of state presented in Ref. [19]. A digital
PID controller regulates the power supply to the bottom band heater, based on the set-point imposed
for the value thus obtained. There are several advantages in performing the control based on this
calculated saturation temperature instead than on direct measurements: (i) the controlled variable
is expected to promptly reacts since it is based on a pressure measurement (less affected by thermal
inertia phenomena), (ii) the same PID parameters can be used throughout the entire operating range,
and (iii) the long transient involved when the setup is heated from cold conditions can be managed
in a more efficient and safe way. In total nine k-type thermocouples measure the wall temperature
at several locations, of which four are used for control purposes and the others for monitoring only.
The power supplies to all the secondary heaters are individually controlled in order to maintain their
temperatures slightly below the saturation value. 7.4.2 Reference Tube control The main purpose of the reference tube (RT) is to bring the fluid it contains at the desired conditions
of super-heating. In turn, this is directly measured as the difference between the temperature in the
RT (from the PT-100 sensor TE2.0 in Fig. 7.4, accuracy 0.1 % of the 400 'C range), and that
measured in the HFT (through TE1.0). A PID controller directly regulates this difference, i.e. the
super-heating, by acting on the heater equipping the RT. 187 Chapter 7 7.4.3 Charge Tube control In order to limit the sources of disturbance for the waves propagating inside the CT, the thermal
control is conceived such that only the external wall temperature is measured through a total of
10 thermocouples distributed along the CT. The second ends of these sensors are connected to
the external wall of the RT, such that the resulting signal is directly the temperature difference
between the RT and the CT wall (''T W RT-CT ). This arrangement aims at exploiting the geometric equivalence among the CT and the RT: being the temperature of the fluid in the RT accurately
measured (TE2.0), if the temperature difference between the external wall of the RT and of the CT
is negligible, i.e. ''T W RT-CT '' 0, it follows that the temperature of the fluid in the CT is equal to what is being measured by TE2.0. In other words, it is expected that imposing on the CT wall the same
temperature measured on the RT wall will result in the same conditions inside the two volumes. A
PID controller modulates the power supply to each individual blanket heater on the CT, aiming at
zeroing ''T W RT-CT . 7.4.4 Low Pressure Plenum control The temperature of the vapour contained in the LPP is measured using a PT-100 sensor (TE4.0 in
Fig. 7.4). A single PID controller modulates the power supply to each of the blankets covering the
LPP, using the temperature as process variable. 7.4.5 Data Acquisition At each of the measurement stations a fully active four arm Wheatstone bridge absolute transducer
measures the pressure at a frequency of 250 kHz with an accuracy of 0.5% of its full scale of 21 bar.
The signal is amplified and connected to the synchronous data acquisition board. A PT-100 sensor
measures the fluid temperature at the end of the tube (TE3.0 in Fig. 7.4, accuracy 0.1% of its 400'C
range). 7.5 Validation This section presents the results of a series of tests aimed at quantitatively characterizing the per-
formance of the FAST setup. 7.5.1 Tightness characterization In order to prevent leakage of the working fluid into the ambient, and of air into the setup, this has
been designed to be leak-tight both when pressurized and under lower-than-atmospheric pressure
conditions. Notably, these requirements must be satisfied within the whole operating temperature
range. To this end, two complementary systems are implemented in the facility: ' Pressurization with inert gas, primarily allowing to check the tightness of the system by adopting common techniques (e.g., helium detectors). Furthermore, (part of) the setup can
be kept pressurized (e.g. with Nitrogen) while not in use. ' Vacuum system, making it possible to independently vacuum different sections of the setup, in order to get rid of the air or of the inert gas possibly present. 188 Commissioning of the FAST setup As anticipated, avoiding the contamination of the working fluid with air is of paramount importance
in order to reduce the risk of thermal decomposition under high temperature within an oxidizing
environment [35]. However, also the contamination by an inert gas has to be avoided. As a matter
of fact, since typically adopted gases features speed of sound values more than 1 order of magnitude
larger than those of the organic compounds of interest, even the smaller contamination can have a
strong influence on the experiments results. A comprehensive series of tests have been conducted up to temperatures of 300'C, for a dura- tion of 72 hours each. This has allowed to assess that the temperature has a negligible influence on
the sealing properties of the equipment. The tightness of the FAST setup has been characterized as
follows, in terms of the average leakage rate LR = ''p V ''t''1 [47], where V is the volume of the
whole setup (i.e. 0.143 m3), and ''p is the pressure drop/rise measured after a time interval ''t (i.e.
259,200 s for all the tests). - Low p ( . 3 mbar abs.): LR < 5E''4 mbar l s''1 (air into the system) - High p ( & 6000 mbar abs.): LR < 5E''2 mbar l s''1 (He to the ambient) These figures are deemed satisfactory. This is particularly true for the results of the vacuum tests which, as explained, were intended to characterize a very critical property of the setup. These
conclusions are confirmed by the fact that periodical gas-chromatography analysis performed on
working fluid samples to investigate possible decomposition have not unveiled any molecular mod-
ification. 7.5.2 Valve Opening Sequence The opening sequence follows a strict pattern: as soon as the clamps are released, see Fig. 7.6,
the spring pushes the slider away, and a small opening is created as the slider leaves the seal and
the flow gets choked close to this position. This is seen in an experiment with initially 4.014 bar
of N2 in the CT and vacuum in the LPP, whose results are shown in Fig. 7.7. The small pressure
drop of approx. 20 mbar in the signal indicates the initial choking (1). As the slider moves further,
the position where the cross-section of the flow is the smallest is changed to a section between the
slider and the inner body. This is seen as a second small drop in pressure of approx. 20 mbar
(2). Only as the slider passes over the venting hole of the inner body, does the designated nozzle
get choked. This corresponds to the large pressure drop in the signal down to approx 2.9 bar (3). The opening time of the fast opening valve, i.e. tFOV, can be estimated by using the method of characteristics. Fig. 7.8 shows a schematic picture of an instantaneous (left) and non-instantaneous
(right) opening. In the ideal case of instantaneous valve opening, all characteristics overlap in a
single point. In the real case, where the opening is non-instantaneous, tFOV is finite and the last
characteristic starts traveling at a later time instant. Since the seal of the FOV is downstream of the
nozzle, the characteristics travel through the nozzle. The nozzle accelerates the fluid, such that the
propagation speed in the nozzle is significantly lower than in the rest of the charge tube, with the
consequence that the later characteristics are curved in this section [48]. The opening time can be estimated by mapping the pressure signals of the sensors to the posi- tion of the valve. For this mapping procedure, the slope of each characteristic has to be determined,
which equals the wave propagation speed and is given by the speed of sound minus the speed of the
fluid in the laboratory reference frame. As the pressure decreases due to the rarefaction, the local
speed of sound decreases, and a flow is started in the opposite direction of the wave propagation,
both contributing to a lower wave propagation speed. The propagation speed can be evaluated as a
function of the pressure drop. The local speed of sound is evaluated by assuming the expansion is 189 Chapter 7 t [s] P [ba r] 1 1.1 1.2 1.3 1.4 1.5 0 1 2 3 4 PIT3, PIT4 PIT1, PIT2 (a) t [s] P [ba r] 0.99 1 1.01 3.96 3.98 4 4.02 PIT4 3 PIT2 PIT3 PIT1 1 2 (b) Figure 7.7: Original signals from an expansion in nitrogen. 7.7a: complete expansion, the two
couples of signals, corresponding to the two measurement stations are visible. 7.7b: detail of the
very first expansion, it is possible to distinguish the four signals and the subsequent pressure drops
corresponding to the FOV opening sequence. isentropic and the fluid velocity after the expansion can be evaluated by using the Riemann invariant
in the undisturbed state in the CT before opening the valve [49]. The estimated value of tFOV does
not take the nozzle into account and is thus higher than the actual valve opening time. However,
for the formation of an RSW, the characteristics should coalesce, so it is the estimated opening time
that we measure using this technique that is important. Fig. 7.9 shows the signals of the same experiment in N2 as displayed in Fig. 7.7, but then mapped to the valve position. The signals now overlap initially, giving evidence of a correct map-
ping procedure. The rarefaction waves propagate through the tube and reflect at the end of the
charge tube. Because the reflection of the first rarefaction wave arrives earlier at the sensor loca-
tion of PT3 than the last unreflected rarefaction wave, a non-simple region is created. This makes
signals PT3 and PT4 unuseful for determination of the valve opening sequence. This shows up in
the mapped signal as diverting from the other signals because the fluid velocity then is incorrectly
evaluated. In order to have a consistent evaluation without disturbance of the noise, the opening time is in this case defined as the difference in time instance when 5% of the pressure drop has occurred until
95% of the pressure drop, based on the mapped signal. An overview of the performed measurements
can be found in table 7.1. The throat area in the nozzle affects the measured opening time as was
expected. With a very small throat area of approx. 68mm2, the opening time measured is between
2.1 and 3.2 ms. With the nominal throat area of approx. 466 mm2, the opening time measured
between 3.5 and 4.5 ms. This can be explained by the fact that the characteristics travel through the
nozzle and are curved. The total opening time, i.e. the duration from the instance the sliding cylinder moves away from the seal until full opening of the valve, increased significantly after many shots in N2, CO2, He, and 190 Commissioning of the FAST setup 'ŽƐŝ'ŽŶ 'ŵ' x Ɛ'ŶƐŽ' ''''ŶƐŝŽŶĨ'Ŷ x ''ů'' (a) Ideal case: instantaneous valve opening 'ŽƐŝ'ŽŶ 'ŵ' x Ɛ'ŶƐŽ' ''''ŶƐŝŽŶĨ'Ŷ x ''ů'' Ž''ŶŝŶŐ'ŵ' 'Ɛ'ŵ'''' Ž''ŶŝŶŐ'ŵ' (b) Real case: non-instantaneous valve open-
ing Figure 7.8: Position-time diagrams of classical expansion fans. In the ideal case with an instan-
taneous valve opening and in absence of a nozzle, all characteristics emerge from a single point. In
the realistic case, the last characteristic starts at a later time instance than the first one, due to the
finite opening time. All characteristics are curved upwards in the nozzle area except the first one,
because of the higher flow velocity in the nozzle, which slows down the wave propagation speed. t [s] P [ba r] 0.97 0.98 0.99 1 1.01 1.02 2 2.5 3 3.5 4 PIT4 PIT2 PIT3 PIT1 (a) t [s] P [ba r] 0.97 0.975 0.98 0.985 0.99 3.96 3.98 4 4.02 PIT1
PIT2
PIT3
PIT4 (b) Figure 7.9: Portions of the signals from an expansion in nitrogen mapped to the valve position,
with two levels of magnification. 191 Chapter 7 number fluid CT P CT T ''P calc. Anozzle opening [bar] ['C] expansion [bar] [mm2] time [ms] 1 He 6.503 50 0.32 67 2.53 2 He 8.472 269.9 0.44 72 3.18 3 He 7.292 269.4 0.33 62 2.12 4 He 4.895 22.7 0.28 79 2.65 5 He 6.086 48.9 1.69 438 3.71 6 He 6.005 17.3 1.74 459 3.92 7 He 6.663 99.2 2.01 483 3.56 8 He 5.984 251 1.74 462 5.00 9 He 6.025 200.6 1.95 522 7.64 10 He 6.015 149.4 1.84 489 4.07 11 air 6.976 95 0.27 61 2.18 12 air 7.133 22.0 0.3 67 2.17 13 air 5.39 20 0.23 68 2.3 14 air 4.857 20 0.205 67 2.28 15 air 4.084 18 0.97 418 4.2 16 air 6.148 49.1 1.615 468 4.15 17 air 6.8 99.5 1.76 461 3.96 18 air 6.312 17.6 1.62 456 4.16 19 air 6.449 149.6 1.72 476 4.2 20 air 6.645 201.3 1.81 488 4.58 21 air 7.088 252.4 1.88 473 4.99 22 air 7.011 19.1 1.81 459 4.23 23 CO2 6.423 50.0 1.59 465 4.58 24 CO2 5.986 18.0 1.5 471 4.86 25 CO2 6.636 100.3 1.64 464 4.13 26 CO2 6.13 149.7 1.5 459 4.4 27 CO2 6.211 201.2 1.51 456 4.56 28 CO2 6.337 200.5 1.57 465 4.63 29 CO2 6.312 249.0 1.56 464 4.5 30 N2 4.000 25.7 1 443 4.12 31 N2 4.014 25.8 1.08 481 4.2 32 N2 1.093 25.3 0.345 576 4.26 33 N2 1.124 25.4 0.33 531 4.39 34 D6 1.257 297.0 0.179 330 5.48 35 D6 2.517 301.1 0.257 254 8.99 36 D6 1.134 254.1 0.175 363 4.87 37 D6 1.265 298.0 0.179 328 7.48 38 D6 2.532 305.1 0.292 286 8.92 39 D6 1.255 293.7 0.151 278 6.61 40 D6 1.257 264.2 0.092 169 7.66 41 D6 1.26 263.2 0.105 193 4.59 42 D6 1.265 300.1 0.14 254 5.62 43 D6 1.285 265.1 0.118 214 8.28 44 D6 2.383 302.3 0.214 220 8.32 Table 7.1: Results from measurements. The nozzle area is calculated using the pressure drop
across the expansion (not possible for siloxane D6). The opening time is inferred from the mapped
signal. air had been performed, attributed to a lack of lubrication. This is not reflected in the measured
estimated opening time as given in table 7.1, which is determined using the large pressure drop
related to the sliding cylinder passing the venting hole. As soon as the first shot in D6 was done, the
total opening time went down immediately, confirming the hypothesis that D6 acts as a lubricant.
On the other hand, the estimated opening time based on the large pressure drop had increased to 5
to 9 ms. These measurements are affected by a large uncertainty due to inaccuracy of the equation
of state in this thermodynamic region. 192 Commissioning of the FAST setup 7.5.3 Wave Speed Measurements To test the capabilities of the measurement system, a shock in air is generated. The pressure in the
CT is lowered to approximately 0.37 bar, while the LPP is kept at atmospheric pressure. The whole
setup is at ambient temperature, equal to '' 18 oC. Upon opening of the FOV, a compression propa- gates into the charge tube, eventually forming a shock. The expected location of shock formation is
estimated using the knowledge on the opening time of the FOV: with tFOV = 4.5 ms, the intersection
of the first and last characteristic is expected to occur at '' 5.2 m from the FOV. Since partial shock formation speeds up the wave, it is expected that complete formation requires more length. It can
indeed be seen that the shock has not yet formed at pressure transducer PT1 and PT2. The shock
seems to have formed when it passes at PT3 and PT4, since the pressure is much steeper compared
to the one given by PT1 and PT2. t [s] P [ba r] 0 2 4 6 8 10 0.4 0.6 0.8 1 1.2 (a) t [s] P [ba r] 2.2 2.21 2.22 2.23 2.24 2.25 0.4 0.6 0.8 PIT4 PIT2 PIT1 PIT3 1 4 1 2 3 (b) Figure 7.10: Pressure signals from a compression in air. 7.10: complete compression from below
atmospheric up to ambient pressure conditions, the four signals are not distinguishable at this level
of detail. 7.10b: detail of the very first compression phase, it is possible to distinguish the four
signals, and the shock wave forming (1 '' 2) and then bouncing back (3 '' 4) in the tube. Since the shock has not formed yet at PT1 and PT2, the compression can be considered a simple compression wave, thus traveling with the speed of the characteristic. By solving the corresponding
Riemann problem, values of 341 m s''1 before and 488 m s''1 after the compression are found as
propagation speeds. By using the time-of-flight method, very similar values are found experimen-
tally, as can be seen in Fig. 7.11. Once the shock has formed, it is expected to travel at a velocity
of 422 m s''1, this value being in extremely good agreement with the experimental observation. It is
demonstrated that the measurement equipment and the devised procedure are best suited to capture
steep pressure variations, i.e. shock waves propagating in the CT, which is also the main objective
of the setup. Weaker phenomena, such as those involved in speed of sound measurements, are also
sensed in a fairly accurate way, but more sophisticated signal analysis techniques than the simple
TOF method adopted here are necessary, as detailed also, e.g., in Ref. [50]. The expected pressure
after the compression, as calculated by the exact solution of the Riemann problem, is 0.6 bar, which 193 Chapter 7 is also in good agreement with (i.e. approx. 50 mbar above) the experimental observation reported
in Fig. 7.10. To be noted also that the expected speed for the RSW is of the order of 100 m s''1,
making it comparatively simpler to be detected than the wave just presented. t [s] W ave spe ed [m s -1 ] 0.04 0.06 0.08 0.1 0.12 0.14 0.16 350 400 450 500 Figure 7.11: Wave speed measurement determined with the time-of-flight method. The black
dots are determined by comparing PIT3 with PIT4, while the white dots PIT1 with PIT2. To fully show the capabilities of the setup, the results of wave speed measurements are presented
for an expansion in siloxane D6 in the classical domain (i.e. outside the BZT region), up to fluid
temperatures close to 300 'C. Fig. 7.12 shows several temperature signals as recorded during the
test campaign. The setup is heated from cold conditions and, as soon as a temperature of 250 'C
is reached, the valve between the HFT and the RT is opened. Part of the liquid is flashed and the
temperature of the liquid therefore drops of several degrees. After '' 11 hours, the super-heating is set to 5 'C. The first opening of the FOV is performed at '' 12 hours. After that, the super- heating is raised to 45 'C, and two more FOV openings are executed. The pressure signals recorded
during the second of these experiments are shown in Fig. 7.13. The procedure is thus repeated
after having increased the saturation temperature up to 290 'C, with 5 'C of super-heating. The
measured fluctuations in temperature in the reference tube and charge tube were of a long period
of the order of 2 hours, and with an amplitude of up to 3 'C. Further optimization of the thermal
control algorithm is planned for experiments at higher temperatures. The TOF method, applied only to the PIT1 and PIT2 signals, is used to evaluated the wave speed in this section as a function of the pressure drop, since PIT3 and PIT4 are disturbed by the
bouncing rarefaction wave, as shown in Fig. 7.13b. Also in this case, the rarefaction waves travel
with a velocity equal to the difference between the speed of sound and the local flow velocity. Since
the fluid is initially at rest, the wave speed estimated by the TOF method for a pressure drop close to
zero tends to the speed of sound, see Fig. 7.14. Being the thermodynamic conditions in the CT mea-
sured, it is possible to obtain an evaluation of the speed of sound also by recurring to the equation
of state of siloxane D6 [19], obtaining a value of 94.8 m s'' 1 (in doing so, the uncertainty in the mea- 194 Commissioning of the FAST setup t [hours] T [ o C ] 0 5 10 15 20 25 0 50 100 150 200 250 300 TE1.0
TE2.0
T sat change in T sat set-point FOV opening Valve opening
(CT charging) change in
superheating
set-point Figure 7.12: Temperature measurements acquired during a test campaign in D6 siloxane at 1.27
bar and 298 'C. Tsat is the saturation temperature calculated starting from the measured pressure.
TE1.0 is the temperature measured by the PT-100 in the vapour generator. TE2.0 is the temperature
measured by the PT-100 in the reference tube. t [s] P [ba r] 4 5 6 0 0.2 0.4 0.6 0.8 1 1.2 1.4 PIT3, PIT4 PIT1, PIT2 (a) t [s] P [ba r] 3.5 3.55 3.6 3.65 3.7 1.05 1.1 1.15 1.2 1.25 PIT4 PIT1 PIT2 PIT3 (b) Figure 7.13: Original signals from an expansion in D6 siloxane at 1.27 bar and 298 'C. 7.13a:
complete expansion, the two couples of signals, corresponding to the two measurement stations are
visible. 7.13b: detail of the first expansion, it is possible to distinguish the four signals. sured quantities has not taken into account). As detailed in Ref. [19], an expanded uncertainty of
the order of 6% can be associated to the specific heat capacity of the fluid. Being the epistemic un-
certainty associated to the cited thermodynamic model unknown, a first and conservative approach 195 Chapter 7 can consist in attributing the same uncertainty to the speed of sound, as reported in Fig. 7.14. It can
be concluded that the facility is effective in performing measurements of wave propagation speed in
high temperature organic vapours, with an accuracy comparable with the available thermodynamic
models. P [bar] w [m /s ] 0 0.02 0.04 0.06 0.08 0.1 80 90 100 110 120 '' Figure 7.14: Wave Speed in D6 siloxane as a function of the pressure drop, evaluated with a
TOF method applied to the PIT1 and PIT2 pressure signals reported in Fig. 7.13. The dotted line
corresponds to the estimation provided by the equation of state presented in Ref. [19], with the
shadowed region representing the preliminary assumed expanded uncertainty of 6%. 7.6 Conclusions & Future Work In this chapter a new Ludwieg tube facility called the FAST is described, that is able to measure
speed and intensity of waves propagating through the fluid contained in the tube. The final objective
of this setup is to provide the first experimental evidence of the rarefaction shock waves (RSWs)
in the dense vapor region of fluids formed by complex organic molecules. The pressure and tem-
perature of the fluid can be regulated independently from each other, such that any thermodynamic
state can be achieved within the limits of the facility ( '' 30 bar and 400 'C). The leakage rate of the facility is found to be acceptable, and the fast opening valve is characterized in terms of its aperture
time, which is found to be compatible to the end of measuring a RSW in D6 siloxane. Tests of
shock formation in air are presented, and used to validate the functioning of the facility and of the
measurement procedure. Preliminary results regarding expansions in D6, up to fluid temperatures
close to 300 'C, further show the capabilities of the FAST of achieving and maintaining the desired
thermodynamic conditions, as well as of obtaining wave speed and intensity measurements. As for
the next step of the work, the RSW experiment will be attempted. 196 Commissioning of the FAST setup Nomenclature s, P = specific entropy [kJ kg''1 K''1], pressure [bar] T , v = temperature ['K], specific volume [m3 kg''1] ρ, c = density [kg m''3], speed of sound [m s''1] A, ' m = flow passage area [m2], mass flow rate [kg s''1] ' V = volumetric flow rate [m3 s''1] Greek symbols ' ' v3 2c2  ''2 P ''v2  s = fundamental derivative of gas dynamics Subscripts CR = critical thermodynamic conditions (liquid-vapour) R = reduced (with respect to critical value) Acronyms MW = Molecular Weight [g mol''1] ORC = Organic Rankine Cycle FAST = Flexible Asymmetric Shock Tube RSW = Rarefaction Shock Wave BZT = Bethe-Zel''dovich-Thompson FOV = Fast Opening Valve CT = Charge Tube LPP = Low Pressure Plenum 197 References [1] P. A. Thompson. Compressible Fluid Dynamics. McGraw-Hill, 1988.
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23(4):1098 '' 1111, 2009. 201 8 Nonclassical Gasdynamics of Vapour Mixtures Part of the contents of this chapter appeared in: A. Guardone, P. Colonna, E. Casati, & E. Rinaldi
Journal of Fluid Mechanics, 741, 681-701 (2014) c Cambridge University Press 2014 - Reprinted with permission Chapter 8 Abstract The nonclassical gasdynamics of binary mixtures of organic fluids in the vapour phase is investigated for the first time. A predictive thermodynamic model is used to compute the relevant
mixture properties, including its critical point coordinates and the local value of the fundamental
derivative of gasdynamics '. The considered model is the improved Peng-Robinson Stryjek-Vera
cubic equation of state, complemented by the Wong-Sandler mixing rules. A finite thermodynamic
region is found where the non-linearity parameter ' is negative and therefore nonclassical gasdy-
namics phenomena are admissible. A non monotone dependence of ' on the mixture composition
is observed in the case of binary mixtures of siloxane and perfluorocarbon fluids, with the mini-
mum value of ' in the mixture being always larger than that of its more complex component. The
observed dependence indicates that non-ideal mixing has a strong influence on the gasdynamics
behaviour''either classical or nonclassical''of the mixture. Numerical experiments of the super-
sonic expansion of a mixture flow around a sharp corner show the transition from the classical con-
figuration, exhibiting an isentropic rarefaction fan centred at the expansion corner, to nonclassical
ones, including mixed expansion waves and rarefaction shock waves, if the mixture composition is
changed. 8.1 Introduction The first scientist who hinted at the possibility of observing rarefaction shock waves in vapours
of molecularly complex organic fluids was Nobel-laureate Hans Bethe, in 1942 [1]. Rarefaction
shock waves are discontinuous solutions to the Euler equations of compressible flows where the
fluid undergoes an irreversible expansion process which results into a discontinuous reduction of
density, pressure, temperature and fluid velocity in the direction of propagation of the shock wave.
As it is well known, rarefaction shock waves are not physically admissible in dilute gases with
constant specific heats. In a broad theoretical study on the theory of shock waves in arbitrary material, Bethe outlined how the occurrence of rarefaction shock waves depends on a peculiar combination of the thermo-
dynamic properties of the material at the states of interest. He noticed that, according to the van
der Waals model [2], rarefaction shock waves would theoretically be possible in the dense vapour
of fluids featuring high values of the heat capacity, if the pre- and post-shock states of the fluid are
close to the vapour-liquid critical point. Nevertheless, he ruled out this possibility on the ground of
what we now know as incorrect physical arguments, see also Ref. [3]. An early contribution is also
due to Zeldovich [4] and Weyl [5]. Though, it was Thompson, see also Refs. [3, 6, 7], who first
provided a systematic treatment of what is now called non classical gas dynamics. A review article
by Kutateladze documents the advancements in non classical gasdynamics until the 80''s [8], while
a more recent review can be found in Ref. [9]. A necessary condition for non classical behaviour to be physically admissible is that the fun- damental derivative of gas dynamics ' ' 1 + ρ c ''c ''ρ ! s = v3 2c2 ''2P ''v2 ! s , (8.1) a thermodynamic property of the fluid first introduced by Hayes [11], is negative. In definition (8.1),
ρ is the density, s is the entropy, P is the pressure, v = 1/ρ is the specific volume, and c is the zero-
frequency speed of sound c ' (''P/''ρ)s. If ' is negative in a finite thermodynamic region, RSWs are admissible, among other so-called non classical waves such as composite and split waves, see,
e.g. Ref. [6]. 204 Nonclassical Gasdynamics of Vapour Mixtures Gas phase ' = 0 ' < 0 ' s > s ' s = s ' s < s ' T = T c ' > 0 Satur ation cur ve Two-phase region Liquid-vapour critical point Liquid phase v / v c P / P c 1.0 1.5 2.0 2.5 0.6 0.8 1.0 1.2 Figure 8.1: From [10]. Liquid-vapour saturation curve ('') and ' < 0 region (shaded region) for
a BZT fluid in the volume-pressure plane computed from van der Waals model under the assumption
of a constant isochoric specific heat cv and for cv/R = 2000, with R gas constant. Selected isentropes
( · · · ) and the critical isotherm T = Tc ('' '') are also indicated. Note that the isentropes are concave down in the ' < 0 region. The isentrope s' is tangent to the ' = 0 line in '. Substances characterized by thermodynamic states featuring negative values of ' in the dense vapour phase are called Bethe-Zel''dovich-Thompson (BZT) fluids. The region of negative ' in the
vapour phase is shown in figure 8.1 in the pressure''specific volume thermodynamic diagram of
a paradigmatic BZT fluid described by the van der Waals fluid model, where the ' = 0 line and
the vapour saturation line delimit the negative-' region. The studies of Thompson sparked quite
some interest in the following years, and many investigations expanded the theory covering several
nonclassical phenomena and aspects, see, e.g., Refs. [12''20]. One of the latest developments is
related to the investigation of nonclassical phenomena in the vapour-liquid critical point region of
any common fluid, see Ref. [21]. Experimental evidence of nonclassical gasdynamics is available only for two-phase vapor- liquid, see Refs. [22''24], or solid-solid systems [25]. In the single-phase vapour region, only
classical gasdynamics phenomena have been observed so far. Notably, in the former Soviet Union,
Borisov made an attempt to experimentally prove the existence of a rarefaction shock wave (RSW),
using a special shock tube [26]. The interpretation of the results of the experiments, arguably a
RSW front developing in the tube, has later been confuted in the light of additional knowledge
and simulation capability [9, 21, 27]. Theoretical studies [28''33], and new simulation capabilities
[34''42], paved the way to a new experimental attempt in 2000 at the University of Boulder [27,
43, 44]. The failed experiment put into evidence one of the major obstacles, namely that the BZT
thermodynamic region (the region comprising the states featuring negative-', see figure 8.1) is very
close to the thermal decomposition temperature of suitable organic fluids, which is in the range
350''400 oC. In addition, the repeatable rupture of the shock-tube diaphragm proved unattainable
due to the relatively small pressure difference and the large acoustic impedance of the fluid [45''47]. Much attention has recently been devoted to the identification of BZT fluids, and to the com- 205 Chapter 8 putation of the negative-' region, see Ref. [48] for a review. More recently Colonna and colleagues
started a new project aimed at the generation and measurement of a rarefaction shock wave in a
newly conceived Ludwieg-tube-type setup [47]. A siloxane fluid, D6 (dodecamethylcyclohexas-
iloxane C12H36O6Si6), has initially been selected as the working fluid. Siloxanes are especially
suited for the RSW experiment because of available knowledge on their thermal stability [49],
thermodynamic properties [51''54]), and their use as working fluids in thermal energy conversion
systems, see, e.g., Refs. [55''57]. Few of the compounds of the siloxane family are candidate BZT
fluids [58]. The design of the rarefaction shock wave experiment drove studies aimed at better identifying the thermodynamic region within which nonclassical phenomena are admissible [59], and the max-
imum pressure difference and shock wave Mach number that can be expected [10]. Given that the
experimental conditions are difficult to realize and that the rarefaction shock wave is expected to be
weak, therefore more challenging to measure, uncertainty quantification applied to flow simulations
has been preliminarily used as an aid in determining the optimal experimental conditions [60]. The present chapter is motivated by several observations about mixtures of organic fluids. Differently from mixtures of ideal gases, thermodynamic properties of dense vapours of multi-
component mixtures do not scale linearly with the mole fractions of each compound, as molecular
interaction among different molecules plays a major role. Typical hallmarks of non-ideal behaviour
of fluids mixtures are the critical temperature, pressure and specific volume of a binary mixture,
which usually differ from that of each of the constituents. The same holds for the melting point and
for most thermodynamic properties. The fundamental derivative of gasdynamics ', being a derived
thermodynamic property, is also affected by non-ideal mixing effects, as preliminarily discussed
in Ref. [61]. In addition, experiments on the thermal stability of siloxane mixtures [49], and a
deeper understanding on the chemistry of thermal decomposition of poly-dymethyl siloxanes [62],
show that, at temperatures close to the so-called temperature stability limit, a pure siloxane un-
dergoes a transformation called rearrangement, whereby small quantities of other compounds of
the same family are formed. Such mixture composition remains then constant at that temperature
over time. The composition of the mixture is therefore a new relevant variable in the study of BZT
fluids, and, importantly, mixtures of organic fluids are also considered for applications in organic
Rankine cycle (ORC) power systems [55, 63''65], one of the possible applications of nonclassical
gasdynamics [39]. In the present preliminary study on mixtures as BZT fluids, siloxanes and perfluorocarbons have been considered as constituents. Suitable thermodynamic models for multi-component fluids
are briefly discussed in §8.2. Their limitation in terms of accuracy of the predicted ' values is also addressed. These models are used to estimate the boundaries of the thermodynamic region of
admissibility of rarefaction shock waves, and the influence of the mixture composition. In §8.3, exemplary simulation of a supersonic flow expanding over a wedge, whereby the composition of
the mixture is varied, are presented to assess the influence of the molecular composition on the
gasdynamics behaviour. Concluding remarks and an outlook on future research are given in §8.4. 8.2 Admissibility Region for Rarefaction Shock Waves in
Dense gas Mixtures
Modelling non-ideal thermodynamic properties of fluid mixtures''including the determination of
the fundamental derivative of gasdynamics '''requires to correctly account for the interaction be-
tween different molecules, an added degree of difficulty with respect to pure-fluid thermodynamics. 206 Nonclassical Gasdynamics of Vapour Mixtures No fundamental and general theory on the interaction of molecules of different type exists yet,
therefore no accurate model is available. For these reasons the estimation of mixture properties is
affected in general by larger uncertainties, if compared to the estimation of pure-fluid properties.
Mixtures of simple molecules, e.g., light gases and simple hydrocarbons, can be modelled with
relatively high accuracy, and reference equations of state have been developed [66]. These semi-
empirical models rely on large sets of accurate fluid property measurements. Unfortunately, accu-
rate property measurements of complex organic compounds are not available. In order to estimate
dense-vapour thermodynamic properties of mixtures of complex organic fluids, simpler so-called
predictive equations of state must be adopted, see, e.g., Refs. [67, 68]. These models rely on a small
set of data related to the pure constituents, and to parameters describing the interaction between dif-
ferent molecules; these parameters can be determined either experimentally or estimated. Predictive
models applicable to mixtures are thermodynamically consistent, but calculated property values are
affected by much larger uncertainties if compared to the estimation of pure-fluid properties. In this study the properties of mixtures of siloxanes and perfluorocarbons are evaluated with either the improved Peng-Robinson Stryjek-Vera cubic equation of state [69], complemented by the
Wong-Sandler mixing rules (iPRSV-WS), see Ref. [70, 71], or the PC-SAFT model [72], which is
formulated in terms of molecular parameters whose value depends on the molecular arrangement.
Since most of the treatment in this chapter is based on the use of the iPRSV-WS model, both the
functional form of the equation of state and the derivation of the adopted mixing-rules are recalled
in Appendix A.1. These models, together with others, are implemented in an in-house computer
library for the calculation of primary and secondary thermodynamic properties of fluids [73]. Information on how the data for the iPRSV-WS model applied to siloxane mixtures were ob- tained can be found in Ref. [55]. The analytical expression of ' for this thermodynamic model is
reported in Ref. [61]. The application of the PC-SAFT model to linear siloxanes is documented in
Ref. [74], and has been extended by the authors to model also cyclic siloxanes. Siloxane/perfluoro-
cabon mixtures are modelled with the iPRSV-WS equation of state starting from experimental val-
ues of the critical point of these mixtures [75], and compared to results from the PC-SAFT model.
Such a comparison is the only possible assessment at the moment, since no other experimental
values are available. Values of ' for the PC-SAFT mixture model are calculated with analytical ex-
pressions obtained by derivation from the equation of state and the isobaric ideal-gas heat capacity
relation, see for example Ref. [48] and [21]. Figure 8.2 shows a comparison between the values of ' calculated along the dew line for the equimolar mixture of propane and pentane using a reference model [66], the iPRSV-WS and the
PC-SAFT models. As it is known, see Refs. [76, 77], predictive models fail to accurately estimate
properties close to the vapour-liquid critical point, therefore also ' values at high reduced temper-
ature ' T = T /Tc deviate from those obtained with the reference model, cf. figure 8.2. A number of evaluations for various fluids modelled by the reference model presented in Ref. [66] revealed
that the iPRSV-WS model performs better than the PC-SAFT model in the critical-point region,
therefore it has been chosen for the analysis presented in §8.3. Figure 8.3 shows the negative-' region (also termed BZT region) in the P-T thermodynamic plane for several selected organic compounds of the family of siloxanes, cloro-fluorocarbons, per-
fluorocarbons and their mixtures, calculated with the iPRSV-WS model. The ensemble of fluid
thermodynamic states featuring a negative value of ' in the dense vapour phase is delimited by
the dew line on the left and by the concave-upward ' = 0 line on the right. An estimate of the
temperature at which thermal break-down in stainless steel is likely to occur is also indicated (TSL,
Thermal Stability Limit). As an example, in table 8.1, the molar fraction x, average molecular weight MW, critical pres- 207 Chapter 8 T/T c ' 0.6 0.7 0.8 0.9 1 0.7 0.75 0.8 0.85 0.9 0.95 1 Figure 8.2: Comparison of ' values along the dew line as a function of the reduced tempera-
ture T /Tc for the equimolar mixture of propane and pentane calculated with the reference model
presented in Ref. [66] (''), the iPRSV-WS ( · · · ), and PC-SAFT ('' '' '') thermodynamic models. Table 8.1: Molar fraction x, average molecular weight MW, critical pressure Pc, critical temper-
ature Tc, critical density ρc and minimum value of the fundamental derivative of gasdynamics 'min
for a mixture of siloxane fluids MDM and MD6M. x MW Pc Tc ρc 'min MDM MD6M [g/mole] [bar] [K] [kg/m3] [-] 1.00 0.00 236.5 14.2 564.1 229.38 0.0917 0.75 0.25 329.2 18.0 653.9 288.41 0.5676 0.40 0.60 459.0 11.7 687.5 260.34 0.2567 0.15 0.85 551.7 8.3 690.3 243.09 -0.1187 0.05 0.95 588.8 7.2 689.6 236.65 -0.3040 0.00 1.00 607.3 6.8 689.0 230.64 -0.4001 208 Nonclassical Gasdynamics of Vapour Mixtures T [ oC] p [ba r] 320 340 360 380 400 420 4 6 8 10 12 14 16 TSL MD 4M D 5 MD 5M MD 6M D 6 PP-10 (a) T [ oC] p [ba r] 320 340 360 380 400 420 4 6 8 10 12 14 16 FC-75 / D 6 0.05 / 0.95 PP-10 / D 4 0.8 / 0.2 PP-10 / D 6 0.8 / 0.2 MD 4M / D6 0.5 / 0.5 FC-75 / D 6 0.05 / 0.95 TSL (b) Figure 8.3: Negative ' region (or BZT region) in the P-T thermodynamic plane for several
pure fluids (8.3a) and some selected mixtures (8.3b): values are calculated with the iPRSV-WS
thermodynamic model. For each fluid, the circle indicate the critical point. It is relevant to future
experiments on non-classical gasdynamic phenomena that the temperature values are close to the
estimated thermal stability limit (TSL) for these organic compounds in contact with stainless steel
( '' 390'C), while the values of pressure are comparatively moderate. The shaded area indicates the range of temperatures where thermal decomposition in stainless steel can be expected. 209 Chapter 8 M W [g/ m ol ], N MD 6 M MD 5 M MD 4 M MD 3 M MD 2 M MD M 0 200 400 600 -0.4 -0.2 0 0.2 ' m in (a) Pure linear siloxanes. x M W [g/ m ol ], N 0 0.2 0.4 0.6 0.8 1 0 100 200 300 400 500 600 -0.4 -0.2 0 0.2 0.4 0.6 ' m in (b) Values for mixtures of MDM/MD6M ( ') and MD5M/MD6M ( '). Figure 8.4: Molecular weight MW (''), active degrees of freedom evaluated at the critical tem-
perature N ( · · · ) and minimum value of ' along the dew line (- - -) for selected linear siloxanes. Properties are calculated with the iPRSV equation of state for the pure fluids, see Ref. [69], while
the equation of state is complemented by the Wong''Sandler mixing rules for the mixtures [78]. sure Pc, critical temperature Tc, critical density ρc and minimum value of the fundamental derivative
of gasdynamics 'min for the mixture of siloxane fluids MDM and MD6M are reported. Thermody-
namic properties are calculated using the iPRSV-WS thermodynamic model. As it is well known,
the critical point coordinates in table 8.1 depend in a non-linear fashion on the mixture composition x, with the critical pressure, temperature and density exhibiting a local maximum. Admittedly, the negative-' region of fluids MD5M and MD6M is partially or completely past the TSL, see figure 8.3. Although mixtures are expected to be more thermally stable than their
pure components, such high values of operating temperatures are unrealistic, if stainless steel is
the containing material. Moreover, for MD5M and MD6M the negative-' region is very close to
the liquid-vapour saturation point, where the value of ' is expected to diverge to infinity [21]. In
this region, an accurate evaluation of the thermodynamic properties, including ', would require the
inclusion of a critical point scaling law and of a cross-over model, linking the latter with the ana-
lytical EoS. In the present qualitative study, fluid MD6M was considered in order to maximize the
strength of non-classical phenomena for illustration purposes; thermal decomposition and critical
point effects are to be carefully assessed before selecting this fluid for the experiments. However, it
is remarkable that, similarly to previous studies on non-classical gasdynamics, the present findings
are directly applicable to less complex molecules, because the qualitative fluid dynamic behaviour
is similar to that of MD6M. Results shown in figure 8.4 are a preliminary evaluation of the dependence of the minimum value of ' on the molecular weight and on the molecular complexity, which is defined here as
the equivalent number of active translational, rotational and vibrational degrees of freedom of the
molecules at the critical temperature and in the dilute gas limit, see Ref. [79]. The molar compo-
sition is also indicated for mixtures. As it is known, in the case of pure fluids the minimum value 210 Nonclassical Gasdynamics of Vapour Mixtures 0.5 1 1.5 2 2.5 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 Sat ura tio n cur ve A B D SL s = s A 'v ' P (a) MD6M 0.5 1 1.5 2 2.5 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 A B Sa tur atio n cu rve D SL s = s A A'' 'v ' P (b) MDM(0.05)/MD6M(0.95) Figure 8.5: Pre- (A) and post-expansion (B) states on the reduced P-v plane. The negative-'
region (dashed line) and DSL are also reported. of ' along the dew line, 'min, decreases monotonically with increasing molecular weight and com-
plexity (figure 8.4a). In addition, the extension of the BZT region in the P-T plane increases with
increasing molecular weight and complexity, cf. figure 8.3a. It is remarkable that the effect of mixing, therefore of intermolecular interaction, alters the non monotone dependency of 'min from molecular weight and complexity. Figure 8.4b shows that
for binary mixtures of the siloxane fluids MDM/MD6M and MD5M/MD6M the estimated value
of 'min does not decrease monotonically with increasing average molecular complexity and weight
of the mixture, similarly to what observed for the values of the critical pressure, temperature and
density in table 8.1. Indeed, for both the MDM/MD6M and the MD5M/MD6M mixtures, the value
of 'min exhibits a maximum, which is at xMDM '' 0.75 for MDM/MD6M, and at xMD 5 M '' 0.9 for MD5M/MD6M. Notably, for the mixture MDM(0.4)/MD6M(0.6) the value of 'min is largely
different, even in sign, from the one predicted for MD4M, which is the homologous pure fluid in
terms of molecular weight and complexity. This type of dependency of 'min on molar composition is
predicted also in case of mixtures of alkanes, by using reference equations of state for the calculation
of thermodynamic properties. In the case presented here, the variation of 'min with the mole fraction of a binary mixture is such that, for any given composition, 'min is always larger than the molar-fraction averaged value
of 'min of the two pure constituents. Due to the large variety of intermolecular forces, it cannot
currently be ruled out that an opposite trend can be observed for different combinations of pure
fluids, namely that the mixing of two or more fluids not considered here leads to values of 'min that
are lower than those of the mixture constituents. From the knowledge of the fundamental derivative of gasdynamics in the vapour phase, the thermodynamic conditions resulting in nonclassical gasdynamics waves can be determined. The
conditions for the admissibility of rarefaction shocks are given by the work of Zamfirescu and 211 Chapter 8 colleagues [59], where the method for determining the so called rarefaction shock region (RSR) is
also reported. In figure 8.5a the RSR of siloxane fluid MD6M is shown, together with a representative isen- trope s = sA. As detailed in Ref. [59], the RSR is the thermodynamic region that includes all
the states that can possibly be upstream and downstream of a rarefaction shock wave. By defini-
tion, the RSR embeds the negative-' region. For pure fluids, the size of the RSR increases with
molecular complexity, similarly to the BZT region. In particular, the RSR is limited by the vapour-
liquid saturation (VLE) curve and by the Double Sonic Line (DSL), which is the locus of all fluid
states that can be connected by a double-sonic shock, whereby the pre- and post-shock states are
sonic. The DSL and the VLE are connected by the two loci representing the upstream state of
upstream-sonic downstream-saturated rarefaction shocks and the downstream state of upstream-
saturated downstream-sonic rarefaction shock wave. Each isentrope intersects the DSL in two points A and B, with vA < vB. At point A the Rayleigh line connecting point A and B is tangent to both the isentrope trough A and the shock adiabat trough
A. At point B, it is tangent to the isentrope trough B and the shock adiabat trough A. Therefore, the
shock connecting point A and B is a double sonic shock, with sonic state in both point A and B.
The RSW connecting point A and B encompasses the largest possible pressure difference, i.e., is
the strongest possible RSW originating from the considered isentrope. Note that in figure 8.5a the
shock adiabat through A and the isentrope s = sA are not distinguishable. The RSR of mixtures is calculated with the same procedure as for pure fluids, with no modifica- tions. An example is given in figure 8.5b, where the RSR for the mixture MDM(0.05)/MD6M(0.95)
is shown. The increase of the MDM percentage in the mixture MDM/MD6M causes the rarefaction
shock region to reduce its size in the P-v plane, if compared to the one of pure MD6M. 8.3 Nonclassical Gasdynamics Behaviour of Dense Gas
Mixtures
A preliminary study on the effect of the mixture composition on the gasdynamic behaviour of mix-
tures of organic fluids is carried out. To this purpose, the supersonic expansion of the dense vapour
of a mixture over a corner is simulated. The selected mixture is composed by MD6M, a BZT fluid, and MDM, a fluid for which no suitable thermodynamic model predicts a negative-' region. To compare results for different mix-
ture composition, a common upstream state was selected in terms of dimensionless quantities. The
upstream state features the same value of the Mach number M, reduced pressure ' P ' P/Pc , and non-dimensional entropy 's = s/s' for all simulations. The locus s = s' is the isentrope tangent to
the saturation line, see figure 8.5. The choice of ' P and 's to identify the upstream flow state is mo- tivated by the fact that they identify homologous thermodynamic states in the P-v thermodynamic
plane, with comparable real gas effects. The values of M, ' P and 's identifying the upstream states for the simulations are reported in table 8.2. The solid surface past the corner forms an angle of -13.169' with respect to the free-
stream direction. These values have been chosen so that in the case of pure MD6M a rarefaction
shock wave with maximum intensity is obtained, which forms an angle of 60' with respect to the
free-stream direction, see Ref. [10]. The computer program used to perform the simulations is a parallel solver for the Navier- Stokes equations on unstructured meshes based on a finite volume formulation and implicit time-
integration [80]. The code has been recently extended to include real gas properties [81] using a 212 Nonclassical Gasdynamics of Vapour Mixtures Table 8.2: Upstream states for the simulations of the supersonic flow of a dense gas mixture over
an expansion corner. MA 'sA ' PA 1.15470 1.00276 1.00217 Table 8.3: Upstream and downstream thermodynamic states for the different mixtures considered
in the simulations. Z is the compressibility factor defined as Z = RT /Pv. Composition x Upstream state A MDM MD6M ' TA ' ρA 'A ZA 1.00 0.00 1.0008 0.8630 1.0823 0.3610 0.75 0.25 1.0133 0.8280 1.1866 0.4510 0.40 0.60 1.0027 0.9234 1.0741 0.3912 0.15 0.85 1.0012 0.9059 0.9290 0.3617 0.05 0.95 1.0008 0.8785 0.8148 0.3577 0.00 1.00 1.0005 0.8824 0.7310 0.3532 Composition x Downstream state B MDM MD6M ' TB ' ρB 'B ZB ' PB 1.00 0.00 0.9833 0.5279 0.2078 0.5072 0.8461 0.75 0.25 1.0013 0.5172 0.5912 0.5661 0.7764 0.40 0.60 0.9931 0.5698 0.3292 0.5291 0.8284 0.15 0.85 0.9919 0.5342 0.1593 0.5241 0.8485 0.05 0.95 0.9910 0.4920 0.1664 0.5395 0.8382 0.00 1.00 0.9902 0.4660 0.2068 0.5551 0.8231 Table 8.4: Downstream Mach number and pressure, temperature, density, and velocity differences
across the expansion waves, where ''( ·) = (·)B '' (·)A. Composition x MDM MD6M MB ''P PA ''T TA '' ρ ρA ''u
uA 1.00 0.00 1.1770 -0.1562 -0.0175 -0.3927 0.4128 0.75 0.25 1.3822 -0.2257 -0.0119 -0.3760 0.3222 0.40 0.60 1.2426 -0.1739 -0.0096 -0.3843 0.3752 0.15 0.85 1.1109 -0.1539 -0.0093 -0.4140 0.4943 0.05 0.95 1.0621 -0.1641 -0.0098 -0.4483 0.6195 0.00 1.00 1.0450 -0.1792 -0.0103 -0.4765 0.7283 213 Chapter 8 general interface to several thermodynamic libraries [73]. An unstructured mesh refinement tech-
nique is adopted to increase the accuracy in regions where the solutions exhibit the largest gradients. Figure 8.6 shows the flow field isobars from flow simulations for different mixtures of MDM/MD6M, whereby the mole fraction of MDM varies from xMDM = 1 in figure 8.6a to xMDM = 0 in figure 8.6f,
under the assumption of negligible fluid viscosity and thermal conductivity. Figure 8.6a displays the supersonic flow of a pure MDM vapour. As expected, since ' > 0, a classical isentropic expansion fan is observed in this case. It is remarkable that differently from
supersonic expansions of a constant specific heats ideal gas, the Mach number M variation across
the expansion is non-monotone, as it can be appreciated from figure 8.7a, where the Mach number
is depicted for a representative streamline across the expansion wave. The present non monotone
behaviour is consistent with the value of the parameter J, namely J(s, ρ, M) = 1 '' '(s, ρ) '' 1 M2 , (8.2) across the expansion wave. Indeed, for isentropic processes from a given state A one has, see
Ref. [82], dM dρ = J(sA, ρ, M) M ρ . (8.3) As shown in figure 8.7b, in the expansion of pure MDM vapour depicted in figure 8.6a, J can have
both negative and positive values and therefore M is non-monotone. Note that for a constant specific
heat ideal gas, J = (1 '' γ)/2 '' 1/M 2 < 0, with γ ratio of the isobaric and isochoric specific heats, and therefore M always increases monotonically during a supersonic expansion. A reversed, nonclassical, behaviour is observed for the supersonic expansion of pure MD6M, shown in figure 8.6f. An oblique nonclassical rarefaction shock wave, which forms an angle of 60'
with respect to the upstream flow direction, is observed. Intermediate situations are observed in the case of mixtures of MDM/MD6M''shown in fig- ures 8.6b, 8.6c, 8.6d and 8.6e''where the supersonic expansions of mixtures of increasing concen-
tration of the more complex component MD6M are depicted. In particular, in figure 8.6b, where the flow of a MDM(0.75)/MD6M(0.25) mixture is shown, a classical rarefaction fan is observed since ' > 0. The angular sector encompassed by the fan is larger
than that observed in figure 8.6a for pure fluid MDM, although the final turning angle θB = ''13.169' is the same in both conditions. Therefore, since the slope of the limiting characteristic line at the
right boundary of the fan is λ(θB) = tan (θB + µ(θB)) where sin µB = 1/MB, one can conclude that
the Mach number at the end of the expansion is larger in this case, as it is confirmed also by the
values in table 8.3 and 8.4. The above can be explained by recalling the dependence of the Mach
number on the local velocity angle θ given by the Prandtl-Meyer relation, see Ref. [7], namely, dθ = '' M2 '' 1 1 '' (' '' 1) M2 dM. (8.4) Indeed, despite the larger average molecular weight, along the considered isentrope the value of J
for the mixture is always lower than that computed for pure MDM, see figure 8.7b, and the Mach
number difference between the upstream and downstream state is larger. In the conditions depicted in 8.6c and 8.6d, 'min > 0, see figure 8.3 and table 8.1, and therefore a classical flow is observed in both cases. In case 8.6c, the Mach number in state B is larger than that
observed in case 8.6a, consistently with the ' and J profiles across the expansion, see figures 8.7c
and 8.7b, respectively. As a consequence, the angle encompassed by the rarefaction fan is larger
than that observed for pure fluid MDM. The opposite situation is found in the case in 8.6d and the
fan is narrower than its pure fluid counterpart. 214 Nonclassical Gasdynamics of Vapour Mixtures (a) MDM (b) MDM(0.75)/MD6M(0.25) (c) MDM(0.40)/MD6M(0.60) (d) MDM(0.15)/MD6M(0.85) (e) MDM(0.05)/MD6M(0.95) (f) MD6M Figure 8.6: Simulated flows of dense vapours of MDM/MD6M expanding over a corner, whereby
the mole fraction of MDM varies from 1 (a) to 0 (f). Fifteen levels of isopressure contour lines are
plotted in the range ' P = [0.8, 1]. The upstream state features the same Mach number M, reduced pressure ' P ' P/Pc and reduced entropy 's = s/s' in all cases. The fluid thermodynamic model is the iPRSV equation of state complemented by the Wong-Sandler mixing rules for the mixtures. 215 Chapter 8 Position along the streamline [-] M ac h [-] 0 0.2 0.4 0.6 0.8 1 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 MDM 75% '' 25% 40% '' 60% 15% '' 85% 5% '' 95% MD6M (a) Mach number Position along the streamline [-] J [-] 0 0.2 0.4 0.6 0.8 1 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 MDM 75% '' 25% 40% '' 60% 15% '' 85% 5% '' 95% MD6M (b) J = 1 '' ' '' 1/M 2 Position along the streamline [-] ' [- ] 0 0.2 0.4 0.6 0.8 1 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 MDM 75% '' 25% 40% '' 60% 15% '' 85% 5% '' 95% MD6M (c) ' Figure 8.7: Variation of the Mach number (top), the parameter J = 1 '' ' '' 1/M2 (middle), and
' (bottom) along a streamline. Different lines correspond to different compositions of the mixture
MDM/MD6M. 216 Nonclassical Gasdynamics of Vapour Mixtures Flow direction [rad] P r [- ] M ac h [- ] 0 0.05 0.1 0.15 0.2 0.75 0.8 0.85 0.9 0.95 1 1.05 1.15 1.2 1.25 1.3 1.35 1.4 1.45 P r Mach (a) MDM Flow direction [rad] P r [- ] M ac h [- ] 0 0.05 0.1 0.15 0.2 0.75 0.8 0.85 0.9 0.95 1 1.05 1.15 1.2 1.25 1.3 1.35 1.4 1.45 P r Mach (b) MDM(0.75)/MD6M(0.25) Flow direction [rad] P r [- ] M ac h [- ] 0 0.05 0.1 0.15 0.2 0.75 0.8 0.85 0.9 0.95 1 1.05 1.15 1.2 1.25 1.3 1.35 1.4 1.45 P r Mach (c) MDM(0.40)/MD6M(0.60) Figure 8.8: Comparison between the numerical integration (- - -) of the Prandtl''Meyer ordinary
differential equation (8.4) and numerical simulation (''). From table 8.1 and figure 8.4, for small concentrations of MDM (xMDM < 0.15), ' assumes negative values in the vapour phase and nonclassical behaviour is admissible. This is the case of
the flow of mixture MDM(0.05)/MD6M(0.95) in figure 8.6e, where the expansion occurs through a
nonclassical composite wave made of a continuous fan that is terminated by a nonclassical rarefac-
tion shock wave, with close-to-sonic downstream state. The expansion is depicted in the thermody-
namic plane in figure 8.5b, which displays the pre- and post-expansion states A and B in the reduced
P-v plane. While for the case of the pure fluid MD6M a single rarefaction shock wave connects the
two states, in the case of the mixture MDM(0.05)/MD6M(0.95), an initial isentropic expansion is
observed from state A to state A'', which lies on the double sonic line. Then, a rarefaction shock
wave expands the fluid from A'' to B. Results are summarized in table 8.4, which displays the downstream Mach number M and the variations of pressure P, the temperature T , the densityρ and the velocity u across the waves for
all the considered different mixture compositions. The entropy difference across composite waves
and the RSW is very small, due to both the relatively small pressure difference across the shock
and the small value of '. Indeed, Landau and Lifshitz showed that a Taylor-series expansion of the
Rankine-Hugoniot jump conditions delivers the following relation ''s '' '' 'A 6 c2 A TA " ''v vA #3 + o 
     " ''v vA #4      , where ''( ·) = (·)B '' (·)A, which is valid for weak shock waves [83]. In the present study, the largest entropy difference was computed by solving the non-linear Rankine-Hugoniot jump conditions for
the RSW in MD6M and it is as small as ''s
sA ' 5 ' 10'' 6. To conclude, figure 8.8 reports the comparison of the numerical integration of the Prandtl'' Meyer ordinary differential equation (8.4) and the numerical simulations for the three classical ex-
pansions of pure fluid MDM and of the mixtures MDM(0.75)/MD6M(0.25) and MDM(0.40)/MD6M(0.60).
The very good agreement obtained by these two different approaches increases the authors'' confi-
dence on the correctness of the presented results. Furthermore, the values of the upstream and 217 Chapter 8 downstream entropy were compared for the three isentropic expansions, for which the exact results
is ''s
sA ' 0 since sA ' sB. Small relative differences of about 10'' 6 confirmed that effects of numerical dissipation were negligible. 8.4 Conclusions Nonclassical gasdynamic phenomena in dense vapours of organic mixtures have been investigated
for the first time. In particular, the effect of non-ideal mixing on the thermodynamic properties
relevant to the fluid dynamics was studied. Predictive equations of state have been used to compute the thermodynamic properties of the mixture, most notably the fundamental derivative of gasdynamics ', for mixtures of siloxanes, per-
fluorocarbons, siloxanes-perfluorocarbons, and cloro- and perfluorocarbons. Some of the exemplary
mixtures display thermodynamic regions of negative nonlinearity for certain compositions. The de-
pendence of the minimum value of ' in the vapour phase from the molar composition has been
analyzed in the paradigmatic case of mixtures of linear siloxanes. It is found that 'min is always
greater than the value of 'min of the most complex molecule in the mixture. In addition the value
'min of a pure linear siloxane whose molecular weight is intermediate with respect to that of the
mixture constituents, is always lower than that of the mixture featuring the same molecular weight
or complexity. Preliminary simulations of a supersonic flow of a dense vapour expanding over a corner are presented. The dense vapour is a binary mixture of linear siloxanes MDM/MD6M, whereby for
each simulation the upstream conditions are kept similar, while the molar composition is varied
from xMDM = 0 to xMDM = 1. The results show how the flow field changes from the classical
expansion fan to a rarefaction shock wave, when the composition is MDM(0.05)/MD6M(0.95). For
MDM(0.15)/MD6M(0.85) a mixed rarefaction shock/fan is predicted. Thermal decomposition of
the fluid and critical point effects are to be carefully assessed before selecting the substance for
experiments. However, it is remarkable that, similarly to previous studies on non-classical flows,
the same gasdynamics behaviour is expected for all considered fluids. We conclude that for the considered mixtures, mixing compounds of the same fluid family does not enhance non-classical gasdynamic phenomena. Given the variety and complexity of molecular
interactions among different molecules, the possibility that the opposite effect occurs for different
mixture compositions cannot be ruled out. Limitations with respect to accuracy and predictive char-
acter of currently available thermodynamic models for mixtures make the analysis of the possibly
large variety of mixtures difficult. In addition, these limitations must be considered also with respect
to the results of this study. Future work will be devoted to the improvement of thermodynamic models suitable for com- plex organic compounds, possibly also by means of property measurements. Indeed, the main
obstacle to such investigation is the lack of experimental thermodynamic data of mixtures of com-
plex organic compounds, or of predictive and accurate thermodynamic models, valid close to the
vapour-liquid critical point. Attention will be dedicated to highly non-ideal mixtures in an attempt to understand if an enhancement of non-classical gasdynamic effects can be achieved by mixing two or more different
organic fluids. This possibility''together with thermal stability''would have a large impact on
experiments aimed at generating and measuring non-classical gasdynamic phenomena. Siloxane
mixtures will also be tested in the experimental facility for generating and measuring rarefaction
shock wave at the Delft University of Technology. 218 Nonclassical Gasdynamics of Vapour Mixtures Acknowledgments The authors acknowledge the contribution of their colleague and friend T.P. van der Stelt for devel-
opment of the mixture thermodynamic models. A.1 iPRSV-WS Thermodynamic Model The thermodynamic model adopted for the multi-component fluids is briefly described here. The
volumetric equation of state (EoS) is provided by the so-called improved Stryjek-Vera Peng-Robinson
(iPRSV) model complemented by a usual polynomial expression for the isobaric ideal-gas specific
heat, see Ref. [69], and by the mixing rules proposed by Wong and Sandler [70]. [84], see also [85], proposed to use the Peng Robinson [86] cubic EoS, with the Soave [87] α-function, but with a different temperature and acentric factor dependence in order to improve
the correlation of vapor pressures for a wide variety of fluids. Notably, the proposed functional
form for α results in the Stryjek-Vera Peng-Robinson (PRSV) EoS featuring a discontinuity in all
the properties at the absolute critical temperature, Tc, for water and alcohols, and at temperature
T = 0.7 · Tc for all the other fluids. Recently, [69] proposed a modification of the PRSV EoS aimed at eliminating the discontinuity in the prediction of thermodynamic properties. The iPRSV EoS is similar to the cubic form characteristic of the PRSV EoS, P = RT v '' b '' a v2 + 2bv '' b2 , (5) where, a =  0.457235 R 2 T 2 c /Pc  α, b = 0.077796 R Tc/Pc, α = h 1 + κ  1 '' p Tr i2 . Here, R = R/µ is the gas constant, with R the universal gas constant, a is the attractive term, b is the co-volume parameter, P and v are the pressure and the specific volume, respectively. The
subscript c indicates properties at the vapour-liquid critical point. The parameter κ depends on the
temperature as follows κ = κ0 + κ1  1 + p Tr  (0.7 '' Tr) , (6) with κ0 = 0.378893 + 1.4897153' '' 0.17131848' 2 + 0.0196554'3, (7) where ' is the acentric factor. The empirical parameter κ1 in eq. (6) is a pure-component parameter
chosen in order to obtain accurate predictions of saturated properties. From low temperatures up to
reduced temperatures of Tr = 0.7, Stryjek and Vera recommend using values for κ1 tabulated in their
papers [84, 85]. Alternatively, κ1 can also be obtained by regressing experimental data. According
to Stryjek and Vera, for water and alcohols the tabulated values can be applied up to the critical
point. For other compounds, slightly better results are obtained with κ1 = 0 for 0.7 < Tr < 1. For
super critical temperatures (Tr > 1) they recommend κ1 = 0, because there would be no advantage
in using eq. (6) in this region. The κ-function therefore introduces a discontinuity in α(T ) either at
Tr = 0.7 or at Tr = 1, and in thermodynamic properties dependent upon and derivatives thereof.
The iPRSV EoS is obtained by modifying the equation for the calculation of the κ-value, such that it
is continuous with the temperature, but by keeping the same parameters κ0 and κ1 in the functional
form, and in such a way that the same values can be used. This is a notable advantage, because 219 Chapter 8 a large amount of data for these parameters that have been obtained so far can still be used. The
κ-function in the iPRSV thermodynamic model is therefore κ = κ0 + κ1 ( q [A '' D (Tr + B)] 2 + E + A '' D (Tr + B) ) p Tr + C, (8) where the value of the coefficients are A = 1.1, B = 0.25, C = 0.2, D = 1.2 and E = 0.01. The
accuracy of the iPRSV thermodynamic model is similar or better than that of the model from which
is derived. The derivatives of κ with respect to the temperature, that are required for the implemen-
tation of a complete thermodynamic model into a computer program, are given in Ref. [69] together
with a thorough discussion on the limits of the thermodynamic model. Wong and Sandler developed a set of mixing rules which satisfy the theoretically correct quadratic composition dependence of the second virial coefficient [70]. The mixing rule is derived
by equating the excess Helmholtz energy AE of an activity coefficient model describing molecular
interaction in the liquid phase to that obtained from the EoS at the so-called infinite-pressure state,
namely, in the limit of a specific volume approaching the co-volume. The mixing rule contains one
additional binary interaction parameter kij in the cross second virial coefficient, see Eq. 11. The
binary interaction parameter can be determined by various approaches, see e.g. Ref. [88]. The
Wong-Sandler mixing rule (WSMR) is used extensively in conjunction with the PRSV EoS. For the
activity coefficient model, a so-called ''solely energetic' model is usually preferred (i.e., a model
which does not have an explicit free-volume term). As it is common practice for the PRSV EoS,
the NRTL model introduced in Ref. [89] is used here to compute the activity coefficient, see also
Ref. [90]. According to the WSMR, the a and b coefficients in (5) are substituted by aM = RT DbM, and bM = Q 1 '' D , (9) respectively, where D = AE '' CEoS + NC X i=1 xiai RT bi , Q = NC X i=1 NC X j=1 xi xj  b '' a RT  ij . The parameter CEoS depends upon the equation of state. For the PRSV EOS, it reads CEoS = '' 2 2 ln  '' 2 '' 1  '' ''0.62323. (10) The following combining rule has been used  b '' a RT  ij = bi + bj '' ai + aj 2RT  1 '' kij  . (11) where a and b are the energy and the co-volume parameter. The subscript M refers to mixture
properties while i and j refer to the components in the mixture. NC is the number of components. From the pressure EoS, a complete thermodynamic model can be finally obtained by specifying the relation between the temperature and the specific heat at constant pressure cP in the dilute gas
limit, see e.g. [91]. In the present study, the following functional form of cP '(T ) = lim v '''' cP(T, v) = C0 + C1 T + C2 T 2 + C 3 T 3 (12) with C0, C1, C2 and C3 constants. The values of the parameters C0, C1, C2 and C3 are given in
Ref. [69] for the fluids of interest here. From the cP definition (12) and the pressure EoS (5) a 220 Nonclassical Gasdynamics of Vapour Mixtures complete thermodynamic model can be obtained. For example, from the reciprocity relation, one
immediately computes the energy EoS as e(T, v) = '(T ) + Z v v0 " T ''P(T, ν) ''v '' P # dν (13) where, from the Meyer''s law of ideal gas, '(T ) = '(R) '' R = limv'''' cv(T, v) is the specific heat at constant volume in the dilute gas limit. All thermodynamic variables can be computed from the
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complex organic compounds as working fluids for the organic Rankine cycle (ORC) power systems
of the future. The material presented is at the basis of several publications on peer-reviewed in-
ternational journals: five papers are already published, one has been accepted for publication, and
two are about to be submitted for publication. The work is divided in self-contained chapters, each
addressing a specific sub-topic, with its own concluding remarks. The general conclusions and their
practical implications are treated in the following, marked with the V and the W sign, respectively. The first part of the thesis presents several contributions to the research in the field of energy con-
version systems, focusing on ORC turbo-generators. Chapter 2 presents the first review work covering the historical developments, the status of the art,
and the future foreseen for the ORC power systems technology. V A comprehensive overview of the applications, technical solutions, and of the ORC plants
which reached commercial operation in the last 20 years is presented, with a collection of
data harvested within the major manufacturers. W The work is intended as a reference for both the Academic and the Industrial audience
and, in the authors'' opinion, could prove particularly useful in avoiding the repetition of
studies/attempts/experiments which have been already carried out in the past. Furthermore,
the presented outlook to the future might help in defining the strategic objectives to be
pursued in order to advance the ORC power systems field. Chapter 3 explores the main envisaged research paths in the field of ORC turbo-expanders design,
i.e., the development of generalized design methodologies, and the assessment of non-conventional
machine architectures. V The first critical evaluation of the centrifugal or radial-outflow turbine (ROT) architecture
as a candidate technology for ORC systems is presented. V It is discussed how the simplifying assumptions usually adopted in the axial turbines practice
are typically not applicable for ROT machines. It is concluded that, in order to design
efficient ROTs, it is needed that the blade discharge geometric angles, the radial chords, the
stage expansion ratios, and the reaction degrees are allowed to vary among each cascade, and
that the diameter and the speed of revolution are included among the optimization variables. V A novel design methodology for the preliminary sizing of ROTs in the power size range
from several MWE down to few kWE is presented, which covers most of the applications
foreseen today. V The in-house mean-line optimization code zTurbo, which allows to determine the prelimi-
nary design of ORC turbines of various configurations and working with different fluids, is
introduced and adopted to verify the novel method by presenting several exemplary design
exercises. V The design of two 1 MWE centrifugal turbines is presented, a transonic six-stage and a
supersonic three-stage machines. These expanders handle an expansion ratio of 60, and
rotate at 3000 RPM. Simplifications derived from the axial-turbines practice are adopted in
order to illustrate their consequences. The results of the design exercise carried out with 230 Conclusions & Perspectives zTurbo confirm that the adopted assumptions lead to unwanted design features, such as
converging meridional channels and large flaring angles on the last stages. The predicted
fluid-dynamic efficiency for the transonic and the supersonic machine is around 86% and
81%, respectively. V The down-scaling potential of the centrifugal architecture is assessed, by applying the novel
design methodology to the sizing of two 10 kWE ROTs, handling an expansion ratio of
45. The design of a 5 stages transonic turbine, and of a 3 stages slightly supersonic one is
presented. The proposed design procedure proves valuable in overcoming the criticality pre-
viously highlighted. In particular, the resulting meridional channel monotonically diverges
maintaining maximum flaring angles lower than 10'. The resulting turbines are projected to
exceed a fluid-dynamic efficiency of 79% and 77%, with speed of revolution around 124000
and 15400 RPM, respectively. W It is demonstrated that the ROT architecture is a promising concept for future ORC power
systems, capable of preserving its features and performance when downscaled, for both
transonic and slightly supersonic configurations. W The proposed methodology and tools are virtually applicable to the preliminary design of
any ROT expander, working with any reasonable fluid. Chapter 4 presents the research related with another innovative component, i.e., a so-called direct
thermal storage system whereby the same fluid is circulated in the heat source, serves as the thermal
storage medium, and acts as the working fluid of the ORC turbo-generator. V Several options are presented regarding the integration of the thermal storage system into the
plant. The most promising solutions seem those decoupling the thermal energy source from
the ORC power block. It is demonstrated how, apart from a substantial simplifications in
terms of both plant layout and operational strategy, this configuration ensures high exergetic
performance of the thermal charge and discharge processes. V A newly conceived variant of the Rankine cycle is introduced, whereby a flashing evap-
oration process precedes the power-generating expansion. The properties of the adopted
complex-molecule working fluids are such that flashing can lead to saturated or superheated
vapor conditions. This characteristic implies further simplifications of the system. The ef-
ficiency of an ORC power plant working according to this complete flashing cycle (CFC)
may be, under the described assumptions, only marginally lower than what observed for a
conventional evaporative ORC power system. V A case study regarding a 100 kWE solar plant is presented: the proposed system features
a constant-pressure thermocline storage system, with vapour generation through external
flashing of the liquid extracted from the storage vessel. The proposed turbo-generator
achieves an estimated 25% efficiency, which corresponds to a solar-to-electric value of 18%
in design conditions for the complete system. With siloxanes compounds, the estimated
values of storage density are around 10 kWhE for a cubic meter of storage volume, which
is around half of what typically achieved with the storage of diathermic oils, but without
considering additional filling materials. The advantages in terms of simplification of the
plant layout could overcome the relatively low values of storage densities, the need of pres-
surization, and the specific cost of the fluids. A dynamic model, developed for the complete
system, is used to investigate the performance under extreme transient conditions. This
allows to preliminary assess the feasibility of remotely controlled operation. 231 Chapter 9 W Feasible and efficient energy storage systems are foreseen to be the enabler technology
for future power plants, such as, notably, those in the field of concentrated solar power
(CSP). Furthermore, small-scale distributed CSP plants co-generating heating and cooling
power will probably gain an important role. As already said, ORC turbo-generators are
good candidates for similar applications but, before this work, no storage system tailored
to this technology was investigated. Therefore, this study has the potential to open up new
possibilities of dissemination for solar-powered ORC engines. With Chapter 5, the focus of the analysis is moved from the component- to the system-level, by
proposing an innovative methodology for the design of flexible energy conversion systems, which
takes dynamic requirements on critical transients into account since a very early phase in the design
cycle. V The new tool DYNDES is presented, which utilizes a multi-objective optimization ap- proach to search for optimal system designs with potentially conflicting objectives. The
main components, notably the heat exchangers in the considered case, are also preliminary
sized at this step. The system dynamic performance is thus enforced as an additional design
criterion, by testing the previously determined optimal system configurations by simulating
the behavior of automatically parametrized dynamic simulations. V It is shown how to exclude those designs which do not satisfy given dynamic requirements
such as, e.g., the tolerance on network frequency variations as a consequence of a strong
load oscillation. V The developed methodology is successfully applied to the case study of an ORC-based
combined cycle power plant for an off-grid oil platform. W The proposed procedures and tools might be valuable for the preliminary design of first-
of-a-kind systems with demanding dynamic requirements, also in fields other than energy
conversion. Chapter 6 addresses another important aspect of modern energy systems, i.e. the operating strategy.
The paradigmatic case of concentrated solar power plants selling energy in a context of time-varying
tariffs is considered. The thermal energy storage (TES) system can be used to shift the production
to the most profitable hours, exploiting the dispatchability capabilities of this technology. V A simplified model of a state-of-the-art central receiver plant has been developed using high-
level modelling languages, and proved to be accurate with respect to the SAM reference
software and literature data. V Optimal control problems have been formulated and solved using high-level modelling lan-
guages. The validity of the analysis is confirmed by previously published results. V As a novelty, different operating strategies are compared based on a detailed financial anal-
ysis over the project life-time. A wide system design space is considered, and the results are
presented for all the foreseeable combinations of solar field size and TES system capacity. V A novel methodology is introduced, which allows to properly assess the potential of optimal
control in terms of both the increased revenue and the reduced investment cost it allows for. V It is demonstrated that optimal control should be taken into account when estimating the
potential plant revenue since its design and sizing phase. V It is shown that, for state-of-the art systems under the assumptions considered, it is always
profitable to exploit optimal control to the end of increasing electricity production. On a
yearly basis, an average gain in the revenue of the order of 5% is obtained with respect to 232 Conclusions & Perspectives usually adopted short-sighted strategies. However, this figure is amplified to more than 10%
in terms of net present value of the investment when applying the complete financial analysis
presented here. Notably, the storage capacity for which maximum profitability occurs seems
to be independent from the considered operating strategy. V The potential of optimal control in terms of investment cost reduction has been unveiled
for the first time. For the case-study technology considered, this follows the possibility of
harvesting the same revenue with a smaller TES capacity. W The results have been obtained with open-source software, and a total of about 50 code lines,
which makes the developed tools quite understandable and user-friendly. The proposed
methodology could be easily implemented as an extension of reference design models, such
as those available within the SAM program. W The proposed methodology constitutes a new tool in the designer''s hands who, depending
on the specific project characteristics and financial framework, may be keen on favouring a
larger electricity production or a comparatively lower investment cost. Notably, this could
be of particular interest for ORC-based CSP systems operating in the envisaged distributed
generation scenario, possibly cogenerating thermal power for heating or cooling purposes. The second part of the thesis is focused on the experimental and numerical investigation of the
non-classical gas dynamic behavior of dense vapors of single- and multi-component organic fluids.
Notably, ORC power systems constitute the first foreseen application for the arguments dealt with
in this part. Chapter 7 describes the commissioning the FAST setup, a new Ludwieg tube facility designed and
built at the Delft University of Technology with the main purpose of providing the first experimen-
tal evidence of the most exotic non-classical gas dynamics effect, i.e., the rarefaction shock wave
(RSW) in the dense vapor region of fluids formed by complex organic molecules. V The setup components and the control & operation strategy devised are proven to be effective
to the end of accurately measuring the speed and the intensity of the propagating waves.
Results for several ideal gases are presented. V The fast opening valve, which is the most critical component, is characterized in terms of its
opening time, which resulted of the order of 2 '' 5 ms. According to previous studies, this should be small enough to ensure the complete formation of the phenomenon of interest, i.e.
a shock wave, within the shock tube. This result is confirmed by analyzing a compression
shock wave propagating in air. V The first published results regarding speed of sound measurements performed in the dense-
gas region of a molecularly complex organic compound, i.e. siloxane D6, are presented. W The FAST setup and the developed measurement procedure constitute unique tools to the
end of proving the existence of the RSW. Furthermore, a number of interesting secondary
results can be obtained, such as, notably, speed of sound measurements. Chapter 8 presents the first theoretical investigation of non-classical gas dynamic phenomena in
dense vapours of organic mixtures. In particular, the effect of non-ideal mixing on the thermody-
namic properties relevant to the fluid dynamics was studied. 233 Chapter 9 V Predictive equations of state have been used to compute the thermodynamic properties of
the mixture, most notably the fundamental derivative of gas dynamics '. V Some of the exemplary mixtures display thermodynamic regions of negative nonlinearity
for certain compositions. V The dependence of the minimum value of ' in the vapour phase from the molar composition
has been analyzed for several paradigmatic mixtures, finding that 'min is always greater than
the value of 'min of the most complex molecule in the mixture. Further, the value 'min of a
pure component whose molecular weight is intermediate with respect to that of the mixture
constituents, is always lower than that of the mixture featuring the same molecular weight
or complexity. V For all the considered mixtures, mixing compounds of the same fluid family does not en-
hance non-classical gas dynamic phenomena. V Preliminary simulations of a supersonic flow of a dense vapour expanding over a corner
are presented. The dense vapour is a binary mixture of linear siloxanes MDM/MD6M,
whereby for each simulation the upstream conditions are kept similar, while the molar com-
position is varied from xMDM = 0 to xMDM = 1. The results show how the flow field
changes from the classical expansion fan to a rarefaction shock wave, when the composition
is MDM(0.05)/MD6M(0.95). For MDM(0.15)/MD6M(0.85) a mixed rarefaction shock/fan
is predicted. W Attention will be dedicated to highly non-ideal mixtures in an attempt to understand if an
enhancement of non-classical gas dynamic effects can be achieved by mixing two or more
different organic fluids. This possibility''together with thermal stability''would have a
large impact on experiments aimed at generating and measuring non-classical gas dynamic
phenomena. 234 Summary A sharp inversion regarding the current trends of energy consumption and related emissions of
global greenhouse gases is needed in order to harmonize our life to the planet resources and, ulti-
mately, in order to survive. It is a shared idea that, to this end, a sustainable energy system has to be
conceived, made to be smarter, more decentralized, and more integrated than what we know today.
In the author''s opinion, energy conversion systems based on the organic Rankine thermodynamic
cycle (ORC) have the potential to play a major role in this envisaged framework, and the work
hereby documented stems primarily from this belief. Several contributions are presented, in order to illustrate the original results of numerical and ex-
perimental research aimed at investigating the potential of molecularly heavy and complex organic
compounds as working fluids for the ORC power systems of the future. This thesis is divided into
two main parts, in turn constituted by self-contained chapters, each addressing a specific sub-topic.
The material presented is at the basis of several publications on peer-reviewed international jour-
nals: five papers are already published, one has been accepted for publication, and two are about to
be submitted for publication. The first part presents the contributions to the research in the field of energy conversion systems,
focusing on ORC turbo-generators. An introductory review on ORC systems, with an overview of their history, the description of the
state-of-the-art from both the academic and the industrial perspective, and an outlook to envisaged
paths of development is contained in Chapter 2. The cumulative global capacity of ORC systems,
which is undergoing a rapid growth started a decade ago, is expected to grow much more in the fu-
ture. The potential for the conversion into electricity of the thermal power coming from renewable
and renewable-like sources is huge, and ORC power systems are one of the most flexible candidate
conversion technologies to this end, both in terms of capacity and temperature levels. A com-
prehensive overview of the applications, technical solutions, and of the ORC plants which reached
commercial operation in the last 20 years is presented, with a collection of data harvested within the
major manufacturers. The work is intended as a reference for both the Academic and the Industrial
audience, and could prove particularly useful in avoiding the repetition of studies/attempts/experi-
ments which have been already carried out in the past. Chapter 3 documents the original research conducted in the field of ORC turbo-expanders, which
constitute the most critical components when efficient systems have to be designed. The variety of
possible working fluids, the complex gas dynamic phenomena encountered, and the lack of simpli-
fied design methods based on experience on similar machines, make the design of efficient turbines
a complicated task. Relevant paths of development may thus be concerned with (i) the development 235 summary of generalized design methodologies, and (ii) the assessment of non-conventional machine architec-
tures: the research presented in this chapter aims at exploring both. The first critical evaluation of
the radial-outflow turbine (ROT) architecture as a candidate technology for ORC turbo-generators
is presented, together with a novel methodological framework for the design of these machines. The
results of several design exercises show that the ROT is a promising concept, which allows for the
realization of efficient, compact, and reliable turbo-expanders in any power-output level of interest. Chapter 4 deals with the assessment of a novel thermal storage systems tailored to high-temperature
ORC systems for concentrating solar power (CSP) applications, stemming from the observation
that the direct storage of the ORC working fluids can be effective thanks to their favourable ther-
modynamic properties. The concept of complete flashing cycle (CFC) is introduced as a mean of
achieving an unmatched system layout simplification, while preserving conversion efficiency. This
is a new variant of the Rankine cycle, whereby the vapour is produced by throttling the organic
working fluid from liquid to saturated vapour conditions. The main trade-offs appearing in the de-
sign phase of such systems, involving the global efficiency, the storage dimensions and pressure,
and the expansion ratio across the turbine, are investigated. Also the dynamic performance of an
exemplary plant are assessed by mean of simulation, preliminary proving the feasibility of remotely
controlled operation. This study has the potential of opening up new possibilities of dissemination
for solar-powered ORC engines. Chapter 5 shifts the focus of the analysis from component- to system-level, presenting a method-
ology for the optimal design of modern power generation systems, accounting for the increasingly
demanding requirements in terms of operational flexibility. The innovative element is the possibility
of considering the dynamic performance since a very early phase of the design procedure. The test
case presented is the preliminary design of an off-grid power plant serving an off-shore platform,
where a gas turbine engine is combined with an ORC power module. The solutions of a stationary
model of this combined plant are used to identify its optimal configurations. A dynamic model of
each of these systems is thus automatically parameterized, by inheriting its parameters values from
the design model results, and used to assess the performance of the modeled system under the tran-
sient scenarios of interest. Again, in the considered example it is shown that the proposed combined
procedure allows to discriminate among the initial set of solutions, in order to provide the designs
that also comply with dynamic requirements. These tools might be valuable for the preliminary
design of first-of-a-kind systems with demanding dynamic requirements, also in fields other than
energy conversion. Chapter 6 explores the potential of innovative operating strategies in the context of thermal energy
storage management for concentrating solar power plants. As the main novelties, a complete finan-
cial analysis is used to this end, and the impact on the system design is investigated. The method-
ology is applied to a test case, a state-of-the-art central receiver plant with direct storage, using
molten salts as working fluid, and selling energy in a context of variable electricity prices. Different
operating strategies are compared, and a wide system design space is considered. The potential of
these techniques is discussed also under the point of view of investment cost reduction, showing
how the same yearly revenue can be harvested with a smaller energy storage, if optimally operated.
The novel method is an additional decision tool allowing to treat the storage operation strategy as
a new variable in the design of next generation energy systems. This could be of particular interest
for ORC-based CSP systems operating in the envisaged distributed generation scenario. 236 The second part of the thesis is focused on the experimental and numerical investigation of the
non-classical gas dynamics behavior of dense vapors of single- and multi-component organic flu-
ids. Notably, ORC power systems constitute the first foreseen application for the arguments dealt
with in this part. Chapter 7 describes the commissioning of the ''Flexible Asymmetric Shock Tube' (FAST) exper-
imental setup designed and built at the Delft University of Technology. The aim of this Ludwieg
Tube facility is to measure the speed of propagation of pressure waves in organic vapors, with the
final objective of providing the first experimental evidence of the most exotic non-classical gas dy-
namics phenomenon, i.e., the rarefaction shock wave (RSW) in the dense vapor region of fluids
formed by complex organic molecules. Furthermore, a number of interesting secondary results can
be obtained, such as, notably, speed of sound measurements. The setup components and the con-
trol & operation strategy devised are proven to be effective to the end of accurately measuring the
speed and the intensity of the propagating waves. Results for several ideal gases are presented. The
fast opening valve, which is the most critical component, is characterized in terms of its opening
time, which resulted small enough to ensure the complete formation of the phenomenon of interest,
i.e. a shock wave, within the shock tube length. This result is confirmed by analyzing a com-
pression shock propagating in air. The preliminary results regarding speed of sound measurements
performed in the dense-gas region of a molecularly complex organic compound, i.e. siloxane D6,
are also discussed. Chapter 8 Presents the first investigation about the non-classical gas dynamics of binary mixtures
of organic fluids in the vapour phase, showing how the composition of the mixture is a new relevant
variable in the study of BZT fluids. This study has practical implications in that mixtures of organic
fluids are considered for applications in ORC power systems, one of the possible applications of
non-classical gas dynamics. Furthermore, multicomponent working fluids are often encountered
in practice due to impurities, and thermal rearrangement effects. A finite thermodynamic region
is predicted where the non-linearity parameter ' is negative, and therefore non-classical gas dy-
namics phenomena are admissible. A non monotone dependence of ' on the mixture composition
is observed in the case of binary mixtures of siloxane and perfluorocarbon fluids, with the mini-
mum value of ' in the mixture being always larger than that of its more complex component. The
observed dependence indicates that non-ideal mixing has a strong influence on the gas dynamics be-
haviour '' either classical or non-classical '' of the mixture. Numerical experiments of the supersonic
expansion of a mixture flow around a sharp corner show the transition from the classical configu-
ration, exhibiting an isentropic rarefaction fan centered at the expansion corner, to non-classical
ones, including mixed expansion waves and rarefaction shock waves, if the mixture composition is
changed. 237 Samenvatting Een scherpe omkering in de huidige trend van energieconsumptie en de gerelateerde emissie van
broeikasgassen is nodig om ons leven in harmonie te brengen met de eindige bronnen van onze
planeet en om uiteindelijk te overleven. Het doel om dit te bereiken dat door velen gedeeld wordt,
is het bedenken van een systeem van duurzame energie dat slimmer, meer gedecentraliseerd en
meer geintegreerd is dan nu. Naar de mening van de auteur heeft de organische Rankine thermody-
namische cyclus het potentieel om een grote rol te spelen in het voorgenomen kader, en het hierbij
gedocumenteerde werk komt voort uit deze overtuiging. Verschillende bijdragen worden getoond om de originele resultaten te laten zien van numeriek en
experimenteel onderzoek met het doel om het potentieel te bestuderen van moleculair zware en
complexe organische stoffen als werkvloeistof voor ORC energie systemen van de toekomst. Dit
proefschrift is in twee delen gesplitst, die verder onderverdeeld zijn in aparte hoofdstukken, elk
hoofdstuk gewijd aan een specifiek sub-onderwerp. Het hierin getoonde materiaal vormt de basis
van verschillende publicaties in peer-reviewed internationale tijdschriften: vijf papers zijn reeds
gepubliceerd, ´e´en is geaccepteerd voor publicatie en twee staan op het punt om ter publicatie ver-
zonden te worden. Het eerste deel van deze thesis toont de bijdragen aan het onderzoek in veld van energie-omzettings
systemen, gericht op ORC turbogeneratoren. Een inleidende recensie van ORC systemen wordt gegeven in hoofdstuk 2, met daarin een overzicht
van hun geschiedenis, beschrijving van de state-of-the-art en het industri¨ele perspectief, en een
blik op de voorgestelde ontwikkelingspaden. De cumulatieve globale capaciteit van ORC syste-
men maakt sinds een decennium geleden een sterke groei door en er wordt verwacht dat deze
in de toekomst doorgroeit. Het potentieel van electriciteitsomzetting van thermische energie uit
hernieuwbare en gelijksoortige bronnen is enorm, en ORC energie systemen zijn een van de meest
flexibele kandidaats-omzettings technologien om dit te doen, zowel wat betreft capaciteit alsmede
de temperatuursniveaus. Een uitgebreid overzicht van de toepassingen, technische oplossingen en
van de ORC machines die in de laatste 20 jaar commercieel operationeel gemaakt zijn, wordt
getoond samen met een data-collectie die van grote fabrikanten afkomstig is. Deze bijdrage is
bedoeld als referentie voor zowel het academische als het industri¨ele publiek, en zou bijzonder nut-
tig kunnen worden om te voorkomen dat studies/pogingen/experimenten herhaald worden die reeds
zijn uitgevoerd. Hoofdstuk 3 documenteert het originele onderzoek gedaan op het gebied van ORC turbo-expanders,
die de meest kritieke componenten vormen aangaande het ontwerp van efficiente systemen. De ho-
eveelheid mogelijke werkvloeistoffen, de aangetroffen complexe gasdynamische fenomenen en het 239 Samenvatting gebrek aan simpele ontwerpmethoden gestoeld op ervaring van gelijksoortige machines, maken
het ontwerp van een efficiente turbine een moeilijke opgave. Relevante ontwikkelingspaden kun-
nen mogelijk te maken hebben met: (i) de ontwikkeling van gegeneraliseerde ontwerpmethodolo-
gin, en (ii) de toetsing van onconventionele machine-bouwstijlen: het gepresenteerde onderzoek
in dit hoofdstuk verkent beide doelen. De eerste kritische evaluatie van de opbouw van een radi-
ale uitstroom turbine (ROT) als kandidaatstechnologie voor ORC turbogeneratoren wordt getoond,
alsmede een nieuw methodologisch raamwerk voor het ontwerp van zulke machines. De resultaten
van verschillende ontwerp-opgaven laten zien dat de ROT een veelbelovend concept is, dat de ver-
wezenlijking van efficiente compacte en betrouwbare turbo-expanders op elk vermogensniveau van
belang mogelijk maakt. Hoofdstuk 4 behandelt de toetsing van nieuwe thermische energie-opslagsystemen specifiek voor
hoge temperatuur ORC systemen voor toepassingen met geconcentreerde zonne-energie, afkomstig
uit de observatie dat directe opslag van ORC werkvloeistoffen effectief kan zijn door hun gunstige
thermodynamische eigenschappen. Het concept van de complete flash cyclus wordt als een middel
voorgedragen om een onovertroffen versimpeling van systeemindeling te bewerkstelligen met be-
houd van effici¨entie. Dit is een nieuwe variant van de Rankine cyclus, waarbij damp geproduceerd
wordt door het smoren van vloeistof tot verzadigde damp. De hoofdafwegingen die zich in het
ontwerp van zo''n systeem voordoen zijn onderzocht, waaronder de globale efficintie, de opslagdi-
mensies en -druk, en de expansieverhouding over de turbine. Ook de dynamische prestatie van een
voorbeeldmachine zijn door middel van simulatie beoordeeld, met als voorlopig resultaat dat het de
haalbaarheid van op afstand geregelde bediening aantoont. Hoofdstuk 5 verschuift de nadruk op de analyse van component naar systeemniveau, waarin een
methodologie voor het optimale ontwerp van moderne energie-opwekkingssystemen voorgelegd
wordt, waarin de immer meer verlangende eisen op het gebied van operationele flexibiliteit in acht
worden genomen. Het innovatieve element is dat de mogelijkheid om de dynamische prestaties
vroeg in het ontwerpproces meegenomen kan worden. De voorgestelde proefopstelling is het
voorontwerp van een off-grid energiecentrale voor een off-shore platform, waarbij een gasturbine
met een ORC energiemodule wordt gecombineerd. De oplossingen van een stationair model van
deze centrale zijn gebruikt om de optimale configuratie te bepalen. Een dynamisch model van ieder
van deze systemen zijn aldus geparametriseerd door de waarde van haar parameters uit de resul-
taten van het ontwerpmodel te gebruiken, en de prestatie van het gemodelleerde systeem onder
interessante transiente scenarios te bepalen. Nogmaals, in het gebruikte voorbeeld is aangetoond
dat de voorgestelde gecombineerde procedure het toelaat om onderscheid te maken tussen de ini-
tiele oplossingen om zodoende de ontwerpen eruit te halen die tevens aan de dynamische eisen
voldoen. Dit gereedschap zou waardevol kunnen zijn voor het voorontwerp van een eerste systeem
met veeleisende dynamische eisen, tevens in andere gebieden dan energie-omzetting. Hoofdstuk 6 verkent de potentie van innovatieve bedieningsstrategin in de context van opslag van
thermische energie voor geconcentreerde zonne-energie centrales. De hoofdnoviteiten zijn dat een
complete financile analyse is gebruikt en de impact op het systeemontwerp is onderzocht. De
methodologie is toegepast op een testcase, een state-of-the-art centrale opvang-machine met directe
opslag, die gesmolten zout als werkvloeistof gebruikt, waarbij energie verkocht wordt afhankelijk
van de variabele electriciteitsprijs. Verschillende bedieningsstrategin zijn met elkaar vergeleken,
en een brede ontwerpruimte is verkend. De potentie van deze technieken is besproken wat betreft
de beperking van investeringskosten, waarbij aangetoond is hoe een gelijk jaarlijks inkomen ge- 240 realiseerd kan worden met een kleinere energieopslag, als deze optimaal bediend wordt. Deze
nieuwe methode is een toegevoegd beslissingsgereedschap dat de opslagbedieningsstrategie als
nieuwe variabele in het ontwerp van volgende generatie energiesystemen behandeld kan worden.
Die zou specifiek nuttig kunnen zijn voor CSP systemen op basis van een ORC die in de voorziene
opwekkingsscenarios werken van gedistribueerde energie-opwekking. Het tweede deel van deze thesis concentreert zich op het experimentele en numerieke onderzoek van
het niet-klassische gasdynamisch gedrag van dichte dampen van organische vloeistoffen bestaande
uit een enkelvoudig component of meervoudige componenten. Opvallend is dat ORC energiesyste-
men de eerste voerziene toepassingen zijn voor de argumenten die in dit deel behandeld worden. Hoofdstuk 7 beschrijft de ingebruikname van de experimentele opstelling ''Flexibele Asymmetrische
Schokbuis' (FAST), die aan de Technische Universiteit Delft ontworpen en gebouwd is. Het doel
van deze Ludwieg Tube faciliteit is het meten van de propagatiesnelheid van drukgolven in or-
ganische dampen, met het uiteindelijke doel om het eerste bewijs te leveren van een van de meest
exotische fenomenen uit de niet-klassische gasdynamica, namelijk de expansie schokgolf (RSW)
in de dichte-damp regio van vloeistoffen van complexe organische moleculen. Verder kunnen een
aantal interessante secundaire resultaten behaald worden, voornamelijk geluidssnelheidsmetingen.
De opstellingscomponenten en de bedachte regel & werkingstrategie zijn effectief gebleken om
nauwkeuring de snelheid en intensiteit van de propagerende golven te meten. Resultaten van enkele
ideale gassen zijn weergegeven. De snel-openende klep, wat het meest kritische component is, is
gekarakteriseerd voor zijn openingstijd, met als resultaat dat deze kort genoeg is om complete for-
matie van het interessante fenomeen, namelijk een schokgolf, binnen de lengte van de schokbuis te
realiseren. Dit resultaat wordt bevestigd door een compressie schok te analyseren die door de buis
gevuld met lucht reist. De voorlopige resultaten aangaande de geluidssnelheid in de dichte damp
regio van een moleculair complexe organische stof, namelijk siloxaan D6, worden ook behandeld. Hoofdstuk 8 geeft het eerste onderzoek weer naar niet-klassische gasdynamica van binaire mengsels
van organische vloeistoffen in de dampfase, waarin wordt aangetoond hoe de samenstelling van het
mengsel een nieuwe relevante variabele is in de studie van BZT vloeistoffen. Dit onderzoek heeft
het praktisch oogpunt dat mengsels van organische vloeistoffen worden overwogen als toepassing in
ORC energiesystemen, een van de mogelijke toepassingen van niet-klassische gasdynamica. Daar-
naast is er regelmatig sprake van een werkvloeistof bestaande uit meerdere componenten vanwege
onzuiverheden en thermische her-rangschik-
kings-effecten. Een eindige thermodynamische regio wordt voorspeld waarin de niet-lineariteitsparameter
negatief is, waarin daarom niet-klassische gasdynamica fenomenen toelaatbaar zijn. Een niet-
monotone afhankelijkheid van op de mengselsamenstelling is waargenomen in het geval van bi-
naire mengsels van siloxanen en perfluorocarbon vloeistoffen, waarbij de minimumwaarde van in
het mengsel altijd groter is dan die van de meer complexe component. De geobserveerde afhanke-
lijkheid laat zien dat het niet ideaal mengen een grote invloed heeft op het gasdynamisch gedrag ''
zowel klassisch als niet-klassisch '' van het mengsel. Numerieke experimenten in de supersone
expansie langs een scherpe hoek laten de transitie zien van de klassische configuratie met een
isentrope expansie waaier gecentreerd op de hoek, naar niet-klassische configuraties met gemenge
waarier-schok expansiegolven en pure expansie-schokgolven zodra de mengselsamenstelling ve-
randerd wordt. 241 Acknowledgement I b el ie v e d u ri n g th es e ye ar s I h av e l ea rne d q uite a lot. This work is als o the resu lt o f th e su pp or t I re ce iv ed fr o m m an y p er so n s. I w ou ld lik e to tha nk my sup erv iso ri nM ila n, Pro f. Do sse na, wh o he lp ed m e du ri ng th e fi rs t st ep s o f m y re se ar ch ac ti vi ty . A sp ec ia l m en tio n to my su pervisor here at T U D elft, Pro f. C olo nn a, fro m w h o m I le ar n ed a lo t, sp ec ia lly w ha tb ein g an Aca dem ic mea ns th ese day s. Ih op ew ew ill be ab le to ke ep o n w o rk in g to g et h er lo n g in th e fu tu re . I am al so gr ate ful to P rof. Ca sella and Prof. Gua rdo ne, no tab le pa rts o f th is th es is w o u ld h av e n o t b ee n po ss ib le w ith out you rh elp .I ho pe Iw ill be off ere da ga in th e op po rt un it y to le ar n fr o m y o u . I al so re m em be r w ith af fe cti on the invalu able participati on o f m y nu m ero us of fic e- m at es an d fr ie n d s, fir st at P oli te cn ico and the na tT UD elf t( yo uk no ww ho yo ua re !) .I w ou ld li k e to es p ec ia ll y th an k A li ce , m y cl os e f rie nd s (a nd th eir children !), a nd my fam ily fo r th ei r co n tin u o u s su p p o rt d u rin g th is pe rio do fse par ati on .I do ub tI wo uld ev er m ad e it w it h o u t fe el in g y o u r p re se nc e. Fi na lly , I wo uld like to express m y gr atit ud e to th e ex am in at io n co m m itt ee .I ap pre ciat eth eir in ter est in my wo rk an d th ei r ti m e d ev o te d to ev al ua te th is dis ser tatio n. Emiliano Casati Firenze, June 22, 2014 About the Author Emiliano I.M. Casati was born in Milan, Italy,
on June the 21st '' 1982. After a more than rea- sonably happy childhood, long story short, he
received his high-school diploma from Liceo
Scientifico Statale G. Galilei - Erba, in Italy.
He then enrolled for a BSc in Energy Engineer-
ing at Politecnico di Milano University. Before
realizing the BSc was done, he found himself
involved in the MSc program ''Energy Conver-
sion' within the same faculty, which finished
at the end of 2008 defending the thesis ''Devel-
opment of aerodynamic probes for pneumatic
measurements in turbines operated with dense
vapors'. The work lasted 18 months as part of a research project involving the company Turboden
(presently part of Mitsubishi Heavy Industries); approximately half of the time was spent working
at Turboden R&D. He then realized he really enjoyed studying, and thus started working as a post-
graduate researcher at Politecnico di Milano for one year, under the supervision of Prof. Dossena.
During the hot summer of 2009 he met Prof. Colonna and decided to go for a PhD program under
the joint-supervision between TU Delft and Politecnico di Milano. The work started in 2010 and,
after four years and few months, here he comes again, but with this nice and well crafted book in
addition! List of publications Journal articles M. Pini, G. Persico, E. Casati, & V. Dossena (2013). Preliminary Design of a Centrifugal Turbine
for Organic Rankine Cycle Applications'. Journal of Engineering for Gas Turbines and Power-
Transactions of the ASME, vol. 135, pp 04231219. E. Casati, A. Galli, & P. Colonna (2013). Thermal Energy Storage for Solar Powered Organic Rank-
ine Cycle Engines'. Solar Energy, vol. 96, pp 205 - 219. A. Guardone, P. Colonna, E. Casati, & E. Rinaldi (2014). Non-Classical Gasdynamics of Vapour
Mixtures'. Journal of Fluid Mechanics, vol. 741, pp 681-701. L. Pierobon, E. Casati, F. Casella, F. Haglind, & P. Colonna (2014). Preliminary Design Method-
ology for Flexible Power Systems Accounting for Dynamic Performance'. Energy, vol. 68, pp
667-679. E. Casati, S. Vitale, M. Pini, G. Persico, & P. Colonna (2014). Centrifugal Turbines for Mini-ORC
Power Systems'. Journal of Engineering for Gas Turbines and Power-Transactions of the ASME,
in print. E. Casati, F. Casella, & P. Colonna (2014). Design of CSP Plants with Optimally Operated Thermal
Storage'. Submitted for publication. T. Mathijssen, E. Casati, M. Gallo, & P. Colonna (2014). Flexible Asymmetric Shock Tube (FAST):
Commissioning of an High Temperature Ludwieg Tube for Rarefaction Shock Wave Measure-
ments'. To be submitted for publication. P. Colonna, E. Casati, J. Larjola, A. Uusitalo, T. Turunen-Saaresti, C. Trapp, & T. Mathijssen
(2014). Organic Rankine Cycle Power Systems: the Path from the Concept to Current Applica-
tions and an Outlook to the Future. To be submitted for publication. T. van der Stelt, E. Casati, N. Chan, & P. Colonna (2014). Development of Technical Equations
of State for Mixtures of Diphenyl-Diphenyl Ether Used as Heat Transfer Fluids'. Submitted for
publication. Conference proceedings E. Casati, P. Colonna, & N. R. Nannan (2011). Supercritical ORC turbogenerators coupled with
linear solar collectors'. In Proceedings of the 30th ISES Biennial Solar World Congress 2011, Kas-
sel - DE. Vol. 5, pp. 40564067. E. Casati, A. Desideri, F. Casella, & P. Colonna (2012). Preliminary assessment of a novel small 247 248 CSP plant based on linear collectors, ORC and direct thermal storage'. In Proceedings of the 18th
SolarPACES conference, Marrakech - MA. E. Casati, E. Rinaldi, A. Guardone, & P. Colonna (2012). Nonclassical gasdynamics of vapor mix-
tures'. In Proceedings of the 6th European Congress on Computational Methods in Applied Sciences
and Engineering '' ECCOMAS 2012. J. Eberhardsteiner, H. J. B¨ohm, & F. G. Rammerstorfer (Eds.)
'' pp. 111. Vienna University of Technology, Vienna - AT. F. Casella, E. Casati, & P. Colonna (2014). Optimal Operation of Solar Tower Plants with Thermal
Storage for System Design'. To be presented at the 19th World Congress of the International Fed-
eration of Automatic Control '' IFAC 2014, Cape Town''ZA. Conference presentations T. Mathijssen, M. Gallo, E. Casati, & P. Colonna (2012). Flow measurements in a Ludwieg tube
type setup for the experimental investigation of rarefaction shock waves: status report'. In Proceed-
ings of the 6th European Congress on Computational Methods in Applied Sciences and Engineering
'' ECCOMAS 2012. J. Eberhardsteiner, H. J. B¨ohm, & F. G. Rammerstorfer (Eds.) '' pp. 12. Vienna
University of Technology, Vienna - AT. P. Colonna, M. Gallo, E. Casati, & T. Mathijssen (2013). Flexible asymmetric shock tube (FAST)
set-up '' Status and first experiences'. Presented at the 2nd International Seminar on ORC Power
Systems '' ASME ORC-2013, Rotterdam - NL. E. Casati, S. Vitale, M. Pini, G. Persico, & P. Colonna (2014). Centrifugal turbines for mini-ORC
power systems'. Presented at the 2nd International Seminar on ORC Power Systems '' ASME ORC-
2013, Rotterdam - NL.

Document Outline

cover PhD_thesis_EC Introduction 1 Introduction 1.1 Energy Scenario 1.2 Thesis Outline I Innovative Concepts 2 ORC Power Systems: from the Concept to Current Applications and an Outlook to the Future Abstract 2.1 Introduction 2.2 Evolution 2.3 State of the art 2.3.1 Technical options 2.3.2 Energy conversion applications 2.4 Future scenarios 2.4.1 Heat Recovery from Automotive Engines 2.4.2 Domestic CHP 2.4.3 Ocean Thermal Energy Conversion - OTEC 2.4.4 Concentrated Solar Power - CSP 2.4.5 Other applications 2.5 Conclusions Nomenclature 3 Centrifugal Turbines for ORC Applications Abstract 3.1 Introduction 3.2 Preliminary Design Method 3.2.1 Mean-line Design Tool for ORC Turbines 3.2.2 Optimization Procedure 3.3 Centrifugal Architecture for ORC applications 3.4 Analysis of the Centrifugal Architecture 3.5 Design of Exemplary 1 MWe Machines 3.5.1 Design Assumptions 3.5.2 Design Methodology 3.5.3 Results: Transonic Turbine 3.5.4 Results: Slightly Supersonic Turbine 3.6 Design of Exemplary 10 kWe Machines 3.6.1 Design Assumptions 3.6.2 Design Methodology 3.6.3 Results: Transonic Turbine 3.6.4 Results: Slightly Supersonic Turbine 3.7 Conclusions Nomenclature 4 Thermal Energy Storage for Solar Powered ORC Engines Abstract 4.1 Introduction 4.2 Siloxanes: High-Temperature ORC Working Fluids 4.3 Concepts of TES Systems for Power Plants 4.4 Direct Storage of Working Fluid in Rankine Power Stations 4.4.1 Storage Methods 4.4.2 Discharge Methods 4.4.3 Storage Systems 4.5 Case Study 4.5.1 Working Principle 4.5.2 Flashing Rankine Cycles with Organic Fluids 4.5.3 Flashing the Organic Vapor Down to Saturated Conditions 4.5.4 Design Analysis Results 4.5.5 Dynamic Modelling 4.5.6 Control Strategy 4.5.7 Dynamic Analysis Results 4.6 Conclusions A.1 Comparison Between Flashing and Evaporative Organic Rankine Cycles A.2 Complete Flash Evaporation as a Working Condition for ORC Power Systems A.3 System Components Dynamic Modelling Nomenclature 5 Design Methodology for Flexible Energy Conversion Systems Accounting for Dynamic Performance Abstract 5.1 Introduction 5.2 Methodology 5.2.1 Multi-Objective Design Optimization 5.2.2 Assessment of Dynamic Performance 5.3 Case of Study 5.4 System Modeling 5.4.1 Preliminary ORC Power Plant Design 5.4.2 Dynamic Modeling 5.4.3 Validation 5.4.4 The DYNDES Tool 5.5 Results and Discussion 5.5.1 Multi-objective Design Optimization 5.5.2 Assessment of Dynamic Performance 5.6 Conclusions Nomenclature 6 Design of CSP Plants with Optimally Operated Thermal Storage Abstract 6.1 Introduction 6.2 Modeling Framework 6.3 Operation Strategy 6.3.1 Reference Operation Strategy 6.3.2 Optimal Control 6.4 Computational Infrastructure 6.5 Results & Discussion 6.6 Conclusions 6.7 Acknowledgements A.1 Solar Fields Design A.2 Financial Analysis A.3 Modelica and Optimica listings Nomenclature II Fundamental Aspects 7 Flexible Asymmetric Shock Tube (FAST): Commissioning of a High Temperature Ludwieg Tube for Wave Propagation Measurements Abstract 7.1 Introduction 7.2 Fundamentals 7.3 The FAST Set-Up 7.3.1 Working Principle 7.3.2 Vapour Generator 7.3.3 Reference Tube 7.3.4 Charge Tube 7.3.5 Fast Opening Valve 7.3.6 Low Pressure Plenum 7.3.7 Condenser and flow return pipe 7.4 Data Acquisition and Control system 7.4.1 Vapour generator control 7.4.2 Reference Tube control 7.4.3 Charge Tube control 7.4.4 Low Pressure Plenum control 7.4.5 Data Acquisition 7.5 Validation 7.5.1 Tightness characterization 7.5.2 Valve Opening Sequence 7.5.3 Wave Speed Measurements 7.6 Conclusions & Future Work Nomenclature 8 Nonclassical Gasdynamics of Vapour Mixtures Abstract 8.1 Introduction 8.2 Admissibility Region for Rarefaction Shock Waves in Dense gas Mixtures 8.3 Nonclassical Gasdynamics Behaviour of Dense Gas Mixtures 8.4 Conclusions A.1 iPRSV-WS Thermodynamic Model Conclusions 9 Conclusions & Perspectives Summary Samenvatting Acknowledgements About the Author List of publications


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