hybrid solar thermal power plants · hybrid solar thermal power plants jorge augusto maciel...

Hybrid Solar Thermal Power Plants

Jorge Augusto Maciel Milhomem Rodrigues

Thesis to obtain the Master of Science Degree in

Mechanical Engineering

Supervisors: Prof. Aires José Pinto dos SantosProf. Viriato Sérgio de Almeida Semião

Examination Committee

Chairperson: Prof. Edgar Caetano FernandesSupervisor: Prof. Aires José Pinto dos Santos

Member of the Committee: Prof. Mário Manuel Gonçalves da Costa

June 2019

To my family.

iii

Acknowledgments

I want to express my very great appreciation to my supervisors, Professor Aires Santos and Professor

Viriato Semiao, for their support throughout the whole process of developing this work. This thesis would

not have been the same without their consistent openness to help and interest in the work. I feel very

fortunate to have had them as my supervisors.

I would also like to thank my friends Francisco Vieira, Joao Ferreira, Joao Formiga, Luıs Fialho, Nuno

Miguel Guerreiro, Pedro Santana, and Shu Kaiyue for their friendship. I cannot let unmentioned that I

am deeply grateful to Francisco for all the academic support through the years in IST, always having my

back in the different academic challenges that we went through.

To my parents and to my brothers, of course, nothing of this would be possible without you. Thank

you for everything.

v

Resumo

A energia solar termica, especialmente quando obtida atraves da implementacao das tecnologias de con-

centracao de energia solar (CSP), representa uma forma de energia renovavel cada vez mais atrativa.

Um dos fatores determinantes no desenvolvimento destas tecnologias e a sua integracao com ciclos de

potencia de forma eficiente. De modo a que as tecnologias CSP se tornem mais populares e competitivas

no mercado de producao de energia eletrica, e importante desenvolver modelos capazes de apresentar

elevadas eficiencias.

O presente trabalho foca-se na analise termodinamica de tres ciclos combinados com regeneracao

no ciclo a gas aqui propostos, nos quais caracterısticas distintivas como a presenca de uma camara de

combustao em serie juntamente com um concentrador solar (CSP) e divisao de caudais apos a turbina

a gas sao estudadas. O calor e fornecido por concentracao de energia solar nos tres modelos, sendo que

em dois deles, uma camara de combustao serve de suporte para o efeito. As analises termodinamicas

sao efetuadas para diferentes fluidos, nomeadamente, CO2, ar, N2, He e H2 para o ciclo de Brayton, e

R-245fa, R-141b, Cyclohexane, n-Pentane e agua para o ciclo de Rankine, resultando num total de 25

combinacoes. As simulacoes sao executadas por um programa desenvolvido em MATLAB.

Os resultados obtidos mostram que a adicao de uma valvula divisora de caudais como unica variavel

entre dois modelos contribui para um melhor aproveitamento da entalpia do fluido apos a sua saıda da

turbina a gas, resultando, em ultima instancia, em eficiencias globais superiores.

Palavras-chave: Concentracao de energia solar, termodinamica, hibridizacao de ciclos de

potencia.

vii

Abstract

Solar thermal energy, especially concentrated solar power (CSP), represents an increasingly attractive

renewable energy source. One of the key factors that determines the development of this technology is its

integration with efficient power cycles. Thus, as to make CSP an attractive alternative to the conventional

thermodynamic cycles present in most of today’s thermal power plants, it is of high relevance to develop

models that provide attractive global efficiencies and cost effective CO2 mitigation.

The present work focuses on the energetic study of three combined Brayton-Rankine cycles hereby

proposed, in which features as having a combustion chamber in series with a solar receiver, and a stream

splitter subsequent to the gas turbine were studied and compared. Heat is provided by concentrated

solar power, having two of the three models to be hybridised with solar and combustion energy. The

thermodynamic analyses are performed for selected working fluids including CO2, air, N2, He and H2 for

the topping cycles, and R-245fa, R-141B, Cyclohexane, n-Pentane, and Water for the bottoming cycle,

resulting in 25 fluid combinations. A MATLAB program was developed to perform the simulations.

The results show that the CO2 and R-245fa fluid pair provides the highest cycle efficiency curves. In

addition, stream splitting proves to be advantageous, compared to other layouts found in literature.

Keywords: Concentrated solar power, thermodynamics, hybrid power cycles.

ix

Contents

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

Resumo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix

List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv

Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii

Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix

1 Introduction 1

1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 State of the Art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2.1 CSP Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2.2 CSP Technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2.3 Solar Thermal Power Plants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.3 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.4 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2 Background 9

2.1 Theoretical Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2 Previous Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.3 Thermodynamic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3 Mathematical Modelling 19

3.1 Model 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.2 Model 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.3 Model 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4 Computational Modelling 31

4.1 Restrictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.1.1 Thermodynamic Properties Restrictions . . . . . . . . . . . . . . . . . . . . . . . . 31

4.1.2 Model Restrictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.2 Numerical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

xi

5 Results and Discussion 37

5.1 Comparison with Reference Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

5.2 MATLAB Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5.2.1 Model 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5.2.2 Model 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

5.2.3 Model 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

6 Conclusions and Future Work 57

6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

6.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

Bibliography 59

xii

List of Tables

2.1 Table caption shown in TOC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2 Brayton cycle peak efficiencies and correspondent values of pressure ratio, volume flow,

temperature at the different states and power generated. Values from [17]. . . . . . . . . . 15

2.3 Combined cycle peak global efficiency values. Values from [17]. . . . . . . . . . . . . . . . 16

2.4 Assumed pressure values in the Rankine cycle. . . . . . . . . . . . . . . . . . . . . . . . . 18

4.1 Minimum temperatures for the Brayton cycle fluids. . . . . . . . . . . . . . . . . . . . . . 32

5.1 Peak global efficiency values obtained from the simulation of the article’s combined cycle. 38

5.2 Peak global efficiency values for each fluid combination with T5 = 825, 850, 875, and 900 K. 40

5.3 Peak power outputs [kW] for each fluid combination with T5 = 825, 850, 875, and 900 K. 40

5.4 Model 2: maximum global efficiency values for T13 = 400 K. . . . . . . . . . . . . . . . . . 48

5.5 Model 2: maximum global efficiency values for T13 = 427 K. . . . . . . . . . . . . . . . . . 49

5.6 Model 1 (with the regenerator effectiveness calculated from the NTU relations): peak

global efficiency values for each fluid combination. . . . . . . . . . . . . . . . . . . . . . . 56

5.7 Model 3: peak global efficiency values for each fluid combination. . . . . . . . . . . . . . . 56

xiii

List of Figures

1.1 CSP projects around the world [4] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 A Parabolic Trough Collector [7]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Schematic representation of a basic LFR system. Each individual reflector tracks the sun

by turning about a horizontal axis normal to the page [9]. . . . . . . . . . . . . . . . . . . 3

1.4 An example of a SPT system in USA [11]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.5 Illustration of a single PDC system. The bowl shaped concentrator reflects the sun rays

onto the power conversion unit placed centred in the axis [13]. . . . . . . . . . . . . . . . . 5

1.6 Basic options to hybridise a Brayton cycle - having the solar energy source placed before

the compressor (Qsol,LP ) or after (Qsol,HP ) [15]. . . . . . . . . . . . . . . . . . . . . . . . 6

1.7 Hybridisation schemes for a gas turbine [14]. . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.1 Schematic representation of the control volume used to develop Eq. (2.1) [18]. . . . . . . . 9

2.2 Schematic representation of the turbine control volume. Adapted from [18]. . . . . . . . . 10

2.3 Counterflow heat exchanger schematic illustration. Adapted from [18]. . . . . . . . . . . . 11

2.4 Brayton cycle scheme [17]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.5 Combined Brayton-Rankine cycle scheme [17] . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.6 Efficiency of a receiver-Carnot heat engine system as a function of receiver temperature

for C = 50, 70, and 100 [17]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.7 Brayton cycle efficiency versus cycle pressure ratio [17] . . . . . . . . . . . . . . . . . . . . 15

2.8 Top cycle efficiency for each configuration of fluids in the combined cycle [17]. . . . . . . . 15

2.9 Top cycle power for each configuration of fluids in the combined cycle [17]. . . . . . . . . . 16

3.1 Schematic presentation of Model 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.2 Diagram representation of the pinch point at the HRSG. . . . . . . . . . . . . . . . . . . . 23



4.1 Phase diagram of CO2 [23]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.2 Flowchart representation of the main employed algorithm. . . . . . . . . . . . . . . . . . . 35

5.1 Brayton cycle results comparison between the results from MATLAB in the present work

and those obtained in the work of Dunham and Lipinski [17]. . . . . . . . . . . . . . . . . 37

xv

5.2 Model 1: cycle global efficiency versus pressure ratio with T5 = 1173 K. . . . . . . . . . . 39

5.3 Model 1: influence of temperature T5 on the global efficiency for each fluid in the Rankine

cycle and CO2 in the Brayton cycle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5.4 Model 1: highest cycle efficiency values for each fluid combination at temperatures T5

equal to 825 K, 850 K, 875 K, and 900 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.5 Model 1: highest cycle power output values for each fluid combination at temperatures T5

equal to 825 K, 850 K, 875 K, and 900 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

5.6 Model 2: global cycle efficiency versus pressure ratio with r = 0.5 and a heat transfer area

of the regenerator equal to 6 m2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

5.7 Model 2: influence of the gas temperatures restrictions on the possible results using CO2

in the Brayton cycle for all Rankine fluids. . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

5.8 Model 2: global efficiency curves for temperature T13 = 400 K and T13 = 427 K at the

inlet of the steam turbine, using CO2 in the Brayton cycle. . . . . . . . . . . . . . . . . . 47

5.9 Model 2: global maximum efficiency values for temperatures T13 = 400 K and T13 = 427

K at the inlet of the steam turbine. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

5.10 Model 2: net power at maximum global efficiency points for temperatures T13 = 400 K

and T13 = 427 K at the inlet of the steam turbine. . . . . . . . . . . . . . . . . . . . . . . 48

5.11 Model 2: global efficiency curves for different values of pinch point temperature difference

with T13 = 400 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

5.12 Model 2: regenerator heat transfer area influence on global cycle efficiency, for the fluid

pair Air and R-245fa, assuming T13 = 400 K, ∆Tpinch point = 10 K and a mass flow ratio

r = m8/m1 = 0.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

5.13 Model 2: mass flow ratio r = m8/m1 influence on global cycle efficiency, for the fluid pair

Air and R-245fa, assuming a regenerator heat transfer area equal to 6 m2, T13=400 K and

∆pinch point = 10 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

5.14 Model 3: global cycle efficiency assuming T5 = 1173 K, a regenerator heat transfer area

equal to 6 m2 and a mass flow ratio r = 0.5. . . . . . . . . . . . . . . . . . . . . . . . . . . 53

5.15 Model 1: global cycle efficiency assuming T5 = 825 K and a regenerator heat transfer area

equal to 6 m2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

5.16 Model 3: global cycle efficiency assuming T5 = 825 K, a regenerator heat transfer area

equal to 6 m2 and a mass flow ratio r = 0.5. . . . . . . . . . . . . . . . . . . . . . . . . . . 55

5.17 Brayton cycle’s regenerator effectiveness values for models 1, 2, and 3, assuming a heat

transfer area of 6 m2 and, for models 2 and 3, a mass flow ratio r = 0.5. . . . . . . . . . . 56

xvi

Nomenclature

Greek symbols

α Radiative absorptivity.

ε Radiative emissivity, effectiveness.

η Efficiency.

ρ Fluid density.

σ Stefan–Boltzmann constant.

ref Reference condition.

Roman symbols

A Surface of a control volume, heat transfer area.

C Solar concentration ratio, heat capacity.

cp Specific heat at constant pressure.

g Gravitational acceleration.

G0 Standard solar irradiation.

h Specific enthalpy.

m Mass flow.

Ma Mach number.

p Pressure.

pR Compressor pressure ratio.

pr Relative pressure.

Q Energy transfer by heat across the boundary of a given control volume.

R Specific gas constant.

s0 Specific entropy.

xvii

T Temperature.

U Heat transfer coefficien.

u Specific internal energy.

V Volume of a control volume, and, when vectorized, velocity of the fluid.

v Control volume velocity, specific volume

W Energy transfer by work across the boundary of a given control volume.

z Vertical coordinate of a given control volume.

Subscripts

b Bottoming cycle.

b, cycle Bottoming cycle.

b, pinch Pinch point at the bottoming cycle side of the heat recovery steam generator.

c Cold side of a heat exchanger..

c Combustion chamber.

e Out direction.

h Hot side of a heat exchanger.

i In direction.

p Pump.

r Ratio.

reg Regenerator.

sol Solar receiver.

t Turbine, topping cycle when appearing in mt.

t, cycle Topping cycle.

t, pinch Pinch point at the topping cycle side of the heat recovery steam generator.

Superscripts

˙ Time derivative.

→ Vector.

xviii

Glossary

CSP Concentrated Solar Power.

HRSG Heat Recovery Steam Generator.

xix

Chapter 1

Introduction

1.1 Motivation

Climate change and global warming are major concerns in the present days. The increasing world

population, accompanied by the growth of energy demand makes the development of sustainable and

clean energy technologies of primary importance in order to reduce emissions of carbon dioxide and other

greenhouse gases. Furthermore, fossil fuels are not unlimited and not easily accessible for most countries,

making them to depend on foreign supplies.

The world still relies heavily on fossil fuels in the present days to meet its growing energy needs,

resulting in the continuous increase of carbon emissions. According to U.S. Energy Information Admin-

istration (EIA) [1], world energy consumption through 2040 will increase, on average, for all fuels other

than coal.

One energy source that is vastly abundant in the nature is the sun, namely, the solar radiation that

arrives to the earth surface. For instance, if 1% of the global deserts area were used to harness solar

energy, that would be sufficient to produce the entire annual primary energy consumption of humankind as

electric power, already taking into consideration the conversion factor to useful energy form of electricity

[2]. Of all the electricity generating systems, power plants are the predominant ones, by means of fluid

expansion in a steam turbine, in most of the cases.

The majority of world-wide heating sources for the purpose of generating electricity is still based on

fossil fuels.

1.2 State of the Art

The global demand for electrical energy is increasing with no signs of slowing down. Alongside with

the electricity consumption, comes the growing amount of pollutant gas emissions, resulting mostly from

the use of fossil resources in combustion processes of the actual working power plants. Thus, there is a

significant incentive to use renewable energy sources to produce electricity. Solar energy is being seen

more and more as a promising energy source to achieve better results in both the environmental and

1

financial aspects. A promising technology is concentrated solar power (CSP), which often offers the most

reliable and dispatchable power generation from sun irradiation [3].

1.2.1 CSP Concept

Concentrated solar power (also known as concentrating solar thermal energy, CST) technologies make use

of the entire solar irradiation spectrum by using mirrors or lenses to concentrate the sun’s rays, providing

a source of heat to generate electricity. Thus, CSP technologies are an alternative to fossil fuels or nuclear

reactions regarding energy production.

1.2.2 CSP Technologies

CSP technology is already implemented in different parts of the world, as shown in Fig. 1.1. Spain is the

world leader in regards to CSP, accounting for more than 2300 MW of power capacity. As also shown

in the map, almost half of the worldwide capacity correspond to under construction or in development

CSP projects. Such demonstrates that the technology is fresh and still increasing in development and

implementation, making it relevant.

Figure 1.1 CSP projects around the world [4]

There is currently a great variety of CSP technologies, but the four most developed and promising

ones [5], are overviewed in the following paragraphs.

Parabolic Trough Collectors

A Parabolic Trough Collector, PTC, is a single-axis linear-focus solar collector, composed of a parabolic-

trough-shaped concentrator that reflects the direct solar radiation onto a receiver or absorber tube located

in the focal line of the parabola. Fig. 1.2 shows an example of a PTC system.

The PTC technology is the most common and mature one among the others. According to Wang et

al. [6], 90% of the actual CSP plants use it. Parabolic troughs can deliver useful thermal energy up

to 400◦ C. However, research on new working fluids promise higher temperatures close to 500◦ C in the

2

midterm [7].

Steel structure

Parabolic trough refector

Absorber tube

l

Figure 1.2 A Parabolic Trough Collector [7].

Linear Fresnel Reflectors

A single-axis Linear Fresnel Reflector system, LFR, is composed of long row reflectors that together

reflect direct solar radiation to an elevated linear tower receiver running parallel to the reflector rotational

tracking axis. A schematic representation of this system can be seen in Fig. 1.3.

The LFR technology is less commercially mature than PTC. However, Linear Fresnel Reflector solar

systems have been considered as a cost effective choice for solar thermal power generations due the their

simple structure when compared to the troughs. On the other hand, LFR systems provide lower thermal

performances per aperture area compared to that of the PTC systems, creating a need in the market to

improve the optical efficiency of the LFR systems [8].

Figure 1.3 Schematic representation of a basic LFR system. Each individual reflector tracks the sun byturning about a horizontal axis normal to the page [9].

Solar Power Towers

Also know as Central Towers (CT), Solar Power Tower systems consist of three main components: he-

liostat field, solar collector, and power-block island. Direct solar radiation is reflected and concentrated

3

by a heliostat field - individual mirror assembly with a two axis solar tracking system - onto a receiver

placed at the top of a tower, as it can be visualized in Fig. 1.4. The direct solar radiation is concentrated

in the receiver reaching a high irradiation flux, which is then converted to thermal energy, heating the

working fluid [10].

Figure 1.4 An example of a SPT system in USA [11].

Parabolic Dish Collectors

The Parabolic Dish Concentrator, PDC, system consists of a base support, a concave dish frame, a re-

flecting sheet, a conversion unit, and a sun-tracking system, as illustrated in Fig. 1.5. The tracking

system is allowed to rotate around the horizontal and vertical axis, having the optical axis of the con-

centrator always pointing towards the sun. The direct solar radiation is then reflected and focused onto

the solar receiver. The receiver captures the high temperature thermal energy into a fluid that is either

the working fluid for a receiver-mounted engine cycle, or is used to transport the energy to ground-based

processes. In the case of a receiver-mounted engine (Stirling engine is often used), a directly coupled

generator converts mechanical energy into electricity.

PDC systems are the less implemented in the group of four technologies. According to Pelay et al.

[12], as of 2017, there were no plants in activity using the PDC technology. Nonetheless, it represented

7–9% of plants under construction and planned, making it a non-negligible technology in the future.

Furthermore, the highest conversion efficiency (>30%) among the actual CSP technologies is reached

with a parabolic dish-type point receiver using a Stirling engine [6]. PDC systems have high optical

efficiencies and low start-up losses leading to highly efficient solar energy engines. This gives parabolic

dishes potential to eventually become one of the least expensive forms of renewable energy.

4

Figure 1.5 Illustration of a single PDC system. The bowl shaped concentrator reflects the sun rays ontothe power conversion unit placed centred in the axis [13].

1.2.3 Solar Thermal Power Plants

In order to generate electricity, the concentrated irradiation is converted to heat, driving a heat engine

(in most cases, a steam turbine [14]) connected to a power cycle.

It is expected that this predominance of CSP implemented with steam turbines continue due to its

relatively low costs and high reliability [15]. However, steam power cycles have a major drawback that

is the large amount of water consumption, given, especially, by the need of having cooling water in the

condenser [14]. Since the most promising locations for solar power are located in arid or desert locations

[16], reducing water consumptions is an important aspect in future projects. Gas turbine power cycles

allow for higher working temperatures, resulting in higher global efficiencies. Water consumption is also

considerably lower [14].

Two configurations for the integration of a combustion chamber and a solar heater in a Brayton cycle

are presented by Nathan et al. [15] (Fig. 1.6). The authors of the mentioned work state that having

the solar heater placed before the compressor increases the required work for compression, decreasing

the global efficiency of the cycle. Spelling, in his PhD Thesis ([14]), presents two configurations for the

heat components - parallel and serial positioning - as shown in Fig. 1.7. As stated by the author, the

parallel scheme is a poor choice thermodynamically, since the inlet temperature to the turbine is below

the maximum value achievable in the combustion chamber. Also, the greater the degree of utilization

of solar energy in the parallel scheme, the lower the temperature entering the turbine. This makes the

serial hybridisation a better choice as it can provide a final inlet temperature to the turbine that is equal

to the combustor outlet temperature. Furthermore, the final temperature delivered to the turbine in the

serial scheme is independent of the degree of solar integration.

5

Figure 1.6 Basic options to hybridise a Brayton cycle - having the solar energy source placed before thecompressor (Qsol,LP ) or after (Qsol,HP ) [15].

(a) Parallel configuration

(b) In series configuration

Figure 1.7 Hybridisation schemes for a gas turbine [14].

Dunham and Lipinski [17] made a thermodynamic energy analysis of the global theoretical efficiencies

and power generation of a Brayton and combined Brayton-Rankine cycles with solar energy as the heat

input, considering a gas microturbine. The analysis was performed for multiple selected working fluids.

With a nominal solar heat input of 150 kW and a 50 kWe gas microturbine, the single Brayton cycle

reached a global efficiency of 15.31% and the combined cycle provided a 21.06% global efficiency.

Among the different literature investigated to pursue a study in CSP power plants, this was the

work that offered the most complete data information to further the authors’ study, and, ultimately, to

contribute to the scientific knowledge on this topic. In addition, the models proposed by the authors do

not contain features that present potential performance improvements and relevance to be studied, such

6

as a stream bifurcation or a combustion chamber. These will be present in the thermodynamic models

proposed in this thesis.

Since this work was the starting point of the present thesis, it will be addressed with more detail in

section 2.2.

1.3 Objectives

The present work consists in proposing three different models of solar heated power cycles, having Dunham

and Lipinski’s work [17] as a starting point. Those are three combined Brayton-Rankine cycles with

regeneration in the Brayton cycle. The first model contains a combustion chamber subsequent to the solar

receiver. The second contains the solar receiver as the only source of heat energy and a stream bifurcation

after the gas turbine to preserve the fluid enthalpy before it enters the Brayton cycle regenerator. The

last model presents both the distinctive feature of the formers - combustor chamber and a stream splitter.

The main objectives of the present work are to:

• Model thermodynamically the three cycles, studying and comparing in detail their performances;

• Study the influence that the selected working fluids have on the cycle performances and their

behaviour in the different configurations and conditions;

• Improve the global performance of the new designed cycles when compared to those developed by

Dunham and Lipinski [17].

1.4 Thesis Outline

This thesis is organized in six chapters. Chapter 1 includes an overview of the present topic in the

context of nowadays society needs. Two sections are dedicated to presenting the state of the art and the

objectives of the present work. Chapter 2 begins with a theoretical introduction, explaining the energy

rate equations that are employed in the implementation of the developed algorithm. A summary of the

article at study is presented subsequently. It is then described how the thermodynamic properties of the

fluids are obtained. The third chapter describes the mathematical modelling of the present work’s models.

In the fourth chapter, it is explained the restrictions that are implemented on the models implementation,

and the computer implementation of the methods explained in the preceding chapter. Chapter 5 presents

a discussion of the results obtained from all the proposed model simulations. Chapter 6, the last one,

gives an overview of the conclusions achieved from this thesis and outlines some relevant future work

points regarding the present work subject.

7

Chapter 2

Background

2.1 Theoretical Introduction

According to Boettener et al. [18], the energy rate balance equation for open systems, in a given control

volume, is given by

Q− W=d

dt

[∫∫∫ (u+

v2

2+ gz

)ρdV

]+

∫∫ (h+

v2

2+ gz

)ρ(~V · ~n)dA (2.1)

where Q and W are, respectively, the net rate of energy transfer by heat and work across the boundary of

the control volume. u is the specific internal energy, v2/2 is the specific kinetic energy, gz is the specific

potential energy, ρ is the fluid density, V is the volume of the control volume, h is the specific enthalpy,

(~V ·~n) is the dot product between the fluid velocity and the normal vector at a given point of the surface

area, A, of the control volume. A schematic representation of the control volume of an open system is

shown in Fig. 2.1.

Considering steady state, the time derivate is null,

d

dt

[∫∫∫ (u+

v2

2+ gz

)ρdV

]= 0

Dashed line definesthe control volume boundary

Inlet i

mi

meControlvolume

zezi

ui +Vi

2___2

+ gzi

ue +Ve

2___2

+ gze

Exit e

Q

W

Figure 2.1 Schematic representation of the control volume used to develop Eq. (2.1) [18].

9

Having kinetic and potential energy variation to be negligible, the following underlined terms are

neglected, ∫∫ (h+

v2

2+ gz

)ρ(~V · ~n)dA→

∫∫h ρ(~V · ~n)dA

Eq. (2.1) is then simplified to

Q− W =

∫∫h ρ(~V · ~n)dA (2.2)

The control volume can be assumed to have a series of one dimensional locations through which mass

enters, i, and exits, e, the system. In this way, the surface integral in Eq. (2.2) can be expressed as the

summation of outlet minus inlet rates of the transported variables,

∫∫h ρ(~V · ~n)dA =

∑e

me he −∑i

mi hi

At steady-state the mass flow is constant and assuming uniform enthalpy at the inlet and exit sections

one finally gets

Q− W = m

(∑e

he −∑i

hi

)(2.3)

Steam and Gas Turbine

Turbines are widely used in thermodynamic cycles to generate power. The power is generated as

superheated steam or gas enters the turbine and expands to lower pressures while passing through a set

of blades attached to a shaft free to rotate.

Selecting the control volume as that enclosing the turbine (Fig. 2.2), the kinetic and potential energy

variations between inlet and outlet are normally negligible.

cvW·

1

2CV

Figure 2.2 Schematic representation of the turbine control volume. Adapted from [18].

Considering that the turbine is adiabatic, i.e., no heat is exchanged with the surroundings (Q = 0),

the power generated is calculated from

Wt = m(h1 − h2)

where 1 and 2 stand, respectively, for the exit and inlet sections.

Compressor and Pump

Contrary to the turbines case, compressors and pumps exploit work provided by a driving motor in

order to, typically by changing the working fluid state, increase its pressure.

10

Having the control volume to enclose the compressor/pump and neglecting the kinetic and potential

energy variation, as well as the heat transfers with the surroundings, the power can be obtained from

Wp = m(h1 − h2)

Furthermore, assuming an ideal pump (i.e. without internal irreversibilities) and an incompressible

flow (i.e. a Mach number Ma << 0.3), the work per unit mass can be expressed as

Wp

m= v(p1 − p2) (2.4)

With the two previous equations one concludes that, for an ideal pump, the change in enthalpy is

equal to h2s− h1 = v(p2− p1), where h2s is the final enthalpy for an isentropic evolution. The real value

h2 is related to h2s through the pump’s isentropic efficiency.

Heat Exchanger

The heat rate between the control volume and the surroundings is negligible, when compared to the

heat transferred from the hot side to the cold one, making Q = 0. No power is generated nor consumed,

so W = 0. As it is implicit from the name, there is an exchange of heat that takes place, usually between

two fluid streams, so, the following expression represents the general energy balance,

0 =∑e

me he −∑i

mi hi

If two different mass flows pass through the hot and cold sides, as schematized in Fig. 2.3, the energy

rate balance takes the following form,

0 = m1(h2 − h1) + m3(h4 − h3)

In the case where the mass flows passing through both sides present the same rates, the energy rate

balance equation simplifies to

h1 − h2 = h4 − h3

CV

Hot side

Cold side

1

3 4

Figure 2.3 Counterflow heat exchanger schematic illustration. Adapted from [18].

A regenerator and an heat recovery steam generator (HRSG) are employed in the models proposed

in this work. Further explanation of these heat exchangers is presented in chapter 3.

11

2.2 Previous Work

Dunham and Lipinski published their work [17] in 2013 about a regenerative Brayton and combined

Brayton-Rankine cycles fuelled by solar energy alone. In that paper, concentration ratios characteristic

of single-axis concentrator collectors, such as LFR and PTC were examined. The authors examined the

cycles efficiencies and power performances for different working fluids in both the topping and bottoming

cycle. This section reviews their work.

The schematic presentations of the thermodynamic cycles are presented in figures 2.4 and 2.5.

The minimum system pressure for all Brayton cycles was set to the atmospheric pressure (1 bar). The

maximum Brayton cycle pressure, at the compressor exit, was initially varied so that the optimal pressure

ratio that provides the maximum cycle efficiency was found. The minimum temperature, T1, was assumed

to be 308 K and the maximum temperature, T4, was obtained assuming a receiver solar concentration

ratio of C = 70. Pressure drops in relation to the pressure at the entrance of the solar receiver and heat

exchanger were assumed to be 5% and 2%, respectively. The efficiency of the compressor, regenerator

and turbine were 0.796, 0.87 and 0.858, respectively. The power input from the solar receiver was taken

as 150 kW.

Figure 2.4 Brayton cycle scheme [17].

At the bottoming cycle, in the combined cycle model, the temperature at the inlet of the pump was

assumed to be 308 K, and the pressure was set to be the saturation pressure at that temperature or the

atmospheric pressure of 1 bar, whichever was greater. The steam turbine inlet temperature was fixed at

400 K. The pinch point temperature difference at the heat exchanger is fixed to 10 K. The maximum

pressure of the Rankine cycle was made to vary up to 20 bar. The isentropic efficiencies of the pump and

the turbine were 0.6 and 0.68, respectively. Table 2.1 presents the considered parameters concisely.

12

Figure 2.5 Combined Brayton-Rankine cycle scheme [17]

Table 2.1 Assumed cycle parameters

Cycle parameter Design point condition

T1 308 K

p1 1 bar

C 70

ηcompressor 79.6 %

ηgasturbine 85.8 %

εregenerator 87 %

Qin 150 kW

T8 308 K

(p9)max 20 bar

∆Tpinch point 10 K

In order to estimate the optimal operating temperature of the solar receiver, Trec, Dunham and

Lipinski employed the following equation to obtain the theoretical efficiency of converting solar heat into

mechanical work,

η=

(αCG0 − εσ(Treceiver)4 − Uconv(Treceiver − Tamb)

CG0

)︸︷︷︸

Receiver efficiency

(1− Tamb

Treceiver

)︸︷︷︸

Carnot efficiency

(2.5)

The different receiver parameters were assumed as follows,

13

• Receiver tubing surface with α = 0.9 and ε = 0.2;

• Overall heat transfer coefficient, Uconv = 10 W/m2K;

• Standard solar irradiation, G0 = 1 Wm−2;

• Atmospheric temperature, Tamb = 303 K;

• Concentration ratio, C = 50, 70, and 100;

• σ is the Stefan-Boltzmann constant (5.67036713×108 Wm−2K−4)

The efficiency was then plotted as shown in Fig. 2.6. The peak efficiency in the curve correspondent

to C = 70 occurred at Treceiver = 831 K. This value was obtained by differentiating Eq. (2.5) with respect

to Treceiver and subsequent equalization to zero. The working fluid was assumed to reach a temperature

of 50 K lower than of the receiver. Thus, T4 was considered to be 781 K in the analysis.

Figure 2.6 Efficiency of a receiver-Carnot heat engine system as a function of receiver temperature forC = 50, 70, and 100 [17].

The Brayton cycle efficiency is obtained from the calculation of the ratio between the cycle power and

the heat input,

ηcycle =Wcycle

Qin

(2.6)

The combined cycle efficiency is calculated as follows,

ηcycle =Wt,cycle + Wb,cycle

Qin

(2.7)

Varying the pressure ratio of the compressor, pR, from 1 to 10, different Brayton cycle efficiency

curves were obtained as shown in Fig. 2.7. The optimal points, as well as the state temperatures, net

cycle power output, and the cycle efficiency for each fluid configuration are presented in Table 2.2. CO2

outperformed the other fluids, providing the highest cycle efficiency of 0.1531.

14

Figure 2.7 Brayton cycle efficiency versus cycle pressure ratio [17]

Regarding the combined Brayton-Rankine cycle, the same analysis was made by obtaining different

values of the global cycle efficiency as a function of the pressure ratio. The peak efficiency and power

results by fluid pair - topping and bottoming fluids combination - are presented in bar charts in Fig. 2.8

and Fig. 2.9. Table 2.3 shows those corresponding specific values. The preponderance of CO2 is notable,

being the fluid that allows for the highest efficiencies and cycle powers.

Figure 2.8 Top cycle efficiency for each configuration of fluids in the combined cycle [17].

Table 2.2 Brayton cycle peak efficiencies and correspondent values of pressure ratio, volume flow, tem-perature at the different states and power generated. Values from [17].

Fluid pR V (m3/s) T1(K) T2(K) T3(K) T4(K) T5(K) T6(K) Wcycle(kW ) ηcycle

CO2 3.0 0.3403 308.0 408.6 646.9 781.0 679.7 445.8 22.96 0.1531Ar 2.0 1.028 308.0 431.6 614.6 781.0 642.0 458.8 11.67 0.0778Air 2.25 0.6667 308.0 408.4 634.5 781.0 667.4 442.7 18.44 0.1229N2 2.25 0.6697 308.0 408.6 633.3 781.0 666.1 442.5 18.37 0.1225He 2.0 1.028 308.0 431.6 614.6 781.0 642.0 459.0 11.56 0.0771H2 2.25 0.6784 308.0 409.0 628.4 781.0 661.2 441.9 17.93 0.1195

15

Figure 2.9 Top cycle power for each configuration of fluids in the combined cycle [17].

Table 2.3 Combined cycle peak global efficiency values. Values from [17].

Fluid CO2 Air H2 N2 Ar He

R-245fa 0.2106 0.1779 0.1741 0.1773 0.1499 0.1495R-141b 0.2068 0.1752 0.1715 0.1746 0.1413 0.1408Cyclohexane 0.1730 0.1416 0.1380 0.1411 0.1033 0.1027HFE7000 0.2076 0.1748 0.1709 0.1741 0.1483 0.1479n-Pentane 0.2059 0.1740 0.1702 0.1734 0.1420 0.1415C6-Fluoroketone 0.1972 0.1639 0.1598 0.1632 0.1351 0.1346

2.3 Thermodynamic Properties

Different fluids are employed for the studied models. In the Brayton cycle, five gases are analysed - CO2,

Air, N2, He, and H2; in the Rankine cycle, five other fluids are examined - R-245fa, R-141b, Cyclohexane,

n-Pentane, and Water. Water is considered for the Rankine cycle given its abundance in nature and its

high exploitation in power cycles.

Thermodynamic properties of the fluids are accessed in every single iteration throughout the com-

putational simulations, and it is therefore relevant to clarify where the corresponding data bases come

from. In this section, it is explained how these data were obtained and used throughout the analyses.

Brayton Cycle Fluids

For an ideal gas, the specific heat at constant pressure, cp(T ), is a function of temperature alone as

described below,

cp(T ) =dh

dT(2.8)

The change in specific enthalpy is obtained integrating Eq. (2.8),

16

h(T2)− h(T1) =

∫ T2

T1

cp(T ) dT (2.9)

In order to obtain specific enthalpy versus temperature, a reference state must be defined and the

above equation can be written as,

h(T ) =

∫ T1

Tref

cp(T ) dT + h(Tref ) (2.10)

where Tref is a reference temperature equal to 0 K at which the enthalpy is null. Thus, at a given

temperature T, specific enthalpy values are obtained from

h(T ) =

∫ T

0

cp(T ) dT (2.11)

In the calculation of Brayton cycles, usually two variables are defined, pr(T ) and the specific entropy

s0(T ), by the following equations [18],

pr(T ) = exp

[s0(T )

R

](2.12)

s0(T ) =

∫ T

0

cp(T )

TdT (2.13)

with R being the specific gas constant of a given gas calculated by dividing the universal gas constant

over its molar mass(R = R/M).

In practical engineering situations, as in the present study, functions (usually polynomial functions)

obtained experimentally are often employed to calculate specific heats. This facilitates the computation

of thermodynamic properties during iterative processes. In the following paragraphs it is exposed the

methodology and polynomial curve fittings that are embedded in the algorithm.

Dunham and Lipinksi [17] obtained their results using the EES (Engineering Equation Solver) soft-

ware, which has its own thermodynamic properties data bases already incorporated. Those data bases,

in turn, rely on polynomial equations presented in the work of McBride et al. [19]. For the sake of

coherency, the same polynomial approximations are employed in this work.

cp(T )/R = a1T−2 + a2T

−1 + a3 + a4T + a5T2 + a6T

3 + a7T4 (2.14a)

h(T )/RT =− a1T−2 + a2 lnT/T + a3 + a4T/2 + a5T

2/3 + a6T3/4 + a7T

4/5 + b1/T (2.14b)

s◦ (T )/R =− a1T−2/2− a2T

−1 + a3 lnT + a4T + a5T2/2 + a6T

3/3 + a7T4/4 + b2 (2.14c)

The values of the coefficients can be accessed from the corresponding reference ([19]).

17

Rankine Cycle Fluids

The thermodynamic properties of the working fluids in the bottoming cycle of each model are obtained

from CoolProp. CoolProp is a C++ library compatible with MATLAB that provides thermodynamic

properties of a large variety of fluids. These are based on the Helmholtz-energy-explicit equations of

state, which is the state-of-the-art of thermodynamic properties evaluation, being employed for many

high-accuracy equations of state available in the literature [20].

To comply with Dunham and Lipinski’s work [17], guaranteeing a fair comparison between the hereby

proposed models results and the same pressures at the inlet and outlet of the pump are used. The authors

say that at the inlet of the pump, it is assumed that the fluid is at its minimum temperature of 308 K

and at a pressure corresponding to its saturation pressure or atmospheric pressure (1 bar), whichever is

greater. The temperature at the inlet of the steam turbine is 400 K for every fluid.

Regarding the water as the Rankine fluid case, which does not appear in those authors’ work, the

pressure is chosen so that the condition of having it at superheated state at the turbine inlet is satisfied.

At 400 K, the maximum pressure value that water can reach without liquefying is 2.4577 bar [21]. The

pressure is then chosen to be 2.45 bar (having then at the turbine’s inlet a pressure of 2.201 bar due to

2% pressure loss in the HRSG).

These property assumptions are succinctly presented in table 2.4.

Table 2.4 Assumed pressure values in the Rankine cycle.

Pressure [bar]

Fluid Pump inlet Pump outlet

R-245fa 2.109 18.75

R-141b 1.126 7.25

Cyclohexane 1 3.25

n-Pentane 1 7.25

Water 1 2.45

18

Chapter 3

Mathematical Modelling

Three new models, whose innovations are explained in detail in the following subsections, are presented

in this work with the objective of, as aforesaid, achieving higher values of the cycles overall efficiencies

and greater power generations, as well as to study the performance of hybrid cycles. The combustor is

placed in series with the solar receiver, having this decision been made based on Spelling’s remarks [14],

mentioned in section 1.2 about this configuration. In the following subsections, the models schematic

representation and their corresponding balance equations are presented in the same order as they are

calculated in the algorithm.

3.1 Model 1

Comparing to the combined cycle presented in the work of Dunham and Lipinski [17], model 1 presented

herein differs from the former in the presence of a combustion chamber placed after the solar receiver.

The model schematic representation is shown in Fig. 3.1.

Pressure losses

The same pressure losses as as those used by Dunham and Lipinski [17] are considered herein, and 2% is

taken as the pressure loss in the combustion chamber. The pressures in all states are then obtained from

the pressure loss conditions, admitting given values of p2, p9 and p10.

Compressor

Knowing the temperature value at state (1), T1 = 308 K, one can obtain the specific enthalpy h1 and pr1

from the thermodynamic properties. The value of pr2s is then obtained from

pr2spr1

=p2

p1(3.1)

Which allows to obtain h2s from the thermodynamic properties. Considering the same value of the

compressor isentropic efficiency as that used by Dunham and Lipinski [17] (0.796), h2 is obtained from

19

Compressor GasTurbine

Receiver Combustor

Pump

Condenser

SteamTurbine

HEX

1

3 4

5

6

2

7

78

9

10 11

12

HRSG

Regenerator

Figure 3.1 Schematic presentation of Model 1.

ηcompressor =h2s − h1

h2 − h1(3.2)

Gas Turbine

The fluid enters the gas turbine, after being heated in the combustion chamber, at a given temperature,

T5, above that of the gas at the receiver outlet. Having that temperature value, h5 and pr5 are obtained

from the thermodynamic properties. Eq. (3.3) is employed to obtain pr6s.

pr5pr6s

=p5

p6(3.3)

Having pr6s, one can obtain h6s, and considering the same isentropic efficiency of the turbine as in

20

Dunham and Lipinski’s work [17] (0.858), h6 is obtained from

ηgas turbine =h5 − h6

h5 − h6s(3.4)

Regenerator

The Brayton cycle regenerator is considered to have an effectiveness as that used by Dunham and Lipinski

[17], εreg = 0.87. Having at this point calculated the specific enthalpies at states (6) and (2), it is now

possible to obtain h3 and h7 from the equations given below,

εreg =h3 − h2

h6 − h2(3.5)

h3 − h2 = h6 − h7 (3.6)

Solar Receiver

At state (4), the gas is, initially, assumed to exit the solar receiver with a temperature, T4, of 781 K

so that h4 is determined from the fluid’s thermodynamic properties. The energy rate supplied by the

receiver, Qsol, is, also initially, assumed to be 150 kW. In this way, the mass flow rate in the topping

cycle, mt, is obtained,

mt =Qsol

h4 − h3(3.7)

The efficiency at which solar heat is converted into mechanical work, presented in 2.2 (Eq. (2.5)), is

expressed as follows,

η=

(αCG0 − εσ(Treceiver)4 − Uconv(Treceiver − Tamb)

CG0

)(1− Tamb

Treceiver

)Knowing that Qsol = GoAcolηreceiver, and having at this point calculated mt from the energy rate

balance equation to the solar receiver, the following equation can be deduced,

Qsol = mt(h4 − h3)⇒

⇒ GoAcol ηreceiver = mt (cp,4T4 − cp,3T3) (3.8)

In to order to obtain a new value of T4, the receiver efficiency equation is substituted into the previous

one. Rearranging the equation, taking into account that Treceiver = T4 + 50, a fourth degree polynomial

equation of T4 is obtained (Eq. (3.9)), which is solved iteratively employing the fsolve toolbox available

in MATLAB.

cpT4 = cpT3 +1

mtGoAcol

(αCG0 − εσ(T4 + 50)4 − Uconv(T4 + 50− Tamb)

CG0

)(3.9)

21

Finally, h4 is obtained as h4 = h(T4).

Pump

The Rankine cycle fluid enters the pump at a temperature, T9, of 308 K and at a given pressure,

p9, dependent on the fluid used (as explained in section 2.3). With these two input values, from the

thermodynamic properties of the Rankine cycle fluids, h9 and the specific volume v9 are obtained.

Making use of the pump equation introduced in section 2.1 (Eq. (2.4)), the specific enthalpy of the

fluid at the exit state for the isentropic process, h10s, is obtained from

h10s − h9 = v9(p10s − p9) (3.10)

Considering a pump isentropic efficiency of 0.6, the specific enthalpy of the exiting fluid, h10, is

calculated from

ηpump =h10s − h9

h10 − h9(3.11)

Heat Recovery Steam Generator

Temperature of the steam at the inlet of the steam turbine, state (11), is fixed at 400 K. The pressure at

the inlet of the Heat Recovery Steam Generator (HRSG) cold side, state (10), is assumed in accordance

with the employed fluid and the pressure at its outlet, state (11), is obtained from the pressure loss

condition. Thus, the specific enthalpy h11 can be obtained from the fluid’s thermodynamic properties.

Since a phase change of the bottoming cycle fluid occurs in the HRSG, a pinch-point analysis is done

to determine the steam mass flow, mb. The pinch point is the location where the temperature difference

between the hot and cold fluids is minimum. This occurs, in this case, when the Rankine fluid is at the

saturation temperature (with a quality of 0%), as represented in Fig. 3.2.

The percentage of heat used to expand the bottoming cycle fluid from saturated liquid to superheated

at the turbine inlet, state (11), is equal to the percentage of heat used to bring the topping cycle gas from

the HRSG inlet, state (7), to the pinch point. The aforesaid can be expressed mathematically as follows,

h11 − hb,pinchh11 − h10

=h7 − ht,pinchh7 − h8

(3.12)

At the bottoming cycle pinch point, Tb,picnch and hb,pinch are obtained knowing the value of p10

and that the quality of the fluid is 0%. With a pinch point difference of 10 K (∆Tpinch = 10 K), the

temperature Tt,pinch is obtained,

Tt,pinch = Tb,pinch + ∆Tpinch (3.13)

Which, from the ideal gas properties, leads to the value of ht,pinch. Now one can obtain h8 from Eq.

(3.12).

22

10

11

7

8 ��ℎ ��

� ��ℎ

� ��ℎ

�

�

Figure 3.2 Diagram representation of the pinch point at the HRSG.

The bottoming cycle mass rate is then calculated from

mt(h7 − h8) = mb(h11 − h10) (3.14)

Steam Turbine

Then, the superheated fluid enters the steam turbine where it expands, producing work in the process.

Its entropy, s11, is obtained from the thermodynamic conditions at this state (knowing h11 and p11).

The outlet specific enthalpy is calculated by starting to obtain its value for an isentropic process. In

an isentropic process, the entropy is conserved (s12s = s11). Knowing s12s and p12, one can now obtain

h12s from the thermodynamic properties.

Finally, considering the same isentropic efficiency as that of Dunham and Lipinski’s work [17] (0.68),

h12 is calculated from

ηsteam turbine =h11 − h12

h11 − h12s(3.15)

Global cycle analysis

The total energy rate input of the combined cycle is the sum of the energy rates supplied by the solar

receiver, Qsol, and by the combustion chamber, Qc,

Qin = Qsol + Qc = mt(h4 − h3) + mt(h5 − h4)

The total power generated by the cycle is expressed mathematically as follows,

Wcycle = Wgas turbine + Wcompressor + Wsteam turbine + Wpump

23

Each of the terms above presented are calculated using the energy mass balance at each cycle com-

ponent at hand. In the compressor’s case, Dunham and Lipinski [17] consider losses in the shaft, having

ηshaft = 0.9797. The work flows on each component is then as follows,

Wgas turbine = mt(h5 − h6)

Wcompressor = mt(h1 − h2)/0.9797

Wsteam turbine = mb(h11 − h12)

Wpump = mb(h9 − h10)

Having the power output and input to the combined cycle, one can now calculate the global cycle

efficiency,

ηcycle =Wcycle

Qin

3.2 Model 2

In the second model, it is proposed an addition of a stream bifurcation subsequent to the gas turbine in

order to distribute, efficiently, the two resultant mass flows for the Brayton cycle and Rankine cycle, as

shown in the model schematic representation in Fig. 3.3. In this way, the temperature of the gas after the

gas turbine is conserved until it reaches the heat exchange with the bottoming cycle fluid, differently from

the previous configuration in which the gas’ temperature decreases when passing through the regenerator

before interacting with the bottoming cycle.

Pressure losses

The same pressure losses are considered. The pressures in all states are then obtained from the pressure

loss conditions, admitting given values for p2, p11 and p12.

Compressor

At the compressor, the same procedure is performed as in the previous model. The enthalpy h2 is

obtained from the isentropic efficiency equation of the compressor.

Gas Turbine

The same procedure is performed as in the previous model. However, in this model, the temperature at

the inlet of the turbine corresponds to that of the solar receiver’s exit. The gas turbine’s outlet specific

enthalpy is obtained from the isentropic efficiency equation of the turbine.

24


Regenerator

Receiver

Pump

Condenser

HRSG

SteamTurbine

HEX

1

3 4

5

2

9

67

11

12 13

8

14

10


Solar Receiver

The specific enthalpy at state (4) is obtained from the same methodology as in the previous model.

Stream Splitting

The stream exiting the gas turbine is divided in two new flow rates. It is considered that the thermody-

namic conditions - specific enthalpy and pressure - are preserved,

h5 = h6 = h8

p5 = p6 = p8

The bifurcation will result in new different mass flow rate values. These will have the following

nomenclature,

25

• m1, from the first state of the cycle to the turbine inlet;

• m8, passing through the regenerator;

• m6, passing through the HRSG.

Then it comes: m1 = m5 = m8 + m6.

Regenerator

The Brayton cycle regenerator is, initially, considered to have an effectiveness, εreg, of 0.87. Having at

this point calculated the specific enthalpies at (8) and (2), one can now obtain h3 from

εreg =h3 − h2

h8 − h2(3.16)

The fact that there are different mass flows crossing the regenerator has to be taken into account for

the calculations. The energy rate balance equation at the regenerator can then be written as follows,

m8(h8 − h9) = m1(h3 − h2) (3.17)

However, at this point, the mass flow rate value in state (8) is unknown. So, the mass flow ratio,

r = m8/m1, is assumed to have a given value, as it is explained in chapter 5. Rearranging the equation,

the specific enthalpy at (9) is calculated from

h9 = h8 −1

r(h3 − h2) (3.18)

The mass flow rate of fluid entering the regenerator’s hot side is then obtained: m8 = r m1.

The regenerator is assumed to be a counterflow type of heat exchanger. According to the effective-

ness–NTU relations ([22]), the effectiveness of the regenerator varies with the mass flow rate values, when

they are different. The heat capacity ratio is given by

Cr =Cmin

Cmax=Ch

Cc=m8 cp,8m1 cp,1

The number of transfer units is

NTU =UA

Cmin

where U is the overall heat transfer coefficient and A is the heat transfer area.

The effectiveness of the regenerator is then finally obtained from the following relation,

εreg =1− exp[−NTU(1− Cr)]

1− Cr exp[−NTU(1− Cr)]

The specific enthalpy exiting the regenerator cold side, h3, and the mass flow rate m1 can now be

updated,

26

h3 = h2 + εreg(h8 − h2)

m1 =Qsol

h4 − h3

Pump

The specific enthalpies at the inlet and outlet of the pump (h11 and h12, respectively) are gotten as in

the first model.


The same procedure as in the previous model is applied, leading to the values of h7 and h13.

Steam Turbine

The value of h14 is obtained likewise h12 in model 1.


The total energy rate input of the combined cycle is provided from the solar receiver, Qsol, alone,

Qin = Qsol = m1(h4 − h3)




ponent at hand,

Wgas turbine = m1(h4 − h5)

Wcompressor = m1(h1 − h2)/0.9797




efficiency,

27

ηcycle =Wcycle

Qin

3.3 Model 3

Model 3 implements both the new features of model 1 and model 2: an addition of a combustion chamber

placed after the solar receiver and a stream splitter at the exit of the gas turbine. The schematic

representation of this model can be viewed in Fig. 3.4.


Regenerator

Receiver Combustor

Pump

Condenser

HRSG

SteamTurbine

HEX

1

3 4

5

6

2

10

78

12

13 14

9

15

11


Pressure losses

The same pressure losses are considered, and 2% is taken as the pressure loss in the combustion chamber.

The pressures in all states are then obtained from the pressure loss conditions, admitting given values of

p2, p12 and p13.

28

Compressor

At the compressor, the same procedure is performed as in the previous model. h2 is obtained from the

isentropic efficiency equation of the compressor.

Gas Turbine

The same procedure is performed as in the previous model, with T5 taking the value of the temperature

of the gas exiting the combustion chamber. h5 is obtained from the isentropic efficiency equation of the

turbine.

Solar Receiver

An equal methodology as in the previous model was executed.

Stream Splitter

The stream exiting the gas turbine is divided into two flow rates. It is considered that the thermodynamic

conditions - specific enthalpy and pressure - are preserved,

h6 = h9 = h7

p6 = p9 = p7

The bifurcation will result in new different mass flow rate values. These will have the following

nomenclature,

• m1, from the first state of the cycle to the turbine’s inlet;

• m9, passing through the regenerator;

• m7, passing through the HRSG.

Then, m1 = m6 = m9 + m7.

Regenerator

The same relations for a counterflow type of heat exchanger as in the previous model are employed,

allowing for the determination of a corrected value of h3 and h10.

Pump

The specific enthalpies at the inlet and outlet of the pump (h12 and h13, respectively) are obtained as in

the previous models.


The same procedure as in the previous model is done, in this case obtaining h8 and h14.

29

Steam Turbine

Similarly to the preceding components, the calculations at the steam turbine repeat, having in this case

the specific enthalpy at its exit to be named h15.


The total energy rate input of the combined cycle is the sum of the energy rates supplied by the solar

receiver, Qsol, and by the combustion chamber, Qc,

Qin = Qsol + Qc = m1(h4 − h3) + m1(h5 − h4)




ponent at hand,

Wgas turbine = m1(h5 − h6)

Wcompressor = m1(h1 − h2)/0.9797




efficiency,

ηcycle =Wcycle

Qin

30

Chapter 4

Computational Modelling

The proposed models presented in the previous chapter are simulated in a MATLAB program developed

for this thesis. This chapter describes the restrictions that are embed in the MATLAB code and explains

the algorithm implemented in the simulations.

4.1 Restrictions

The implementation of restrictions is crucial to guarantee the reliability of the results in a real life context.

This section describes those restrictions, being organized in two subsections: thermodynamic properties

restrictions, which are applicable across all three models; model restrictions, having some nuances that

vary with the used model.

4.1.1 Thermodynamic Properties Restrictions

Each working fluid in the topping and bottoming cycle of the models are constrained to operate in a

certain limited temperature range. In the case of the bottoming cycle, CoolProp has these thermodynamic

restrictions incorporated, preventing the program to keep running when the range values are not verified.

In the Brayton cycle, however, restrictions have to be implemented given that there is no such library.

These are incorporated by programming in the code so that situations such as fluid condensation do not

occur.

As explained more thoroughly in the next chapter, temperatures at the exit of the Brayton cycle

regenerator and at the exit of the HRSG (both cases at pressures close to 1 bar) can attain excessively

low temperatures, which brings to the necessity to have temperature restrictions. Table 4.1 shows the

minimum temperatures for each gas at which the program is allowed to run. Except for CO2, those

correspond to the triple point temperatures, and since they are used by Dunham and Lipinksi [17], the

same was done in this work. In the CO2 case, however, because its triple point temperature is too high

comparing to the others (216.6 K), its restriction is pushed further down to 195 K in order to increase

the span of results (the increase is not extreme, but it is significant). This is the chosen value because,

at the critical states as the one mentioned above, the gas is at around 1 bar, which, as shown in Fig. 4.1,

31

CO2 can operate on. The point (-78.5◦ C/194.5 K, 1 atm/1.01 bar) in the diagram is used as a reference

point for this decision.

Table 4.1 Minimum temperatures for the Brayton cycle fluids.

Fluid Lower limit temperature

CO2 195.0 K

Air 60.0 K

N2 63.151 K

He 2.1768 K

H2 13.957 K

Figure 4.1 Phase diagram of CO2 [23].

4.1.2 Model Restrictions

As mentioned before, there is also a set of model restrictions that have to be implemented into the

developed program. Several restrictions are implemented with the purpose of rejecting solutions that

result from physics incoherences occurring in intermediate steps and others aiming for the models to

comply with the desired design conditions.

Starting with the physical meaning, the models are restricted to operate in a set of conditions that,

for instance, avoid a component to exhibit thermal energy rate input (e.g. solar receiver) greater than

that leaving the equipment (in this case, the condition h4 > h3 has to be verified). These constraints

have to be introduced into the program code since the software does not have any physics considerations

or sensibility incorporated. This type of restriction is applied to the following components: regenerator,

solar receiver, combustion chamber, and HRSG, avoiding negative energy rates and negative mass flow

rates.

Regarding the models intended design characteristics, a few more restrictions are implemented.

32

Heat dissipation for the fluid to reach initial conditions

It is desired that no other source of energy is added to the cycle to get the Brayton cycle fluid to

achieve the initial cycle conditions (308 K, 1 bar) at the compressor inlet. In this way, the fluid at states

(8)/(10)/(11) in models 1/2/3 is restricted to have temperatures equal or greater than 308 K.

Brayton cycle regenerator

In models 2 and 3, the efficiency is calculated from the NTU relations (as described in chapter 3).

As in the recurrently mentioned work [17], the effectiveness is fixed at 0.87 (which one can percept as

relatively high value in the heat exchangers domain), in the mentioned models the regenerator is designed

to provide maximum effectiveness values at around 0.87.

Combustion chamber

The purpose of adding a combustion chamber in models 1 and 3 is to have it as a support to the

solar receiver, operating together so that the cycles generate higher electric powers at higher efficiencies.

Accordingly, in order to avoid a combustion chamber providing the fluids with disproportionally higher

values of heat than the solar receiver, the models are restricted to run by the following restriction:

Qc < Qs.

4.2 Numerical Model

In this section it is described the algorithm used do implement the models described in Chapter 2.

In order to study the performance of the models proposed in the present work, the pressure ratio in

the Brayton cycle (pR = p2/p1) and the temperature at the exit of the combustion chamber (T5, in the

cases of model 1 and model 3) constitute the first variable inputs of the system. The ratio, r, between the

mass flow rates resulting from the stream splitting in models 2 and 3 is assumed to have a given value.

The main algorithm employed is presented in the form of flowchart schematized in Fig. 4.2.

The program, developed in MATLAB, follows the following steps:

1. Start by selecting the model chosen by the user that is firstly simulated.

2. Select the gas used in the Brayton cycle. Depending on the selected gas, different thermodynamic

property data bases are loaded and become ready to be called in. Restrictions are also considered

accordingly.

3. Select the Rankine cycle fluid. Different fluids result in different thermodynamic properties, and in

different pressure values at the inlet and outlet of the pump (as mentioned in section 2.3).

4. Read the input variables. The values to be iterated by the computer code correspond to the entries

in the chosen vectors of pressure ratio, ~p2, and temperature at the exit of the combustor, ~T5. Given

increment values, ∆p and ∆T , are taken such that: ~p2(i + 1) = ~p2(i) + ∆p and ~T5(i + 1) =

~T5(i) + ∆T5. These values are then specified and explained in chapter 5. The iterations are made

till the last entries of pressure and temperature, np and nT , respectively, are reached.

33

5. Evaluate the model that was selected and decides whether it starts an iterative process by varying

T5 or not. As aforesaid, this process is not applied to model 2 given the absence of a combustion

chamber.

6. Assume the first entry value of ~T5, if applied, and, subsequently, the first value of ~p2.

7. For each value of p2 and T5, Brayton and Rankine cycles’ outputs are calculated.

8. Perform post-processing of data so that a comprehensive analysis of the systems output variation

with the variable inputs (e.g., plots, bar charts) is possible.

After getting the results from these iterations, further simulations are made in order to study the

models behaviour with other variables, such as the mass flow ratio that governs the stream splitter after

the gas turbine in models 2 and 3 and the regenerator design - heat transfer area - (models 2 and 3).

The method to accomplish the results of these studies is identical to the one presented in the previously

mentioned Flowchart.

Regarding the fixed parameters, the same values as those used by Dunham and Lipinksi [17] article

are taken. In terms of components efficiencies, the gas and steam turbines have an isentropic efficiency

of 0.858 and 0.68, respectively. The isentropic efficiency values taken for the compressor and the pump

are 0.796 and 0.6, respectively. The solar receiver operates at a solar concentration ratio of C = 70. For

the heat recovery steam generator, the temperature difference at the pinch point is assumed to be 10 K

until varied in upcoming simulations presented in the next chapter.

34

Start

Select Brayton cycle

fluid

Select Rankine cycle

fluid

Input vectors:

2, 5

Select Model

Evaluate

Model

Model 1 or Model 3

T

T

5 assumes the first

entry value of T5

p2 assumes the first

entry value of p2

Model 2

Calculate Brayton

cycle outputs

Calculate Rankine

cycle outputs

Calculate Global

cycle outputs

p2 + p

Post Processing

T5 + T

p2 p2 n

p2 = p2 n

T5 T5 n

5 = 5

p

T T n

T

p

T

p

Figure 4.2 Flowchart representation of the main employed algorithm.

35

Chapter 5

Results and Discussion

5.1 Comparison with Reference Results

As the models previously proposed and described are coded into a computer program developed from

scratch in MATLAB, a comparison with the ones obtained in Dunham and Lipinski’s [17] work is per-

formed.

Fig. 5.1 displays the global efficiency curves obtained in the present work and the ones obtained in

the previously mentioned work. One can observe that the results match, validating the program and the

thermodynamic properties data base.

pR

1 2 3 4 5 6 7 8 9 10

ηcycle

0

0.05

0.1

0.15

0.2

CO2

Air

N2

He

H2

(a) MATLAB (b) Dunham and Lipinski’s [17] obtained results

Figure 5.1 Brayton cycle results comparison between the results from MATLAB in the present workand those obtained in the work of Dunham and Lipinski [17].

In regards to the combined cycle, Table 5.1 shows the results from the MATLAB simulations. Com-

paring to the results obtained in the previous work (section 2.2, Table 2.3), these do not distance with

any considerable magnitude from the ones previously obtained, have the highest deviation to be on the

fluid pair He & Cyclohexane, presenting a difference of ηprevious − ηMATLAB = 0.0234. With respect to

the results per fluid pair compared to the others within each set of results, the same tendency is verified.

37

The differences of the absolute values can be explained from the distinct thermodynamic properties data

bases (recalling section 2.3, in the present work the CoolProp’s library was used).

Table 5.1 Peak global efficiency values obtained from the simulation of the article’s combined cycle.

Fluid CO2 Air N2 He H2

R-245fa 0.2090 0.1745 0.1734 0.1312 0.1690R-141b 0.1977 0.1640 0.1631 0.1182 0.1593Cyclohexane 0.1619 0.1279 0.1271 0.0793 0.1233n-Pentane 0.1987 0.1647 0.1638 0.1194 0.1598

5.2 MATLAB Results

This section presents the results obtained in MATLAB for each of the three models. In the plots shown,

dotted line curves represent results without restrictions applied, whilst the solid lines refer to the results

with restrictions, sometimes mentioned as acceptable results.

5.2.1 Model 1

Higher gas temperatures at the turbine inlet translates into greater expansion ratios of the gas resulting

in higher power generation values. According to Aichmayer et al. [24], the gas micro-turbine has a

metallurgical temperature limit of 1173 K. As such temperature is a chosen input to the system (outlet of

the combustion chamber), it was first thought to study the Brayton cycle with T5 = 1173 K. The range

of pressure ratio values considered goes from 1 to 20. The resultant global efficiencies of the cycle versus

pressure ratio for T5 are shown in Fig. 5.2. The efficiencies are, as expected, higher than those of the

work of Dunham and Lipinski [17]. However, one can observe that no possible results are present (no

solid lines), due to the following reasons:

– The combustion chamber provides disproportionally higher heat values than the solar receiver;

– The temperature, T5, of the gas entering the gas turbine is so high that, for several values of the

pressure ratio, pR, T3 > T4, i.e., the temperature at the exit of the regenerator exceeds the selected

temperature at the exit of the solar receiver, which is physically impossible.

Thus, the value of T5 was lowered. An iterative process has led to a selection of temperatures at

which the model gives physically acceptable results. The selected temperatures, T5, were 825 K, 850 K,

875 K, and 900 K.

Increasing T5 causes similar qualitative effects on the results, regardless of the operating working

fluids. Thus, for the sake of conciseness, Fig. 5.3 presents only the global efficiency results for CO2 in

the Brayton cycle.

It is observed that the increase of temperature T5 yields higher values of efficiency, while also reducing

the spectrum of possible results. Thus, higher temperatures do not necessarily imply higher efficiencies.

For instance, for the CO2 and Cyclohexane case (Fig. 5.3c), one can observe that, due to thermodynamic

constraints, the highest possible efficiency obtained with 900 K is lower than the highest at 875 K.

38

pR

0 5 10 15 20

ηcycle

0

0.1

0.2

0.3

0.4

0.5

R-245fa

R-141b

Cyclohexane

n-Pentane

Water

(a) CO2

pR

0 5 10 15 20

ηcycle

0

0.1

0.2

0.3

0.4

0.5

R-245fa

R-141b

Cyclohexane

n-Pentane

Water

(b) Air

pR

0 5 10 15 20

ηcycle

0

0.1

0.2

0.3

0.4

0.5

R-245fa

R-141b

Cyclohexane

n-Pentane

Water

(c) N2

pR

0 5 10 15 20

ηcycle

0

0.1

0.2

0.3

0.4

0.5

R-245fa

R-141b

Cyclohexane

n-Pentane

Water

(d) He

pR

0 5 10 15 20

ηcycle

0

0.1

0.2

0.3

0.4

0.5

R-245fa

R-141b

Cyclohexane

n-Pentane

Water

(e) H2

Figure 5.2 Model 1: cycle global efficiency versus pressure ratio with T5 = 1173 K.

39

A bar chart presenting the highest efficiency points in all fluid combinations is shown in Figure 5.4

and each global efficiency peak value is displayed in table 5.2. Those values, when compared to the values

obtained by Dunham and Lipinski [17] (presented in Table 2.3) are overall considerably higher.

Regarding the power outputs, Fig. 5.5 shows bar charts and table 5.3 displays the values of power

generated at the maximum global efficiency points. The variation of the peak power values follows the

same trends as the global efficiencies. They are presented to give the reader an insight into their order

of magnitude, compared to the values obtained in the work of Dunham and Lipinski [17]. The obtained

values are overall considerably higher than those obtained in the mentioned article.

Table 5.2 Peak global efficiency values for each fluid combination with T5 = 825, 850, 875, and 900 K.

T5 = 825 K T5 = 850 K

CO2 Air N2 He H2 CO2 Air N2 He H2

R-245fa 0.2327 0.1989 0.1978 0.1550 0.1947 0.2525 0.2199 0.2189 0.1775 0.2154

R-141b 0.2189 0.1855 0.1846 0.1387 0.1820 0.2376 0.2056 0.2048 0.1605 0.2018

Cyclohexane 0.1832 0.1492 0.1484 0.0992 0.1455 0.2020 0.1695 0.1688 0.1213 0.1656

n-Pentane 0.2206 0.1870 0.1861 0.1409 0.1832 0.2395 0.2074 0.2065 0.1628 0.2033

Water 0.1703 0.1364 0.1357 0.0842 0.1328 0.1885 0.1562 0.1556 0.1063 0.1527

T5 = 875 K T5 = 900 K


R-245fa - 0.2395 0.2386 0.1983 0.2347 - - - - -

R-141b 0.2527 0.2244 0.2236 0.1808 0.2203 0.2360 0.2284 0.2271 0.1931 0.2310

Cyclohexane 0.2160 0.1885 0.1879 0.1420 0.1845 0.1955 0.1898 0.1884 0.1528 0.1933

n-Pentane 0.2555 0.2263 0.2256 0.1832 0.2221 - 0.2322 0.2308 0.1968 0.2341

Water 0.2004 0.1748 0.1742 0.1269 0.1712 0.1757 0.1722 0.1708 0.1348 0.1770

Table 5.3 Peak power outputs [kW] for each fluid combination with T5 = 825, 850, 875, and 900 K.

T5 = 825 K T5 = 850 K


R-245fa 48.14 39.59 39.28 29.78 38.02 63.14 51.39 51.42 39.77 49.07

R-141b 46.04 37.37 37.09 27.22 35.99 60.83 49.59 49.17 36.58 46.92

Cyclohexane 38.84 30.27 30.02 19.47 28.99 52.42 40.88 41.03 28.22 38.98

n-Pentane 46.22 37.67 37.39 27.33 36.00 60.94 49.44 49.01 37.12 47.28

Water 36.25 27.87 27.65 16.51 26.47 49.69 38.17 37.82 24.73 36.41

T5 = 875 K T5 = 900 K


R-245fa - 67.35 66.65 52.53 62.82 - - - - -

R-141b 75.47 65.16 64.48 49.19 61.76 70.64 68.42 67.51 56.47 69.05

Cyclohexane 64.52 55.79 55.18 38.64 51.72 58.52 56.83 56.00 44.68 57.78

n-Pentane 76.32 64.63 65.04 49.85 61.22 - 69.53 68.62 57.55 69.98

Water 59.87 51.73 51.16 35.63 48.91 52.59 51.58 50.78 39.41 52.90

40

pR

0 5 10 15 20

ηcycle

0

0.1

0.2

0.3

0.4

0.5

T5 = 825 K

T5 = 850 K

T5 = 875 K

T5 = 900 K

(a) R-245fa

pR

0 5 10 15 20

ηcycle

0

0.1

0.2

0.3

0.4

0.5

T5 = 825 K

T5 = 850 K

T5 = 875 K

T5 = 900 K

(b) R-141b

pR

0 5 10 15 20

ηcycle

0

0.1

0.2

0.3

0.4

0.5

T5 = 825 K

T5 = 850 K

T5 = 875 K

T5 = 900 K

(c) Cyclohexane

pR

0 5 10 15 20

ηcycle

0

0.1

0.2

0.3

0.4

0.5

T5 = 825 K

T5 = 850 K

T5 = 875 K

T5 = 900 K

(d) n-Pentane

pR

0 5 10 15 20

ηcycle

0

0.1

0.2

0.3

0.4

0.5

T5 = 825 K

T5 = 850 K

T5 = 875 K

T5 = 900 K

(e) Water

Figure 5.3 Model 1: influence of temperature T5 on the global efficiency for each fluid in the Rankinecycle and CO2 in the Brayton cycle.

41

R-245fa R-141b Cyclohexane n-Pentane Water

ηcycle

0

0.05

0.1

0.15

0.2

0.25

0.3

825 K

850 K

875 K

900 K

(a) CO2


ηcycle

0

0.05

0.1

0.15

0.2

0.25

0.3

825 K

850 K

875 K

900 K

(b) Air


ηcycle

0

0.05

0.1

0.15

0.2

0.25

0.3

825 K

850 K

875 K

900 K

(c) N2


ηcycle

0

0.05

0.1

0.15

0.2

0.25

0.3

825 K

850 K

875 K

900 K

(d) He


ηcycle

0

0.05

0.1

0.15

0.2

0.25

0.3

825 K

850 K

875 K

900 K

(e) H2

Figure 5.4 Model 1: highest cycle efficiency values for each fluid combination at temperatures T5 equalto 825 K, 850 K, 875 K, and 900 K.

42


Pow

erOutput[kW

]

0

10

20

30

40

50

60

70

80825 K

850 K

875 K

900 K

(a) CO2


Pow

erOutput[kW

]

0

10

20

30

40

50

60

70

80825 K

850 K

875 K

900 K

(b) Air


Pow

erOutput[kW

]

0

10

20

30

40

50

60

70

80825 K

850 K

875 K

900 K

(c) N2


Pow

erOutput[kW

]

0

10

20

30

40

50

60

70

80825 K

850 K

875 K

900 K

(d) He


Pow

erOutput[kW

]

0

10

20

30

40

50

60

70

80825 K

850 K

875 K

900 K

(e) H2

Figure 5.5 Model 1: highest cycle power output values for each fluid combination at temperatures T5

equal to 825 K, 850 K, 875 K, and 900 K.

43

The results displayed in figures 5.3, 5.4, and 5.4 lead to the following conclusions:

• The maximum power output value at a highest global cycle efficiency point (76.32 kW) occurs with

the fluid pair CO2 and n-Pentane at a temperature T5 = 875 K, which also corresponds to the

highest global efficiency point (0.255);

• Power outputs and global efficiencies tend to rise with the increase of temperature T5, for 825 K

< T5 < 875 K. For temperatures T5 higher than 875 K, this tendency is not always verified due to

the imposed restrictions to the combined Brayton-Rankine cycle.

• CO2 consistently provides the highest global cycle efficiencies, excluding the cases at which no

results complying with the restrictions are obtained.

5.2.2 Model 2

The second model novelty, compared with those in the reviewed literature, is the addition of a stream

splitter after the gas turbine, maintaining solar energy as the only source of energy. Since there is no

combustion chamber added, the temperature T4 of the gas entering the gas turbine is calculated from an

energy balance to the solar receiver.

The range of values of the pressure ratio varies between 1 and 10, as this span covers the results of

interest to the study.

The regenerator effectiveness, which depends on the mass flow rates and temperatures on its cold and

hot side, was calculated from the effectiveness - NTU relations, as explained in 3.2.

An iterative process consisting in varying values of mass flow ratio, r = m8/m1, and heat transfer area

of the regenerator led to the decision of choosing 0.5 and 6 m2 as their values, respectively, to perform

the subsequent simulations. Considering the appropriate restrictions presented in section 4.1, the global

efficiency is plotted against the pressure ratio in Fig. 5.6.

Analysing the results, one can notice that all the efficiency curves maintain the trend of reaching

a maximum value at a certain pressure ratio value. However, comparing to model 1, the global cycle

efficiency values fall more abruptly after reaching their peaks. Another important difference, comparing

figures 5.6 (model 2) and 5.3 (model 1), is the fact that, in the latter case, possible operation points

spread around maximum efficiency, except for T5 = 875 K and T5 = 900 K, whereas in the former, they

are always located beyond that point, i.e., the global cycle efficiency never reaches its maximum value.

This happens mainly due to the gas temperature restrictions, explained in section 4.1.1. In order to get

an insight on how these restrictions influence the possible results, Fig. 5.7 shows the results of global

efficiency with (left) and without (right) temperature restrictions, using CO2 in the Brayton cycle.

One might wonder why temperature constraints have such a larger impact on the results of model 2

(and model 3, as well) than on those of model 1.

As explained before, the stream splitter has the advantage of supplying fluid to the HRSG at a

larger enthalpy compared to model 1. However, it can be too large to meet the system’s requirements.

Recalling the pinch point equation presented in section 3.1 (eq. (3.12)), that can be rearranged yielding

h8 − h10 = (h7 − h10) − A × (h7 − ht,pinch), where A = (h11 − h10)/(h11 − hb,pinch) > 1. By fixing the

44

enthalpies of the Rankine cycle and the pinch point difference, A becomes a constant, as well as ht,pinch.

From the above equation, one concludes that h8 < h10 whenever h7 > (ht,pinch × A − h10)/(A − 1).

In other words, there is a threshold value for the enthalpy at the inlet of the HSRG hot side, above

which the enthalpy at the hot side outlet is smaller than the enthalpy at the cold side inlet, which is

obviously physically impossible. An equivalent analysis can be applied to model 2, replacing states 7, 8,

10, 11 by 6, 7, 12, 13 (likewise for model 3, replacing 10, 11 by 13, 14). Models 2 and 3 provide higher

temperatures at the inlet of the HRSG hot side. In fact, those values may be so high that it results in

too low temperatures at its outlet, making it difficult to comply with the thermodynamic constraints

mentioned previously. This is the main reason why models 2 and 3 have their results considerably more

restricted than those of model 1, and also explains the huge difference in Fig. 5.7 between the results

with and without these constraints.

To allow the system to work with high enthalpy values h6, thus avoiding thermodynamic constraints,

two strategies were implemented:

1. Increase the value of the enthalpy h13 at the steam turbine inlet;

2. Increase the pinch point temperature difference.

These two options can be mathematically justified by the enthalpy threshold value mentioned pre-

viously. Similarly to what happens in model 1, in model 2 the condition h7 < h12 is met whenever

h6 > (ht,pinch×A−h12)/(A− 1), where A = (h13−h12)/(h13−hb,pinch). Therefore, to avoid unrealistic

solutions, the threshold value h6,max = (ht,pinch×A−h12)/(A−1) must be as large as possible. Differenti-

ating h6,max with respect to A, one concludes that h6,max increases when A decreases and, differentiating

A with respect to h13, the conclusion is similar, i.e., A decreases when h13 increases. Therefore, h6,max is

a monotone increasing function of h13, which explains the first strategy. The mathematical explanation

for the second strategy is much more straightforward, since, from the equation of h6,max, it is obvious

that h6,max increases with ht,pinch.

45

pR

0 2 4 6 8 10

ηcycle

0

0.1

0.2

0.3

0.4

0.5

R-245fa

R-141b

Cyclohexane

n-Pentane

Water

(a) CO2

pR

0 2 4 6 8 10

ηcycle

0

0.1

0.2

0.3

0.4

0.5

R-245fa

R-141b

Cyclohexane

n-Pentane

Water

(b) Air

pR

0 2 4 6 8 10

ηcycle

0

0.1

0.2

0.3

0.4

0.5

R-245fa

R-141b

Cyclohexane

n-Pentane

Water

(c) N2

pR

0 2 4 6 8 10

ηcycle

0

0.1

0.2

0.3

0.4

0.5

R-245fa

R-141b

Cyclohexane

n-Pentane

Water

(d) He

pR

0 2 4 6 8 10

ηcycle

0

0.1

0.2

0.3

0.4

0.5

R-245fa

R-141b

Cyclohexane

n-Pentane

Water

(e) H2

Figure 5.6 Model 2: global cycle efficiency versus pressure ratio with r = 0.5 and a heat transfer areaof the regenerator equal to 6 m2

46

pR

0 2 4 6 8 10

ηcycle

0

0.1

0.2

0.3

0.4

0.5

R-245fa

R-141b

Cyclohexane

n-Pentane

Water

(a) Gas temperatures restrictions applied

pR

0 2 4 6 8 10

ηcycle

0

0.1

0.2

0.3

0.4

0.5

R-245fa

R-141b

Cyclohexane

n-Pentane

Water

(b) No gas temperatures restrictions applied.

Figure 5.7 Model 2: influence of the gas temperatures restrictions on the possible results using CO2 inthe Brayton cycle for all Rankine fluids.

Increase of T13

The temperature T13 was raised from 400 K to 427 K, given that 427 K is the lowest temperature of

all the critical points (which corresponds to R-245fa, according to CoolProp [20]). The increase of h13

also implies an increase in the steam turbine expansion, i.e., in the net power output of the Rankine cycle.

Figures 5.8 and 5.9 show the global efficiency and power outputs obtained from the implementation of

the first strategy. As the behaviour is similar for every gas, only the results for CO2 are presented. The

rise of the temperature at the steam turbine inlet increases the range of physically acceptable results, as

well as the global cycle efficiencies, but not to the extent desired, since in Fig. 5.8 the possible solutions

are still far from the point of maximum efficiency.

The results for the power outputs are shown in Fig. 5.10. The most striking feature in figures 5.9 and

5.10 is the increase in global efficiency and net power output for the pair of fluids CO2 and R-245fa.

pR

0 2 4 6 8 10

ηcycle

0

0.1

0.2

0.3

0.4

0.5

R-245fa

R-141b

Cyclohexane

n-Pentane

Water

(a) Global efficciency curves for T13 = 400 K

pR

0 2 4 6 8 10

ηcycle

0

0.1

0.2

0.3

0.4

0.5

R-245fa

R-141b

Cyclohexane

n-Pentane

Water

(b) Global efficciency curves for T13 = 427 K

Figure 5.8 Model 2: global efficiency curves for temperature T13 = 400 K and T13 = 427 K at the inletof the steam turbine, using CO2 in the Brayton cycle.

47

CO2

Air N2

He H2

ηcycle

0

0.05

0.1

0.15

0.2

0.25

R-245fa

R-141b

Cyclohexane

n-Pentane

Water

(a) 400K

CO2

Air N2

He H2

ηcycle

0

0.05

0.1

0.15

0.2

0.25

R245FA

R141b

Cyclohexane

nPentane

Water

(b) 427K

Figure 5.9 Model 2: global maximum efficiency values for temperatures T13 = 400 K and T13 = 427 Kat the inlet of the steam turbine.

CO2

Air N2

He H2

Pow

erOutput[kW

]

0

5

10

15

20

25

30


(a) 400K

CO2

Air N2

He H2

Pow

erOutput[kW

]

0

5

10

15

20

25

30


(b) 427K

Figure 5.10 Model 2: net power at maximum global efficiency points for temperatures T13 = 400 K andT13 = 427 K at the inlet of the steam turbine.

In order to compare the results obtained with the ones from the work of Dunham and Lipinski [17],

tables 5.4 and 5.5 show the maximum global efficiency values of model 2 at temperatures at the steam

turbine’s inlet 400 and 427 K, respectively. For the pair of fluids CO2 and R-245fa, mentioned previously,

the increase in global efficiency equals 41.4 %.

Table 5.4 Model 2: maximum global efficiency values for T13 = 400 K.


R-245fa 0.1182 0.1589 0.1564 0.1427 0.1664R-141b 0.1774 0.1758 0.1745 0.1647 0.1848Cyclohexane 0.1350 0.1328 0.1362 0.1175 0.1421n-Pentane 0.1667 0.1704 0.1688 0.1602 0.1792Water 0.1375 0.1316 0.1315 0.1150 0.1386

48

Table 5.5 Model 2: maximum global efficiency values for T13 = 427 K.



Increase of ∆Tpinch point

In the second strategy, the value T13 = 400 K was kept constant and the pinch point temperature

difference was raised above 10 K. In Fig. 5.11, results are presented for the CO2 and R-245fa, Air and

R-141b fluid pairs, having each plot different curves corresponding to different pinch point temperature

differences. These two fluid pairs were chosen randomly to demonstrate that the same tendency is verified,

regardless of the working fluids.

As observed, the increase of the pinch point temperature difference decreases the global efficiency val-

ues, while also broadening the span of acceptable results. However, for the former fluid pair (which is the

most affected by the restrictions implemented), even at the lowest efficiency curves (highest ∆Tpinch point),

the global cycle efficiency is higher than the value obtained with a pinch point temperature difference

equal to 10 K, due to thermodynamic constraints. As it is not realistic to have ∆Tpinch point values as

high as 100 K, and as it would lower every other configuration’s global efficiency, its value should not

differ much from the value of 10 K mentioned in the work of Dunham and Lipinski [17].

pR

0 2 4 6 8 10

ηcycle

0

0.1

0.2

0.3

0.4

0.5

∆Tpinch=10 K

∆Tpinch=25 K

∆Tpinch=50 K

∆Tpinch=100 K

(a) CO2 & R-245fa

pR

0 2 4 6 8 10

ηcycle

0

0.1

0.2

0.3

0.4

0.5

∆Tpinch=10 K

∆Tpinch=25 K

∆Tpinch=50 K

∆Tpinch=100 K

(b) Air & R-141b

Figure 5.11 Model 2: global efficiency curves for different values of pinch point temperature differencewith T13 = 400 K.

Regenerator Heat Transfer Area

Other specification of the model cycles that influences its performance is the regenerator design and,

more specifically, its heat transfer area. Thus, the behaviour of the global efficiency curves when the heat

transfer area of the regenerator varies is analysed, keeping a mass flow ratio, m8/m1, equal to 0.5, and a

temperature at the inlet of the steam turbine T13 = 400 K. For the sake of conciseness, the fluid pair Air

49

and R-245fa was chosen, since the global efficiency curves show the same behaviour.

Fig. 5.12 shows the global efficiency evolution with the variation of the heat transfer area. The

larger the regenerator heat transfer area, the greater the global cycle efficiency, since the regenerator

effectiveness increases with its area of heat transfer (section 3.2). Furthermore, the pressure ratio at

which the curves reach their maximum level tends to decrease with the area increase. However, the range

of physically acceptable results does not improve. It is also worth noticing that no acceptable results are

obtained for areas of 8 m2 or higher.

pR

0 2 4 6 8 10

cycle

0

0.1

0.2

0.3

0.4

0.5

1m2

2m2

4m2

6m2

8m2

Figure 5.12 Model 2: regenerator heat transfer area influence on global cycle efficiency, for the fluid pairAir and R-245fa, assuming T13 = 400 K, ∆Tpinch point = 10 K and a mass flow ratio r = m8/m1 = 0.5.

Mass Flow Ratio

The mass flow ratio r = m8/m1 also affects the regenerator effectiveness. In the results presented in

Fig. 5.13, the regenerator heat transfer area was kept constant and equal to 6 m2.

The results show that the increase of the mass flow ratio implies a reduction of global efficiencies,

which can be explained by the following reasons:

– From the NTU relations (3.2), the increase of m8/m1 decreases the regenerator effectiveness and,

therefore, the Brayton cycle efficiency;

– The mass flow through the HRSG (m6 = m1(1 − r)) decreases, which results in a decrease of the

bottoming cycle mass flow, (mb = m6(h6 − h7)/(h13 − h12)) and, consequently, of the Rankine

power output and efficiency.

It is noteworthy that, with the increase of the mass flow ratio, the pressure ratios at which global

efficiencies reach their maximum values tend to be relocated to higher values, and that the curves inter-

section with the horizontal axis occurs for lower pR values. Regarding the range of acceptable results,

(solid lines) a tendency towards a broader spectrum can be observed when the mass flow ratio increases,

despite the lower efficiencies.

50

pR

0 2 4 6 8 10

ηcycle

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.20

0.35

0.50

0.65

0.80

Figure 5.13 Model 2: mass flow ratio r = m8/m1 influence on global cycle efficiency, for the fluid pairAir and R-245fa, assuming a regenerator heat transfer area equal to 6 m2, T13=400 K and ∆pinch point =10 K.

Nevertheless, the maximum global efficiency obtained in the work of Dunham and Lipinski [17]

(0.2106) could to not be reached, which can be explained by the following reasons:

• In the mentioned authors work, the regenerator effectiveness is considered constant and equal to

0.87, whilst in the present model it depends on different parameters such as the heat transfer area,

mass flow rates and specific heats, the maximum value being 0.87. Such disparities prevent a

possible and fair comparison between those cycles to be obtained. This issue will be addressed in

the next section;

• This model forces the Brayton cycle fluids to go to more extreme conditions due to its own config-

uration by having the stream bifurcation, which implies more severe restrictions in the operating

conditions.

On the other hand, however, efficiencies for several fluid combinations were raised, compared to

Dunham and Lipinski’s work [17]. Those correspond to the combinations: Air - R-141b, He - R-141b, He

- Cyclohexane, He - n-Pentane, H2 - R-141b, H2 - Cyclohexane, and H2 - n-Pentane.

5.2.3 Model 3

This model, compared to the previous one, brings the novelty of having a combustion chamber placed

after the solar receiver.

In a first approach, it is expected that this model provides the highest global efficiency values, com-

pared to the other two, due to the implementation of a combustion chamber, which increases the expansion

in the gas turbine. However, the analysis is not so straightforward.

Fig. 5.14 presents the global cycle efficiency results for the metallurgical temperature limit of the gas

turbine, T5 = 1173 K, assuming mass flow ratio of r = m9/m1 = 0.5, and a regenerator heat transfer

area equal to 6 m2. The two last parameters were chosen in order to make a comparison with the results

51

of model 2. The pR values range from 1 to 40 for this first simulation and are bounded to 20 thereafter,

since there are no relevant results above that value.

As expected, the efficiencies are overall higher than the ones obtained with model 2, which can

be observed comparing figures 5.14 and 5.6, and no acceptable results are obtained. However, when

compared to the peak efficiencies in model 1, using the same temperature T5 = 1173 K (Fig. 5.2), the

global efficiencies of model 3 are considerably lower. Such outcome is mainly due to the fact that in

model 1 (as well as in the work of Dunham and Lipinski [17]) the regenerator effectiveness was considered

constant and equal to 0.87, whereas in models 2 and 3 this parameter was calculated using the NTU

relations, imposing a maximum value of 0.87. To make a comparison on equal terms, the same procedure

should be applied to model 1. Efficiency curves are presented in Fig. 5.15 (model 1) and Fig. 5.16 (model

3), assuming a temperature at the inlet of the gas turbine T5 = 825 K and a regenerator heat transfer

area of 6 m2. The peak efficiency values are presented in tables 5.6 and 5.6 .

52

pR

5 10 15 20 25 30 35 40

ηcycle

0

0.1

0.2

0.3

0.4

0.5

R-245fa

R-141b

Cyclohexane

n-Pentane

Water

(a) CO2

pR

5 10 15 20 25 30 35 40

ηcycle

0

0.1

0.2

0.3

0.4

0.5

R-245fa

R-141b

Cyclohexane

n-Pentane

Water

(b) Air

pR

5 10 15 20 25 30 35 40

ηcycle

0

0.1

0.2

0.3

0.4

0.5

R-245fa

R-141b

Cyclohexane

n-Pentane

Water

(c) N2

pR

5 10 15 20 25 30 35 40

ηcycle

0

0.1

0.2

0.3

0.4

0.5

R-245fa

R-141b

Cyclohexane

n-Pentane

Water

(d) He

pR

5 10 15 20 25 30 35 40

ηcycle

0

0.1

0.2

0.3

0.4

0.5

R-245fa

R-141b

Cyclohexane

n-Pentane

Water

(e) H2

Figure 5.14 Model 3: global cycle efficiency assuming T5 = 1173 K, a regenerator heat transfer areaequal to 6 m2 and a mass flow ratio r = 0.5.

53

pR

0 5 10 15 20

ηcycle

0

0.05

0.1

0.15

0.2

0.25

0.3

R-245fa

R-141b

Cyclohexane

n-Pentane

Water

(a) CO2

pR

0 5 10 15 20

ηcycle

0

0.05

0.1

0.15

0.2

0.25

0.3

R-245fa

R-141b

Cyclohexane

n-Pentane

Water

(b) Air

pR

0 5 10 15 20

ηcycle

0

0.05

0.1

0.15

0.2

0.25

0.3

R-245fa

R-141b

Cyclohexane

n-Pentane

Water

(c) N2

pR

0 5 10 15 20

ηcycle

0

0.05

0.1

0.15

0.2

0.25

0.3

R-245fa

R-141b

Cyclohexane

n-Pentane

Water

(d) He

pR

0 5 10 15 20

ηcycle

0

0.05

0.1

0.15

0.2

0.25

0.3

R-245fa

R-141b

Cyclohexane

n-Pentane

Water

(e) H2

Figure 5.15 Model 1: global cycle efficiency assuming T5 = 825 K and a regenerator heat transfer areaequal to 6 m2.

54

pR

0 5 10 15 20

ηcycle

0

0.05

0.1

0.15

0.2

0.25

0.3

R-245fa

R-141b

Cyclohexane

n-Pentane

Water

(a) CO2

pR

0 5 10 15 20

ηcycle

0

0.05

0.1

0.15

0.2

0.25

0.3

R-245fa

R-141b

Cyclohexane

n-Pentane

Water

(b) Air

pR

0 5 10 15 20

ηcycle

0

0.05

0.1

0.15

0.2

0.25

0.3

R-245fa

R-141b

Cyclohexane

n-Pentane

Water

(c) N2

pR

0 5 10 15 20

ηcycle

0

0.05

0.1

0.15

0.2

0.25

0.3

R-245fa

R-141b

Cyclohexane

n-Pentane

Water

(d) He

pR

0 5 10 15 20

ηcycle

0

0.05

0.1

0.15

0.2

0.25

0.3

R-245fa

R-141b

Cyclohexane

n-Pentane

Water

(e) H2

Figure 5.16 Model 3: global cycle efficiency assuming T5 = 825 K, a regenerator heat transfer areaequal to 6 m2 and a mass flow ratio r = 0.5.

55

Table 5.6 Model 1 (with the regenerator effectiveness calculated from the NTU relations): peak globalefficiency values for each fluid combination.


R-245fa 0.1618 0.1500 0.1500 - 0.1482R-141b 0.1615 0.1395 0.1391 - 0.1360Cyclohexane 0.1291 0.1074 0.1070 - 0.1041n-Pentane 0.1649 0.1425 0.1419 - 0.1388Water 0.1159 0.0949 0.0945 - 0.0920

Table 5.7 Model 3: peak global efficiency values for each fluid combination.



The results show that model 3 outperforms model 1. With the exception of the pair CO2 and R-245fa,

every fluid combination in model 3 yields higher peak global efficiencies than in the case of model 1. It

is worth pointing that no acceptable results are obtained in model 1 for He.

To understand the influence of the stream splitter on the regenerator effectiveness, Fig. 5.17 presents

the effectiveness values for the three models, under the same design conditions, imposing a maximum

effectiveness value of 0.87. The effectiveness for the first model is considerably lower. Since there is

no stream splitter in model 1, the larger mass flow on the regenerator hot side is the reason for this

behaviour.

pR

0 5 10 15 20

ηreg

0

0.2

0.4

0.6

0.8

0.87

1

CO2

Air

N2

He

(a) Model 1

pR

0 2 4 6 8 10

ηreg

0

0.2

0.4

0.6

0.8

0.87

1

CO2

Air

N2

He

H2

(b) Model 2

pR

0 5 10 15 20

ηreg

0

0.2

0.4

0.6

0.8

0.87

1

CO2

Air

N2

He

H2

(c) Model 3

Figure 5.17 Brayton cycle’s regenerator effectiveness values for models 1, 2, and 3, assuming a heattransfer area of 6 m2 and, for models 2 and 3, a mass flow ratio r = 0.5.

These results, reconciled with the global efficiencies results, show the degree of influence that the

regenerator effectiveness has in the cycles performances and how the stream splitting provides better

results.

56

Chapter 6

Conclusions and Future Work

6.1 Conclusions

The main goal of this work was to study the performance of three combined Brayton-Rankine cycles with

solar thermal power generation and, if possible, improve the results of the work of Dunham and Lipinski

[17].

The main conclusions are:

1. The fluid pair CO2 and R-245fa provides the highest global cycle efficiency curves for all the models.

In the case of model 2 and 3, however, due to the stream splitting, this pair is the most affected

in terms of thermodynamic restrictions, resulting in the lowest global efficiencies, despite having

better maximum efficiencies.

2. In model 1, with its regenerator effectiveness calculated from the NTU relations, the fluid pair CO2

and n-Pentane stands out as the best pair, providing an efficiency value of 0.1649. The fluid pair

H2 and R-141b provides the best cycle performance for model 2, leading to a global efficiency of

0.1848. In regards to model 3, the best fluid pair is CO2 and R-141b, providing an efficiency value

of 0.2045.

3. With the model operating with the same Brayton cycle regenerator design conditions, as in the

work of Dunham and Lipinski [17] (εreg = 0.87), having a combustion chamber supporting the solar

receiver in the generation of heat (with Qc < Qsol) provides higher global efficiencies than with

solar alone. This also supports the idea that the combination of both types of energy can feed a

power cycle more efficiently.

4. With εreg being obtained from the NTU-effectiveness relations, models 2 and 3 outperform model

1, which is similar to the cycle studied in the work of Dunham and Lipinski [17]. Such results allow

us to conclude that the implementation of the stream splitter is beneficial.

57

6.2 Future Work

As mentioned in chapter 1, technologies for the exploitation of solar energy are developing at a significant

pace due to the present environmental and economical context. Therefore, research in this field is very

relevant and some suggestions can be made regarding future work:

1. In addition to the energy analysispresented in this work, an exergetic analysis should also be done,

in order to identify the components of the cycle with major exergy destructions.

2. A further analysis on a wider range of fluids.

3. Finally, as in any engineering study, an economic analysis is paramount. As the goal is to maxi-

mize gains and minimize costs, these conflicting objectives can be studied using a multi-objective

optimization, which examines the required trade-off between increased electricity production and

additional investment cost. This analysis should also take into account CO2 emissions, which will

be increasingly penalized by taxes and regulations, in the near future.

58

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