Receiver Design Methodology for Solar Tower Power Plants

Department of Energy Technology Receiver Design Methodology for Solar Tower Power Plants

Master Thesis

Joseph Stalin Maria Jebamalai

Supervisors: Dipl.-Ing. Peter Sch¨ottl,Internal Supervisor, Fraunhofer ISE, Freiburg

Dr. Bj¨ornLaumert, External Supervisor, KTH Royal Institute of Technology

KTH School of Industrial Engineering and Management Department of Energy Technology Division of Heat and Power Technology SE - 100 44, Stockholm August 2016

Master of Science Thesis EGI_2016: 070 MSC EKV1157

Receiver Design Methodology for Solar Tower Power Plants

Joseph Stalin Maria Jebamalai

Approved Examiner Supervisor 16th August 2016 Dr. Björn Laumert Dipl.-Ing. Peter Schöttl

Dr. Björn Laumert

Commissioner Contact person

Dr. Björn Laumert

Abstract – Swedish

Centrala solmottagarsystem (CRS) är på frammarsch på grund av deras höga koncentrationsfaktor och höga potential att minska kostnaderna genom att öka kapacitetsfaktorn av solkraftanläggningar med lagring. I CRS kraftanläggningar är solljuset fokuserat på mottagaren genom arrangemanget av tusentals speglar för att omvandla solstrålning till värme för att driva värmecykler. Solmottagare används för att överföra värmeflux från solen till arbetsmediet. Generellt arbetar solmottagare i driftpunkter med hög temperatur och därför genereras strålningsförluster. Vidare har solmottagaren en betydande påverkan på den totala kostnaden för kraftverket. Således har konstruktion och modellering av mottagaren en signifikant påverkan på kraftanläggningseffektivitet och kostnad. Målet med detta examensarbete är att utveckla en designmetodik för att beräkna geometrin hos solmottagaren och dess verkningsgrad. Denna designmetodik riktar sig främst till stora kraftverk i området 100 MWe, men även skalbarheten av designmetoden har studerats. Den utvecklade konstruktionsmetoden implementerades i in-house designverktyg devISEcrs som även integrerar andra moduler som modellerar solspegelfält, lagring och kraftblocket för att beräkna den totala kraftverksverkningsgraden. Designmodeller för de andra komponenterna är delvis redan implementerade, men de är modifierade och/eller utvidgade för att integrera den nya CRS mottagarmodellen. Slutligen har hela mottagarmodellen validerats genom att jämföra resultaten med testdata från litteraturen. Abstract

Central Receiver Systems (CRS) are gaining momentum because of their high concentration and high potential to reduce costs by means of increasing the capacity factor of the plant with storage. In CRS plants, sunlight is focused onto the receiver by the arrangement of thousands of mirrors to convert the solar radiation into heat to drive thermal cycles. Solar receivers are used to transfer the heat flux received from the solar field to the working fluid. Generally, solar receivers work in a high-temperature environment and are therefore subjected to different heat losses. Also, the receiver has a notable impact on the total cost of the power plant. Thus, the design and modelling of the receiver has a significant influence on efficiency and the cost of the plant. The goal of the master thesis is to develop a design methodology to calculate the geometry of the receiver and its efficiency. The design methodology is mainly aimed at large-scale power plants in the range of 100 MWe, but also the scalability of the design method has been studied. The developed receiver design method is implemented in the in-house design tool devISEcrs and also it is integrated with other modules like solar field, storage and power block to calculate the overall efficiency of the power plant. The design models for other components are partly already implemented, but they are modified and/or extended according to the requirements of CRS plants. Finally, the entire receiver design model is validated by comparing the results of test cases with the data from the literature.

ii Receiver Design Methodology for Solar Tower Power Plants Acknowledgement

I express my sincere gratitude to Fraunhofer Institute of Solar Energy Systems (ISE) and KTH Royal Institute of Technology for providing this wonderful opportunity to carry out my master thesis in Germany. It was an incredible experience for me as I have gained lots of knowledge on CSP power plants.

I would take this opportunity to thank my supervisor at Fraunhofer ISE, Dipl.-Ing. Peter Schöttl for his continuous guidance and knowledge sharing throughout the thesis. I extend my gratitude to my academic supervisor, Dr. BjörnLaumert for his support. Special thanks to KTH and Fraunhofer ISE for providing financial support and all the necessary facilities.

I am also thankful to Anna Heimsath, Bernhard Seubert, Claudia Sutardhio, De Wet Van Rooyen, Pankaj Deo, Raymond Branke, Shaab Rohani and Thomas Fluri for their contributions and dis- cussion about the project. Furthermore, I would like to thank all the staﬀ members who helped me through all phases of my thesis.

Finally, I would like to thank my parents and my friends, Abhishek Srujan, Anand Bhaskaran and Sai Janani Ramachandran for their continuous support and motivation all days, especially during my hard times.

Receiver Design Methodology for Solar Tower Power Plants iii Contents

Contents iv

List of Figures vi

List of Tables viii

Nomenclature ix

1 Introduction 1 1.1 Solar Radiation...... 1 1.2 Concentrated Solar Power (CSP)...... 2 1.3 Central Receiver Systems (CRS)...... 4 1.4 Research Statement...... 6 1.5 Thesis Overview...... 7

2 Literature Review8 2.1 Tubular Receivers...... 8 2.1.1 Water/Steam...... 8 2.1.2 Molten Salt...... 9 2.1.3 Liquid Sodium...... 10 2.1.4 Sodium/Salt Binary...... 10 2.2 Design Criteria...... 11 2.2.1 Receiver Design Methodology...... 11 2.2.2 Allowable Peak Flux Limit...... 12 2.2.3 Receiver Sizing...... 13 2.2.4 Receiver Aspect Ratio...... 13 2.2.5 Tube Diameter Selection...... 14 2.2.6 Fluid Flow Path Selection...... 14 2.2.7 Tower Sizing...... 15 2.3 Cavity Speciﬁc Design Criteria...... 15 2.3.1 Cavity Receiver Geometry...... 16 2.3.2 Cavity Opening Angle...... 16 2.3.3 Lip Height (Aperture-to-Total Height Ratio)...... 16 2.3.4 Cavity Inclination...... 17 2.4 Heat Transfer Model...... 17 2.4.1 External Receiver...... 18 2.4.2 Cavity Receiver...... 21

3 Design Methodology 25 3.1 Design Approach...... 25 3.2 General Receiver Design Model...... 27 3.2.1 Receiver Thermal Power...... 27 3.2.2 Calculation of HTF Properties...... 27 iv Receiver Design Methodology for Solar Tower Power Plants CONTENTS

3.2.3 Receiver Sizing...... 27 3.2.4 Receiver Surface Temperature Calculation...... 28 3.2.5 Mass Flow Rate Calculation...... 29 3.2.6 Pressure Loss and Pump Power Calculation...... 29 3.3 External Receiver Design Model...... 30 3.3.1 Geometry Design...... 30 3.3.2 Tube and Panel Design...... 30 3.3.3 Tower Height Design...... 32 3.3.4 Receiver Thermal Eﬃciency...... 33 3.4 Cavity Receiver Design Model...... 34 3.4.1 Geometry Design...... 34 3.4.2 Tube and Panel Design...... 36 3.4.3 Tower Height Design...... 36 3.4.4 Receiver Thermal Eﬃciency...... 37

4 Implementation 39 4.1 devISEcrs - A Design Tool...... 39 4.2 Implementation Structure...... 40 4.3 Interface of Receiver Classes...... 41 4.3.1 Receiver Class...... 41 4.3.2 External Receiver Class...... 41 4.3.3 Cavity Receiver Class...... 41

5 Validation and Results 44 5.1 Receiver Design Validation...... 44 5.1.1 External Receiver...... 44 5.1.2 Cavity Receiver...... 48 5.2 Receiver Thermal Losses Validation...... 49 5.2.1 External Receiver...... 49 5.2.2 Cavity Receiver...... 50 5.3 Eﬀect of Spillage Loss on Heliostat Size...... 51

6 Conclusion and Future Work 53 6.1 Conclusion...... 53 6.2 Future Work...... 53

Bibliography 54

Receiver Design Methodology for Solar Tower Power Plants v List of Figures

1.1 Direct, diffuse and reflected radiation [8]...... 1 1.2 World solar DNI map [50]...... 2 1.3 Example of solar thermal power plant with four subsystems [3]...... 3 1.4 Types of CSP collectors [5]...... 4 1.5 Gemasolar 20MW solar tower power plant in Sevilla, Spain [6]...... 5 1.6 Optical losses in the heliostat field...... 5 1.7 Solar receivers [9]...... 6

2.1 Tubular receivers from Solar Two plant (left) and PS10 plant (right) [52].....8 2.2 Flow layout of water/steam central receiver system [2]...... 9 2.3 Flow layout of molten salt central receiver system [52]...... 9 2.4 Flow layout of liquid sodium central receiver system [22]...... 10 2.5 Flow layout of sodium/salt binary central receiver system [22]...... 11 2.6 Tubular receivers: a) External receiver, b) Cavity receiver [10]...... 11 2.7 Receiver peak flux value for different HTF and materials with respect to life cycles [22]...... 13 2.8 Eight possible fluid flow configuration by Wagner [52]...... 14 2.9 Solar tower for external and cavity receivers [23]...... 15 2.10 Cavity receiver geometry with four receiver panels [23]...... 16 2.11 Lip height of cavity receiver [33]...... 17 2.12 Cavity inclination angle [33]...... 17 2.13 Variation of Richardson number with respect to wind velocity for cavity receiver [48] 22 2.14 Two-zone model of the cavity receiver [25]...... 23

3.1 Receiver design methodology for tubular receivers...... 26 3.2 External receiver geometry [45]...... 30 3.3 Tube diameter correlation with respect to receiver thermal power...... 31 3.4 Variation of tower height with respect to receiver thermal power [22]...... 32 3.5 Tower height correlation with respect to receiver thermal power for external receiver 33 3.6 Geometry of cavity receiver [23]...... 34 3.7 Internal angle geometry of cavity receiver [23]...... 35 3.8 Tower height correlation with respect to receiver thermal power for cavity receiver 36 3.9 Internal heat transfer area of the cavity receiver [43]...... 37

4.1 Modules of the devISEcrs design tool...... 39 4.2 Class inheritance structure of the receiver module in devISEcrs...... 40

5.1 Total and individual loss component comparison for external receiver...... 50 5.2 Total and individual loss component comparison for cavity receiver...... 51 5.3 External receiver spillage loss of diﬀerent power plant sizes with respect to heliostat size...... 52 vi Receiver Design Methodology for Solar Tower Power Plants LIST OF FIGURES

5.4 Cavity receiver spillage loss of diﬀerent power plant sizes with respect to heliostat size...... 52

Receiver Design Methodology for Solar Tower Power Plants vii List of Tables

2.1 Receiver ﬂux limit for diﬀerent HTF [22]...... 13 2.2 Nusselt correlation for forced convection of external receivers [43]...... 20

3.1 Properties of solar salt [55]...... 27 3.2 Tube diameter used in various commercial power plants [49][39] [51]...... 31

4.1 Input parameters and its default value of the receiver class...... 41 4.2 Input parameters and its default value of the external receiver class...... 42 4.3 Output parameters of the external receiver class...... 42 4.4 Input parameters and its default value of the cavity receiver class...... 42 4.5 Output parameters of the cavity receiver class...... 43

5.1 Solar Two power plant characteristics [51]...... 45 5.2 Comparison of Solar Two receiver design parameters...... 45 5.3 Gemasolar power plant characteristics [36]...... 46 5.4 Comparison of Gemasolar receiver design parameters...... 46 5.5 Crescent Dunes power plant characteristics [37]...... 47 5.6 Comparison of Crescent Dunes receiver design parameters...... 48 5.7 PS10 power plant characteristics [44]...... 48 5.8 Comparison of PS 10 receiver design parameters...... 49 5.9 Validation of molten salt external receiver thermal losses...... 49 5.10 Validation of molten salt cavity receiver thermal losses...... 50

viii Receiver Design Methodology for Solar Tower Power Plants Nomenclature

Abbrevations

CRS Central Receiver Systems

CSP Concentrated Solar Power

DNI Direct Normal Irradiance

HTF Heat Transfer Fluid

Greek symbols

α Absorptance -

β Volumetric expansion coeﬃcient 1/K

Emissivity -

η Eﬃciency -

µ Dynamic viscosity kg/ms

ν Kinematic viscosity m2/s

ρ Density kg/m3

σ Stefan-Boltzmann constant W/m2K4

θ Cavity opening angle -

Symbols

∆P Pressure diﬀerence N/m2 m˙ Mass ﬂow rate kg/s

Q˙ Energy W cp Speciﬁc heat J/kgK

Ks Surface roughness - uwind Wind velocity m/s

2 qo Allowable peak ﬂux W/m A Area m2

D Diameter m d Diameter of the receiver tube m

Receiver Design Methodology for Solar Tower Power Plants ix NOMENCLATURE f Darcy friction factor - g Acceleration due to gravity m/s2 Gr Grashof number - H Height m h Heat transfer coefficient W/m2 K k Thermal conductivity W/m K L Length m n Count - Nu Nusselt number - P Pressure N/m2 Pr Prandtl number - R Thermal Resistance K/W r Radius m Ra Rayleigh number - Re Reynolds number - Ri Richardson number - SM Solar multiple - T Temperature K v Velocity m/s W Width m Subscripts abs Absorber amb Ambient avg Average c Characteristic cond Conduction conv Convection eff Effective el Electric env Envelope f Film for Forced htf Heat transfer fluid x Receiver Design Methodology for Solar Tower Power Plants NOMENCLATURE i Inner inc Incident max Maximum min Minimum mix Mixed nat Natural o Outer pb Power block rad Radiation rec Receiver ref Reflection s Surface th Thermal tot Total tube Receiver tube w Wall

Receiver Design Methodology for Solar Tower Power Plants xi Chapter 1

Introduction

The growing global energy demand and environmental pollution urge humanity to focus on renewable energy. In order to meet the increasing energy demand in a sustainable way, solar energy has the potential to act as a future energy source. One challenge with solar energy is that it is a variable source of energy. This can be tackled with Concentrated Solar Power (CSP) coupled with storage technology which assures dispatchability of energy. Hence, CSP can act as a promising alternative source of energy in the future. CRS plant is one of the types of CSP plants, for which the receiver design methodology will be developed in this thesis. This chapter explains about basic concepts of CSP technology, research statement and the thesis overview.

1.1 Solar Radiation

Figure 1.1: Direct, diﬀuse and reﬂected radiation [8]

Solar irradiance is the rate of radiant energy per unit area over a period of time produced from the sun. The units of solar irradiance are W/m2 [45] and suns. One sun is equal to 1000 W/m2. The atmosphere scatters and absorbs some of the solar radiation that is incident on the earth surface before reaching the ground. This is mainly due to the dust particles, gaseous molecules and clouds in the atmosphere. The amount of solar radiation reﬂected, scattered and absorbed depends on

Receiver Design Methodology for Solar Tower Power Plants 1 CHAPTER 1. INTRODUCTION

Figure 1.2: World solar DNI map [50] the distance travelled by the solar radiation, levels of dust particles and water vapour present in the atmosphere. Figure 1.1 shows the three types of radiation which are explained below:

• Direct radiation - The radiation which is coming straight through the atmosphere without getting scattered is called direct radiation and it is directional.

• Diﬀuse radiation - The radiation, which gets scattered by the particles and molecules in the atmosphere, but still made it down to the earth surface, is called diﬀuse radiation.

• Reflected radiation - The radiation which has been reflected due to obstacles such as buildings and ground is called reflected radiation.

CSP plants convert only Direct Normal Irradiance (DNI) into electrical energy [14]. The minimum threshold DNI necessary for the CSP technology is 2000 KW h/m2/year because of economic constraints [14]. In order to have an idea about DNI, world solar DNI map is shown in the Figure 1.2.

1.2 Concentrated Solar Power (CSP)

CSP technology mainly works on the principle of concentrating vast area direct insolation onto absorbers to convert it into thermal energy. Mirrors are used to focus the solar radiation onto absorbers. Absorbers are used to transfer the obtained solar thermal energy to a Heat Transfer Fluid (HTF). Then, the thermal energy in the HTF is used to generate steam and electricity is produced by a conventional power cycle. Solar radiation is a variable source of energy, which cannot be controlled. Thus, it is advisable to incorporate storage into the system. Consequently, CSP technology mainly consists of four subsystems [11] which are shown in the Figure 1.3:

2 Receiver Design Methodology for Solar Tower Power Plants CHAPTER 1. INTRODUCTION

Figure 1.3: Example of solar thermal power plant with four subsystems [3]

• Solar collector/field • Solar receiver • Storage system • Power conversion system The solar collector mainly differs with the shape of the collector surface. There are line focusing systems, which can be a parabolic trough or a linear fresnel collector, and point focusing systems, which can be a dish collector or a central receiver. The four types of commercially accomplished CSP collectors [11] are depicted in Figure 1.4. Point focusing systems have a higher concentration ratio compared to the line focusing systems. Thus, higher temperatures can be easily achieved by point focusing systems [11]. Solar receivers are the main focus of this thesis, therefore they are discussed in a separate section. The main technologies used in the storage system are sensible or latent heat storage. Some of the different types of storage system are listed below: • Storage systems – Two-tank direct – Two-tank indirect – Single-tank thermocline • Storage media – Sensible heat storage – Latent heat storage

Receiver Design Methodology for Solar Tower Power Plants 3 CHAPTER 1. INTRODUCTION

Figure 1.4: Types of CSP collectors [5]

Two-tank molten salt HTF is widely used as a storage technology in CSP plants [16] because molten salt is economically cheap [28] and it has large-scale industrial experience as a coolant in heat transport systems [26].

The power conversion system is a conventional Rankine, Brayton or combined cycle consisting of turbine, generator, and condenser.

1.3 Central Receiver Systems (CRS)

CRS plants have thousands of mirrors (called heliostats) concentrating solar radiation onto the receiver. The receiver is placed on top of the tower at the focal point of the heliostats as shown in Figure 1.5. CRS plants have the following four subsystems: • Heliostat field • Solar receiver • Storage system • Power conversion unit The heliostat field consists of an array of two-axis tracking mirrors which always focuses the radiation onto the receiver. There are two types of heliostat field orientation: Surround fields are roughly circular with the heliostats surrounding the tower, North/south fields have all heliostats on either north or south of the tower. The former are suitable for the equatorial region and the

4 Receiver Design Methodology for Solar Tower Power Plants CHAPTER 1. INTRODUCTION

Figure 1.5: Gemasolar 20MW solar tower power plant in Sevilla, Spain [6] latter are suitable for the northern/southern hemisphere due to the sun's path in the respective region.

Solar radiation undergoes various optical losses before it reaches the receiver. Figure 1.6 depicts various optical losses in the heliostat field. The cosine efficiency of the heliostat is the major effect which determines the optimum heliostat field layout [45]. This efficiency depends on both the sun's position and the location of the individual heliostat relative to the receiver [45]. The tracking mechanism is used to position the heliostat so that its surface normal bisects the angle between the sun's rays and the reflected radiation from the heliostat to the receiver. The effective reflection area of the heliostat is reduced by the cosine of one half of this angle [45] and the loss due to this effect is called cosine loss. Shadowing losses are due to the shadows casted by neighbouring heliostats on the heliostat under consideration. The effect of radiation from one heliostat to the receiver being blocked by another heliostat is called blocking loss. Attenuation loss occurs due to the dust particles in the path of the radiation to the receiver. The effect of reflected radiation from the heliostat which does not hit the receiver is called spillage loss. This occurs when the reflected image of the heliostat is larger than the receiver aperture. Heliostat field design has to take into account optical losses. The radial staggered pattern is the most widely used layout for designing solar fields for CRS plants [42][40].

Figure 1.6: Optical losses in the heliostat ﬁeld

Receiver Design Methodology for Solar Tower Power Plants 5 CHAPTER 1. INTRODUCTION

Figure 1.7: Solar receivers [9]

The main types of CRS receivers are shown in the Figure 1.7 and also listed below:

• Tubular receivers

– External receiver – Cavity receiver

• Volumetric receivers

– Open volumetric air receiver – Pressurized air receiver

• Solid particle receivers

Tubular receivers are the most widely used receiver technology [27]. Hence, the design methodology is limited to tubular receivers in this study. In case of tubular receivers, external and cavity are the two most commonly used receivers in CRS plants. The type of receiver directly affects the shape of the solar field. External receivers are combined with surround type solar fields whereas cavity receivers are combined with either a north or south field. In case of external receivers, all the outer surfaces of absorber tubes are exposed to the field whereas in cavity receivers, absorber tubes are enclosed in the cavity. The radiation enters the cavity through the aperture opening, to hit the absorbing tube surfaces. The enclosure of cavity receivers reduces thermal losses compared to external receivers. Since the cavity enclosure restricts the entry of concentrated solar radiation, spillage loss is higher as compared to external receivers.

In PS10, the cavity opening angle for cavity receiver is 180 degrees and so it looks like a half cylinder [23]. However, it is possible to increase the cavity opening angle. Moreover, multiple cavities can be formed to cover the radiation from the solar ﬁeld [45].

1.4 Research Statement

In the recent years, several publications covered receiver design, optimisation and assessment of receiver thermal efficiency [30][53][31][41][24]. Solar receivers cost around 10 - 15% of the total capital investment cost of a power plant [38]. Plant performance, capital cost and the cost of energy produced are significantly affected by the receiver efficiency [43].

6 Receiver Design Methodology for Solar Tower Power Plants CHAPTER 1. INTRODUCTION

Therefore, it is essential to design the receiver carefully in order to increase the plant performance and to minimise the energy cost. In case of CRS plants, receivers are one of the crucial parts to design because they should be capable of withstanding high working temperatures and solar ﬂux transients that cause thermal stress and creep failure [38]. Hence, the main focus of this thesis is on the design of receivers. Due to their high commercial relevance, only tubular receivers are covered.

This research focuses on developing the design methodology for tubular receivers which includes external and cavity receivers. Also, this work includes implementation of the developed design method in the Fraunhofer ISE in-house design tool, devISEcrs. The entire receiver geometry will be designed by devISEcrs and also the thermal losses will be calculated.

1.5 Thesis Overview

This thesis is structured with six chapters starting with this introduction chapter explaining the basic CSP technologies. Chapter 2 discusses the literature about various tubular receiver systems, receiver design methodology, design criteria and the heat transfer model. Chapter 3 explains about the developed design methodology based on the study of literature. Chapter 4 describes the implementation of the developed design method, which includes the structure of implementation and interface of the receiver classes. Chapter 5 shows the results and validation of the developed design method. Finally, Chapter 6 concludes the work and discusses possible future work.

Receiver Design Methodology for Solar Tower Power Plants 7 Chapter 2

Literature Review

In this chapter, diﬀerent design methodologies of tubular receivers are studied. Also, an overview of the design criteria is given and the existing heat transfer models of tubular receivers are discussed.

2.1 Tubular Receivers

Tubular receivers are the most widely used state-of-the-art receiver technology [27]. Two examples are shown in the Figure 2.1. There are four common system options available based on the receiver and storage ﬂuid. Among these four, water/steam and molten salt systems are commercially most relevant and liquid sodium is still in research phase.

Figure 2.1: Tubular receivers from Solar Two plant (left) and PS10 plant (right) [52]

2.1.1 Water/Steam Figure 2.2 depicts the water/steam central receiver system. Water is used as a Heat Transfer Fluid (HTF) in this type of system. Hence, there is a direct steam generation in the receiver itself. One of the main advantages of this system is that there is no need of a heat exchanger, if storage is not considered. The disadvantages of this system are as follows:

• Low receiver peak ﬂux limit (0.3 to 0.6 MW/m2)[22].

• Storing energy in the form of high-pressure steam is uneconomical, so energy must be trans- ferred to some other medium with heat exchangers resulting in higher exergy loss.

8 Receiver Design Methodology for Solar Tower Power Plants CHAPTER 2. LITERATURE REVIEW

Figure 2.2: Flow layout of water/steam central receiver system [2]

• The phase change in the HTF adds additional restrictions to the receiver design, which have a negative inﬂuence on the eﬃciency.

• The pioneer CSP power plant, Solar One used oil/rock thermocline storage. The maximum temperature limitation of oil is 315 ◦C. As a consequence, the output steam from the storage has comparatively low temperature which results in the low turbine gross eﬃciency [22].

2.1.2 Molten Salt

A molten salt central receiver system is shown in the Figure 2.3. Molten salt is an attractive HTF for CSP plants with storage due to its low cost and its commercial availability. Some of the attractive features [22] are:

Figure 2.3: Flow layout of molten salt central receiver system [52]

• High receiver peak ﬂux limit compared to water/steam system (0.6 to 0.8 MW/m2).

• State-of-the-art technology with 40 years of operational experience as a HTF.

• Non-toxic and stable over an extended period of time when protected from the environment and overheating.

• Molten salt is 2 to 3 times cheaper than sodium.

Receiver Design Methodology for Solar Tower Power Plants 9 CHAPTER 2. LITERATURE REVIEW

Figure 2.4: Flow layout of liquid sodium central receiver system [22]

2.1.3 Liquid Sodium A liquid sodium central receiver system is shown in the Figure 2.4. Attributing to the fact that liquid sodium has very good heat transfer properties, it has low thermal losses due to the reduced area of the receiver. Mostly, sodium receivers are external type with already reduced losses, hence further loss reduction with cavity type receiver is not shown to be beneﬁcial [22]. Compared to molten salt, liquid sodium has very good heat transfer properties [22] as indicated below: • High thermal conductivity results in operating the receiver with high incident solar ﬂux (in excess of 1.5 MW/m2). • Sodium freezes at 100 ◦C which is two times lower when compared to molten salt. • Sodium has a high boiling point (873 ◦C) [13] which allows it to operate in high-temperature Brayton power cycles.

• Receiver size and thermal losses are reduced due to the higher operational flux resulting in a better receiver efficiency. But, there are many limiting factors which act as a hindrance for sodium receiver to be commercially accomplished. Some of them [22] are stated below: • The relatively high cost and low specific heat of sodium limit its usage as sensible heat storage medium. • Low volumetric heat capacity of sodium makes the storage tank large and costly. • The main point to note is that the highly reactive nature of sodium and water has to be considered while designing and it adds a high risk.

2.1.4 Sodium/Salt Binary Sodium/salt binary central receiver system is shown in the Figure 2.5. Sodium is used as a receiver fluid and molten salt is used as a storage fluid in sodium/salt binary system. It combines the attractive features of both fluids, but an additional heat transfer loop is needed for the system to run, which adds complexity. The risk of sodium fire is reduced, because it is restricted within the concrete tower. However, the reaction between sodium and molten salt is not well-known. Current indications are that it would be strongly exothermic and release the gaseous product, which may lead to pressurisation problem [22].

10 Receiver Design Methodology for Solar Tower Power Plants CHAPTER 2. LITERATURE REVIEW

Figure 2.5: Flow layout of sodium/salt binary central receiver system [22]

2.2 Design Criteria

This section summarises critical receiver design parameters.

2.2.1 Receiver Design Methodology This section summarises the various receiver design methodologies that are available in the literature. Figure 2.6 depicts the sketch of external and tubular receivers.

Figure 2.6: Tubular receivers: a) External receiver, b) Cavity receiver [10]

Falcone [1986] Falcone [22] suggested the following steps for tubular receiver design:

1. Calculate the thermal rating of the receiver based on system level requirements like plant output, type of receiver ﬂuid and storage media, nature of power cycle and solar multiple.

2. Select the ﬂux limit based on working ﬂuid and tube material of the receiver.

3. Calculate the required receiver absorber area for the given allowable ﬂux limit.

4. Design the receiver geometry, taking into account thermal loss and the practical size of the receiver. The minimum receiver size is largely a function of spillage considerations based on the size of reﬂected heliostat image. The maximum practical size is limited by the height of receiver panels due to shipping constraints.

Receiver Design Methodology for Solar Tower Power Plants 11 CHAPTER 2. LITERATURE REVIEW

Zavoico [2001]

Zavoico [55] suggested the following steps for tubular receiver design:

1. Establish the allowable incident ﬂux as a function of bulk salt temperature, allowable cumu- lative tube strains and corrosion rates at the salt ﬁlm temperature.

2. Estimate the receiver size based on the maximum allowable ﬂux.

3. Estimate the heat losses for various combinations of receiver height and diameter.

4. The aspect ratio should be selected for the maximum receiver eﬃciency and low cost.

Lata [2008]

Lata et al. [30] tried to optimize the receiver dimensions in order to increase the allowable peak ﬂux of molten salt receiver from 0.85 MW/m2 to 1 MW/m2. Basically, this design methodology is similar to others. In addition, the authors tried to optimise the following receiver dimensions.

1. Receiver size optimisation to minimise the thermal losses (Aspect ratio selection).

2. Selection of small tube diameter to maximise the receiver thermal eﬃciency and to prevent fatigue-creep damage (Tube diameter selection).

3. Selection of thin tube wall to improve thermal eﬃciency (Tube wall thickness selection).

4. Minimise the pressure losses by optimising the number of panels and molten salt circuit routeing (Number of panels and ﬂuid path selection).

5. Selection of high nickel alloy material with excellent mechanical properties (Material selection).

System Advisory Model (SAM)

The performance model of SAM uses the TRNSYS components developed at the University of Wisconsin [52]. The solar ﬁeld optimisation algorithm is based on the DELSOL3 model developed at the Sandia national laboratory [52]. It is capable of operating in two modes. The ﬁrst one calculates the performance of an existing system. The second one is an optimisation of system design.

In the optimisation process, the tower height and receiver sizes are iteratively evaluated to ﬁnd out the minimum possible cost of electricity output. The optimisation process needs the initial guess deﬁned by the user. They have developed an objective function for the minimisation of the energy cost.

2.2.2 Allowable Peak Flux Limit The typical range of flux limit for the receiver fluids is listed in the Table 2.1. It depends on the tube material and the required number of life cycles. Figure 2.7 shows the dependency of the peak allowable flux on the receiver life time for different HTF and materials [22]. With one cycle per day, 30 years receiver lifetime would lead to 11000 cycles. Also, one should take into account for transients due to weather conditions. Alternatively, the allowable peak flux, qo can be calculated based on a model using the allowable thermal strain, thermal expansion and the poisson ratio of the material [32]. The average flux can be calculated by the peak-to-average flux ratio. According to Stine and Harrigan [46], the peak-to-average flux ratio can be between 2 to 3.

12 Receiver Design Methodology for Solar Tower Power Plants CHAPTER 2. LITERATURE REVIEW

Figure 2.7: Receiver peak ﬂux value for diﬀerent HTF and materials with respect to life cycles [22]

Name of the HTF Flux limit range Unit Water/Steam 0.3 to 0.6 MW/m2 Molten Salt 0.6 to 1.2 MW/m2 Liquid Sodium 1.2 to 1.75 MW/m2

Table 2.1: Receiver ﬂux limit for diﬀerent HTF [22]

2.2.3 Receiver Sizing Incident receiver thermal power should be estimated in order to size the receiver. Then, the allowable average flux should be determined based on the HTF and material (see section 2.2.2) to calculate the absorber area required to handle the flux. Selection of the allowable peak flux has to be done carefully to avoid thermal stress and fatigue-creep failure. Generally, one-half to one-third of the peak flux [46] is selected as an average flux. The receiver is sized for the average flux in order to ensure that it will not fail.

For cavity receivers, the inner surfaces of the receiver are exposed to re-radiation because of the enclosed structure, which may lead to overheating. According to Falcone [22], the receiver size for cavity receivers is 25 percent larger than the external receiver for the same incident receiver thermal power. So, the average ﬂux is selected accordingly for the cavity receivers in order to ensure that it will not fail.

2.2.4 Receiver Aspect Ratio According to Falcone [22], the receiver aspect ratio (height-to-diameter ratio) should be between 1 to 2. It should be optimised based on the trade-oﬀ between thermal and spillage losses. According to Zavoico [55], the receiver aspect ratio will be in the range of 1.2 to 1.5 and it should be selected for maximum receiver eﬃciency. For cavity receivers, it is usually in the range of 0.7 to 1 [22]. Some additional design considerations from literature are:

• The shipping constraint of the sub-assembly of panel tubes and the maximum continuous

Receiver Design Methodology for Solar Tower Power Plants 13 CHAPTER 2. LITERATURE REVIEW

length of available seamless tubing limit the receiver height to 30m [22]. However, there are some power plants which slightly cross this limit. Crescent Dunes Solar Energy Project in US has the receiver height of 30.48 m [4] and the Atacama-1 project in Chile has been planned with a receiver height of 32 m [1].

• A taller height receiver is desirable so that the spillage is minimised [55].

• A larger diameter receiver is desirable to maximise the interior space available to place all the receiver components, however large diameter will increase the thermal losses. So, space allocation design analysis should also be considered to optimise the aspect ratio [55].

2.2.5 Tube Diameter Selection The receiver tube diameter can vary between 20 mm to 45 mm [30]. The tube material is generally stainless steel or Incoloy. The analysis by Lata [30] states the following:

• Small diameters increase the receiver efficiency due to the increased salt velocity and heat transfer coefficient. However, small diameters increase the manufacturing cost and the pressure drop. The pressure drop is directly proportional to the length of the salt circuit and to the square of the salt velocity and it is inversely proportional to the tube diameter. There- fore, a trade-off between pressure drop and receiver efficiency should be done to optimise the tube diameter.

• Thin tube walls increase the heat transfer rate due to the reduced conductive resistance in the tubes. However, in practise, the wall thickness is limited to commercial values.

2.2.6 Fluid Flow Path Selection

Figure 2.8: Eight possible fluid flow configuration by Wagner [52]

The fluid flow path is chosen in such a way that it can distribute the local peak flux on the receiver evenly. The number of fluid flow paths has an influence on the pressure drop. Falcone [22] states that upward fluid flow is preferable so that the buoyancy force of the fluid does not counteract with the pumping pressure. Molten salt has a high volumetric heat capacity, which results in low volume flow for a given power level [22]. Thus, for molten salt receivers, multi-pass flow is needed to get high velocities and high wall heat transfer coefficients. Consequently, it is difficult to realise upward flow configurations in all panels. Hence, serpentine flow (up and down) is a reasonable alternative flow configuration. Wagner [52] developed a receiver model to analyse the behaviour of solar power plants and studied eight possible fluid flow configurations of the receiver, which are

14 Receiver Design Methodology for Solar Tower Power Plants CHAPTER 2. LITERATURE REVIEW depicted in the Figure 2.8. The following suggestions are given by Wagner to design an eﬃcient receiver:

• It is observed that the configuration with a single flow path has high pressure drop, which increases the parasitic pump power. Hence, two parallel flow paths in the receiver are suggested in order to obtain better overall efficiency of the plant.

• In Northern hemisphere, the northern panels will receive high flux due to the sun position during peak hours. If cold fluid enters through the high flux northern panels, it will lead to high thermal losses. Thus, the south to north flow configuration gives high efficiency in the northern hemisphere. However, in this configuration, the hot fluid from the south side will not be able to cool the high flux northern panels during peak hours. Consequently, the northern panels are exposed to high thermal stresses, which is not recommendable. Hence, in the Northern hemisphere, the north to south flow configuration with two parallel flow path with or without a crossover is recommended.

Rodriguez-Sanchez [39] simulated the same eight flow configurations as Wagner to select the best with the aim of increasing the receiver availability and the global efficiency of the CRS plant. She obtained results similar to that of Wagner and proposed the north to south flow configuration with one crossover in the middle as the best configuration based on the considerations of receiver thermal efficiency, distributed flux, tube temperature and thermal stress.

2.2.7 Tower Sizing

The tower height is mainly a function of the receiver thermal power of the plant [22]. The tower height is also influenced by the type of solar field. Falcone [22] presented a graph (see Figure 3.4) which shows the range of tower height for a given receiver thermal power and the type of solar field. The towers can be built of steel or concrete. Figure 2.9 shows both steel and concrete type tower. The tower investment cost increases with increasing height.

Figure 2.9: Solar tower for external and cavity receivers [23]

2.3 Cavity Speciﬁc Design Criteria

The following section consists of design criteria speciﬁc for cavity receivers. There is no speciﬁc design criteria needed for external receivers.

Receiver Design Methodology for Solar Tower Power Plants 15 CHAPTER 2. LITERATURE REVIEW

2.3.1 Cavity Receiver Geometry The cavity receiver geometry is designed to reduce thermal losses by enclosing the absorber tubes inside a protecting cavity. The receiver aspect ratio acts as a primary design parameter for the cavity receiver geometry, which is shown in the Figure 3.4.1. It is usually in the range of 0.7 to 1 [22]. The aspect ratio determines the width and height of the aperture opening and the radius of the cavity. All the piping and headers are placed inside the cavity, so there is some space needed on the top and bottom of the absorber tubes. This needs to be considered while designing the cavity receiver geometry. Generally, these headers are not exposed to direct irradiation and can be covered by a lip to reduce heat losses. The design of the lip is explained in the subsection 2.3.3. Similar to active surfaces, the inactive surfaces are also heated up due to re-radiation and hence, careful selection of receiver allowable ﬂux is necessary.

Figure 2.10: Cavity receiver geometry with four receiver panels [23]

2.3.2 Cavity Opening Angle The cavity opening angle depends on the solar field arrangement. The cavity opening angle should be similar to the covered angle of the radiation to the receiver from the solar field, so that the spillage loss will be reduced. Most commercial plants are designed with a cavity opening angle of 180◦ [23]. Lukas [23] calculated the receiver thermal efficiency with varying cavity opening angle. He observed that the receiver thermal efficiency increases with increasing cavity opening angle more than 180◦. Since increasing the cavity opening angle more than 180◦ decreases the aperture opening for a single cavity receiver, heat loss will be reduced. However, it is not possible to distribute the heat flux uniformly for a high cavity opening angle. Therefore, it can't be applied in real applications [23].

2.3.3 Lip Height (Aperture-to-Total Height Ratio) The lip height is usually calculated by using the aperture-to-total height ratio. The diﬀerence between the total height to aperture height is known as lip height, which is shown in the Figure 2.11. The lip which is placed above the aperture, is called upper lip, whereas the lip which is placed

16 Receiver Design Methodology for Solar Tower Power Plants CHAPTER 2. LITERATURE REVIEW

Figure 2.11: Lip height of cavity receiver [33] below the aperture, is called lower lip. Generally, the upper lip reduces the heat losses while the lower lip doesn't have much inﬂuence on the latter [29]. The value of aperture-to-total height ratio used by Lukas is 0.75 [23]. If the aperture-to-total height ratio is further increased, the spillage loss is increased. Hence, a trade-oﬀ should be done in order to optimise the aperture-to-total height ratio.

2.3.4 Cavity Inclination

The cavity inclination can vary from 0◦ to 90◦, which is depicted in the Figure 2.12. The convective heat loss of the cavity receiver depends on the wind speed, wind direction and cavity inclination. Flesch [25] conducted a cryogenic wind tunnel experiment and observed the influence of wind on the convective loss for head-on and side-on wind direction. Cavity inclination reduces convective heat losses [18][19]. However, wind speed increases convective heat losses particularly for inclined cavities. From the analysis of cryogenic wind tunnel experiment, Flesch [25] observed that the cavities should be designed in such a way, that the wind flow is parallel to the aperture plane in order to have a positive or at least non-negative influence of wind. Moreover, cavity inclination is recommended in order to reduce the convection losses [25].

Figure 2.12: Cavity inclination angle [33]

2.4 Heat Transfer Model

This section covers heat loss models from literature for external convection, radiation and reﬂec- tion. Conduction loss to the back side of the receiver panel is small compared to other losses [46], so it is neglected in this study. An overview of various heat transfer models is summarised in this section. It is divided into two subsections, external and cavity receivers.

Receiver Design Methodology for Solar Tower Power Plants 17 CHAPTER 2. LITERATURE REVIEW

2.4.1 External Receiver In case of external receivers, the entire absorber area is exposed to the surroundings. Hence, there are higher thermal losses from the receiver to the surroundings compared to cavity receivers [22]. The main thermal losses are convection and radiation heat loss.

Convective Heat Loss The heat transfer equations for the convection heat loss of cylindrical receivers are comparable to the correlations found in common heat transfer literature. However, the Nusselt correlation that can be applied to large-scale receivers is an ambiguous field, in which a lot of research is being carried out [43][15]. For cylindrical receivers, convective heat transfer is influenced by both natural and forced convection. Hence, mixed convection is usually considered [43]. In order to find out which heat transfer is dominant, the Richardson number is used [48], which is explained in the subsection 2.4.2.

According to literature [15][43], heat transfer coeﬃcient for mixed convection, hmix can be calculated with the following correlation. According to Cengel [15], the value m lies between 3 and 4. The value close to 3 suits better for vertical surfaces and the larger values are suited for horizontal surfaces. Siebers [43] studied this value and estimated the best-suited value of 3.2 for external receivers. m m 1/m hmix = (hnat + hfor) (2.1) where

2 • hnat = Heat transfer coeﬃcient due to natural convection, W/m K

2 • hfor = Heat transfer coeﬃcient due to forced convection, W/m K Natural Convection Loss Natural convection loss occurs due to buoyancy eﬀects and Nusselt correlations are given by many authors. The Nusselt correlation which can be applied for large-scale solar external receiver is given below:

Churchill and Chu [1975]: This correlation is used for the design of base-load nitrate salt central power plants by Abengoa [49]. This research is carried out in Sandia national lab in US Tamb+Ts [49]. All the fluid properties are calculated at the film temperature, Tf = 2 . !2 0.387Ra1/6 Nu = 0.825 + L Ra < 1012 (2.2) nat 8/27 L 1 + (0.492/Pr)9/16 For laminar flows, the following correlation is slightly more accurate. It is observed that a transition 9 from laminar to turbulent boundary flow occurs when RaL exceeds 10 . This correlation is valid up to 109. ! 0.67Ra1/4 Nu = 0.68 + L 10−1 < Ra < 109 (2.3) nat 4/9 L 1 + (0.492/Pr)9/16 Rayleigh number, Ra is defined as the product of Grashof number and the Prandtl number and it is given in the form of equation below:

Ra = Gr · P r (2.4)

The Grashof number, Gr can be calculated by the following equation:

3 Gr = g · β · (Ts,avg − Tamb) · Hrec/νfluid (2.5) where

18 Receiver Design Methodology for Solar Tower Power Plants CHAPTER 2. LITERATURE REVIEW

• g = Acceleration due to gravity, m/s2

• β = Volumetric expansion coeﬃcient, 1/K

• Ts,avg = Average surface temperature of the receiver, K

• Tamb = Ambient temperature, K

• Hrec = Height of the receiver, m

2 • νfluid = Kinematic viscosity, m /s

The Prandtl number, P r is defined as the ratio of viscous diffusion rate and thermal diffusion rate. It can be calculated by using the equation below:

µ/ρ c µ Pr = = p (2.6) k/cpρ k where

• µ = Dynamic viscosity, kg/ms

• ρ = Density, kg/m3

• k = Thermal conductivity, W/mK

• cp = Speciﬁc heat, J/kgK

Siebers and Kraabel [1984] [43]: This correlation is widely used for the convective heat loss calculation of solar receivers [17]. The authors stated that there is nearly 40 percent uncertainty in the equation [43]. All the ﬂuid properties are calculated at the ambient temperature, Tamb.

1/3 −0.14 Nunat = 0.098 · Gr · (Ts/Tamb) (2.7)

Forced Convection Loss The forced convection loss occurs due to the inﬂuence of wind. Nusselt correlations which can be applied to the large-scale solar external receiver are described below:

Churchill and Bernstein [1977] [15]: The following correlation is valid for Re · P r > 0.2 [15]. Christian and Clifford [17] stated that this correlation is valid for Reynold’s number up to 4 × 105. Therefore, this correlation can't be used for high Reynold’s number due to high wind speeds [17]. All the fluid properties are calculated at the film temperature, Tf .

" #4/5 0.62 · Re1/2 · P r1/3 Re 5/8 Nu = 0.3 + 1 + (2.8) for [1 + (0.4/P r)2/3]1/4 282000

Reynolds number, Re is deﬁned as the ratio of inertial and the viscous forces. It can be calculated using the following equation: u · D Re = wind rec (2.9) νair where

• uwind = Wind velocity, m/s

• Drec = Diameter of the receiver, m

Receiver Design Methodology for Solar Tower Power Plants 19 CHAPTER 2. LITERATURE REVIEW

Reynolds Number Range Correlation

Ks/Drec = 0 (A smooth cylinder) 0.8 0.5 Re 0.625 (1) All Re Nufor = 0.3 + 0.488 · Re · 1 + 282000 −5 Ks/Drec = 75 × 10 (2) Re ≤ 7.0 × 105 Use correlation (1) 5 7 −3 0.98 (3) 7.0 × 10 < Re < 2.2 × 10 Nufor = 2.57 × 10 · Re 7 0.81 (4) Re ≥ 2.2 × 10 Nufor = 0.0455 · Re −5 Ks/Drec = 300 × 10 (5) Re ≤ 1.8 × 105 Use correlation (1) 5 6 0.89 (6) 1.8 × 10 < Re < 4 × 10 Nufor = 0.0135 · Re (7) Re ≥ 4 × 106 Use correlation (4) −5 Ks/Drec = 900 × 10 (8) Re ≤ 1 × 105 Use correlation (1) (9) Re > 1 × 105 Use correlation (4)

Ks is the radius of the receiver tube, m

Table 2.2: Nusselt correlation for forced convection of external receivers [43]

Siebers and Kraabel [1984] [43]: This correlation is widely used for the convective heat loss calculation of solar receivers [17]. The correlations are shown in the Table 2.2. All the ﬂuid properties are calculated at the ﬁlm temperature, Tf .

Cengel [2003] [15]: In this correlation, the ﬂuid can be either gas or liquid but it is valid between the Reynolds number range of 4 × 104 − 4 × 105. This correlation is used for the design of base-load nitrate salt central power plant by Abengoa [49]. This research is carried out in Sandia national lab in US [49].

0.805 1/3 Nufor = 0.027 · Re · P r (2.10)

Long-wave Radiation Heat Loss

The radiation heat loss, Q˙ loss,rad is simple for external receivers and it can be calculated using Stefan-Boltzmann law. The external receiver is coated with the black coating to increase the absorptivity. Generally, black pyromark is used to coat the receiver panels and housing [55].

˙ 4 4 Qloss,rad = σ · eff · Aproj · (Ts,avg − Tamb) (2.11) The eﬀective emittance is given by the following equation [54]: eff = 2 (2.12) + (1 − ) · π where • σ = Stefan-Boltzmann constant, 5.670 · 10−8W/m2K4

• rec = Emissivity of the receiver

2 • Aproj = Projected area of the receiver, m

20 Receiver Design Methodology for Solar Tower Power Plants CHAPTER 2. LITERATURE REVIEW

• Ts,avg = Average surface temperature, K

• Tamb = Ambient temperature, K.

The average surface temperature of the receiver, Ts,avg can be calculated using mean radiant temperature. It can be given by the following equation:

1/4 T 4 + T 4 ! T = s,hot s,cold (2.13) s,avg 2 where

• Ts,hot = Hot surface temperature, K

• Ts,cold = Cold surface temperature, K The calculation for surface temperature of the receiver is explained in the subsection 3.2.4.

Reflection Heat Loss The part of the radiation which is reflected away from the receiver surface is called reflective heat loss. It can be calculated by using the absorptance of the receiver coating. The following equation gives the reflective heat loss, Q˙ loss,ref from the receiver surface:

Q˙ loss,ref = (1 − αeff ) · Q˙ th,rec (2.14)

With αeff = Eﬀective absorptance due to the curvature of receiver tubes. The curvature of the tubes has to be taken into account while calculating the absorptance. The eﬀective absorptance, αeff can be calculated by [54]: α αeff = 2 (2.15) α + (1 − α) · π

2.4.2 Cavity Receiver In this subsection, the heat transfer models speciﬁc for cavity receivers are discussed. In cavity receivers, the absorber tubes are enclosed in a cavity to reduce the thermal losses. Similar to external receivers, the main thermal losses in cavity receivers are convection heat loss and radiation heat loss.

Convective Heat Loss In order to find out which convective heat transfer is predominant, the Richardson number can be used [48]. With the help of this number, it is easy to find out what kind of convection mechanism has to be included in the heat transfer model. The Richardson number, Ri is defined as the ratio of the Grashof number to the square of the Reynolds number.

Ri = Gr/Re2 (2.16)

• If the Richardson number is much greater than unity, natural convection dominates over forced convection. • If it is much lower than unity, natural convection is negligible and forced convection dominates the heat transfer. In order to have an idea about Richardson number, Teichel [48] plotted the Richardson number with respect to varying wind speed, which is shown in the Figure 2.13. From the Figure 2.13, one can conclude that natural convection is dominant for wind velocities less than 5 m/s while forced convection dominates for wind velocities higher than 25 m/s.

Receiver Design Methodology for Solar Tower Power Plants 21 CHAPTER 2. LITERATURE REVIEW

Figure 2.13: Variation of Richardson number with respect to wind velocity for cavity receiver [48]

Generally, the maximum wind velocity will be nearly 20 m/s at the height of the receiver [48] and as a result, only natural convection or mixed convection can be expected in the large CRS receivers. However, the wind velocity can exceed the previously stated value depends on the site.

However, the forced convection on large-scale cavity receivers has not been suﬃciently studied. But, there are several studies on small scale cavity receivers [35][47] and the heat losses due to wind velocity and direction [33][25] are also studied. Therefore, it is not well known whether these correlations can be applied to large central receivers of CSP towers.

Natural Convection Loss

Convection heat loss for the cavity receiver can be well explained with the two-zone model. Figure 2.14 shows the stagnant zone and convective zone of the cavity receiver.

• The stagnant zone is the region, where the air is standing still and the temperature is close to the wall temperature [25].

• The convection zone is the region, where the cold air enters through the aperture opening, gets heated up and leaves through the upper part of the aperture [25].

Increasing wind speed can shrink the stagnant zone [25]. This can be seen as a reason for the low wind dependency of non-inclined cavities, as their stagnant zone is comparatively small.

Clausing(1983): In 1983, Clausing [19] published analytical and experimental modelling results for test cavities in a cryogenic wind tunnel experiment conducted at the University of Illinois, Urbana-Champaign. Based on the results, he developed a natural convection heat transfer correlation. According to Clausing, the circulating flow inside the cavity is mainly due to the buoyancy effects at boundary layers of the active surfaces [23]. However, it can be affected by the wind inflow and its direction. Clausing considered the wind velocity in the bulk flow velocity inside the cavity. Convection heat losses will not be greatly influenced by wind velocities lower than 8 m/s. He developed a correlation which allows calculating a heat transfer coefficient specific for each surface.

22 Receiver Design Methodology for Solar Tower Power Plants CHAPTER 2. LITERATURE REVIEW

Figure 2.14: Two-zone model of the cavity receiver [25]

The correlation can be applied only if the heat transfer is dominated by internal resistances and wind eﬀects don't have a large inﬂuence. This model is valid for Rayleigh numbers greater than 1.6 × 109 and the temperature ratio of wall to ambient being between 1 and 2.6. It is numerically validated for no-wind and head-on wind conditions. According to Teichel [48], the temperature ratio of a typical receiver is between 1.8 and 3.4, so it is out of range for some conditions.

Clausing(1987): Clausing [20] updated his previous model by experimental investigation of smooth, isothermal cubic cavities with a variety of side facing apertures to predict the convection loss for large-scale solar receivers. The large-scale receivers are modelled using the cryogenic wind tunnel at the University of Illinois, Urbana Champaign. Using the results, Clausing came up with a correlation which is valid for large Rayleigh numbers and the large temperature ratio of wall to ambient, hence it can be applied to large-scale solar receivers.

Unlike the previous model, this model was developed with only one heat transfer coeﬃcient using the aperture area for the calculation of the convective losses of the entire cavity. This model is 7 10 valid for 3 × 10 ≤ Ra ≤ 3 × 10 and 1 ≤ Tw/Tamb ≤ 3. Higher Rayleigh numbers can occur for large-scale receivers, hence it might not be valid for all cases [48].

Siebers and Kraabel (1984): Siebers and Kraabel [43] came up with natural convection heat transfer correlation in 1984, which was based on the experimental work on cubical cavities by Kraabel. They considered natural convection in large cavities to be similar to large vertical ﬂat plates. They developed a Nusselt correlation for a simple cavity receiver with a validity range of 105 ≤ Gr ≤ 1012. A correction factor is introduced in order to account for the aperture lips and the tilt angle of the cavity. This model is validated with experimental measurements and it shows good accordance with their results.

Forced Convection Loss Forced convection has a significant influence on the convective heat transfer, but no reliable correlations are available to predict the forced convection heat transfer for cavity receivers. The only simple correlation that can be applied to cavity receivers is the correlation by Siebers and Kraabel [43]. They used the forced convection correlation for vertical flat plate in order to account

Receiver Design Methodology for Solar Tower Power Plants 23 CHAPTER 2. LITERATURE REVIEW for the wind eﬀect. Their correlation was validated with the experimental data. The overall heat transfer coeﬃcient for cavity receivers can be obtained by using the value of m as 1 in Equation 2.1

While this correlation was validated with a 4.5 MW test receiver at Sandia Lab, the forced convection values are mostly over-predicted. Thus, the model is conservative. The authors state that the equation is expected to have an uncertainty of more than 50 percent [43].

Long-wave Thermal Radiative Heat Loss The thermal radiation from the active surfaces of a cavity receiver will directly or indirectly reach all the inactive surfaces and ﬁnally some part of the radiation will leave to ambient through the aperture opening. It is complex to determine the radiation heat losses accurately. Still, it can be calculated using view factors and there are two widely used methods to calculate radiation heat loss [48]. They are

• Radiosity method • F-hat method The view factors can be calculated using analytical or by ray tracing method. The analytical method is limited to the speciﬁc cavity geometry with four receiver panels and for other geometries, ray tracing is used.

Reflection Heat Loss Similar to long-wave thermal radiative heat loss, reflection heat loss can also be calculated with view factors using the same two methods as specified in subsection 2.4.2.

24 Receiver Design Methodology for Solar Tower Power Plants Chapter 3

Design Methodology

In this chapter, the design approach for tubular receivers and the receiver design model for both external and cavity receivers are discussed.

3.1 Design Approach

In this section, the steps required to design the receiver are summarised and shown in Figure 3.1. Furthermore, they are covered in detail in subsequent sections.

1. Calculate the incident receiver thermal power with the desired receiver output power and the receiver thermal eﬃciency, which is assumed initially (see section 3.2.1).

2. Select receiver ﬂuid and material.

3. Calculate the allowable peak flux limit on the receiver based on the type of HTF and the receiver material. Subsequently, calculate the average allowable flux and size the receiver using the average allowable flux (see section 3.2.3).

4. Design the receiver outer geometry using the aspect ratio (height-to-diameter ratio). It has to be chosen considering the factor of minimal thermal and spillage loss of the receiver (see section 3.3.1 for external receivers).

5. Fix the additional parameters like cavity opening angle, aperture-to-total height ratio and cavity inclination to design the receiver outer geometry for cavity receivers (see section 3.4.1).

6. Select the receiver tube diameter in such a way that the pressure loss is minimised and the receiver eﬃciency is increased. A small diameter results in higher eﬃciency while in the other hand, it tends to increase the pressure losses (see section 3.3.2).

7. Select the tube wall thickness based on the pressure exerted by the ﬂuid on the tube. Thin wall will lead to higher receiver eﬃciency, but it is limited by typical values of commercial tubes. Moreover, it should be able to hold the pressure and the tubes should not break (see section 3.3.2).

8. Calculate the mass flow rate (see section 3.2.5) and fix the design fluid flow velocity. Then, the cross-sectional area required for the fluid flow is calculated using the mass flow rate, the velocity and the density of the fluid. Once the cross-sectional area is known, the number of tubes and panels can be calculated by selecting the number of flow paths (see section 3.3.2).

9. Calculate the heat losses for the designed receiver and the actual eﬃciency is known. Hence, the previous steps are iteratively repeated until convergence is reached (see section 3.3.4 for external receivers and section 3.4.4 for cavity receivers).

Receiver Design Methodology for Solar Tower Power Plants 25 CHAPTER 3. DESIGN METHODOLOGY

10. Size the tower height with the receiver thermal power and the type of solar ﬁeld (see section 3.3.3 for external receivers and section 3.4.3 for cavity receivers).

Figure 3.1: Receiver design methodology for tubular receivers

26 Receiver Design Methodology for Solar Tower Power Plants CHAPTER 3. DESIGN METHODOLOGY

3.2 General Receiver Design Model

This section describes the receiver design model which is common for both external and cavity receivers.

3.2.1 Receiver Thermal Power The first step is to calculate the incident receiver thermal power from the solar field. For this purpose, the receiver output power is calculated and the receiver thermal efficiency is assumed. Then, the receiver thermal power, Q˙ th,rec is calculated by

Q˙ th,pb Q˙ th,rec = · SM (3.1) ηrec,guess where

• Q˙ th,pb = Thermal power required for power block, W

• ηrec,guess = Assumed receiver thermal eﬃciency • SM = Solar multiple

3.2.2 Calculation of HTF Properties The properties of HTF play a main role in the receiver design. Correlations for the properties of solar salt, hitec, hitec XL, therminol, liquid sodium and for some gases [12] are implemented. The properties for any other fluid can be given as an input to design the receiver with the particular fluid. The properties needed for the receiver model are density, specific heat capacity, dynamic viscosity and thermal conductivity. In this thesis, the focus is on molten salt receivers. Therefore, correlations to calculate solar salt properties are given in the Table 3.1.

Property Equation Units

3 Density ρ = 2090 − (0.636 · Tmean,htf ) kg/m

Speciﬁc heat capacity Cp = 1443 + 0.172 · Tmean,htf J/kgK

−4 2 −7 3 3 Dynamic viscosity µ = (22.714 − (0.120 · Tmean,htf ) + (2.281 × 10 · Tmean,htf ) − (1.474 × 10 · Tmean,htf ))/10 Pa s

−4 Thermal conductivity k = 0.443 + 1.9 · 10 · Tmean,htf W/m K

◦ Tmean,htf is the mean ﬂuid temperature, C

Table 3.1: Properties of solar salt [55]

3.2.3 Receiver Sizing Receiver sizing is done based on the allowable flux on the receiver. The allowable flux on the receiver depends on the receiver material and the type of HTF. Generally, the allowable peak flux for molten salt receivers built with 316 Stainless steel material is 0.83 MW/m2 [22]. For receivers built with Incoloy 800H, the allowable peak flux is 1 MW/m2 [32][55]. So, these values are used as the default values in the model.

The average allowable flux can be calculated with the peak-to-average flux ratio. Falcone used a specific value of 1.78 for external receivers and 2.65 for cavity receivers [22]. Because of the cavity enclosure, the inner surfaces of the receiver are exposed to re-radiation, which may lead to overheating. Consequently, cavity receivers have high peak-to-average flux ratio. Therefore, the absorber area is larger for the same receiver thermal power. The value used by Falcone is also in

Receiver Design Methodology for Solar Tower Power Plants 27 CHAPTER 3. DESIGN METHODOLOGY accordance with the Gemasolar design ﬂux [36] and therefore, it is used in this model. Using the average allowable ﬂux, the area of the receiver, Arec can be calculated by

Q˙ th,rec Arec = (3.2) qavg,flux where

2 • qavg,flux = Allowable average ﬂux of the receiver, W/m

• Q˙ th,rec = Incident receiver thermal power, W

3.2.4 Receiver Surface Temperature Calculation

It is assumed that the receiver has a uniform surface temperature. The heat transfer through the tube walls is calculated. The calculation takes into account conduction through the tube wall thickness and then convection to the receiver ﬂuid. The surface temperature of the receiver is calculated by calculating the resistance due to conduction and convection. The receiver surface temperature, Ts,avg can be obtained by:

Ts,avg = Q˙ fluid · (Rcond + Rconv) + Thtf,avg (3.3)

With Thtf,avg = Average temperature of the receiver ﬂuid, K. The resistance due to conduction through the tube walls, Rcond can be given by:

ln(ro,tube/ri,tube) Rcond = (3.4) 2 · π · Hrec · ktube · ntube where

• ro,tube = Radius of the receiver outer tube, m

• ri,tube = Radius of the receiver inner tube, m

• ntube = Total number of tubes in the receiver

The resistance due to internal convection between tube wall and the receiver ﬂuid, Rconv can be given by: 1 Rconv = (3.5) hinner · π · ri,tube · Hrec · ntube

The heat transfer coeﬃcient of internal convection between tube wall and the receiver ﬂuid, hinner can be given by the following equation:

hinner = Nu · kfluid/Lc (3.6)

With Lc = Characteristic length, which is the inner receiver tube diameter, di,tube. The Nusselt correlation by Dittus-Boelter [12] is used:

Nu = 0.023Re0.8P r0.4 (3.7)

The above equation is valid for 0.7 < P r < 120 and 104 < Re < 1.2 × 105. Using these equations, the surface temperature of the receiver is calculated.

28 Receiver Design Methodology for Solar Tower Power Plants CHAPTER 3. DESIGN METHODOLOGY

3.2.5 Mass Flow Rate Calculation The design mass flow rate of the receiver fluid is calculated with the absorbed receiver thermal power. The minimum limitation of the mass flow rate to avoid any damage is given by the constraint that the flow has to be turbulent. Thus, the Reynolds number has to be greater than or equal to 4000 [39]. The mass flow rate,m ˙ htf is calculated by:

Q˙ inc,rec · ηrec m˙ htf = (3.8) cp,htf,avg · (Thtf,hot − Thtf,cold) where

• ηrec = Receiver thermal eﬃciency

• cp,htf,avg = Speciﬁc heat of the receiver ﬂuid, J/kg K

• Thtf,hot = Outlet temperature of the hot receiver ﬂuid, K

• Thtf,cold = Inlet temperature of the cold receiver ﬂuid, K

3.2.6 Pressure Loss and Pump Power Calculation

The pressure drop in the receiver tubes, ∆Ptube is given by the following equation [15]. The pressure loss due to the bends is not considered in this model.

2 Hrec vfluid ∆Ptube = ρfluid · f · · (3.9) Dtube,inner 2

With f = (0.790lnRe − 1.64)−2 for smooth tubes valid for 104 < Re < 106 and for rough tubes /D √1 2.51√ f = −2.0 log 3.7 + Re f . where

• vfluid = Velocity of the receiver ﬂuid, m/s • /D = Relative roughness

The pressure drop for pumping the ﬂuid up to the receiver, ∆Ptower is given by:

∆Ptower = ρfluid · g · Htower (3.10)

With Htower = Height of the tower, m. The net presure drop across the receiver panels, ∆Pnet is given by: npanels ∆Pnet = ∆Ptube · + ∆Ptower (3.11) nflowpath where

• npanels = Number of panels in the receiver

• nflowpath = Number of ﬂow path in the receiver

The energy required to pump the receiver ﬂuid through the receiver, Q˙ pump is given by:

m˙ htf ∆Pnet · ρfluid Q˙ pump = (3.12) ηpump

With ηpump = Pump eﬃciency.

Receiver Design Methodology for Solar Tower Power Plants 29 CHAPTER 3. DESIGN METHODOLOGY

3.3 External Receiver Design Model 3.3.1 Geometry Design In case of external receivers, the outer geometry design includes diameter and height of the receiver. Figure 3.2 depicts the geometry of external receiver.

Figure 3.2: External receiver geometry [45]

In order to design the outer geometry, the parameter receiver aspect ratio, AR (height to diameter ratio) is introduced. Generally, for an external receiver, the aspect ratio lies between 1 to 2 [22]. In this model, the default value of receiver aspect ratio is set as 1.5. The area of the receiver, Arec can be derived as:

Arec = π · Drec · Hrec · π/2 (3.13) The factor, π/2 is used to take into account curvature of the tubes in the receiver. The above equation can be reformulated in terms of the receiver aspect ratio and the geometry can be calculated as: p Drec = Arec/(π · AR · π/2) (3.14)

Hrec = AR · Drec (3.15)

3.3.2 Tube and Panel Design The tube outer diameter, the tube thickness and the number of flow paths in the receiver have to be selected in order to design receiver tubes and panels. The tube outer diameter usually varies between 20 mm to 45 mm [30]. It is related to receiver thermal power, because of the fact that the mass flow rate of the HTF depends on the required receiver thermal power. Consequently, the fluid velocity is adapted to meet the required mass flow. The cross-sectional area is adjusted to maintain the fluid velocity within the allowable limits.

Scalability of the power plant is addressed by developing a linear correlation for tube outer diameter with receiver thermal power. The data used to develop the correlation is tabulated in the Table 3.2. The developed linear correlation for tube outer diameter, do,tube is shown in Figure 3.3:

−4 do,tube = (0.2682 × 10 · Q˙ th,rec) + 0.02268 (3.16)

30 Receiver Design Methodology for Solar Tower Power Plants CHAPTER 3. DESIGN METHODOLOGY

Power plant name Receiver thermal power, MWth Tube diameter, mm Solar Two 43 23 Gemasolar 120 25 Crescent Dunes 540 42 Abengoa Solar 795 40.9

Table 3.2: Tube diameter used in various commercial power plants [49][39][51]

Figure 3.3: Tube diameter correlation with respect to receiver thermal power

With receiver thermal power, Q˙ th,rec in MWth. Tube thickness depends on the pressure exerted by the ﬂuid onto the tube. For instance, direct water/steam receivers needs thicker tubes to withstand the higher pressure. In case of molten salt receivers, it can be as low as 1 mm [37]. As a conservative approach, the default value of tube thickness is selected as 1.2 mm in this model.

Wagner [52] suggested the use of two ﬂow path branches, which is selected by default in this model. The total number of receiver tubes, ntube,rec can be calculated as:

π · Drec ntube,rec = (3.17) do,tube

The number of tubes per panel, ntube,panel can be calculated with the cross-sectional area of the ﬂuid: Asec ntube,panel = 2 (3.18) π · (di,tube/2) · nflowpath

The total cross-sectional area of the ﬂuid ﬂow path, Asec can be calculated as:

m˙ htf Asec = (3.19) ρfluid · vfluid

Once the number of tubes per panel is calculated, the number of receiver panels, npanels can be calculated as: ntube,rec npanels = (3.20) ntube,panel

Receiver Design Methodology for Solar Tower Power Plants 31 CHAPTER 3. DESIGN METHODOLOGY

While designing, it should be taken care that the number of panels will also be even, if the number of ﬂow path is even. In this model, the number of panels are rounded to the next even number.

3.3.3 Tower Height Design

Figure 3.4: Variation of tower height with respect to receiver thermal power [22]

Currently, there is no reliable tower height model in the literature. Tower height is given as a user input in all the commercial design softwares. Falcone [22] has given a graph for tower height with respect to receiver thermal power, which is shown in Figure 3.4. Therefore, a correlation is developed by curve ﬁtting with his values. However, the values are not in accordance with commercial power plants, because the data is quite old. So, another correlation is developed using state-of-the-art commercial power plant and it is depicted in the Figure 3.5. The correlation for calculating tower height for surround ﬁelds based on Falcone is given below:

˙ −3 ˙ 2 Htower,min = 36.30075 + (0.3013896 · Qth,rec) − (0.1004369 × 10 · Qth,rec) (3.21)

˙ −3 ˙ 2 Htower,max = 54.91579 + (0.3070526 · Qth,rec) − (0.1039793 × 10 · Qth,rec) (3.22) H + H H = tower,min tower,max (3.23) tower 2 where

• Qth,rec = Receiver thermal power, MWth.

• Htower,min = Minimum tower height, m

• Htower,max = Maximum tower height, m

• Htower = Tower height, m The following correlation is developed using state-of-the-art commercial power plant data:

Htower = 0.2552 · Q˙ th,rec + 82.60 (3.24)

With Qth,rec = receiver thermal power in MWth.

32 Receiver Design Methodology for Solar Tower Power Plants CHAPTER 3. DESIGN METHODOLOGY

Figure 3.5: Tower height correlation with respect to receiver thermal power for external receiver

3.3.4 Receiver Thermal Eﬃciency

The receiver thermal eﬃciency, ηrec is calculated by deﬁning all thermal losses from the receiver.

Q˙ loss,tot ηrec = 1 − (3.25) Q˙ th,rec

With Q˙ loss,tot = Total heat loss from the receiver in W . The heat loss model includes heat loss due to reﬂection, external convection and radiation. The conduction to the back side of the receiver panel is small compared to other losses and it is neglected [46].

Q˙ loss,tot = Q˙ loss,conv + Q˙ loss,rad + Q˙ loss,ref (3.26) where

• Q˙ loss,conv = Heat loss due to external convection, W

• Q˙ loss,rad = Heat loss due to long-wave thermal radiation, W

• Q˙ loss,ref = Heat loss due to reﬂection, W

Convection Heat Loss The external receiver is usually approximated as a vertical cylinder. The following condition has to be met to treat the receiver as vertical plate for the heat transfer correlations.

Drec 35 ≥ 1 (3.27) Hrec Gr 4 The external convection heat loss equation is given below with the mixed convection heat transfer coeﬃcient. Q˙ loss,conv = hmix · Arec · (Ts,avg − Tamb) (3.28) Mixed convection: According to literature [43], most of the external solar receivers will undergo mixed convection. It is calculated with equation 2.1.

Receiver Design Methodology for Solar Tower Power Plants 33 CHAPTER 3. DESIGN METHODOLOGY

Natural convection:

The heat transfer coeﬃcient for natural convection, hnat can be calculated with the following equation: hnat = Nunat · kair/Hrec (3.29) In this thesis, Siebers and Kraabel correlation is used for the heat transfer model because of its wide validity range. Furthermore, it was developed especially for large-scale solar receivers based on experiments. Siebers and Kraabel correlation is given in the equation 2.7.

Forced convection:

The heat transfer coeﬃcient for forced convection, hfor can be calculated with the following equation: hfor = Nufor · kair/Drec (3.30) Similar to natural convection, Siebers and Kraabel correlation is also used for forced convection due to its wide validity range. Nusselt correlations for smooth and rough cylinders are shown in the Table 2.2.

Long-wave Thermal Radiation Heat Loss The model for radiative heat losses is explained in section 2.4.1.

Reﬂection Heat Loss The model for reﬂective heat losses is explained in section 2.4.1.

3.4 Cavity Receiver Design Model 3.4.1 Geometry Design Geometry design includes the radius of the cavity, height of the receiver, height of the absorber, lip height, width and height of the aperture, cavity opening angle and the cavity inclination angle. The aspect ratio usually ranges between 0.7 to 1 for cavity receivers [22]. The outer geometry of cavity receiver is shown in the Figure 3.6.

Figure 3.6: Geometry of cavity receiver [23]

The following steps show how to calculate the width and height of the receiver aperture.

34 Receiver Design Methodology for Solar Tower Power Plants CHAPTER 3. DESIGN METHODOLOGY

Once the absorber area is calculated with the allowable heat ﬂux, width and height of the receiver can be calculated by ﬁxing the aspect ratio, AR and the cavity opening angle, θrec. θ π A = rec · π · r · H · (3.31) abs π rec abs 2 where

2 • Aabs = Receiver absorber area, m

• rrec = Radius of the receiver, m

• Habs = Height of the absorber, m

Figure 3.7: Internal angle geometry of cavity receiver [23]

The radius and height of the absorber can be calculated by rewriting the above equation in terms of the aspect ratio, which is shown below. In order to have an idea of receiver radius and its internal angle geometry, the cavity geometry is depicted in Figure 3.7. s Aabs rrec = (3.32) θrec 2 π · π · AR

Habs = 2 · AR · rrec (3.33)

The aperture width, Waper can be calculated from the following equation with the assumption of receiver width always being equal to aperture width or by ﬁxing the aperture-to-total width ratio, Waper : Wtot ratio π − θrec Waper Waper = 2 · rrec · cos · (3.34) 2 Wtot ratio In order to accommodate the receiver pipings and headers inside the cavity, extra space above the absorber area is needed. After including the space, the overall height can be calculated with the Hgap parameter gap-to-absorber height ratio, H : abs ratio Hgap Hrec = Habs · 1 + (3.35) Habs ratio

The aperture height, Haper can be calculated with the aperture-to-total height ratio of the receiver, Haper H . It is chosen as 0.75 [48]. tot ratio Haper Haper = · Hrec (3.36) Htot ratio

Receiver Design Methodology for Solar Tower Power Plants 35 CHAPTER 3. DESIGN METHODOLOGY

The lip height, Hlip can be calculated with total height of the receiver and the aperture. Only the upper lip is considered in the current model. The lip height of the receiver, Hlip can be calculated by:

Hlip = Hrec − Haper (3.37)

3.4.2 Tube and Panel Design The receiver tube and panel design is similar to external receivers except the calculation of number of receiver tubes in the receiver. The number of receiver tubes can be calculated by

θrec π · rrec · π ntube,rec = (3.38) do,tube

3.4.3 Tower Height Design Similar to external receivers, the tower height for cavity receivers is calculated by the correlation developed by curve ﬁtting Falcone values. The correlation is shown below:

˙ ˙ 2 Htower,min = 58.31818 + (0.4377023 · Qth,rec) − (0.0001802198 · Qth,rec) (3.39)

˙ ˙ 2 Htower,max = 76.02273 + (0.4571479 · Qth,rec) − (0.0002080919 · Qth,rec) (3.40) H + H H = tower,min tower,max (3.41) tower 2 The correlation was updated by developing a new correlation using state-of-the-art commercial power plants, which is shown in the Figure 3.8.

Htower = 0.6806 · Q˙ th,rec + 106.6 (3.42)

Figure 3.8: Tower height correlation with respect to receiver thermal power for cavity receiver

36 Receiver Design Methodology for Solar Tower Power Plants CHAPTER 3. DESIGN METHODOLOGY

3.4.4 Receiver Thermal Efficiency The general procedure for calculation of receiver thermal efficiency is similar to that of external receivers. The heat losses which are calculated differently for cavity receivers are shown below.

Convection Heat Loss It is assumed that the inactive surfaces and the air inside the cavity have higher temperatures due to re-radiation.

Natural convection: The following Nusselt correlation by Siebers and Kraabel [43] can be used to calculate the natural

Figure 3.9: Internal heat transfer area of the cavity receiver [43] heat transfer coeﬃcient: T 0.18 Nu = 0.088Gr1/3 s,avg 105 ≤ Gr ≤ 1012 (3.43) Tamb The correction factors are introduced to account for the eﬀect of aperture lip and the cavity inclination. It is shown below: n A1 A3 hnc = hnc,0 (3.44) A2 A1 where ◦ 0.63 θrec<30 • n = → ◦ 0.8 θrec>30

• Area A1, A2 and A3 are shown in the Figure 3.9.

The area used for heat transfer is the total interior surface of the cavity receiver, A1.

Forced convection: The following Nusselt correlations by Siebers and Kraabel [43] can be used to calculate the forced heat transfer coeﬃcient: Nu = 0.0287Re0.8P r1/3 (3.45)

Receiver Design Methodology for Solar Tower Power Plants 37 CHAPTER 3. DESIGN METHODOLOGY

The area used for heat transfer is the aperture area of the cavity receiver.

Long-wave Thermal Radiation Heat Loss The thermal radiation heat loss equation for the cavity receivers is given with the view factor:

˙ 4 4 Qloss,rad = σS · eff · Fsurf−aper · Asurf · (Ts,avg − Tamb) (3.46)

In this thesis, a simple thermal radiation loss model is derived with the aperture opening area, assuming uniform temperature inside the cavity and using reciprocity and enclosure rules. If all the surfaces inside the cavity are considered as a single surface, then the reciprocity rule for cavity receivers is given by: Faper−surf · Aaper = Fsurf−aper · Asurf (3.47) With a view from the aperture to the cavity surface, the enclosure rule for cavity receivers is given by: N X Faper−surf = 1 (3.48) surf=1 Using these above equations, the view factor is replaced by specifying the aperture area:

Aaper = Fsurf−aper · Asurf (3.49)

The following equation is used to calculate the radiation heat loss from the cavity receiver:

˙ 4 4 Qloss,rad = σS · eff · Aaper · (Ts,avg − Tamb) (3.50)

This is assumed to be valid, if the average surface temperature of all surfaces inside the cavity is used. The eﬀective emittance is given by the following equation [54]: eff = (3.51) + (1 − ) · Aaper Aproj The cavity receiver is coated with black coating to increase the absorptivity. Generally, black Pyromark is used to coat the receiver panels [55].

Reflection Heat Loss The reflection heat loss is reduced because of the enclosing cavity structure. The reflected radiation can only leave through the aperture to reach the surroundings. The simple reflection loss equation is derived by assuming the receiver thermal power is uniformly distributed in the receiver. Similar to the thermal radiation approach, the following equation is used to calculate the reflected heat loss from the cavity receiver:

Q˙ th,rec Q˙ loss,ref = (1 − αeff ) · · Aaper (3.52) Aproj where

2 • Aaper = Area of the aperture, m

2 θrec • Aproj = Projected area, m = π · π · rrec · Habs

38 Receiver Design Methodology for Solar Tower Power Plants Chapter 4

Implementation

This chapter discusses the implementation of the design method, its structure and the interface for external and cavity receivers to the in-house CRS plant design tool devISEcrs.

4.1 devISEcrs - A Design Tool

Figure 4.1: Modules of the devISEcrs design tool

There are six modules in the devISEcrs tool, which are shown in the Figure 4.1 and their functionality is discussed brieﬂy below:

• The Design Point module calculates the design point conditions for which the power plant will be designed.

• The Power Block module in the design tool computes the required thermal power, eﬃciency, mass ﬂow rate and the gross-to-net conversion factor based on the design point calculations.

• A two tank molten salt storage is modelled in the Storage module, which computes the thermal power required for the storage, total mass and volume of the molten salt along with the tank dimensions.

• Based on the storage calculations, the Solar Multiple module calculates the solar multiple which is used to design the solar field and the receiver. The solar multiple is used to define the oversizing of the solar field, which is necessary to take into account the energy required for storage.

• The Receiver module designs the receiver and computes the thermal losses. It is based on the methodology derived in section3.

Receiver Design Methodology for Solar Tower Power Plants 39 CHAPTER 4. IMPLEMENTATION

• The Solar Field module designs the solar ﬁeld layout and calculates the optical losses of the solar ﬁeld.

4.2 Implementation Structure

As the devISEcrs tool is written in Python, the receiver module is also implemented in Python. The implementation is highly object-oriented. The code documentation is done using the doxygen style. The implementation structure of the receiver design method and the main functions are shown in the Figure 4.2.

Figure 4.2: Class inheritance structure of the receiver module in devISEcrs

The receiver module includes the design method for both types of receivers. As they share some common functionality, the External Receiver class and the Cavity Receiver class inherit from a more general Receiver class. The sub-division of the design methodology as described in section 3 is implemented using functions.

Due to this structure, it is possible to use the receiver module for the design of the entire receiver or the distinct investigations on speciﬁc aspects. Additionally, it is possible to manually overwrite almost all default values used in the implementation.

40 Receiver Design Methodology for Solar Tower Power Plants CHAPTER 4. IMPLEMENTATION

The current model allows the user to design the receiver with molten salt and liquid sodium as a HTF. Furthermore, other HTFs can be integrated into the model with ease.

4.3 Interface of Receiver Classes

In this section, the input and output parameters of the receiver classes and the default values of input parameters are described.

4.3.1 Receiver Class Table 4.1 shows required inputs and the default values which are used, if the user does not specify an input value.

Name Default value Unit Thermal power required for power block - W Solar multiple - - Assumed receiver thermal efficiency 0.9 - Temperature of hot fluid out 565 C Temperature of cold fluid in 288 C Ambient temperature 298 K Absorptivity of the receiver surface 0.95 - Velocity of the receiver fluid 4 m/s Wind velocity 8 m/s Emissivity of the receiver surface 0.88 - Absolute viscosity of air 1.846 × 10−5 Kg/ms Kinematic viscosity of air 1.568 × 10−5 m2/s Specific heat of air 1005 J/kgK Volumetric expansion coefficient of air 3.43 × 10−3 1/K Thermal conductivity of air 0.0257 W/mK Thermal conductivity of receiver tube 23.9 W/mK Efficiency of pump 0.8 -

Table 4.1: Input parameters and its default value of the receiver class

4.3.2 External Receiver Class Table 4.2 shows the input parameters that are speciﬁc for external receivers. It is possible to specify manually output parameters such as area, height, diameter, number of panels, number of tube per panel and tower height to calculate losses for the existing receiver. Table 4.3 shows the output parameters of the external receiver class.

4.3.3 Cavity Receiver Class Table 4.4 shows the input parameters that are speciﬁc for cavity receivers. Similar to external receivers, some outer parameters can be speciﬁed manually to calculate the thermal losses for an existing cavity receiver. Table 4.5 shows the output parameters of the cavity receiver class.

Receiver Design Methodology for Solar Tower Power Plants 41 CHAPTER 4. IMPLEMENTATION

Name Default value Unit Heat transfer ﬂuid Molten salt - Receiver aspect ratio 1.5 - Outer diameter of receiver tube Diameter correlation m Thickness of receiver tube 0.0012 m Number of ﬂow path 2 - Tower height Tower correlation m

Table 4.2: Input parameters and its default value of the external receiver class

Name Unit Area of the receiver m2 Height of the receiver m Diameter of the receiver m Outer diameter of receiver tube m Thickness of receiver tube m Number of panels - Number of tubes per panel - Tower height m Mass flow rate of the fluid kg/s Minimum allowable mass flow rate kg/s Incident receiver thermal power W

Table 4.3: Output parameters of the external receiver class

Name Default value Unit Heat transfer ﬂuid Molten salt - Receiver aspect ratio 1 - Cavity opening angle 180 degrees Aperture to total height ratio 0.75 - Aperture to total width ratio 1 - Outer diameter of receiver tube Diameter correlation m Thickness of receiver tube 0.0012 m Number of ﬂow path 2 - Cavity inclination angle 0 degrees Tower height Tower correlation m Tower Orientation 180 degrees

Table 4.4: Input parameters and its default value of the cavity receiver class

42 Receiver Design Methodology for Solar Tower Power Plants CHAPTER 4. IMPLEMENTATION

Name Unit Area of the receiver m2 Total height of the receiver m Diameter of the receiver m Lip height m Outer diameter of receiver tube m Thickness of receiver tube m Number of panels - Number of tubes per panel - Cavity opening angle degrees Cavity inclination angle degrees Tower height m Mass flow rate of the fluid kg/s Minimum allowable mass flow rate kg/s Incident receiver thermal power W Receiver normal vector -

Table 4.5: Output parameters of the cavity receiver class

Receiver Design Methodology for Solar Tower Power Plants 43 Chapter 5

Validation and Results

This chapter discusses the validation of the design method and the further results obtained using this model.

5.1 Receiver Design Validation

The receiver design methodology is validated using selected reference plants. The reference plants are chosen in such a way that they are commercially well established and the plant data is available in the literature. Then, a new receiver is designed for the reference case speciﬁcations using the developed model and is compared against the reference plant to check the validity of the developed design method. This validation procedure is applied to external and cavity receivers.

5.1.1 External Receiver The external receiver model is only validated with molten salt as HTF. Though other HTFs can be used, the validation is limited to molten salt receiver in this thesis. Three solar power plants of diﬀerent sizes are used as reference cases. These are the 10 MW Solar Two power plant in California, the 20 MW Gemasolar power plant in Spain and the 110 MW Crescent Dunes power plant in Nevada. All three are using the molten nitrate salt receiver technology.

Solar Two Power Plant The Solar Two power plant is a 10 MW CRS plant with 3 hours of storage located in California, USA [51]. It was the ﬁrst power plant developed with molten salt storage technology in 1996 [51] and it was demolished in 2009. A 43 MWth external nitrate salt receiver was constructed to meet the demand of net electric power [51]. The plant location and characteristics are tabulated in Table 5.1.

Using the plant location and speciﬁcations, a new receiver is designed with the developed design method. The receiver is designed for the desired receiver thermal power. The resulting receiver design is compared with the actual Solar Two plant values.

Table 5.2 shows the results of devISEcrs model and the values of Solar Two power plant. On comparing receiver absorber area, it has a deviation of nearly 7 percent from the reference plant value, which is due to the deviation in allowable average design flux on the receiver. Solar Two power plant used an average solar flux value of 430 KW/m2 and 465 KW/m2 is used in this model. The receiver diameter and height will be affected by the deviation of absorber area. Furthermore, the selection of receiver aspect ratio differs.

44 Receiver Design Methodology for Solar Tower Power Plants CHAPTER 5. VALIDATION AND RESULTS

Location Latitude 34.51◦ N Longitude 116.53◦ W Plant Characteristics Electric Power 10 MWe Storage Capacity 3 hours Receiver parameters Receiver thermal power 43 MWth Receiver ﬂuid Molten salt

Table 5.1: Solar Two power plant characteristics [51]

The tube diameter is selected using the correlation implemented in this model. The correlation is based on four commercial power plants, so it is a rather rough model of selecting the tube diameter. However, the selected receiver tube diameter is pretty close to the actual plant data. The selected receiver tube thickness also agrees quite well with the reference plant.

Design parameters Solar Two plant devISEcrs default devISEcrs model Absorber area 99.29 m2 [51] 92.39 m2 92.39 m2 Receiver diameter 5.1 m [51] 4.4 m 4.4 m Receiver height 6.2 m [51] 6.7 m 6.7 m Diameter of receiver tube 23 mm [51] 24 mm 24 mm Thickness of receiver tube 1.2 mm [51] 1.2 mm 1.2 mm No. of receiver panels 24 [51] 34 24 No. of tubes per panel 32 [51] 17 24 Tower height 76 [34] 94 94

Table 5.2: Comparison of Solar Two receiver design parameters

The selected number of receiver panels and tubes per panel deviates from the reference plant value. This can be explained with the small tube diameter deviation and the selected design velocity. The default design velocity used in the model is 4 m/s. If the design velocity to the model is given as 2.8 m/s, which is close to the reference plant value, the number of panels and tubes per panel are 24 and 24 respectively.

Comparing the above values with the reference plant, it can be concluded that the developed model designs the receiver within a reasonable limit.

Gemasolar Power Plant The Gemasolar plant is a 20 MW CRS plant with 15 hours of storage located in the province of Seville, Spain [36]. It is built based on the experience of the Solar Two power plant with molten salt as a heat storage technology. A 120 MWth external receiver was constructed to meet the demand of net electric power [36]. The plant location and the characteristics are tabulated in the Table 5.3.

Like the Solar Two receiver, a new receiver is designed using the developed design method for

Receiver Design Methodology for Solar Tower Power Plants 45 CHAPTER 5. VALIDATION AND RESULTS the respective plant location and speciﬁcations. The receiver is designed for the desired receiver thermal power and the resulting receiver design is compared with the actual Gemasolar plant values.

Location Latitude 37.33◦ N Longitude 5.19◦ W Plant Characteristics Electric Power 19.9 MWe Storage Capacity 15 hours Receiver parameters Receiver thermal power 120 MWth Receiver ﬂuid Molten salt

Table 5.3: Gemasolar power plant characteristics [36]

The actual and designed receiver design parameters are listed in the Table 5.4. The designed absorber area is smaller when compared to the actual plant value. This is because of the difference in allowable average design flux on the receiver. In the Gemasolar power plant, the allowable average design flux used is 445 KW/m2, whereas this model uses 465 KW/m2. The receiver diameter and height are influenced by the absorber area, which therefore also deviates to some extent. Moreover, the aspect ratio used is also different between the actual plant and the model. Gemasolar is using an aspect ratio of 1.3 and the model is using 1.5 as a default value.

Design parameters Gemasolar plant devISEcrs model devISEcrs model Absorber area 269.6 m2 [36] 256.64 m2 256.64 m2 Receiver diameter 8.1 m [36] 7.2 m 7.2 m Receiver height 10.6 m [36] 11.3 m 11.3 m Diameter of receiver tube 25 mm [7] 26 mm 26 mm Thickness of receiver tube 1.65 mm [37] 1.2 mm 1.2 mm No. of receiver panels 16 [37] 22 16 No. of tubes per panel 64 [37] 40 56 Tower height 140 m [21] 114 m 114 m

Table 5.4: Comparison of Gemasolar receiver design parameters

The designed tube diameter is close to the actual tube diameter, because the correlation of the tube diameter is developed based on state-of-the-art commercial plants. There is a deviation in tube thickness, which is kept constant for molten salt receivers in the model. The tube thickness has to be selected based on the pressure exerted by the ﬂuid, so that the tube can withstand the pressure. Mostly, pressure is not crucial for molten salt receivers. In case of water/steam receivers, care should be taken to design the tube thickness according to the high operating pressure in the receiver.

Though the tube diameter is close to the actual value, the number of panels and tubes per panel are diﬀerent due to the selected design velocity. If the design velocity is given as 2.8 m/s, which

46 Receiver Design Methodology for Solar Tower Power Plants CHAPTER 5. VALIDATION AND RESULTS is close to the reference plant value, the number of panels and the tubes per panel are 16 and 56 respectively. The small diﬀerence in tubes per panel from the reference plant can be explained with the small absorber area and receiver diameter. Tower height model is rather rough and therefore there is some deviation in the tower height. However, the developed design method designs a reasonable receiver that accords to that of commercial plants.

Crescent Dunes Power Plant The Crescent Dunes power plant is a 110 MW solar tower power plant with 10 hours of storage located in Tonopah, Nevada, USA [37]. It is a large scale power plant with molten salt technology and is developed by SolarReserve. A 540 MWth external molten salt receiver is used for the required net electric power [37]. There is no detailed literature for the receiver thermal power used in Crescent Dunes power plant. Therefore, the receiver thermal power is calculated with the design mass ﬂow rate of the plant (1280 kg/s), which is found in the literature [37]. Rodriguez [37] mentioned that the Crescent Dunes plant generates four times more electric power than Gemasolar which is in accordance with the calculated receiver thermal power. The plant location and the speciﬁcations are tabulated in the Table 5.5.

Location Latitude 38.14◦ N Longitude 117.22◦ W Plant Characteristics Electric Power 110 MWe Storage Capacity 10 hours Receiver parameters

Receiver thermal power 540 MWth Receiver ﬂuid Molten salt

Table 5.5: Crescent Dunes power plant characteristics [37]

Using the plant location and speciﬁcations, the developed design method designs a new receiver. Similar to the previous reference cases, the receiver is designed for the desired receiver thermal power. The resulting receiver design is compared with the actual reference plant values.

The actual and designed receiver design parameters are listed in the Table 5.6. The actual receiver thermal power is calculated with the design mass ﬂow rate and it might not be accurate. Hence, there will be a deviation in absorber area, which in turn inﬂuences the receiver diameter and height. However, the deviation of the designed absorber area from the real value is less than 5 %.

The tube diameter has a deviation of 5 mm from the reference plant. However, the tube diameter can be selected over a wide range for the same receiver thermal power. The number of panels and the tubes per panel will be changed according to the tube diameter and ﬂuid velocity. For the design velocity of 4 m/s, the number of panels and the tubes per panel are 16 and 83 respectively. The result is close to the actual plant data. As explained in the previous section, a constant tube wall thickness is used in this model.

Comparing the designed receiver parameters to the actual plant data, the results correspond to the commercial power plants.

Receiver Design Methodology for Solar Tower Power Plants 47 CHAPTER 5. VALIDATION AND RESULTS

Design parameters Crescent Dunes plant devISEcrs model Absorber area 1105.28 m2 [37] 1155.77 m2 Receiver diameter 17.6 m [37] 15.6 m Receiver height 20 m [37] 23.6 m Diameter of receiver tube 42 mm [37] 37 mm Thickness of receiver tube 1.65 mm [37] 1.2 mm No. of receiver panels 16 [37] 16 No. of tubes per panel 76 [37] 83 Tower height 195 m [4] 220 m

Table 5.6: Comparison of Crescent Dunes receiver design parameters

By validating 10 MW, 20 MW and 110 MW molten salt power plant, it is conﬁrmed that the developed design methodology gives reasonable results for small scale to large scale power plants.

5.1.2 Cavity Receiver The current cavity receiver implementation uses molten salt as HTF. There is no commercial molten salt cavity receiver available for validation. However, the model can be used to design the outer geometry of the receiver to compare with currently available water/steam cavity receivers. Since the ﬂuid properties would be needed to design the internal tube geometry, the part is left out. The outer geometry of the cavity receiver is validated using the PS10 solar power plant.

PS10 Power Plant PS10 is a 10 MW CRS plant with 0.5 hours of storage located in the province of Seville, Spain [44]. It is using the direct water/steam solar receiver technology and the pressurised superheated steam is stored in tanks for 30 minutes. A 40 MWth cavity receiver is used to meet the required

Location Latitude 37.26◦ N Longitude 6.15◦ W Plant Characteristics Electric Power 10 MWe Storage Capacity 0.5 hours Receiver parameters Receiver thermal power 40 MWth Receiver ﬂuid Water

Table 5.7: PS10 power plant characteristics [44] net electric power. The plant location and speciﬁcations are listed in the table 5.7.

A new receiver is designed using the developed design method for the respective plant speciﬁca- tions. The receiver is designed for the desired receiver thermal power and the resulting receiver

48 Receiver Design Methodology for Solar Tower Power Plants CHAPTER 5. VALIDATION AND RESULTS design is compared with the reference plant values.

Design parameters PS 10 plant devISEcrs model Absorber area 260 m2 [23] 248 m2 Cavity radius 7 m [23] 6.2 m Receiver height 12 m [23] 12.7 m Receiver width 14 m [23] 12.4 m Aperture width 14 m [23] 12.4 m Aperture height 9 m [23] 9.5 m Lip height 3 m [23] 3.2 m Tower height 120 m [44] 133 m

Table 5.8: Comparison of PS 10 receiver design parameters

Table 5.8 shows the actual and designed receiver parameters. The allowable design flux for water/steam fluid is used as given by Falcone [22]. In case of water/steam receiver, the allowable design flux is lower compared to molten salt HTF. As all the outer design parameters agree well with the designed data, the developed design methodology designs cavity receivers in accordance with the commercial references.

5.2 Receiver Thermal Losses Validation

For the validation of receiver thermal losses, the test cases used in Falcone [22] is used. 320 MWth molten salt external and cavity receivers are evaluated for the purpose of thermal losses validation.

5.2.1 External Receiver

A 320 MWth external receiver is designed and the thermal losses are calculated. Generally, the receiver thermal efficiency depends highly on the assumptions made in the model, in particular the chosen material coating properties. The absorptivity of the coating will have a large influence on receiver thermal efficiency. So, it is difficult to reproduce the exact efficiency, unless the exact assumptions and the used coating properties are known. However, it can be proved that the calculated efficiency and individual loss components are reasonably close to the reference. Table 5.9 shows the thermal losses and the receiver efficiency of reference plant and devISEcrs model.

Parameters Reference plant devISEcrs model

Receiver thermal power 320 MWth [22] 320 MWth

Total loss 35.2 MWth [22] 38.19 MWth

Convection loss 5.12 MWth [22] 4.88 MWth

Radiation loss (Emitted and Reﬂected) 30.08 MWth [22] 33.31 MWth Receiver eﬃciency 89.0 [22] 88.06

Table 5.9: Validation of molten salt external receiver thermal losses

Receiver Design Methodology for Solar Tower Power Plants 49 CHAPTER 5. VALIDATION AND RESULTS

Figure 5.1: Total and individual loss component comparison for external receiver

The absorptance used in the model is 0.95. The calculated receiver efficiency agrees reasonably well with the reference plant receiver efficiency. Figure 5.1 shows the comparison of convection and radiation losses contribution for designed and actual external receiver. In this model, 0 m/s is used as a design wind velocity [37]. The radiation loss includes the emitted and reflected radiation. The estimated convective loss is quite close to the reference value and there is some deviation in radiation losses. This can be explained with the deviation in coating properties. However, the calculated values are in the reasonable range. Hence, the developed loss model is assumed to be valid for molten salt external receivers.

5.2.2 Cavity Receiver

Similar to the external receiver, a 320 MWth molten salt cavity receiver is designed and the thermal losses are calculated. Table 5.10 shows the thermal losses and the receiver eﬃciency of both reference plant and devISEcrs model.

Parameters Reference plant devISEcrs model

Receiver thermal power 320 MWth [22] 320 MWth

Total loss 29.44 MWth [22] 23.42 MWth

Convection loss 10.24 MWth [22] 8.37 MWth

Radiation loss (Emitted and Reﬂected) 19.2 MWth [22] 15.05 MWth Receiver eﬃciency 90.8 [22] 92.68

Table 5.10: Validation of molten salt cavity receiver thermal losses

50 Receiver Design Methodology for Solar Tower Power Plants CHAPTER 5. VALIDATION AND RESULTS

Figure 5.2: Total and individual loss component comparison for cavity receiver

The absorptance used in the model is 0.95. The calculated receiver efficiency is 92 percent which is close to the actual efficiency of 91 percent. Figure 5.2 shows the comparison of convection and radiation losses contribution for designed and actual cavity receiver. Similar to external receiver, 0 m/s is used as a design wind velocity for cavity receiver also. The radiation loss consists of both emitted and reflected radiation. The deviation of radiation losses can be explained with the assumptions made in this model and the deviation in coating properties. However, the model is estimating thermal losses in the reasonable range and therefore, it is assumed to be valid for molten salt cavity receiver.

5.3 Eﬀect of Spillage Loss on Heliostat Size

Spillage loss has to be within a reasonable limit. After careful analysis using the devISEcrs tool, it is found that the spillage loss is largely inﬂuenced by the heliostat size, particularly for small-scale power plants.

Due to astigmatism, the reﬂected beam size on the receiver increases with increasing heliostat size. In case of large-scale power plants, the receiver size is big enough to accept the large reﬂec- ted beam produced by large heliostats. However, care should be taken while determining heliostat size for small scale receivers in order to restrict spillage loss to a reasonable limit.

Figure 5.3 shows the external receiver spillage loss for different power plant sizes with respect to heliostat size. The effect of increased spillage is most significant for small-scale power plants. General trade-off between high spillage losses and high heliostat field costs which arise for using a very high number of heliostats.

It is shown in the Figure 5.3 that small size power plants are more prone to high spillage losses with respect to heliostat size. So, it is essential to select an appropriate heliostat size in order to restrict the spillage loss to a reasonable limit.

Receiver Design Methodology for Solar Tower Power Plants 51 CHAPTER 5. VALIDATION AND RESULTS

Figure 5.3: External receiver spillage loss of diﬀerent power plant sizes with respect to heliostat size

Figure 5.4: Cavity receiver spillage loss of diﬀerent power plant sizes with respect to heliostat size

Figure 5.4 depicts the cavity receiver spillage loss for diﬀerent power plant sizes with respect to heliostat size. The spillage loss is lower for cavities than external receivers because of large aperture size for the same receiver thermal power. Therefore, the size of the power plant selected for the cavity receivers is restricted to the 10 MW power plant. Similar to external receivers, cavity receivers are also more prone to spillage loss with respect to heliostat size for small-scale power plants. Hence, it is suggested to use a heliostat size that corresponds to the receiver size for small-scale power plants.

52 Receiver Design Methodology for Solar Tower Power Plants Chapter 6

Conclusion and Future Work

6.1 Conclusion

A methodology was developed to design molten salt tubular receivers by using and adapting existing design criteria available in the literature. It was implemented in Python and embedded in the Fraunhofer ISE tool, devISEcrs.

The developed receiver will be able to design/calculate: • Outer receiver geometry • Internal tube geometry • Loss estimation

The developed design methodology was validated by comparing to four diﬀerent commercial power plants. The resulting receiver designs are in accordance with the commercial power plants. Moreover, the scalability of the design method is considered and the model is able to design small to large-scale power plants.

Spillage losses depending on heliostat and receiver size were studied.

6.2 Future Work

Possible future improvements may include:

• Development of a method to calculate the allowable peak flux with the given receiver fluid and material. • Inclusion of the aiming point strategy to estimate the flux on the receiver surface. • Implementation of a more detailed pressure loss calculation considering pressure loss due to bends and headers. • Development of a method to calculate cavity inclination angle for cavity receivers. • Replacement of the tower height model with a more sophisticated one.

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