Thermo-Economic Analysis of a Solar Thermal Power Plant with a Central Tower Receiver for Direct Steam Generation

Ranjit Desai KTH Royal Institute of Technology April-September 2013. ([email protected]) EMN, École des Mines de Nantes. KTH, Royal Institute of Technology. BME, Budapest University QUB, Queen’s University, Belfast UPM, Universidad Politécnica de Madrid

Ranjit Desai Index Note

Master’s Thesis

Ranjit Desai Index Note

Master’s Thesis

Supervised by

Institute Tutor Academic Tutor Rafael E. Guédez Dr. Claire Gerente KTH Royal Institute of Technology Ecole des Mines de Nantes Concentrating Solar Power Group GEPEA UMR CNRS 6144, Department of Energy Technology/ Heat and Power Division 4 Rue Alfred Kastler, BP 20722. Brinellvägen 68, SE-100 44. 44307, Nantes Cedex 03, Stockholm, SWEDEN. Nantes, FRANCE.

Ranjit Desai Index Note

Master’s Thesis

INDEX NOTE Report Title: Thermo-Economic Analysis of a Solar Thermal Power Plant with a Central Tower Receiver for Direct Steam Generation

Placement Title: Research Internship

Author: Ranjit Desai

Institute: KTH Royal Institute of Technology

Address: KTH Royal Institute of Technology

Department of Energy Technology/ Heat and Power Division, Brinellvägen 68, SE-100 44.

Stockholm, SWEDEN.

Institute Tutor: Rafael E. Guédez

Role: Research Assistant

Academic Tutor: Dr. Claire Gerente

Summary:

Amongst the different Concentrating Solar Power (CSP) technologies, central tower power plants with direct steam generation (DSG) emerge as one of the most promising options. These plants have the benefit of working with a single heat transfer fluid (HTF), allowing them to reach higher temperatures than conventional parabolic trough CSP plants; this increases the efficiency of the power plant. The goal of the study is to evaluate the thermodynamic and economic performance of one of these plants by establishing a dynamic simulation model and coupling it with in-house cost functions. In order to do so, the TRNSYS simulation studio is used together with MATLAB for post processing calculations. Furthermore, a valuable expected outcome of the work is the development, verification and validation of new DSG component models in TRNSYS for performance estimation; such as a central tower receiver model and steam accumulators for storage. Lastly, thermo-economic optimization of the power plant performance and costs will be addressed using a multi-objective optimization tool to determine the trade-offs between conflicting objectives, such as water depletion and the levelized electricity cost (LEC).

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Contents

Index Note ...... iii

List of Tables ...... v

List of Figures ...... v

Nomenclature ...... vi

ACRONYMS ...... VI GREEK LETTERS ...... VII SUBSCRIPTS ...... VII

1 Introduction ...... 1

2 Objectives ...... 2

3 Theoretical Framework ...... 3

3.1 LINE-FOCUSING CSP ...... 3 3.1.1 PARABOLIC TROUGH CONCENTRATOR ...... 3 3.1.2 LINEAR FRESNEL REFLECTOR ...... 3 3.2 POINT-FOCUSING CSPS ...... 4 3.2.1 DISH STIRLING ...... 4 3.2.2 SOLAR CENTRAL TOWER SYSTEM ...... 5

4 Methodology ...... 6

4.1 POWER BLOCK ...... 6 4.2 THERMODYNAMIC MODEL OF POWER BLOCK ...... 7 4.2.1 STODOLA EXPANSION MODEL ...... 7 4.2.2 THE NTU-EFFECTIVENESS METHOD ...... 8 4.2.3 FEED WATER PUMP ...... 9 4.2.4 INDIRECT AIR-COOLED CONDENSER ...... 9 4.3 RECEIVER MODELLING ...... 9 4.3.1 LITERATURE REVIEW ...... 10 4.3.2 THE MODEL ...... 10 4.4 CRITICALITY OF THE DIMENSIONS ...... 13 4.4.1 CRITICAL METAL TEMPERATURE ...... 13 4.4.2 PRESSURE DROP ...... 14

5 Analysis...... 16

5.1 OPTIMIZATION BASED ON DIMENSIONS ...... 16 5.2 ECONOMIC ANALYSIS ...... 17 5.3 SELECTED DESIGN...... 18

6 Future work ...... 19

6.1 FORTRAN PROGRAMMING ...... 19

7 Conclusion ...... 20

8 References ...... 21 iv

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Appendix ...... 24

APPENDIX A: TUBE SELECTION HANDBOOK FOR AISI 316L ...... 24 APPENDIX B: OPTIMIZED STATES FROM POWER BLOCK ...... 25 APPENDIX C: GNATT CHART...... 26 APPENDIX D: FORTRAN PROGRAM WINDOW IN MVS 2008 ...... 27 APPENDIX E: ANALYSIS GRAPHS FOR SH SECTION AND RH SECTION ...... 28 SH SECTION ...... 28 RH SECTION ...... 29

LIST OF TABLES

Table 1 Operating Parameters of the Ivanpah Power Plant ...... 6 Table 2 Standard Heat Transfer Coefficients and Minimum Approach Temperature ...... 9 Table 3 NTU-Effectiveness Relationship ...... 9 Table 4 Correlations for Nusselt Number w.r.t. Reynolds Number ...... 13 Table 5 Two Phase Pressure Drop ...... 15

LIST OF FIGURES Figure 1 : Parabolic Trough Concentrator ...... 3 Figure 2 : Andasol 1 PTC Power Plant ...... 3 Figure 3 : Linear Fresnel Reflector ...... 4 Figure 4 : Compact Linear Fresnel Reflector ...... 4 Figure 5 : LFR Power Plant, France ...... 4 Figure 6 : Dish Stirling System ...... 5 Figure 7 : Dish Stirling CSP Plant, USA ...... 5 Figure 8 : Solar Central Tower System ...... 5 Figure 9 : Gemasolar Power Plant ...... 5 Figure 10 : Methodology ...... 6 Figure 11 : Power Plant Layout ...... 7 Figure 12 : Stodola’s Ellipse Law for Off-Design Turbine Operation ...... 8 Figure 13 : Vertical view of the cavity receiver ...... 10 Figure 14 : The integrated Solar Receiver ...... 10 Figure 15 : Receiver Panel Representation ...... 11 Figure 16 : Heat Transfer in receiver ...... 11 Figure 17 : Pressure Drop Vs No of Tubes...... 16 Figure 18 : Efficiency Vs No. of Tubes ...... 17 Figure 19 : Material Cost Vs No. of Tubes ...... 18 Figure 20 : TRNSYS Proforma Design ...... 19 Figure 21 : SH: Pressure Drop Vs No. of Tubes ...... 28 Figure 22 : SH: Efficiency Vs No. of Tubes ...... 28 Figure 23 : SH: Material Cost Vs No. of Tubes ...... 29 Figure 24 : RH: Pressure Drop Vs No. of Tubes ...... 29 Figure 25 : RH: Efficiency Vs No. of Tubes ...... 30 Figure 26 : RH: Material Cost Vs No. of Tubes ...... 30

Ranjit Desai List of Tables

Master’s Thesis

NOMENCLATURE

푄̇ Energy per unit of time [W, watts] h Heat transfer coefficient [W/m2K] F Face Factor T Temperature [K] A Area [m2] H Height of the receiver [m] L Length (height) of the receiver [m] K Conductive heat transfer coefficient [W/mK] g Acceleration due to gravity [m/s2] Re Reynolds Number Nu Nusselt Number Pr Prandlt Number Gr Grashof Number Ra Rayleigh’s Number Cp Specific heat [kJ/kgK]

Acronyms

Btu British Transfer Unit CSP Concentrated Solar Power CT Central Tower CLFR Compound Linear Fresnel Reflector DNI Direct Normal Irradiance [W/m2] DSG Direct Steam Generation FORTRAN FORmula TRANslation language FWP Feed Water Pump HPT High Pressure Turbine HTF Heat Transfer Fluid LFR Linear Fresnel Reflector LPT Low Pressure Turbine MATLAB MATrix LABoratory MLD Mixed Logical Dynamical MW Mega Watt [106] NTU Number of Transfer Units PB Power Block ppm Parts per million PTC Parabolic Trough Concentrator RH Reheater vi

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SCTS Solar Central Tower System SH Superheater SHS Superheated steam SL Saturated liquid STPP Solar Thermal Power Plant TRNSYS TRaNsient SYStems USA United States of America

Greek Letters

𝜎 Stefan-Boltzman’s constant [5.68 × 10 −8 푊/푚2퐾 ] ρ Density (kg/m3) Ф Mass-Flow coefficient 휀 Emissivity, Effectiveness 훽 Volumetric Expansion Coefficient [1/K] 휇 Dynamic Viscosity [Ns/m2] 휐 Kinematic Viscosity [m2/s] 훼 Thermal Diffusivity [m2/s]

Subscripts

fluid Physical State as Liquid out Position of the working fluid in Position of the working fluid, inside gains Energy received by working fluid losses Energy lost by working fluid max maximum min Minimum nom Nominal inc Incident Energy hs Hot Side cs Cold Side conv Convective Heat Transfer Losses rad Radiative Heat Transfer Losses ref Reflective Heat Transfer Losses amb Ambient G Gas pf Pressure correction factor r Ratio sky Sky s Surface vii

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nat Natural nb Nucleate Boiling tp Two-phase for Forced avg Average L Along the Length or length being characteristic dimension, Liquid rec Receiver mixed Mixed (natural and forced)

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1 INTRODUCTION The ever growing population and industrialized world of 21st century is facing severe problems such as climate change and ozone layer depletion. The 20th century saw the industrial revolution of mankind, which majorly increased fossil fuel consumption to many folds. During such period, the business pragmatism was of utter importance and environmental impacts were thrown aside. It was not until the beginning of the 21st century when mankind raised concerns about climate change due to the increasing levels of CO2 emissions, notwithstanding the ever swelling energy demand. In fact, at present CO2 emissions have already exceeded the upper safety limit of 350 ppm [1], and the energy demand is also expected to reach the 550 quadrillion BTU [2] by the end of year 2013. It is even of higher concern that the continuous population growth and increasing use of modern heavy energy technologies (which could lead to increasing CO2 emissions) will be worsening the situation. Hence, the search of sustainable means of power generation should be considered.

In such a jeopardy, renewable energy sources are proving to be a feasible solution, mankind to rely on. Indeed, nowadays the world receives approximately 17-18% of its energy from renewables, including about 9% from ‘traditional biomass’ and about 8% from other renewable sources [3]. These renewable shares are ideally expected to grow in the energy outlook, to bring down carbon emissions along with providing energy.

Concentrating Solar Power (CSP) is one of such renewable energy sources which came into light in the late 2oth and early 21st century. In CSP technology, the incident solar radiations are reflected onto the receiver placed at the focal point (or along the focal line, in case of line-focusing CSP) to increase the temperature of the surface up to even 1400 0C. The gained heat energy by heat transfer fluid (HTF) or working fluid is then transformed into the usable form of energy such as electricity, using turbines and generators.

Historically, CSP was first introduced by Archimedes to repel the invading army [4], but it was not until the late 19th century when the first parabolic trough technology [5] using steam for power generation was demonstrated. Today CSP represents a reliable technology for electricity generation with a global installed capacity that exceeds the 2GWe. Further, based on the number of projects that are being planned or currently under construction the International Energy Agency has estimated that, even in the case of a conservative scenario, CSP installed capacity will exceed the 10 GWe by 2020 [6]. In such regard, it is worth highlighting the construction of Ivanpah Solar power plant [7] located in the Mojave Desert in California, which will have a nominal capacity of approximately 320MWe, being the largest CSP project ever deployed. It is expected to go online in September 2013 in United States of America (USA) at Primm city of Nevada province [7] [8].

Using Ivanpah Solar as a reference plant for the current work, the main objective is thus to perform a thermoeconomic evaluation and analysis of a CSP direct steam generation (DSG) system. Specifically, the work aims to develop a model for the dynamic simulation of the central tower (CT) receivers used in such power plants, which will then lead to perform further analysis.

The objectives section enlists the interim goals of this project. The theoretical framework explains the background of CSP technologies, and spreads light on the central tower receiver technology to end with. In methodology, the model is explained in details to be followed by economic analysis, results and discussions.

Ranjit Desai Introduction

Master’s Thesis

2 OBJECTIVES The project was set to achieve a dynamic simulation of a DSG solar thermal power plant to be used to compare it with other power plants based on other power producing technologies especially with various CSP technologies. In path to reach the final goal various interim objectives were attained. These objectives were as follow 1. Decide an appropriate architecture for DSG receiver design from available resources 2. Develop a thermal model of the receiver to get possible design solutions 3. Select an optimized design 4. Economic analysis based on material for the selected design 5. Develop a FORTRAN model for the selected design 6. Create new TRNSYS components for DSG

Ranjit Desai Objectives

Master’s Thesis

3 THEORETICAL FRAMEWORK The geographical location of the power plants based on CSP technologies is instrumental due to the fact that CSP deals with the assimilation of incident solar irradiation, normally denoted as DNI (Direct Normal Irradiance) and measured in terms of solar energy incident per unit area (푊/푚2). Modern day CSP technology has evolved many folds from the initial attempts and put into use for many different applications such as power production and process steam generation etc. The choice of technology to be implemented therefore, depends upon the end usage and the required highest temperature. These technologies can be distinguished on their focusing paradigms such as line focusing and point focussing. The present chapter deals with the different CSP technologies with an example of the existing power plants based on the respective technology as well as the highlighting differences between these technologies.

3.1 Line-focusing CSP In line-focusing CSP technologies, the incident solar energy is reflected onto the receiver placed along the focal point of the reflector. The line-focusing technologies are generally employed to reach temperature up to 400 0C [9] for which molten salts, oils or water inclusively can be used as heat transfer fluid. Currently, there are two main types of line-focusing CSP technologies, namely parabolic trough and linear Fresnel. These are briefly described in the subsequent sections of the chapter.

3.1.1 Parabolic Trough Concentrator In Parabolic Trough Concentrator (PTC), parabolic geometry is the working principle, which says the incident rays perpendicular to the plane of parabola are reflected and concentrated at the focus. The working fluid is passed through the receiver, which is made up of a metal pipe enveloped inside a vacuum tube to minimize mainly the convective losses. For power generation, many PTCs are connected in series to reach up to 400 0C [9] needed as per the end use. The PTC have tracking systems which allow them to track the Sun in the search of maintaining the perpendicularity of the incident rays [10]. A general schematic of such power plant is shown in Figure 1. The PTC plants represent around 80% of the total CSP installed capacity worldwide [11], being worth to mention the ANDASOL [12] complex in southern Spain [13]. It consists of three 50MWe CSP plants that commenced in 2006 and where the use of storage using a molten salts system was first demonstrated at large scale, thus boosting the development of CSP and encouraging new research fields. The Figure 2 shows parabolic trough in ANDASOL 1 power plant.

Figure 1 : Parabolic Trough Concentrator [14] Figure 2 : Andasol 1 PTC Power Plant [15]

3.1.2 Linear Fresnel Reflector In Linear Fresnel Reflector (LFR) technology, flat mirror reflectors reflect and concentrate onto the receiver through which working fluid is pumped [16]. A typical LFR is shown in Figure 3. Compared to PTCs, LFRs are less expensive and also allow for larger reflective areas [6]. Furthermore, recent developments in LFR demonstrate that arrangements accounting for two receivers can yield a better overall performance. Such arrangement is known as Compact Linear Fresnel Reflector (CLFR) [17] as shown in Figure 4. Indeed when compared against PTCs, although cheaper, LFRs have other issues such as more optical losses and building complex tracking systems. Given that LFRs are flat mirror reflectors, these are easier to manufacture and install (that is why they are cheaper) and 3

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this is why they are typically used in hybridization modes (together with coal). The Puerto Errado 2 [18] power plant is a pure linear Fresnel plant. However, the largest LFR power plant with 100 MWe gross capacity is being constructed in India in Dhursar district of Rajasthan [19]. The Figure 5 shows one of such LFR power plant of 12 MWe gross capacity located at Ghisonaccia (Corsica Island), France [20].

Figure 3 : Linear Fresnel Reflector [21] Figure 4 : Compact Linear Fresnel Reflector

Figure 5 : LFR Power Plant, France [22]

3.2 Point-Focusing CSPs In Point-Focusing CSPs, the receiver is placed at the focal point of the reflector field. These technologies are usually employed to achieve very high temperatures, hence are used in power production. The temperature range, these technologies can achieve is up to 1500 0C [9] because of the very high concentration ratios [9].

3.2.1 Dish Stirling This system consists of stand-alone parabolic concentrator with a Stirling engine mounted at the focal point onto which the rays are concentrated. Because of its construction, this kind of concentrator can track Sun’s movement along both the axes, i.e. Sun’s position with respect to equator as seasonal tracking and Sun’s movement throughout the day as daily tracking. Dish Stirling has the highest Solar-to-electric energy efficiency because of high concentration ratios and two-axial tracking [10]. The Figure 6 shows a typical Dish Stirling System.

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Figure 6 : Dish Stirling System [21] Figure 7 : Dish Stirling CSP Plant, USA [23]

The complexity of construction and costs in manufacturing, installation and maintenance have limited this technology from penetrating CSP market. In turn, commercial power plants using this technology are very few [6] [24]. One such power plant exists in California shown in Figure 7, USA with 300 MWe gross capacity [23].

3.2.2 Solar Central Tower System The Solar Central Tower systems (SCTS) consists of a centrally located receiver mounted at the top of a tower surrounded by a heliostats field. This heliostats field consists of large number of flat mirrors attached to the metallic frame and supported by stands on the ground. These heliostats track the Sun though out the year with seasonal and daily tracking. The maximum temperature that can be achieved with SCTS is approximately 1200 0C [9].

Figure 8 illustrates the Solar Central Tower system. After PTC, Solar Tower has been the most successful technology used for CSP plants [6]. In case of molten salts, the heat is transferred to water in a heat exchanger to convert to steam however, in case of water as a working fluid, steam is directly produced out of the receiver hence usually referred as direct steam generation (DSG). In Spain, Gemasolar Power plant [25] uses molten salt as working fluid and has 19.9 MWe [26] of gross capacity. The Figure 9 shows a filed photograph of Gemasolar power plant.

Figure 8 : Solar Central Tower System [21] Figure 9 : Gemasolar Power Plant [26]

Moreover, Spain also hosts a DSG power plant located in Sevila known as PS-10 and PS-20 with 11 MW and 20 MW of gross capacities respectively. The most recent solar thermal power plant with DSG technology is being constructed in USA, which is known as Ivanpah Solar thermal power plant. The Ivanpah Solar Thermal power plant is installed with the gross capacity of 392 MW and comprises of three tower and heliostat field systems. The working pressure in the power cycle is 160 bar with the receiver outlet temperature of steam is 580 0C [8].

Ranjit Desai Theoretical Framework

Master’s Thesis

4 METHODOLOGY The methodology for this work is shown in Figure 10. To analyse the STPP with SCTS having a central receiver based on DSG principle by dynamic simulations in TRNSYS, the necessary step was to design the receiver component using FORTRAN programing language. However, to design such a component, finding out dimensions of the receiver was the prior step. To calculate these dimensions, a receiver model was developed in MATLAB. The optimum mass flow rate was determined by simulating a power block of the complete plant to generate 123 MWe [7] [8]; similar to the capacity of one out of three towers at the Ivanpah Solar Thermal Power plant.

Power Block Optimization Mass Flow

MATLAB simulation Receiver Dimensions

FORTRAN component design Receiver Component

TRANSYS dynamic Simulation

Thermo-Economic Performance Evaluation

Figure 10 : Methodology

4.1 Power Block The power block (PB) was designed on the basis of limited available information of the Ivanpah CSP plant, which is given in Table 1. The PB works on the regenerative Rankine cycle of power generation. The entire power block schematic is shown in Figure 11. The numbers are used to represent the thermodynamic states of the working fluid, here water. However, to simulate this power block some key assumptions regarding the physical form of the water have been made (either quality ‘zero’ or ‘one’). These key assumptions were 1. Saturated Liquid at States namely 1, 2, 3, 4, 5, 6, 7 and State 8. 2. Saturated Steam at States namely 9 and 11. 3. Superheated Steam at States 10 and 12. 4. There is no mass leakage therefore, the heat and mass transfer with the make-up water which exists in the actual power plant has been neglected. 5. The work done on the working fluid by pumps is neglected as it is very small compared to the work done by the working fluid. Table 1 Operating Parameters of the Ivanpah Power Plant [7] [8]

Parameter Quantity Heat Transfer Fluid (HTF) Water Receiver Inlet Temperature 249 0C Receiver Outlet Temperature 586 0C Change in Temperature in receiver 270 0C Pressure in Power Cycle 160 bar Turbine Capacity (gross) 392 MWe

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12 SHS 24 HPT 1 LPT 1 22 LPT 2 LPT 3

10 SHS

11 S 21 23 SH 13 S RH 9 SS 25 CONDENSER

14 15 S 16 S 20 1 SL

P1 2 SL

P-13 18 BOILER 7 SL 4 SL 3 SL

5 SL 17 SL 19 SL

8 SL PH-HE1 PH-HE2 6 SL

Figure 11 : Power Plant Layout

The turbine used for this power plant has 8 stages and has mass extractions after 2nd and 6th stage [27] [8]. This power block was then simulated using MATLAB, and an optimized mass flow rate was calculated for the 123 MW as it is the capacity of the one solar tower out of three at Ivanpah[7] [8].

4.2 Thermodynamic Model of Power Block The operating parameters of Ivanpah power plant once found out were used to develop the complete power plant layout. The live-stream conditions were necessarily kept the same as that of Ivanpah to generate the electricity gross output of that of 123 MW (as specified in Table 1). A selection of the turbine is done by using catalogues of the turbine manufacturers which enlisted the specific turbines which could be used for such live stream conditions. The SST-900 [27] was one of the appropriate turbines for this work. The outlet pressures were calculated using the Stodola Expansion Model [28] for the turbines.

4.2.1 Stodola Expansion Model The off-design operation of a multi-stage axial turbine can be modelled using Stodola’s ellipse [29]. It uses the mass flow co-efficient (Ф) and pressure ratio across the unit of the turbine. The mass-flow co-efficient can be defined in terms of mass flow rate through that section of the turbine, pressure, fluid density and absolute temperature. [30]. It is stated in equation 4.1. For each expansion section of the turbine with a given backpressure

(푃표푢푡 ), a simple relationship may be developed [28] [29], allowing the expansion to be considered to be similar to that of a nozzle, this is known as Stodola’s Ellipse. The relationship is stated in equation 4.2. The Stodola’s ellipse is shown is Figure 12. This law is valid over a wide range of pressure ratios but does not give accurate mass flow once the chocking begins [29] because below the critical back pressure (푃푇 ) sonic flow conditions occur within the section. The outlet pressure can be found out using equation 4.3, as a function of ′푀̇ ′ (mass flow through the given section) and Y is the ellipse constant. ‘Y’ is stated in equation 4.4, as a function of the pressure ratio, mass flow constant for that segment.

푀̇ 푀̇ √푇 4.1 Φ = = √𝜌푃 푃 4.2 푃 2 Φ ∝ √1 − ( 표푢푡) 푃

Ranjit Desai Methodology

Master’s Thesis

Figure 12 : Stodola’s Ellipse Law for Off-Design Turbine Operation [28]

4.3 2 2 푃표푢푡 = √푃𝑖푛 − 푀̇ ∙ 푇𝑖푛 ∙ 푌

2 2 푃𝑖푛,푛표푚 − 푃표푢푡,푛표푚 4.4 Y = 2 2 푃𝑖푛,푛표푚 ∙ Φ𝑖푛,푛표푚

4.2.2 The NTU-Effectiveness Method The Heat Exchangers in the PB are modelled using NTU-Effectiveness method. Using nominal inlet conditions for both sides (hot and cold) and nominal mass flow rates, the heat load and the required surface area can be found out using this method [31]. The first step for this method is to define the maximum possible heat transfer rate between two fluids, which is achieved in counter flow heat exchanger

̇ ℎ푠 푐푠 푄푚푎푥 = 퐶푚𝑖푛(푇𝑖푛 − 푇𝑖푛 ) 4.5

Where ‘퐶푚𝑖푛’ is smaller specific heat of the two. The actual rate would be smaller to than this rate thus the efficiency can be of this heat exchanger can be defined as ratio of actual heat transferred to the maximum possible heat exchange. The actual heat exchange can therefore be stated as (equation 4.6). Thus, by knowing the inlet conditions of the two streams, for a given heat exchanger of a given capacity, the total heat load can be determined. Further, for any given heat exchanger, it can be shown that the efficiency is a function of ratio of heat capacities and the number of transfer units (NTU) [31] as shown in equation 4.7. The NTU and ‘퐶푟’ are defined in equations 4.8 and 4.9. In equation 4.8 ‘U’ is overall heat transfer co-efficient and ‘A’ is the surface area of the heat exchanger.

Therefore, the efficiency ‘휀’ in terms of ‘Δ푇푚𝑖푛’ (the minimum approach temperature). The value of ‘Δ푇푚𝑖푛’ are standardized with respect to stream type and can be found out using the Table 2. The NTU-Effectiveness relationship changes with respect to the type of the heat exchanger. For the counter-flow heat exchanger this relation is tabulated in Table 3.

̇ ℎ푠 푐푠 푄 = 휀푄푚푎푥 = 휀퐶푚𝑖푛(푇𝑖푛 − 푇𝑖푛 ) 4.6

휀 = 푓(푁푇푈, 퐶푟) 4.7

푈퐴 4.8 푁푇푈 = 퐶푚𝑖푛

퐶푚𝑖푛 4.9 퐶푟 = 퐶푚푎푥

Δ푇푚𝑖푛 4.10 휀 = 1 − ℎ푠 푐푠 (푇𝑖푛 − 푇𝑖푛 )

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Table 2 Standard Heat Transfer Coefficients and Minimum Approach Temperature [28]

Stream Type Heat Transfer Co-efficient Δ푇푚𝑖푛/2 Gas Stream 60 [푊/푚2퐾] 20 [K] Liquid Stream 560 [푊/푚2퐾] 5 [K] Evaporating Stream 1600 [푊/푚2퐾] 3 [K] Condensing Stream 3600 [푊/푚2퐾] 2 [K]

Table 3 NTU-Effectiveness Relationship

휀-NTU Relationship Condition 1 휀 − 1 퐶 < 1 푁푇푈 = ln ( ) 푟 퐶푟 − 1 휀퐶푟 − 1 휀 푁푇푈 = 퐶푟 = 1 1 − 휀

4.2.3 Feed water Pump The FWP works is required to raise the pressure of water to the required input to the next component of the power cycle. The FWP is modelled to find out the power requirements by the pump [28]. For this model some assumptions were made as follows 1. No heat exchange between pump and the environment 2. Change in kinetic and potential energy are neglected 3. Internal dissipation is characterized by hydraulic efficiency The Pump power is calculated as stated in equation 4.11 using hydraulic efficiency. This Hydraulic efficiency can be calculated as a function of temperature inputs and outputs (as stated in equation 4.12).

1 Δ푃 4.11 푃푝푢푚푝̇ = 푀̇ ( ) 휂ℎ 𝜌

1 − 휂ℎ Δ푃 4.12 푇표푢푡 = 푇𝑖푛 + ( ) 휂ℎ 𝜌퐶푝푤

4.2.4 Indirect Air-Cooled Condenser Similar to that of FWP, condenser model is also developed to calculate the mechanical power required to drive the circulating pumps and air draught fans as well as heat exchange areas for the surface condenser and the air-cooler. This model is developed along the same lines to those of published by J. Spelling in his PhD thesis [30]. The power required by the cooling fan can be given as follows (equation 4.13). Moreover, the equations required to calculate

‘푀̇ 푎𝑖푟’are as follows in equations 4.14 and 4.15.

푟푎 푀̇ 푎𝑖푟퐶푝푎푇푎 4.13 푎𝑖푟 퐶푝푎 푃푓푎푛̇ = [(1 + 푓푑푃 ) − 1] 휂푓푎푛

퐶푝푤 4.14 푀̇ 푎𝑖푟 = 푀̇ 푐표표푙 퐶푝푎

푀̇ 푐표표푙Δℎ푐표푛푑 4.15 푀̇ 푐표표푙 = 퐶푝푤(푇푐표푛푑 − ∆푇푐표푛푑 − (푇푎 + ∆푇푎𝑖푟))

4.3 Receiver Modelling For the modeling of the central receiver component, available information from previous research works on the design of CTSTPPs and vertical once-through high-pressure boilers has been used. Furthermore, all accessible information concerning the design of the receiver used in the Ivanpah Solar system has been collected and has been used as a reference. In the following sub-sections first there are highlighted the main aspects from the 9

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literature survey performed and subsequently the modeling approach considering both the heat transfer and mechanical structure of the component.

4.3.1 Literature Review Several researchers have proposed different techniques for the modelling and analysis of central tower receivers for CSP appliances. The first model considered was a hybrid model developed by using a Mixed Logical Dynamical (MLD) approach confirms that continuous and discrete characteristics modelling is possible in a single model [32]. However, this model could not be incorporated to find out the dimensions of a receiver system, as needed for this work because it is completely theoretical and has not applied to any of the existing central tower receivers. Alternatively, a model developed [33] for the dynamic simulation of the receiver at DAHAN CSP plant in China, explains the functioning of a cavity receiver, as shown in Figure 13. Such receiver is similar to that at Gemasolar CSP plant, which is based on molten salts as HTF. The issue in applying this model to for this work could have been the practical problems not possibly studied in changing the working fluid from that of molten salts to water. Thus, this model is discarded from the available options.

Figure 13 : Vertical view of the cavity Figure 14 : The integrated Solar Receiver [34] receiver [33]

On the other hand, a simulation of an integrated steam generator for solar tower [34] based on a structural modification of already existing receiver designs was developed and proved to achieve higher optical and thermal efficiencies. Furthermore, the authors of such work have applied their model to a larger-scale CSP plant with superheated steam at 550 0C and of 150 bars similar conditions to those of Ivanpah Plant (as previously stated in Table 1). Therefore, this model was selected as a main reference for this thesis work. The construction of this receiver is shown in Figure 14. The proposed structure has pipes flowing along the height of the receiver and placed along the circumference. The outer pipes comprise to be evaporator pipes of the boiler part of the receiver, whereas the superheater (SH) section is enveloped inside to boiler section. Such envelope structure helps in reducing the thermal losses, thereafter cancelling out the need of having a different section for the SH. Moreover, the radiation spillage around the receiver cavity to the SH from heliostats field is firstly intercepted by the boiler section, situated near the cavity. Thus, the energy which would have lost otherwise in radiation and spillage is used to do the useful work. In turn, this modified architecture of receiver claims to be thermally more efficient and economically cheaper than the rest [34].

4.3.2 The Model Firstly, the heat transfer across the receiver system is modelled. However, only the boiler section is modelled first considering heat transfer in the boiler and the receiver section would be in same lines fundamentally. The SH and reheater (RH) section would necessarily be having the similar heat transfer except the working temperatures and pressures. One such receiver panel is shown in Figure 15. The evaporating tubes are in contact with each other and they run along the height of the receiver.

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Di Do

Figure 15 : Receiver Panel Representation

The energy will be reflected by the heliostat field on to the receiver, which will be absorbed by the working fluid passing through the boiler. The energy absorbed by the working fluid would be the difference between total incident energy and total losses through the receiver. These losses comprise of 1. Convective losses because of the air surrounding the receiver, 2. Radiative losses because of the radiations emitted by the hot surface to the surrounding, 3. Reflective losses because of the material properties. This heat transfer has been shown in Figure 16.

Steam OUT

Q conv H Q inc

Q ref

Q rad

Water IN

Figure 16 : Heat Transfer in receiver

This absorbed heat is equal to the energy gains from the solar field.

푄̇푓푙푢𝑖푑 = 푄̇표푢푡 − 푄̇𝑖푛 4.16

푄̇푓푙푢𝑖푑 = 푄̇푔푎𝑖푛푠 − 푄̇푙표푠푠푒푠 4.17

푄̇푙표푠푠푒푠 = 푄̇푐표푛푣 + 푄̇푟푎푑 + 푄̇푟푒푓 4.18

푄̇푓푙푢𝑖푑 = 푄̇𝑖푛푐 − (푄̇푐표푛푣 + 푄̇푟푎푑 + 푄̇푟푒푓 ) 4.19

4.3.2.1 Radiative losses The radiative heat transfer losses are dominant losses at high temperatures. The heat loss due to radiation is calculated using equation 4.22. as a function of both ambient air temperature and effective sky temperature [35] In this case the ambient temperature, plays a very important role and is calculated by using the Duffie-Beckman equation stated as in equation 4.23 [36]. The Equations 4.20-4.22 [37] show the relationship between the sky temperature, ambient air temperature and radiative heat transfer losses. 2 2 ℎ푟푎푑,푎푚푏 = 𝜎휀퐹푠,푎푚푏 (푇푠 + 푇푎푚푏 )(푇푠 + 푇푎푚푏 ) 4.20

2 2 ℎ푟푎푑,푠푘푦 = 𝜎휀퐹푠,푠푘푦 (푇푠 + 푇푠푘푦 )(푇푠 + 푇푠푘푦 ) 4.21

푄̇푟푎푑 = ℎ푟푎푑,푎푚푏 ∙ 퐴푠 ∙ (푇푠 − 푇푎푚푏 ) + ℎ푟푎푑,푠푘푦 ∙ 퐴푠 ∙ (푇푠 + 푇푠푘푦 ) 4.22

1.5 푇푠푘푦 = 0.552 ∙ (푇푎푚푏 ) 4.23 11

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4.3.2.2 Convective losses The volumetric flow rate is very large is needed for such a power plant. The system possesses very large Reynolds number (Re) as result of high volumetric flow rate and comparatively small tube diameters. For such very large values of Reynolds numbers (greater than 10 5), the convective heat transfer correlations are different than the traditional ones. Further, due to abnormally large geometry of the external cylinder, the natural convection from the receiver is assumed to be similar to that of from the vertical flat-plate.

4.3.2.2.1 Natural convection The Nusselt number is calculated using either equation 4.24 as introduced by Siebers and Kraabel [35] or equation 4.25 known as Churchill and Chu [31]. The choice between these two equations depends upon the values of Grashof Number (Gr) to be calculated using equation 4.26. The equation 4.24 is valid for Gr < 1012 however, the Churchill and Chu correlation (equation 4.25) is valid for Gr > 1013. For this correlation the long vertical tube is approximated 4 9 9 13 as a vertical plate [for laminar flow (10 ≤ 푅푎퐿 ≤ 10 ) and for turbulent flow (10 ≤ 푅푎퐿 ≤ 10 )]. To use these two correlations some other entities are required such as Grashof Number (Gr), Rayleigh’s Number (Ra) and Prandlt Number, which are calculated using equations 4.26, 4.27 and 4.28 respectively.

−.14 4.24 1/3 푇푠 푁푢푠푠푒푙푡푛푎푡 = 0.098 ∙ 퐺푟퐻 ( ) 푇푎푚푏 2 0.387 ∙ 푅푎 1/6 4.25 푁푢 = {0.825 + 퐿 } 퐿 [1 + (0.492/푃푟)9/16]8/27

3 퐻 푟푒푐 4.26 퐺푟푛푎푡 = 푔 ∙ 훽 ∙ (푇푠,푎푣푒 − 푇푎푚푏 ) ∙ 2 휐 푎푚푏 푔 ∙ 훽 ∙ (푇 − 푇 ) ∙ 퐿3 4.27 푅푎 = 퐺푟 ∙ Pr = 푠 ∞ 퐿 퐿 휐 ∙ 훼 퐶 ∙ 휇 4.28 푃푟 = 푝 Κ

4.3.2.2.2 Forced Convection Similar to that of Natural Convection, Nusselt Number calculation is the prior step to calculate the convective heat transfer coefficient (forced). In this particular case, as there will be a lot variation in the thermo-physical properties of the water with time, the choice of correlation is made from several available options. The forced convection correlations are provided as a set of curves that are applied for a specific range of Reynolds number and for a specific surface roughness. These correlations are tabled below in Table 4.

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Table 4 Correlations for Nusselt Number w.r.t. Reynolds Number [35]

Reynolds Number Range Correlation

퐾푠 ⁄퐷 = 0 (A smooth cylinder) 0.8 1. All Re 푅푒 0.635 푁푢 = 0.3 + 0.488 ∙ 푅푒0.5 (1 + ( ) ) 282000

−5 퐾푠 ⁄퐷 = 75 × 10 5 2. 푅푒 ≤ 7.0 × 10 Use smooth cylinder correlation as in row 1. 5 7 −3 0.98 3. 7.0 × 10 < 푅푒 < 2.2 × 10 푁푢 = 2.57 × 10 ∙ 푅푒 7 0.81 4. 푅푒 ≥ 2.2 × 10 푁푢 = 0.0455 ∙ 푅푒 −5 퐾푠 ⁄퐷 = 300 × 10 5 5. 푅푒 ≤ 1.8 × 10 Use smooth cylinder correlation as in row 1. 5 6 0.89 6. 1.8 × 10 < 푅푒 < 4.0 × 10 푁푢 = 0.0135 ∙ 푅푒 7. 푅푒 ≥ 4.0 × 10 6 Use the same correlation as in row 4. −5 퐾푠 ⁄퐷 = 900 × 10 5 8. 푅푒 ≤ 1.0 × 10 Use smooth cylinder correlation as in row 1. 5 9. 푅푒 > 1.0 × 10 Use the same correlation as in row 4.

−3 The surface roughness used for this work was 퐾푠 = 2.5 × 10 [35]. In particular for this work, the values of Nusselt Number and Reynolds Number are very large; both natural and forced convection play the important roles in determining the resulting convective heat transfer. Therefore, a mixed convection correlation is used and is given by equation 4.29 [38].

1 4.29 푚 푚 푚 ℎ푚𝑖푥푒푑 = (ℎ푛푎푡 + ℎ푓표푟 ) Where, ‘m’ denotes the degree of dominance of either of the two convection coefficients viz. forced and natural convection coefficients. As ‘m’ increases the value of ′ℎ푚𝑖푥푒푑 ′will be influenced by the larger effect of the two. The value of ‘m’ is selected as 3.2 based on the studies [35] [38] which, indicate a relatively strong dependence on the larger of the two convective heat transfer coefficients viz. natural and forced.

4.4 Criticality of the Dimensions The heat loss calculations were necessarily meant to get the dimensions of the tubes in the receiver. However, there were two checks employed to keep the design under the safety and operative limits. The first is metal property known as ‘critical metal temperature’ (Tcrit) and pressure drop across the receiver. The metal temperature and pressure drop as they would vary with respect to number of tubes and the selected diameter of the tubes. The following section explains how these properties were calculated.

4.4.1 Critical Metal Temperature The dimensions of the receiver are finalized by the model explained in the section 4.3 and based on the critical design parameters of the material referred from pipe selection handbook [39]. These parameters include allowable working pressure of the tube and corresponding maximum continuous working temperature of the selected tube corresponding to the diameter. To evaluate this criticality, the phenomenon of Log-Mean-Temperature-Difference (LMTD) is used. LMTD is calculated from equation 4.30.

푄̇ 4.30 퐿푀푇퐷 = 푔푎𝑖푛 퐴푠푢푟푓 ∙ ℎ𝑖푛푡푒푟푛푎푙 푇 − 푇 4.31 퐿푀푇퐷 = 표푢푡 𝑖푛 푇 − 푇 푙푛 ( 푚 𝑖푛 ) 푇푚 − 푇표푢푡 13

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The internal convective heat transfer coefficient was calculated using Gnielinski correlation [31], stated in equation

4.33. The equation 4.31 gives ‘Tm’, which is metal temperature and is seen to be always smaller than the critical metal temperature (Tcrit) selected from pipe handbook.

4.4.1.1 Boiling in boiler section In boiler section as water will change its phase to saturated steam, while calculating internal heat transfer coefficient, boiling in a vertical tube was also considered to compare with that of only convective heat transfer. The boiling correlations were taken from Steiner-Taborek method [40]. The value of ℎ퐿 was found out using Gnielinski correlation of Nusselt Number (stated in equation 4.33) as a function of Reynolds Number, Prandlt Number and Fanning friction factor. This factor is calculated using equation 4.34.

1 4.32 3 3 3 ℎ푡푝 = ((ℎ푛푏,0 ∙ 퐹푛푏 ) + (ℎ퐿 ∙ 퐹푡푝 ) ) 푓 ( ⁄ ) ∙ (푅푒 − 1000) ∙ 푃푟 4.33 ℎ퐿 ∙ 푑𝑖푛 8 퐿 퐿 푁푢퐿 = = 1 퐾 푓 ⁄2 2 ⁄ ⁄3 1 + 12.7 ( 8) ∙ (푃푟퐿 − 1) −2 푓 = [0.794 ln(푅푒퐿) − 1.64] 4.34

Further, the two-phase multiplier 퐹푡푝 is calculated using equation 4.35 and the nucleate boiling correction factor

퐹푛푏 is calculated using equation 4.36. The value of 푅푝,0 is taken as 1휇푚. Moreover, the equations 4.37 to 4.39 show calculations of rest of the above mentioned factors (such as ‘퐹푝푓 ’, ‘푛푓’ and ‘퐹(푀)’) where, M is the molecular weight 2 2 of the fluid. The values of ′푞0′ and ‘ℎ푛푏,0 ′ are taken as 150000 W/m and 25580 W/m respectively according to Khandilkar et.al [40].

1.1 1.5 0.6 𝜌퐿 0.35 4.35 퐹푡푝 = [(1 − 푥) + 1.9 ∙ 푥 ∙ ( ) ] 𝜌퐺 −0.4 0.133 4.36 푞 푛푓 푑 푅푝 퐹푛푏 = 퐹푝푓 ∙( ) ∙ ( ) ∙ ( ) ∙ 퐹(푀) 푞0 푑𝑖,0 푅푝,0

0.45 1.7 3.7 4.37 퐹푝푓 = 2.816 ∙ 푃푟퐿 + (3.4 + 7) ∙ 푃푟퐿 1 − 푃푟퐿

푛푓 = 0.8 − 0.1 ∙ exp (1.75 푃푟퐿) 4.38 퐹(푀) = 0.377 + 0.199 ln 푀 + 0.000028427 푀2 4.39

4.4.2 Pressure Drop One of the most important designing parameters in this process is a permissible pressure drop across the receiver tubes. Pressure drop is calculated using Bernoulli’s principle, which is stated in equation 4.40. In general, the following are the main contributors to the resulting pressure drop 1. Pressure drop due to a sudden change in the flow caused by different bends and valves, known as singularity losses, Δ푃푠 2. Due to friction between pipe walls and fluid, known as frictional pressure loss, Δ푃푓 3. Momentum change loss caused due to acceleration or deceleration in the flow, Δ푃푚 4. Gravity loss or hydrostatic loss or static head Δ푃푔. In this particular system, pressure losses are calculated per section separately (boiler, SH and RH) and incorporated in the PB simulations to calculate the pressure input for the next section. It is calculated using the necessary correlations as explained in the following sub-sections of this chapter.

Δ푃 = Δ푃푠 + Δ푃푓 + Δ푃푚 + Δ푃푔 4.40 The singularity and momentum losses are negligible in this system because the tubes are straight and there are no acceleration imposed on the fluid. The pressure loss due to gravity is calculated using equation 4.41, where H stands for height of the tower. For all the sections of the receiver except frictional losses, rest of the losses are calculated in similar fashion.

Δ푃푔 = H ∙ ρ ∙ g 4.41 The frictional losses for SH and RH section are calculated using equation 4.42. 14

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2 Δ푃푓 = 2f HG ⁄퐷ℎ𝜌 4.42 Where, f denotes Frictional fanning factor and calculated using equation 4.34. However, in boiler section the water is converted into steam to be supplied to the SH. The two phase frictional loss0 estimated from the corresponding 2 pressure drop for single-phase flow and multiplied by ‘Two-phase friction multiplier’ denoted as ‘휙푙표 ’. Equation 4.43 shows the method to calculate two-phase frictional drop.

2 2 2퐿 퐺 2 4.43 Δ푃푓 = 휙푙표 Δ푃푓,푙표 = 푓푙표 휙푙표 퐷ℎ 푔푐𝜌푙

Where, ′푔푐′is a constant whose value is 1 in SI units and L denotes the height of the tower. The two-phase friction multiplier is calculated using two different correlations known as Friedel correlation and Chisholm correlation, stated in Table 5. Table 5 Two Phase Pressure Drop*

Correlation Parameters

2 For 휇푙⁄휇푣 < 1000 and 퐺 < 100 푘푔⁄푚 푠 Friedel correlation [41] 𝜌 푓 퐸 = (1 − 푥)2 + 푥2 푙 푣표 퐹퐻 𝜌 푓 휙 2 = 퐸 + 3.23 ∙ 푣 푙표 푙표 퐹푟0.045푊푒0.035 퐹 = 푥0.78 ∙ (1 − 푥)0.24 𝜌 0.91 휇 0.19 휇 0.7 퐻 = ( 푙 ) ∙ ( 푣) ∙ (1 − 푣) 𝜌푣 휇푙 휇푙 퐺2 퐹푟 = 2 푔퐷ℎ𝜌ℎ표푚 2 퐺 퐷ℎ 푊푒 = 2 𝜎𝜌ℎ표푚 1 푥 (1 − 푥) = + 𝜌ℎ표푚 𝜌푣 𝜌푙 퐺 = 𝜌 ∙ 푓푙표푤 푣푒푙. 2 For 휇푙⁄휇푣 > 1000 and 퐺 > 100 푘푔⁄푚 푠 0.5 Chisholm correlation [41] 푌 = (Δ푃푣⁄Δ푃푙) 2 2 푛∗ 푛∗ 2−푛 2 휙푙표 = 1 + (푌 − 1) ∙ [퐵푥 (1 − 푥) + 푥 ] 2 ∙ 푓푣 ∙ 퐺 Δ푃푣 = 2 − 푛 퐷ℎ𝜌푣 푛 ∗= 2 2 2 ∙ 푓푙 ∙ 퐺 Δ푃푙 = 퐷ℎ𝜌푙 푛 = 0.25 4.8 퐺 < 500 퐵 = {2400⁄퐺 500 ≤ 퐺 < 1900} 푓표푟 푌 ≤ 9.5 55⁄퐺0.5 퐺 ≥ 1900 520⁄푌퐺0.5 퐺 ≤ 600 퐵 = { } 푓표푟 9.5 < 푌 ≤ 28 21⁄푌 퐺 > 600 퐵 = 15000⁄(푌2퐺0.5) 푓표푟 푌 > 28

* E, F, H, Y and B are the local parameters and are defined in this table; rest are in SI units. 15

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5 ANALYSIS The results obtained from the above described model is analysed to select a design for the Fortran component. This chapter deals with elaborations over the strategy to get the optimized solution. Firstly, this section explains how material constraints were applied to get the feasible solutions and further it explains the economic analysis.

5.1 Optimization based on dimensions A pool of solutions was developed by using the model and the design constraints were applied to find out a set of feasible solutions out of all the theoretically solutions. The constraints were 1. The metal temperature was always below the Critical Metal Temperature (Tcrit) and 2. The pressure drop was limited to below 3% across the receiver in all the three sections namely, boiler, SH and RH. The constraint of ‘Tcrit’ is applied because the metal temperature crossing this limit is practically beyond the physical limits of the material for the selected diameter and allowable working pressure. The diameter of the tube is decided using the tube selection handbook. The selection is based on allowable working pressure for a particular diameter and ‘Tcrit’. The dimensions when they are selected they are selected in such a way that the metal temperature due to internal heat-transfer never exceeds the critical metal temperature (Explained in Section 4.4.1.). Along with the diameter the important design parameter is the height of the receiver. The height was varied from 30m to 50m keeping the middle ground similar to that of Ivanpah

(37.49m) [42]. The tube selection handbook gives the diameter, thickness, and ‘Tcrit’ (for the given working pressure).

Likewise, the constraint of 3% in pressure drop is applied because a CT receiver can be approximated to that of vertical once through high-pressure boiler because such a boiler also works at the similar live stream conditions and also contains tubes running vertically along the length of the boiler, which is structurally similar to that of CT receiver system of this project. For these boilers the pressure drop across the boiler is conventionally assumed to be 3-5% of the inlet pressure [43]. As well as with the increase in pressure loss higher pumping power is required, hence the power needed by the pump increases. Throughout the complete system the pressure drop gets added from each section and this results in heavy pumping power requirements as an external input, leading to less overall efficiency. Thus, to limit the power input to minimum possible this constraint is very important.

The pressure drop decreases with the increase in number of tubes because the flow velocity decreases and thus the frictional pressure loss, which is the major factor in a flow system of a long length (Explained in section 4.4.2). It can be depicted from Figure 17 that for longer length there is more pressure loss. Thus, if a solution is selected for the minimum pressure drop, it will be more expensive compared because of the material cost. Therefore, the number of tubes are selected in such a way that the pressure drop is not more than 3% as well as the cost of the material is kept minimum. For SH and RH section the analysis follows the similar pattern and the graphs are given in Appendix E.

BOILER SECTION: PRESSURE DROP 5 4.5 4 3.5 3 H=30m 2.5 H=37.49m 2 H=40m 1.5

PRESSURE PRESSURE DROP (%) 1 H=50m 0.5 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 NO. OF TUBES

Figure 17 : Pressure Drop Vs No of Tubes 16

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5.2 Economic Analysis The economic analysis is majorly based on the material cost required. The material cost increases with the increase in number of tubes. Therefore, the selection of the optimized solution is also based upon the thermal efficiency of the component. The efficiency is calculated in terms of energy losses and energy gains as stated in equation 5.1. The efficiency is in terms of energy gains and losses which are already calculated as explained in section 4.3.2.

푄푔푎𝑖푛 5.1 휂푡ℎ = (푄푔푎𝑖푛 + 푄푙표푠푠푒푠) The efficiency of the boiler decreases with the increase in number of tubes as though the mass flow rate decreases there is increase in surface area and it increases the radiative losses. Although these losses are proportional to that of ‘T4’, in this case the variation with respect to temperature is not that dominating as the outlet and inlet temperatures remain the same for all the cases (leading to the SH inlet and then the live stream conditions). This restricts from the surface temperatures to small variation. However, the radiative losses being directly proportional to surface area with the increase in number of tubes the radiative losses increase. As well as for the same number of tubes the efficiency is higher for smaller length because of the same reason that the surface area would be smaller.

In case of convective loss, they do not have as dominating effect as radiative losses because these losses majorly take place because of the surrounding air conditions and the flow properties. Although mass flow changes the variation it causes in total as compared to radiative losses is not dominating. The Figure 18 shows the trends in which the variation of efficiency with respect to increasing number of tubes for different heights. For the SH and RH section the analysis remains the same and the graphs can be seen in Appendix E.

BOILER:THERMAL EFFICIENCY 100

80 H=30m 70 H=37.49m 60 H=40 EFFICIENCY EFFICIENCY (%) 50 H=50 40

30 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 NO. OF TUBES

Figure 18 : Efficiency Vs No. of Tubes

The material cost is calculated using the density and the total weight of the material requited for the receiver construction. The Figure 19 shows the variation of material cost with respect to increasing number of tubes for different lengths of the receivers. The material cost increases with number of tubes and also with the length because the material volume required increases.

In all the analysis sections the calculations are compared with the height of the Ivanpah CSP plant because if this plant is constructed using the same architecture as that of this project, the results obtained should have the comparable results. Further, the length of the tower is restricted to 30m because for the heights below this the diameter of the tubes changes and the metal temperature reaches very close to critical metal temperature. The complete analysis repeated for the SH and RH section.

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BOILER:MATERIAL COST 12100000

10100000

8100000 H=30m 6100000 H=37.49m 4100000 H=40 H=50 MATERIAL MATERIAL (USD) COST 2100000

100000 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 NO. OF TUBES

Figure 19 : Material Cost Vs No. of Tubes

5.3 Selected Design The selection of the optimized design though completely based upon the material and operational limits, financial estimations are done to discard the options of higher costs. The optimized design for the boiler section, 100 DN 80 tubes of outer diameter (OD) of 88.90mm. For SH section, 100 DN 32 tubes with OD 42.16mm and same 300 tubes for RH section.

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Master’s Thesis

6 FUTURE WORK In order to achieve the final goal of this six month project necessarily a TRNSYS component needs to be developed. This component will allow the Concentrating Solar Energy research group at KTH to generate numerous dynamic simulations of DSG Solar thermal PP. The results of all these simulations will be used to compare those of with various other solar thermal technologies with different locations and different operating conditions. It will also allow to study the functioning of Ivanpah Solar Thermal PP as a case study. The TRNSYS component is designed and programmed in FORTRAN. The following subsections mention about the selected solution from the above described optimization and analysis.

6.1 FORTRAN Programming This particular task need two different special software those are 1. A FORTRAN Compiler and 2. Microsoft Visual Studio (MVS). A TRNSYS component is written in FORTRAN and it can be done in two ways. The first is using the programmer’s way that is writing the whole program using the compiler and MVS. Otherwise, one can use the in- built option of creating a proforma. The Figure 20 shows the TRNSYS window of a new component design through proforma.

Figure 20 : TRNSYS Proforma Design

In this particular work the second option was preferred to not to waste a lot of time in basic programming. However, because of the time limits in producing this work and the compatibility issue between TRNSYS 17, Intel Visual Fortran Compiler 11.1, MVS 2008 and Microsoft Windows 7 not getting sorted out, the complete designing of this component is not completed. (See Appendix D: Fortran Program window in MVS 2008)

For this component the selected dimensions for the receiver were as follows. For boiler section, 200 DN 90 AISI 316L tubes with internal diameter (ID) of 85.4 mm. Similarly for SH section 100 DN 32 tubes with ID 33.1 mm and for RH section 300 DN 32 tubes with diameter of 38.9 mm. 19

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7 CONCLUSION The DSG is one of the ways of using immense solar energy to generate electricity and the complex factor of using synthetic oil or molten salts is also eliminated because of use of water as a working fluid. The complex nature of CT receiver architecture is still a matter of complex engineering. During this project I learnt to deal with such complex thermo-physical phenomenon in process.

The selected architecture of CT receiver on the basis of literature review is the most recent design studied for the maximum efficiency. It also addresses issues such as radiation spillage and economically cheap option. The mathematical model developed of this receiver design explains the heat-transfer phenomena in and around the receiver components.

The complete power block was designed for the regenerative Rankine power generation cycle for the large scale power plant of 123 MW to decide the optimized mass flow rate. The determination of this mass flow rate was important from the objective of establishing the heat transfer phenomena and to apply the physical constraints to the receiver. The components such as turbines, feed water heater, heat exchangers, pump and condenser.

The selection process of the optimized design was a trade-off between thermal performance, practical feasibility of available solutions and financial expenditures for the material. The selected design will be eventually used for the component design in FORTRAN. TRNSYS will then take inputs from such a component to run the required simulations for the CT solar thermal PP.

The latest commercial solar thermal PP will be put into production in near future will be based upon DSG using CTS. This technology is seen to push forward the developments in solar thermal sector. If Ivanpah proves its efficacy, this technology will set the ball rolling in wide scale commercialization of solar thermal technologies. Such sustainable means of energy production is the need of the hour.

This project undertaken at KTH Heat and Power Division in the context to develop dynamic simulation of DSG PP was a rewarding experience and gain me the opportunity to learn in detail about a CT receiver system. The opportunity to be a part of one of the core research group and to work with experts can be the highlight of this internship, least to mention. It allowed me to integrate and apply the inter-disciplinary courses which I had undertaken throughout this ME3 program.

Ranjit Desai Conclusion

Master’s Thesis

8 REFERENCES

[1] Co2now.org, “CO2 Now.” [Online]. Available: http://co2now.org/. [Accessed: 17-May-2013].

[2] Eia.gov, “AEO Table Browser - Energy Information Administration,” 2013. [Online]. Available: http://www.eia.gov/oiaf/aeo/tablebrowser/#release=IEO2011&subject=0-IEO2011&table=1- IEO2011®ion=0-0&cases=Reference-0504a_1630. [Accessed: 17-Jun-2013].

[3] E. Matrinot, “Renewables Global Futures Report 2013,” Paris, France, 2013.

[4] T. W. Africa, “Archimedes Through the Looking Glass,” The Classical World, vol. 68, no. 5, pp. 305–308, 1975.

[5] C. M. Meyer, “From troughs to triumph: SEGS and gas,” Ee pulblishers.co.za, 22, p. 1, Apr-2013.

[6] (Internationl Energy Agency) IEA, “Concentrating solar power roadmap, 2010,” Paris, France, 2010.

[7] BrightSource, “BrightSource Ivanpah | Proven Leadership in Solar Energy,” 2013. [Online]. Available: http://ivanpahsolar.com/.

[8] NREL, “NREL: Concentrating Solar Power Projects - Ivanpah Solar Electric Generating System,” 2013. [Online]. Available: http://www.nrel.gov/csp/solarpaces/project_detail.cfm/projectID=62. [Accessed: 06-May-2013].

[9] H. L. Zhang, J. Baeyens, J. Degrève, and G. Cacères, “Concentrated solar power plants: Review and design methodology,” Renewable and Sustainable Energy Reviews, vol. 22, pp. 466–481, Jun. 2013.

[10] Sargent&Lundy, “Assessment of Parabolic Trough and Power Tower Solar Technology Cost and Performance Forecasts. NREL/SR-550-34440.,” Chicago, Illinois, USA, 2003.

[11] NREL, “NREL: Concentrating Solar Power Projects - Parabolic Trough Projects,” 2011. [Online]. Available: http://www.nrel.gov/csp/solarpaces/parabolic_trough.cfm. [Accessed: 11-Jul-2013].

[12] COBRA-Group, “Cobra Group - Welcome,” 2013. [Online]. Available: http://www.grupocobra.com/. [Accessed: 11-Jul-2013].

[13] “Solar Millennium AG - Home,” 2013. [Online]. Available: http://www.solarmillennium.de/index,lang2.html. [Accessed: 11-Jul-2013].

[14] NREL, “NREL: TroughNet - Parabolic Trough Solar Field Technology,” 2010. [Online]. Available: http://www.nrel.gov/csp/troughnet/solar_field.html. [Accessed: 10-Jul-2013].

[15] Green-Planet-Solar-Energy.com, “Solar Steam Generator: AndaSol-1,” 2012. [Online]. Available: http://www.green-planet-solar-energy.com/solar-steam-generator-2.html. [Accessed: 11-Jul-2013].

[16] Green-India, “The Solar Thermal Breakthrough: Ausra’s Compact Linear Fresnel Reflector (CLFR) and Lower Temperature Approach,” Mumbai, India, 2010.

[17] “APP - Current Research > Solar thermal energy > CLFR technology.” [Online]. Available: http://www.physics.usyd.edu.au/app/research/solar/clfr.html. [Accessed: 10-Jul-2013].

[18] NREL, “NREL: Concentrating Solar Power Projects - Puerto Errado 2 Thermosolar Power Plant,” 2012. [Online]. Available: http://www.nrel.gov/csp/solarpaces/project_detail.cfm/projectID=159. [Accessed: 30-May-2013].

[19] NREL, “NREL: Concentrating Solar Power Projects - Dhursar.” [Online]. Available: http://www.nrel.gov/csp/solarpaces/project_detail.cfm/projectID=272. [Accessed: 11-Jul-2013]. 21

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Master’s Thesis

[20] NREL, “NREL: Concentrating Solar Power Projects - Alba Nova 1.” [Online]. Available: http://www.nrel.gov/csp/solarpaces/project_detail.cfm/projectID=221. [Accessed: 11-Jul-2013].

[21] Green-Rhino-Energy-Ltd., “Concentrated Solar Thermal | Technologies,” 2013. [Online]. Available: http://www.greenrhinoenergy.com/solar/technologies/cst_technologies.php. [Accessed: 11-Jul-2013].

[22] Solar-Euro-Med, “Thermodynamic Solar Concentration in | Solar Euromed,” 2012. [Online]. Available: http://www.solareuromed.com/fr/. [Accessed: 11-Jul-2013].

[23] “Concentrated Solar Power:Parabolic Dish,” 2008. [Online]. Available: https://www.mtholyoke.edu/~wang30y/csp/ParabolicDish.html. [Accessed: 11-Jul-2013].

[24] NREL, “NREL: Concentrating Solar Power Projects - Dish/Engine Projects,” 2011. [Online]. Available: http://www.nrel.gov/csp/solarpaces/parabolic_trough.cfm. [Accessed: 11-Jul-2013].

[25] NREL, “NREL: Concentrating Solar Power Projects - Gemasolar Thermosolar Plant,” 2011. [Online]. Available: http://www.nrel.gov/csp/solarpaces/project_detail.cfm/projectID=40. [Accessed: 11-Jul- 2013].

[26] Torresol-Energy, “Torresol Energy - Gemasolar thermosolar plant,” 2010. [Online]. Available: http://www.torresolenergy.com/TORRESOL/gemasolar-plant/en. [Accessed: 16-Apr-2013].

[27] (Siemens AG), “SST-900 Industrial Steam Turbines,” Erlangen, Germany, 2009.

[28] J. D. Spelling, “Steam Turbine Optimisation Solar Thermal Power Plant Operation for,” KTH Royal Institute of Technology, Stockholm, Sweden, 2011.

[29] D. Cooke, “Modeling of Off-Design Multistage Turbine Pressures by Stodola’s Ellipse,” in Energy Incorporated, 1983.

[30] J. D. Spelling, “Hybrid Solar Gas-Turbine Power Plants A Thermoeconomic Analysis,” KTH Royal Institute of Technology, Stockholm, Sweden, 2013.

[31] F. P. Incropera, D. P. Dewitt, T. L. Bergman, and A. S. Lavine, Fundamentals of Heat and Mass Transfer, 7th ed. John Wiley & Sons, Inc., 2011, p. 1076.

[32] O. Behar, A. Khellaf, and K. Mohammedi, “A review of studies on central receiver solar thermal power plants,” Renewable and Sustainable Energy Reviews, vol. 23, pp. 12–39, Jul. 2013.

[33] Q. Yu, Z. Wang, E. Xu, X. Li, and M. Guo, “Modeling and dynamic simulation of the collector and receiver system of 1MWe DAHAN solar thermal power tower plant,” Renewable Energy, vol. 43, pp. 18–29, Jul. 2012.

[34] R. Ben-Zvi, M. Epstein, and a. Segal, “Simulation of an integrated steam generator for solar tower,” Solar Energy, vol. 86, no. 1, pp. 578–592, Jan. 2012.

[35] M. J. Wagner, “Simulation and Predictive Performance Modeling of Utility-Scale Central Receiver System Power Plants by,” University of Wisconsin-Madison, 2008.

[36] T. H. Mehlitz, Temperature Influence and Heat Management Requirements of Microalgae Cultivation in Photobioreactors. GRIN Verlag, 2009, p. 152.

[37] T. Taumoefolau, S. Paitoonsurikarn, G. Hughes, and K. Lovegrove, “Experimental Investigation of Natural Convection Heat Loss From a Model Solar Concentrator Cavity Receiver,” Journal of Solar Energy Engineering, vol. 126, no. 2, p. 801, 2004.

[38] Siebers and Kraabel, “Estimating convective energy losses from solar central receivers- SAND-84-8717,” Livermore, CA (USA), 1984. 22

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Master’s Thesis

[39] AS, “Pressure Rating Tables for Stainless Steel Pipe Notes to the tables of allowable working pressures.,” 2010.

[40] S. G. Khandilkar, M. Shoji, and V. K. Dhir, Handbook of Phase Change: Boiling and Condensation. Philadelphia, USA: Taylor & Francis, 1999, p. 788.

[41] G. E. Hewitt, “Gas-Liquid Flow,” in in Handbook of Heat Exchanger Design, G. E. Hewitt, Ed. New York, United States of America, 1992, pp. 1–33.

[42] M. (BrightSource) Bobinecz, “BrightSource Energy Ivanpah Solar Electric,” 2012.

[43] S. Teir and A. Kulla, “Steam/Water Circulation Design,” Helsinki, 2002.

Ranjit Desai References

Master’s Thesis

APPENDIX

Appendix A: Tube Selection Handbook for AISI 316L

700

3.80

2.50

1.30

1.00

4.20

2.90

1.40

1.00

4.50

3.10

1.60

1.10

4.90

3.40

1.90

1.30

5.50

4.00

2.30

1.60

5.20

3.60

2.50

1.50

6.10

4.30

3.20

1.90

6.70

4.80

3.70

2.10

8.10

5.80

4.70

2.70

675

4.90

3.30

1.70

1.40

5.50

3.80

1.90

1.30

5.80

4.10

2.10

1.40

6.30

4.50

2.40

1.70

7.20

5.10

3.00

2.00

6.80

4.70

3.30

1.90

7.90

5.60

4.10

2.40

8.70

6.20

4.80

2.80

7.60

6.10

3.50

10.60

650

6.30

4.20

2.20

1.70

7.00

4.80

2.40

1.60

7.50

5.20

2.70

1.90

8.10

5.70

3.10

2.10

9.20

6.60

3.80

2.60

8.70

6.00

4.20

2.50

7.10

5.30

3.10

8.00

6.10

3.50

9.70

7.80

4.50

10.10

11.20

13.50

625

8.20

5.50

2.80

2.30

9.10

6.30

3.10

2.10

9.70

6.80

3.50

2.40

7.40

4.00

2.80

8.60

4.90

3.40

7.80

5.40

3.20

9.30

6.90

4.00

7.90

4.60

5.90

10.50

11.90

11.40

13.20

14.60

10.40

17.60

12.60

10.20

600

6.80

3.50

2.80

7.80

3.90

2.70

8.40

4.40

3.00

9.30

5.00

3.40

6.10

4.20

9.70

6.80

4.00

8.60

5.00

9.90

5.70

7.30

10.20

11.40

12.10

13.10

14.90

10.70

14.20

16.40

11.60

18.10

12.90

21.90

15.70

12.70

575

8.00

4.10

3.30

9.20

4.50

3.10

9.90

5.10

3.50

5.90

4.00

7.20

4.90

8.80

4.70

5.90

6.70

8.60

11.90

13.30

14.20

15.40

10.90

17.40

12.50

16.60

11.40

19.30

13.60

10.00

21.30

15.20

11.60

25.70

18.50

14.90

550

8.70

4.40

3.60

4.90

3.40

5.60

3.80

6.40

4.40

7.80

5.30

8.60

5.10

6.40

7.30

9.30

12.90

14.40

10.00

15.40

10.70

16.70

11.80

18.90

13.60

18.00

12.40

20.90

14.70

10.90

23.10

16.40

12.60

27.90

20.00

16.10

525

9.00

4.60

3.70

5.10

3.50

5.70

3.90

6.60

4.50

8.00

5.50

8.90

5.20

6.50

7.50

9.60

13.30

14.90

10.20

15.90

11.00

17.20

12.10

19.40

14.00

18.50

12.70

21.50

15.20

11.20

23.70

16.90

12.90

28.70

20.60

16.60

500

9.00

4.60

3.70

5.10

3.50

5.70

3.90

6.60

4.50

8.00

5.50

8.90

5.20

6.50

7.50

9.60

13.30

14.90

10.20

15.90

11.00

17.20

12.10

19.40

14.00

18.50

12.70

21.50

15.20

11.20

23.70

16.90

12.90

28.70

20.60

16.60

475

9.00

4.60

3.70

5.10

3.50

5.80

4.00

6.60

4.50

8.10

5.60

9.00

5.20

6.60

7.60

9.70

13.40

15.00

10.30

16.00

11.10

17.40

12.20

19.60

14.10

18.70

12.90

21.70

15.30

11.30

24.00

17.10

13.10

29.00

20.80

16.70

Allowable Working Pressure (MPa) Pressure Working Allowable

450

9.10

4.60

3.80

5.20

3.50

5.80

4.00

6.70

4.60

8.20

5.60

9.00

5.30

6.70

7.70

9.80

13.50

15.10

10.40

16.20

11.20

17.50

12.30

19.80

14.20

18.90

13.00

21.90

15.40

11.40

24.20

17.20

13.20

29.20

21.00

16.90

425

9.30

4.70

3.80

5.30

3.60

5.90

4.10

6.80

4.70

8.30

5.70

9.20

5.40

6.80

7.80

9.90

13.80

15.40

10.60

16.50

11.40

17.80

12.60

20.20

14.50

19.20

13.20

22.30

15.70

11.60

24.60

17.60

13.40

29.80

21.40

17.20

400

9.40

4.80

3.90

5.30

3.60

6.00

4.10

6.90

4.70

8.40

5.80

9.30

5.40

6.80

7.90

13.90

15.60

10.70

16.60

11.50

18.00

12.70

20.40

14.60

19.40

13.30

22.50

15.90

11.70

24.80

17.70

13.50

30.00

21.60

17.40

10.00

375

9.50

4.80

3.90

5.40

3.70

6.00

4.10

6.90

4.80

8.50

5.80

9.40

5.50

6.90

7.90

14.00

15.70

10.80

16.80

11.60

18.20

12.80

20.50

14.80

19.60

22.70

16.00

11.80

25.10

17.90

13.70

30.30

21.80

17.50

10.10

135.00

350

9.60

4.90

4.00

5.50

3.70

6.20

4.20

7.10

4.80

8.60

5.90

9.50

5.60

7.00

8.10

14.30

16.00

11.00

17.10

11.90

18.50

13.00

20.90

15.00

19.90

13.70

23.10

16.30

12.10

25.50

18.20

13.90

30.90

22.20

17.80

10.30

325

9.90

5.00

4.10

5.60

3.80

6.30

4.30

7.20

5.00

8.90

6.10

9.80

5.70

7.20

8.30

14.70

16.40

11.30

17.50

12.20

19.00

13.40

21.50

15.40

20.40

14.10

23.70

16.70

12.40

26.20

18.70

14.30

31.70

22.70

18.30

10.60

7.11

3.40

2.77

8.56

6.02

3.05

2.11

8.08

5.74

3.05

2.11

7.62

5.49

3.05

2.11

7.01

5.16

3.05

2.11

5.54

3.91

2.77

1.65

5.08

3.68

2.77

1.65

4.55

3.38

2.77

1.65

4.55

3.38

2.77

1.65

10.97

Thickness

Temperature Temperature

80S

40S

10S

80S

40S

10S

80S

40S

10S

80S

40S

10S

80S

40S

10S

80S

40S

10S

80S

40S

10S

80S

40S

10S

80S

40S

10S

Sch No Sch

88.90

73.03

60.33

48.26

42.16

33.40

141.30

114.30

101.60

D_out

125 100

DN 24

Ranjit Desai Appendix

Master’s Thesis

Appendix B: Optimized States from Power Block T P H S X V U FR Cp Temp. Pressure Enthalpy Entropy Quality Sp. Internal Mass flow Specific Volume Energy rate Heat 0C bar kJ/kg kJ/kgK m3/kg kJ/kg kg/s kJ/kgK

Ranjit Desai Appendix

Master’s Thesis

Appendix C: Gnatt Chart

October

September

August

July

June

May

April

ProjectCompletionpresentation KTH and

ResultAnalysis

TRNSYS Model TRNSYS

TRNSYS Simulation TRNSYS

Fortran Program Fortran

FinalDefense and Report inMadrid

Fortran Program Fortran

Fortran Compiler VisualFortran and Studio

TRNSYS Programmer's Guide Programmer's TRNSYS

LiteratureReview

Fortran Model Fortran

MATLAB Model FinalizationModel MATLAB

Tube SelectionTube

PressureCalculations Loss

Heat-Transfer PhenomenaHeat-Transfer

Mid-term ReportMid-term

Heat-Transfer PhenomenaHeat-Transfer

Mass FlowOptimization Rate Mass

PowerDesignBlock

MATLAB Model MATLAB

FinalizingReceiver Architecture

ReceiverDesign

Summary

Ivanpah Solar Thermal PowerThermalSolarIvanpahPlant

Solar CentralSystemsSolarTower Solar Thermal TechnologiesThermalSolar Literature Review Literature

Ranjit Desai Appendix

Master’s Thesis

Appendix D: Fortran Program window in MVS 2008

Ranjit Desai Appendix

Master’s Thesis

Appendix E: Analysis Graphs for SH section and RH section

SH Section

SH SECTION: PRESSURE DROP 0.45 0.4 0.35 0.3 0.25 H=30m 0.2 H=37.49m 0.15 H=40m

PRESSURE PRESSURE DROP (%) 0.1 H=50m 0.05 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 NO. OF TUBES

Figure 21 : SH: Pressure Drop Vs No. of Tubes

SH SECTION:THERMAL EFFICIENCY 100 90 80 70 H=30m 60 H=37.49m 50 H=50m 40 H=40 EFFICIENCY EFFICIENCY (%) 30 20 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 NO. OF TUBES

Figure 22 : SH: Efficiency Vs No. of Tubes

Ranjit Desai Appendix

Master’s Thesis

SH SECTION:MATERIAL COST 3509000

3009000

2509000

2009000 H=30m

1509000 H=37.49m H=40 1009000 H=50 MATERIAL MATERIAL (USD) COST 509000

9000 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 NO. OF TUBES

Figure 23 : SH: Material Cost Vs No. of Tubes

RH Section

RH SECTION: PRESSURE DROP 18 16 14 12 10 H=30m 8 H=37.49m 6 H=40m

PRESSURE PRESSURE DROP (%) 4 H=50m 2 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 NO. OF TUBES

Figure 24 : RH: Pressure Drop Vs No. of Tubes

Ranjit Desai Appendix

Master’s Thesis

RH SECTION:THERMAL EFFICIENCY 100

80 H=30m 60 H=37.49m 40 H=50m 20 EFFICIENCY EFFICIENCY (%) H=40 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 NO. OF TUBES

Figure 25 : RH: Efficiency Vs No. of Tubes

RH SECTION:MATERIAL COST 990000 910000 830000 750000 670000 590000 H=30m 510000 H=37.49m 430000 350000 H=40 270000 H=50 MATERIAL MATERIAL (USD) COST 190000 110000 30000 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 NO. OF TUBES

Figure 26 : RH: Material Cost Vs No. of Tubes

Ranjit Desai Appendix