Ranjit Desai Index Note

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.

(ranjitd@kth.se)

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

i

Ranjit Desai Index Note

Master’s Thesis

ii

Institute Tutor

Rafael E. Guédez

KTH Royal Institute of Technology

Concentrating Solar Power Group

Department of Energy Technology/ Heat and Power Division

Brinellvägen 68, SE-100 44.

Stockholm, SWEDEN.

Academic Tutor

Dr. Claire Gerente

Ecole des Mines de Nantes

GEPEA UMR CNRS 6144,

4 Rue Alfred Kastler, BP 20722.

44307, Nantes Cedex 03,

Nantes, FRANCE.

Supervised by

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Master’s Thesis

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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

Ranjit Desai List of Tables

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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 Nomenclature

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NOMENCLATURE

�̇� 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

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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 𝑊/𝑚2𝐾 ]

ρ Density (kg/m3)

Ф Mass-Flow coefficient

𝜀 Emissivity, Effectiveness

𝛽 Volumetric Expansion Coefficient [1/K]

𝜇 Dynamic Viscosity [Ns/m2]

𝜐 Kinematic Viscosity [m2/s]

𝛼 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

G

pf

Ambient

Gas

Pressure correction factor

r Ratio

sky Sky

s Surface

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nat

nb

tp

Natural

Nucleate Boiling

Two-phase

for Forced

avg Average

L Along the Length or length being characteristic dimension, Liquid

rec Receiver

mixed Mixed (natural and forced)

Ranjit Desai Introduction

Master’s Thesis

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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 thermo-

economic 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 Objectives

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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 Theoretical Framework

Master’s Thesis

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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 (𝑊/𝑚2). 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

Ranjit Desai Theoretical Framework

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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.

Ranjit Desai Theoretical Framework

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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 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].

Figure 8 : Solar Central Tower System [21]

Ranjit Desai Methodology

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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.

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

Power Block Optimization

MATLAB simulation

FORTRAN component design

TRANSYS dynamic Simulation

Thermo-Economic Performance Evaluation

Mass Flow

Receiver Dimensions

Receiver Component

Figure 10 : Methodology

Ranjit Desai Methodology

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P-13

8 SL

9 SS

10 SHS

11 S

25

12 SHS

21

22 24

23

15 S 16 S

13 S

20 1 SL

2 SL

3 SL7 SL 4 SL

5 SL

6 SL

14

17 SL 19 SL

18BOILER

SH

RH

HPT 1 LPT 1 LPT 2 LPT 3

P1

P2

PH-HE1 PH-HE2

CONDENSER

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

(𝑃𝑜𝑢𝑡 ), 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 (𝑃𝑇 ) sonic flow conditions occur within the

section. The outlet pressure can be found out using equation 4.3, as a function of ′𝑀′̇ (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.

Φ = �̇�

√𝜌𝑃=

�̇�√𝑇

𝑃

4.1

Φ ∝ √1 − (𝑃𝑜𝑢𝑡

𝑃)

2

4.2

Ranjit Desai Methodology

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

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

Where ‘𝐶𝑚𝑖𝑛’ 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 ‘𝐶𝑟’ 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 ‘𝜀’ in terms of ‘Δ𝑇𝑚𝑖𝑛 ’ (the minimum approach temperature). The value of ‘Δ𝑇𝑚𝑖𝑛 ’ 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.

𝑃𝑜𝑢𝑡 = √𝑃𝑖𝑛2 − �̇�2 ∙ 𝑇𝑖𝑛 ∙ 𝑌

4.3

Y = 𝑃𝑖𝑛,𝑛𝑜𝑚

2 − 𝑃𝑜𝑢𝑡,𝑛𝑜𝑚2

𝑃𝑖𝑛,𝑛𝑜𝑚2 ∙ Φ𝑖𝑛,𝑛𝑜𝑚

2 4.4

𝑄𝑚𝑎𝑥 ̇ = 𝐶𝑚𝑖𝑛(𝑇𝑖𝑛

ℎ𝑠 − 𝑇𝑖𝑛𝑐𝑠) 4.5

𝑄 ̇ = 𝜀𝑄𝑚𝑎𝑥 = 𝜀𝐶𝑚𝑖𝑛(𝑇𝑖𝑛

ℎ𝑠 − 𝑇𝑖𝑛𝑐𝑠) 4.6

𝜀 = 𝑓(𝑁𝑇𝑈, 𝐶𝑟) 4.7

𝑁𝑇𝑈 =𝑈𝐴

𝐶𝑚𝑖𝑛

4.8

𝐶𝑟 =𝐶𝑚𝑖𝑛

𝐶𝑚𝑎𝑥

4.9

𝜀 = 1 −Δ𝑇𝑚𝑖𝑛

(𝑇𝑖𝑛ℎ𝑠 − 𝑇𝑖𝑛

𝑐𝑠)

4.10

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

Stream Type Heat Transfer Co-efficient Δ𝑇𝑚𝑖𝑛/2

Gas Stream 60 [𝑊/𝑚2𝐾] 20 [K]

Liquid Stream 560 [𝑊/𝑚2𝐾] 5 [K]

Evaporating Stream 1600 [𝑊/𝑚2𝐾] 3 [K]

Condensing Stream 3600 [𝑊/𝑚2𝐾] 2 [K]

Table 3 NTU-Effectiveness Relationship

𝜀-NTU Relationship Condition

𝑁𝑇𝑈 =1

𝐶𝑟 − 1ln (

𝜀 − 1

𝜀𝐶𝑟 − 1)

𝐶𝑟 < 1

𝑁𝑇𝑈 =𝜀

1 − 𝜀 𝐶𝑟 = 1

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).

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

‘�̇�𝑎𝑖𝑟 ’are as follows in equations 4.14 and 4.15.

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

�̇�𝑝𝑢𝑚𝑝 =1

𝜂ℎ

�̇� (Δ𝑃

𝜌)

4.11

𝑇𝑜𝑢𝑡 = 𝑇𝑖𝑛 +1 − 𝜂ℎ

𝜂ℎ

(Δ𝑃

𝜌𝐶𝑝𝑤

) 4.12

�̇�𝑓𝑎𝑛 =�̇�𝑎𝑖𝑟𝐶𝑝𝑎𝑇𝑎

𝜂𝑓𝑎𝑛

[(1 + 𝑓𝑑𝑃𝑎𝑖𝑟)

𝑟𝑎𝐶𝑝𝑎 − 1]

4.13

�̇�𝑎𝑖𝑟 = �̇�𝑐𝑜𝑜𝑙

𝐶𝑝𝑤

𝐶𝑝𝑎

4.14

�̇�𝑐𝑜𝑜𝑙 = �̇�𝑐𝑜𝑜𝑙Δℎ𝑐𝑜𝑛𝑑

𝐶𝑝𝑤(𝑇𝑐𝑜𝑛𝑑 − ∆𝑇𝑐𝑜𝑛𝑑 − (𝑇𝑎 + ∆𝑇𝑎𝑖𝑟))

4.15

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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.

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.

Figure 13 : Vertical view of the cavity receiver [33]

Figure 14 : The integrated Solar Receiver [34]

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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.

H

Water IN

Steam OUT

Q conv

Q inc

Q ref

Q rad

Figure 16 : Heat Transfer in receiver

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

�̇�𝑓𝑙𝑢𝑖𝑑 = �̇�𝑜𝑢𝑡 − �̇�𝑖𝑛 4.16

�̇�𝑓𝑙𝑢𝑖𝑑 = �̇�𝑔𝑎𝑖𝑛𝑠 − �̇�𝑙𝑜𝑠𝑠𝑒𝑠 4.17

�̇�𝑙𝑜𝑠𝑠𝑒𝑠 = �̇�𝑐𝑜𝑛𝑣 + �̇�𝑟𝑎𝑑 + �̇�𝑟𝑒𝑓 4.18

�̇�𝑓𝑙𝑢𝑖𝑑 = �̇�𝑖𝑛𝑐 − (�̇�𝑐𝑜𝑛𝑣 + �̇�𝑟𝑎𝑑 + �̇�𝑟𝑒𝑓 ) 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.

ℎ𝑟𝑎𝑑,𝑎𝑚𝑏 = 𝜎𝜀𝐹𝑠,𝑎𝑚𝑏 (𝑇𝑠2 + 𝑇𝑎𝑚𝑏

2)(𝑇𝑠 + 𝑇𝑎𝑚𝑏 ) 4.20

ℎ𝑟𝑎𝑑,𝑠𝑘𝑦 = 𝜎𝜀𝐹𝑠,𝑠𝑘𝑦 (𝑇𝑠2 + 𝑇𝑠𝑘𝑦

2)(𝑇𝑠 + 𝑇𝑠𝑘𝑦 ) 4.21

�̇�𝑟𝑎𝑑 = ℎ𝑟𝑎𝑑,𝑎𝑚𝑏 ∙ 𝐴𝑠 ∙ (𝑇𝑠 − 𝑇𝑎𝑚𝑏 ) + ℎ𝑟𝑎𝑑,𝑠𝑘𝑦 ∙ 𝐴𝑠 ∙ (𝑇𝑠 + 𝑇𝑠𝑘𝑦 ) 4.22

𝑇𝑠𝑘𝑦 = 0.552 ∙ (𝑇𝑎𝑚𝑏 1.5) 4.23

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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

as a vertical plate [for laminar flow (10 4 ≤ 𝑅𝑎𝐿 ≤ 10 9) and for turbulent flow (10 9 ≤ 𝑅𝑎𝐿 ≤ 10 13)]. 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.

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.

𝑁𝑢𝑠𝑠𝑒𝑙𝑡𝑛𝑎𝑡 = 0.098 ∙ 𝐺𝑟𝐻 1/3 (

𝑇𝑠

𝑇𝑎𝑚𝑏

)−.14

4.24

𝑁𝑢𝐿 = {0.825 +0.387 ∙ 𝑅𝑎𝐿

1/6

[1 + (0.492/𝑃𝑟)9/16]8/27}

2

4.25

𝐺𝑟𝑛𝑎𝑡 = 𝑔 ∙ 𝛽 ∙ (𝑇𝑠,𝑎𝑣𝑒 − 𝑇𝑎𝑚𝑏 ) ∙𝐻3

𝑟𝑒𝑐

𝜐2𝑎𝑚𝑏

4.26

𝑅𝑎𝐿 = 𝐺𝑟𝐿 ∙ Pr =𝑔 ∙ 𝛽 ∙ (𝑇𝑠 − 𝑇∞ ) ∙ 𝐿3

𝜐 ∙ 𝛼

4.27

𝑃𝑟 = 𝐶𝑝 ∙ 𝜇

Κ

4.28

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

Reynolds Number Range Correlation

𝐾𝑠 𝐷⁄ = 0 (A smooth cylinder)

1. All Re 𝑁𝑢 = 0.3 + 0.488 ∙ 𝑅𝑒0.5 (1 + (

𝑅𝑒

282000)

0.635

)

0.8

𝐾𝑠 𝐷⁄ = 75 × 10−5

2. 𝑅𝑒 ≤ 7.0 × 10 5 Use smooth cylinder correlation as in row 1.

3. 7.0 × 10 5 < 𝑅𝑒 < 2.2 × 10 7 𝑁𝑢 = 2.57 × 10 −3 ∙ 𝑅𝑒0.98

4. 𝑅𝑒 ≥ 2.2 × 10 7 𝑁𝑢 = 0.0455 ∙ 𝑅𝑒0.81

𝐾𝑠 𝐷⁄ = 300 × 10−5

5. 𝑅𝑒 ≤ 1.8 × 10 5 Use smooth cylinder correlation as in row 1.

6. 1.8 × 10 5 < 𝑅𝑒 < 4.0 × 10 6 𝑁𝑢 = 0.0135 ∙ 𝑅𝑒0.89

7. 𝑅𝑒 ≥ 4.0 × 10 6 Use the same correlation as in row 4.

𝐾𝑠 𝐷⁄ = 900 × 10−5

8. 𝑅𝑒 ≤ 1.0 × 10 5 Use smooth cylinder correlation as in row 1.

9. 𝑅𝑒 > 1.0 × 10 5 Use the same correlation as in row 4.

The surface roughness used for this work was 𝐾𝑠 = 2.5 × 10−3 [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].

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 ′ℎ𝑚𝑖𝑥𝑒𝑑 ′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.

ℎ𝑚𝑖𝑥𝑒𝑑 = (ℎ𝑛𝑎𝑡 𝑚 + ℎ𝑓𝑜𝑟

𝑚)1𝑚

4.29

𝐿𝑀𝑇𝐷 = �̇�𝑔𝑎𝑖𝑛

𝐴𝑠𝑢𝑟𝑓 ∙ ℎ𝑖𝑛𝑡𝑒𝑟𝑛𝑎𝑙

4.30

𝐿𝑀𝑇𝐷 = 𝑇𝑜𝑢𝑡 − 𝑇𝑖𝑛

𝑙𝑛 (𝑇𝑚 − 𝑇𝑖𝑛

𝑇𝑚 − 𝑇𝑜𝑢𝑡)

4.31

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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 co-

efficient, 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 ℎ𝐿 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.

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

𝐹𝑛𝑏 is calculated using equation 4.36. The value of 𝑅𝑝,0 is taken as 1𝜇𝑚. Moreover, the equations 4.37 to 4.39 show

calculations of rest of the above mentioned factors (such as ‘𝐹𝑝𝑓 ’, ‘𝑛𝑓’ and ‘𝐹(𝑀)’) where, M is the molecular weight

of the fluid. The values of ′𝑞0

′ and ‘ℎ𝑛𝑏,0 ′ are taken as 150000 W/m2 and 25580 W/m2 respectively according to

Khandilkar et.al [40].

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, Δ𝑃𝑠 2. Due to friction between pipe walls

and fluid, known as frictional pressure loss, Δ𝑃𝑓 3. Momentum change loss caused due to acceleration or

deceleration in the flow, Δ𝑃𝑚 4. Gravity loss or hydrostatic loss or static head Δ𝑃𝑔. 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.

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.

The frictional losses for SH and RH section are calculated using equation 4.42.

ℎ𝑡𝑝 = ((ℎ𝑛𝑏,0 ∙ 𝐹𝑛𝑏 )3 + (ℎ𝐿 ∙ 𝐹𝑡𝑝 )

3)13

4.32

𝑁𝑢𝐿 = ℎ𝐿 ∙ 𝑑𝑖𝑛

𝐾=

(𝑓

8⁄ ) ∙ (𝑅𝑒𝐿 − 1000) ∙ 𝑃𝑟𝐿

1 + 12.7 (𝑓

8⁄ )1

2⁄

∙ (𝑃𝑟𝐿

23⁄ − 1)

4.33

𝑓 = [0.794 ln(𝑅𝑒𝐿) − 1.64]−2 4.34

𝐹𝑡𝑝 = [(1 − 𝑥)1.5 + 1.9 ∙ 𝑥0.6 ∙ (𝜌𝐿

𝜌𝐺

)0.35 ]1.1

4.35

𝐹𝑛𝑏 = 𝐹𝑝𝑓 ∙(𝑞

𝑞0

)𝑛𝑓 ∙ (𝑑

𝑑𝑖,0

)

−0.4

∙ (𝑅𝑝

𝑅𝑝,0

)

0.133

∙ 𝐹(𝑀) 4.36

𝐹𝑝𝑓 = 2.816 ∙ 𝑃𝑟𝐿0.45 + (3.4 +

1.7

1 − 𝑃𝑟𝐿7) ∙ 𝑃𝑟𝐿

3.7 4.37

𝑛𝑓 = 0.8 − 0.1 ∙ exp (1.75 𝑃𝑟𝐿) 4.38

𝐹(𝑀) = 0.377 + 0.199 ln 𝑀 + 0.000028427 𝑀2 4.39

Δ𝑃 = Δ𝑃𝑠 + Δ𝑃𝑓 + Δ𝑃𝑚 + Δ𝑃𝑔 4.40

Δ𝑃𝑔 = H ∙ ρ ∙ g 4.41

Ranjit Desai Methodology

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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

pressure drop for single-phase flow and multiplied by ‘Two-phase friction multiplier’ denoted as ‘𝜙𝑙𝑜2’. Equation

4.43 shows the method to calculate two-phase frictional drop.

Where, ′𝑔𝑐′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

For 𝜇𝑙 𝜇𝑣⁄ < 1000 and 𝐺 < 100 𝑘𝑔 𝑚2𝑠⁄

Friedel correlation [41]

𝜙𝑙𝑜2 = 𝐸 + 3.23 ∙

𝐹𝐻

𝐹𝑟0.045𝑊𝑒0.035

𝐸 = (1 − 𝑥)2 + 𝑥2𝜌𝑙

𝜌𝑣

𝑓𝑣𝑜

𝑓𝑙𝑜

𝐹 = 𝑥0.78 ∙ (1 − 𝑥)0.24

𝐻 = (𝜌𝑙

𝜌𝑣

)0.91

∙ (𝜇𝑣

𝜇𝑙

)0.19

∙ (1 −𝜇𝑣

𝜇𝑙

)0.7

𝐹𝑟 = 𝐺2

𝑔𝐷ℎ𝜌ℎ𝑜𝑚2

𝑊𝑒 = 𝐺2𝐷ℎ

𝜎𝜌ℎ𝑜𝑚2

1

𝜌ℎ𝑜𝑚

=𝑥

𝜌𝑣

+(1 − 𝑥)

𝜌𝑙

𝐺 = 𝜌 ∙ 𝑓𝑙𝑜𝑤 𝑣𝑒𝑙.

For 𝜇𝑙 𝜇𝑣⁄ > 1000 and 𝐺 > 100 𝑘𝑔 𝑚2𝑠⁄

Chisholm correlation [41]

𝜙𝑙𝑜2 = 1 + (𝑌2 − 1) ∙ [𝐵𝑥𝑛∗(1 − 𝑥)𝑛∗ + 𝑥2−𝑛]

𝑛 ∗= 2 − 𝑛

2

𝑌 = (Δ𝑃𝑣 Δ𝑃𝑙⁄ )0.5

Δ𝑃𝑣 = 2 ∙ 𝑓𝑣 ∙ 𝐺2

𝐷ℎ𝜌𝑣

Δ𝑃𝑙 = 2 ∙ 𝑓𝑙 ∙ 𝐺2

𝐷ℎ𝜌𝑙

𝑛 = 0.25

𝐵 = {

4.8 𝐺 < 5002400 𝐺⁄ 500 ≤ 𝐺 < 1900

55 𝐺0.5⁄ 𝐺 ≥ 1900} 𝑓𝑜𝑟 𝑌 ≤ 9.5

𝐵 = {520 𝑌𝐺0.5⁄ 𝐺 ≤ 600

21 𝑌⁄ 𝐺 > 600} 𝑓𝑜𝑟 9.5 < 𝑌 ≤ 28

𝐵 = 15000 (𝑌2𝐺0.5)⁄ 𝑓𝑜𝑟 𝑌 > 28

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

Δ𝑃𝑓 = 2f HG2 𝐷ℎ𝜌⁄ 4.42

Δ𝑃𝑓 = 𝜙𝑙𝑜2Δ𝑃𝑓,𝑙𝑜 = 𝑓𝑙𝑜

2𝐿

𝐷ℎ

𝐺2

𝑔𝑐𝜌𝑙

𝜙𝑙𝑜2

4.43

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Master’s Thesis

16

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.

Figure 17 : Pressure Drop Vs No of Tubes

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600

PR

ES

SU

RE

DR

OP

(%

)

NO. OF TUBES

BOILER SECTION: PRESSURE DROP

H=30m

H=37.49m

H=40m

H=50m

Ranjit Desai Analysis

Master’s Thesis

17

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.

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.

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.

30

40

50

60

70

80

90

100

100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600

EF

FIC

IEN

CY

(%

)

NO. OF TUBES

BOILER:THERMAL EFFICIENCY

H=30m

H=37.49m

H=40

H=50

𝜂𝑡ℎ =𝑄𝑔𝑎𝑖𝑛

(𝑄𝑔𝑎𝑖𝑛 + 𝑄𝑙𝑜𝑠𝑠𝑒𝑠)

5.1

Ranjit Desai Analysis

Master’s Thesis

18

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.

100000

2100000

4100000

6100000

8100000

10100000

12100000

100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600

MA

TE

RIA

L C

OS

T (

US

D)

NO. OF TUBES

BOILER:MATERIAL COST

H=30m

H=37.49m

H=40

H=50

Ranjit Desai Future work

Master’s Thesis

19

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.

Ranjit Desai Conclusion

Master’s Thesis

20

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 References

Master’s Thesis

21

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&region=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].

Ranjit Desai References

Master’s Thesis

22

[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.

Ranjit Desai References

Master’s Thesis

23

[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 Appendix

Master’s Thesis

24

APPENDIX

Appendix A: Tube Selection Handbook for AISI 316L

Tem

pera

ture

0 C32

535

037

540

042

545

047

550

052

555

057

560

062

565

067

570

0

DND_

out

Sch

No

Thic

knes

s

mm

mm

2533

.40

5S1.

6510

.60

10.3

010

.10

10.0

09.

909.

809.

709.

609.

609.

308.

607.

305.

904.

503.

502.

70

33.4

010

S2.

7718

.30

17.8

017

.50

17.4

017

.20

16.9

016

.70

16.6

016

.60

16.1

014

.90

12.7

010

.20

7.80

6.10

4.70

33.4

040

S3.

3822

.70

22.2

021

.80

21.6

021

.40

21.0

020

.80

20.6

020

.60

20.0

018

.50

15.7

012

.60

9.70

7.60

5.80

33.4

080

S4.

5531

.70

30.9

030

.30

30.0

029

.80

29.2

029

.00

28.7

028

.70

27.9

025

.70

21.9

017

.60

13.5

010

.60

8.10

3242

.16

5S1.

658.

308.

107.

907.

907.

807.

707.

607.

507.

507.

306.

705.

704.

603.

502.

802.

10

42.1

610

S2.

7714

.30

13.9

013

.70

13.5

013

.40

13.2

013

.10

12.9

012

.90

12.6

011

.60

9.90

7.90

6.10

4.80

3.70

42.1

640

S3.

3818

.70

18.2

017

.90

17.7

017

.60

17.2

017

.10

16.9

016

.90

16.4

015

.20

12.9

010

.40

8.00

6.20

4.80

42.1

680

S4.

5526

.20

25.5

025

.10

24.8

024

.60

24.2

024

.00

23.7

023

.70

23.1

021

.30

18.1

014

.60

11.2

08.

706.

70

4048

.26

5S1.

657.

207.

006.

906.

806.

806.

706.

606.

506.

506.

405.

905.

004.

003.

102.

401.

90

48.2

610

S2.

7712

.40

12.1

011

.80

11.7

011

.60

11.4

011

.30

11.2

011

.20

10.9

010

.00

8.60

6.90

5.30

4.10

3.20

48.2

640

S3.

6816

.70

16.3

016

.00

15.9

015

.70

15.4

015

.30

15.2

015

.20

14.7

013

.60

11.6

09.

307.

105.

604.

30

48.2

680

S5.

0823

.70

23.1

022

.70

22.5

022

.30

21.9

021

.70

21.5

021

.50

20.9

019

.30

16.4

013

.20

10.1

07.

906.

10

5060

.33

5S1.

655.

705.

605.

505.

405.

405.

305.

205.

205.

205.

104.

704.

003.

202.

501.

901.

50

60.3

310

S2.

779.

809.

509.

409.

309.

209.

009.

008.

908.

908.

608.

806.

805.

404.

203.

302.

50

60.3

340

S3.

9114

.10

13.7

013

5.00

13.3

013

.20

13.0

012

.90

12.7

012

.70

12.4

011

.40

9.70

7.80

6.00

4.70

3.60

60.3

380

S5.

5420

.40

19.9

019

.60

19.4

019

.20

18.9

018

.70

18.5

018

.50

18.0

016

.60

14.2

011

.40

8.70

6.80

5.20

6573

.03

5S2.

116.

105.

905.

805.

805.

705.

605.

605.

505.

505.

304.

904.

203.

402.

602.

001.

60

73.0

310

S3.

058.

908.

608.

508.

408.

308.

208.

108.

008.

007.

807.

206.

104.

903.

803.

002.

30

73.0

340

S5.

1615

.40

15.0

014

.80

14.6

014

.50

14.2

014

.10

14.0

014

.00

13.6

012

.50

10.7

08.

606.

605.

104.

00

73.0

380

S7.

0121

.50

20.9

020

.50

20.4

020

.20

19.8

019

.60

19.4

019

.40

18.9

017

.40

14.9

011

.90

9.20

7.20

5.50

8088

.90

5S2.

115.

004.

804.

804.

704.

704.

604.

504.

504.

504.

404.

003.

402.

802.

101.

701.

30

88.9

010

S3.

057.

207.

106.

906.

906.

806.

706.

606.

606.

606.

405.

905.

004.

003.

102.

401.

90

88.9

040

S5.

4913

.40

13.0

012

.80

12.7

012

.60

12.3

012

.20

12.1

012

.10

11.8

010

.90

9.30

7.40

5.70

4.50

3.40

88.9

080

S7.

6219

.00

18.5

018

.20

18.0

017

.80

17.5

017

.40

17.2

017

.20

16.7

015

.40

13.1

010

.50

8.10

6.30

4.90

9010

1.60

5S2.

114.

304.

204.

104.

104.

104.

004.

003.

903.

903.

803.

503.

002.

401.

901.

401.

10

101.

6010

S3.

056.

306.

206.

006.

005.

905.

805.

805.

705.

705.

605.

104.

403.

502.

702.

101.

60

101.

6040

S5.

7412

.20

11.9

011

.60

11.5

011

.40

11.2

011

.10

11.0

011

.00

10.7

09.

908.

406.

805.

204.

103.

10

101.

6080

S8.

0817

.50

17.1

016

.80

16.6

016

.50

16.2

016

.00

15.9

015

.90

15.4

014

.20

12.1

09.

707.

505.

804.

50

100

114.

305S

2.11

3.80

3.70

3.70

3.60

3.60

3.50

3.50

3.50

3.50

3.40

3.10

2.70

2.10

1.60

1.30

1.00

114.

3010

S3.

055.

605.

505.

405.

305.

305.

205.

105.

105.

104.

904.

503.

903.

102.

401.

901.

40

114.

3040

S6.

0211

.30

11.0

010

.80

10.7

010

.60

10.4

010

.30

10.2

010

.20

10.0

09.

207.

806.

304.

803.

802.

90

114.

3080

S8.

5616

.40

16.0

015

.70

15.6

015

.40

15.1

015

.00

14.9

014

.90

14.4

013

.30

11.4

09.

107.

005.

504.

20

125

141.

305S

2.77

4.10

4.00

3.90

3.90

3.80

3.80

3.70

3.70

3.70

3.60

3.30

2.80

2.30

1.70

1.40

1.00

141.

3010

S3.

405.

004.

904.

804.

804.

704.

604.

604.

604.

604.

404.

103.

502.

802.

201.

701.

30

141.

3040

S7.

119.

909.

609.

509.

409.

309.

109.

009.

009.

008.

708.

006.

805.

504.

203.

302.

50

141.

3080

S10

.97

14.7

014

.30

14.0

013

.90

13.8

013

.50

13.4

013

.30

13.3

012

.90

11.9

010

.20

8.20

6.30

4.90

3.80

Allo

wab

le W

orki

ng P

ress

ure

(MPa

)

Ranjit Desai Appendix

Master’s Thesis

25

Appendix B: Optimized States from Power Block

T P H S X V U FR Cp

Temp. Pressure Enthalpy Entropy Quality Sp. Volume

Internal Energy

Mass flow rate

Specific Heat

0C bar kJ/kg kJ/kgK m3/kg kJ/kg kg/s kJ/kgK

Ranjit Desai Appendix

Master’s Thesis

26

Appendix C: Gnatt Chart

34

56

78

910

1112

1314

1516

1718

1920

2122

2324

2526

2728

29

Lite

ratu

re R

evie

w

Sola

r The

rmal

Tec

hnol

ogie

s

Sola

r Cen

tral

Tow

er S

yste

ms

Ivan

pah

Sola

r The

rmal

Pow

er P

lant

Sum

mar

y

Rece

iver

Des

ign

Fina

lizin

g Re

ceiv

er A

rchi

tect

ure

MA

TLA

B M

odel

Pow

er B

lock

Des

ign

Mas

s Fl

ow R

ate

Opt

imiz

atio

n

Hea

t-Tr

ansf

er P

heno

men

a

Mid

-ter

m R

epor

t

Hea

t-Tr

ansf

er P

heno

men

a

Pres

sure

Los

s Ca

lcul

atio

ns

Tube

Sel

ecti

on

MA

TLA

B M

odel

Fin

aliz

atio

n

Fort

ran

Mod

el

Lite

ratu

re R

evie

w

TRN

SYS

Prog

ram

mer

's G

uide

Fort

ran

Com

pile

r and

Vis

ual S

tudi

o

Fort

ran

Prog

ram

Fina

l Rep

ort a

nd D

efen

se in

Mad

rid

Fort

ran

Prog

ram

TRN

SYS

Sim

ulat

ion

TRN

SYS

Mod

el

Resu

lt A

naly

sis

Proj

ect C

ompl

etio

n an

d KT

H p

rese

ntat

ion

Oct

ober

Sept

embe

rA

pril

May

June

July

Aug

ust

Ranjit Desai Appendix

Master’s Thesis

27

Appendix D: Fortran Program window in MVS 2008

Ranjit Desai Appendix

Master’s Thesis

28

Appendix E: Analysis Graphs for SH section and RH section

SH Section

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

Figure 22 : SH: Efficiency Vs No. of Tubes

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600

PR

ES

SU

RE

DR

OP

(%

)

NO. OF TUBES

SH SECTION: PRESSURE DROP

H=30m

H=37.49m

H=40m

H=50m

20

30

40

50

60

70

80

90

100

100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600

EF

FIC

IEN

CY

(%

)

NO. OF TUBES

SH SECTION:THERMAL EFFICIENCY

H=30m

H=37.49m

H=50m

H=40

Ranjit Desai Appendix

Master’s Thesis

29

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

RH Section

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

9000

509000

1009000

1509000

2009000

2509000

3009000

3509000

100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600

MA

TE

RIA

L C

OS

T (

US

D)

NO. OF TUBES

SH SECTION:MATERIAL COST

H=30m

H=37.49m

H=40

H=50

0

2

4

6

8

10

12

14

16

18

100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600

PR

ES

SU

RE

DR

OP

(%

)

NO. OF TUBES

RH SECTION: PRESSURE DROP

H=30m

H=37.49m

H=40m

H=50m

Ranjit Desai Appendix

Master’s Thesis

30

Figure 25 : RH: Efficiency Vs No. of Tubes

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

0

20

40

60

80

100

100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600

EF

FIC

IEN

CY

(%

)

NO. OF TUBES

RH SECTION:THERMAL EFFICIENCY

H=30m

H=37.49m

H=50m

H=40

30000

110000

190000

270000

350000

430000

510000

590000

670000

750000

830000

910000

990000

100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600

MA

TE

RIA

L C

OS

T (

US

D)

NO. OF TUBES

RH SECTION:MATERIAL COST

H=30m

H=37.49m

H=40

H=50