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
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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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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).
Ranjit Desai Index Note
iv 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 FORTRANPROGRAMMING ... 19
7 Conclusion ... 20
8 References ... 21
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Appendix ... 24
APPENDIX A:TUBE SELECTION HANDBOOK FOR AISI316L ... 24
APPENDIX B:OPTIMIZED STATES FROM POWER BLOCK ... 25
APPENDIX C:GNATT CHART... 26
APPENDIX D:FORTRAN PROGRAM WINDOW IN MVS2008 ... 27
APPENDIX E:ANALYSIS GRAPHS FOR SH SECTION AND RH SECTION ... 28
SHSECTION ... 28
RHSECTION ... 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
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NOMENCLATURE
𝑄̇ 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
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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.
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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
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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.
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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]
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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
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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
7 SL 4 SL 3 SL
5 SL
6 SL 14
17 SL 19 SL
BOILER 18 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 = 𝑀̇
√𝜌𝑃=𝑀̇√𝑇
𝑃 4.1
Φ ∝ √1 − (𝑃𝑜𝑢𝑡
𝑃 )
2
4.2
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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− 𝑀̇2∙ 𝑇𝑖𝑛∙ 𝑌 4.3
Y = 𝑃𝑖𝑛,𝑛𝑜𝑚2− 𝑃𝑜𝑢𝑡,𝑛𝑜𝑚2
𝑃𝑖𝑛,𝑛𝑜𝑚2∙ Φ𝑖𝑛,𝑛𝑜𝑚2
4.4
𝑄𝑚𝑎𝑥 ̇ = 𝐶𝑚𝑖𝑛(𝑇𝑖𝑛ℎ𝑠− 𝑇𝑖𝑛𝑐𝑠) 4.5
𝑄̇ = 𝜀𝑄𝑚𝑎𝑥 = 𝜀𝐶𝑚𝑖𝑛(𝑇𝑖𝑛ℎ𝑠− 𝑇𝑖𝑛𝑐𝑠) 4.6
𝜀 = 𝑓(𝑁𝑇𝑈, 𝐶𝑟) 4.7
𝑁𝑇𝑈 = 𝑈𝐴 𝐶𝑚𝑖𝑛
4.8
𝐶𝑟= 𝐶𝑚𝑖𝑛 𝐶𝑚𝑎𝑥
4.9
𝜀 = 1 − Δ𝑇𝑚𝑖𝑛
(𝑇𝑖𝑛ℎ𝑠− 𝑇𝑖𝑛𝑐𝑠)
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
‘𝑀̇𝑎𝑖𝑟’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
𝑃̇𝑝𝑢𝑚𝑝= 1 𝜂ℎ𝑀̇ (Δ𝑃
𝜌 ) 4.11
𝑇𝑜𝑢𝑡= 𝑇𝑖𝑛+1 − 𝜂ℎ
𝜂ℎ ( Δ𝑃
𝜌𝐶𝑝𝑤) 4.12
𝑃̇𝑓𝑎𝑛=𝑀̇𝑎𝑖𝑟𝐶𝑝𝑎𝑇𝑎
𝜂𝑓𝑎𝑛 [(1 + 𝑓𝑑𝑃𝑎𝑖𝑟)
𝑟𝑎
𝐶𝑝𝑎− 1] 4.13
𝑀̇𝑎𝑖𝑟= 𝑀̇𝑐𝑜𝑜𝑙
𝐶𝑝𝑤 𝐶𝑝𝑎
4.14
𝑀̇𝑐𝑜𝑜𝑙 = 𝑀̇𝑐𝑜𝑜𝑙Δℎ𝑐𝑜𝑛𝑑
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.
𝑄̇𝑓𝑙𝑢𝑖𝑑 = 𝑄̇𝑜𝑢𝑡 − 𝑄̇𝑖𝑛 4.16
𝑄̇𝑓𝑙𝑢𝑖𝑑 = 𝑄̇𝑔𝑎𝑖𝑛𝑠 − 𝑄̇𝑙𝑜𝑠𝑠𝑒𝑠 4.17
𝑄̇𝑙𝑜𝑠𝑠𝑒𝑠 = 𝑄̇𝑐𝑜𝑛𝑣+ 𝑄̇𝑟𝑎𝑑 + 𝑄̇𝑟𝑒𝑓 4.18
𝑄̇𝑓𝑙𝑢𝑖𝑑 = 𝑄̇𝑖𝑛𝑐 − (𝑄̇𝑐𝑜𝑛𝑣+ 𝑄̇𝑟𝑎𝑑 + 𝑄̇𝑟𝑒𝑓 ) 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+ 𝑇𝑎𝑚𝑏2)(𝑇𝑠 + 𝑇𝑎𝑚𝑏 ) 4.20
ℎ𝑟𝑎𝑑,𝑠𝑘𝑦 = 𝜎𝜀𝐹𝑠,𝑠𝑘𝑦 (𝑇𝑠2+ 𝑇𝑠𝑘𝑦2)(𝑇𝑠 + 𝑇𝑠𝑘𝑦 ) 4.21
𝑄̇𝑟𝑎𝑑 = 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 ) ∙𝐻3𝑟𝑒𝑐
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 ⁄ = 0 (A smooth cylinder) 𝐷
1. All Re
𝑁𝑢 = 0.3 + 0.488 ∙ 𝑅𝑒0.5(1 + ( 𝑅𝑒 282000)
0.635
)
0.8
𝐾𝑠 ⁄ = 75 × 10𝐷 −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 ⁄ = 300 × 10𝐷 −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 ⁄ = 900 × 10𝐷 −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)𝑚1 4.29
𝐿𝑀𝑇𝐷 = 𝑄̇𝑔𝑎𝑖𝑛
𝐴𝑠𝑢𝑟𝑓∙ ℎ𝑖𝑛𝑡𝑒𝑟𝑛𝑎𝑙
4.30
𝐿𝑀𝑇𝐷 = 𝑇𝑜𝑢𝑡− 𝑇𝑖𝑛
𝑙𝑛 (𝑇𝑚− 𝑇𝑖𝑛
𝑇𝑚− 𝑇𝑜𝑢𝑡)
4.31
