Study of Solar Thermoelectric Generators Coupled with Concentrated Solar Power Systems
Thesis submitted to the faculty of San Francisco State University In partial fulfillment of A 2> the requirements for the Degree 3 G
j a w Master of Science
' £ 5 6 In
Engineering: Energy Systems
by
Bitul Sinha
San Francisco, California
January 2017 Copyright by Bitul Sinha CERTIFICATION OF APPROVAL
I certify that I have read Study of Solar Thermoelectric Generators Coupled with
Concentrated Solar Power Systems by Bitul Sinha, and that in my opinion this work meets the criteria for approving a thesis submitted in partial fulfillment of the requirement for the degree Master of Science in Engineering: Energy Systems at San
Francisco State University.
Ahrr Professor Study of Solar Thermoelectric Generators Coupled with Concentrated Solar Power Systems
Bitul Sinha San Francisco, California 2016
Thermoelectricity, although being a fairly new technology, is making new paths into energy generation. One of the drawbacks of thermoelectric generators is its low efficiency (3%-4%), which is why it has not been utilized in a large scale energy production.
In this thesis, I discuss the possibility of implementing thermoelectric generators into solar thermal concentrator tubes, which can generate electricity without any significant effect on thermal power generated for energy production or industrial process heating. The calculations provided in this thesis are based on theoretical heat transfer models and reasonable assumptions.
I certify that the Abstract is a correct representation of the content of this thesis. ACKNOWLEDGEMENTS
I would like to thank Assistant Professor A.S Cheng who helped me in every way possible with this thesis. I have learned a lot from his immense knowledge and experience in the area of renewable energy and heat transfer. He has been very patient with me and always has been ready to discuss any hurdle we have faced in achieving results and conclusion while writing this thesis. It was his infectious motivation and guidance that helped me write this thesis.
I also would like to thank Professor Ahmad Ganji for being on my supervising committee. His guidance was crucial for the completion of this thesis.
v TABLE OF CONTENTS
LIST OF TABLES...... VII
LIST OF FIGURES...... VIII
LIST OF APPENDICES...... IX
1. INTRODUCTION...... 1
1.1. Objective...... l
2. CONCEPTS...... 4
2.1. Concentrated Solar Power (CSP) Systems...... 4 2.1.1. Parabolic Trough...... 4 2.1.2. Solar Power Tower...... 6 2.1.3. Compact Linear Fresnel Reflectors (CLFR)...... 7 2.1.4. Dish Stirling...... 8 2.2. Thermoelectricity ...... 9 2.3. Thermoelectric Generator (TEG)...... 11 2.4. Previous work done by researchers on STEGs ...... 13
3. MODELING AND CALCULATIONS...... 18
3.1. Proposed Design...... 18 3.2. Assumptions...... 20 3.3. Heat Transfer Model...... 21 3.4. Thermal Losses...... 28 3.5. Thermoelectric Generator Performance...... 30 3.6. Model Parameters...... 31 3.6.1. Absorber and Mirror...... 31 3.6.2. Heat Transferring Fluid...... 32 3.6.3. Thermoelectric Material...... 33 3.6.4. Temperatures...... 35 3.6.5. Energy Balance Equations...... 35 3.6.6. Temperatures at the Origin...... 36 4. MATLAB...... 39
5. RESULTS...... 40
6. CONCLUSION...... 44
7. REFERENCES 45 LIST OF TABLES
Table Page
1. Estimates of Effective Optical Efficiency Terms...... 26 2. Values of C and m for corresponding Reynolds numbers...... 30 3. Table of Constants Used...... 38 LIST OF FIGURES
Figures Page
1. Basic diagram explaining working of parabolic trough solar concentrator...... 6 2. Solucar PS 10 Solar Thermal Power Plant...... 7 3. Compact Fresnel Linear Reflector...... 8 4. Dish Stirling System...... 9 5. Thermoelectricity generated in a semiconductor thermocouple due to Seebeck effect...... 10 6. Thermoelectric Generator (TEG)...... 13 7. Schematic of the STEG proposed by Kraemer...... 15 8. Schematic of the integrated heat pipe type evacuated tube solar collector with direct incorporation ofTEGs...... 16 9. Schematic of model prposed by Miljkovic et. al...... 17 10. Proposed Model...... 19 11. Heat Transfer Diagram...... 25 12. Schott PTR 70 HCE installed on LS-2 Collector...... 32 13. Thermoelectric material, Pb0 98Sr0 2TexNa0A chosen from the UC Santa Barbara Material Research Laboratory’s database...... 34 14. HTF fluid temperature versus length of the tube for various different values of solar insolation...... 40 15. Hot side TEG temperature versus length of the tube for various different values of solar insolation...... 41 16. Cold side TEG temperature versus length of the tube for various different values of solar insolation...... 41 17. Glass envelope temperature versus length of the tube for various different values of solar insolation...... 42 18. Heat incident by the hot side of the TEG versus length of the tube for various different values of solar insolation...... 42 19. Heat transferred to the fluid by the cold side of the TEG versus length of the tube for various different values of solar insolation...... 43 20. Thermoelectric efficiency of individual module versus length of the tube for various different values of solar insolation...... 43 21. Thermoelectric power generated (flux) versus length of the tube for various different values of solar insolation...... 44 LIST OF APPENDICES
Appendix Page
1. Syltherm 800 Datasheet...... 48 2. MATLAB Codes...... 49
ix 1
1. Introduction
The use of fossil fuels is damaging to our environment, and their scarcity has made us strive to attain independence from such sources of energy and move towards alternative and renewable energy sources. Damage to the environment in terms of methane emissions from hydro-power facilities has made us rethink suitable alternative and renewable energy sources. Advanced solar and wind power technologies are emerging as the better options. It is essential for us to switch to renewable forms of energy to sustain mankind, amongst which solar energy is the most abundant and easily accessible. Solar energy is one of the most used sources of energy among the renewable sources of energy. Solar energy has been harnessed for human benefits since the beginning and has been proving helpful even now.
Although solar is being implemented on a large scale via solar photovoltaic (PV) and solar thermal facilities, it is crucial to make these alternative technologies more efficient than ever so that they can sustain the electricity demand of the population on Earth. Research into solar PV and solar thermal technologies have provided us with high efficiency solar panels and high temperature concentrator tubes. In order to further increase the efficiency, it is necessary for us to discover newer avenues or technologies.
1.1. Objective
Although solar photovoltaic is one of the most commercialized technologies for harnessing solar energy, solar thermal does have some notable advantages, which can be summarized as: 2
• Feasibility of constructing large scale systems with outputs in several megawatts
Ability to store thermal energy (using molten salts) for generating power during night
• Utilization of a wide range of the solar radiation spectrum
Durability against damage during high temperature operation under intense radiation and high temperature environments.
Thermoelectric Generators (TEG) have recently emerged as a promising alternative amongst other renewable technologies, owing to their solid state nature and silent operation due to the absence of moving parts. Although TEGs are plagued by low efficiency, the reliability and lifetime has kept researchers interested in them.
The vision to combine solar power with TEG has been experimented by various researches in the past. In 1888. Edward Weston received a patent for a device which concentrated solar radiation onto a thermoelectric module with a black surface [1]. Coblentz also received a patent for a solar thermoelectric generator in 1913 which implemented optical concentration [2] although he does not predict that optical concentration would lead to increased efficiency. Coblentz built this device, but he managed to measure an efficiency of less than one hundredth of one percent [3]. Maria Telkes reported the first experimental STEG efficiency using flat-plate collectors in combination with a ZnSb/BiSb thermocouple in 1954 [4], The device demonstrated 0.6% efficiency, which increased to 3.4% when a 50-fold concentrating lens was added [5]. Since then, research into solar thermoelectric generators had been reduced due to extremely low efficiency values and inability to attain high temperatures in a thermocouple without significant radiative and convective losses. In 2011, Kraemer et. al. [6] experimentally demonstrated 4.6% efficiency in a Bi2Te3 nanostructured STEG [5]. 3
The objective of this thesis is to formulate and analyze the performance of a solar concentrator tube, which is utilized in a parabolic trough collector, embedded with thermoelectric elements, also known as Solar Thermoelectric Generators (STEGs). 4
2. Concepts
In order to understand the analysis of the proposed design in this thesis, it is important to understand the concepts and principles of operation of these technologies.
2.1. Concentrated Solar Power (CSP) Systems
Solar energy, radiant light and heat from the sun, is harnessed using a range of ever- evolving technologies such as solar heating, solar photovoltaics, solar thermal electricity, solar architecture and artificial photosynthesis. The Earth’s surface receives around 2.4 kWh/m2 per day to 5.9 kWh/m2 per day of solar energy after the reflection by the atmosphere and absorption by clouds.
In today’s world, solar energy is harnessed mainly using solar photovoltaic panels or concentrated solar power (CSP). CSP utilizes the thermal energy of the sun’s rays, which is concentrated using mirrors or lenses onto a point, in order to generate high temperatures. This creates a high temperature in that small area. In order to recover heat and transfer it from this region to the point of use, a heat transfer fluid (HTF) is utilized. The HTF, usually a fluid with high specific heat capacity, enters the high temperature region and receives thermal energy, resulting in a temperature rise. This fluid is then transferred to the point of use to generate steam or to be used for Industrial Process Heating (IPH).
2.1.1. Parabolic Trough
A parabolic trough is an apparatus to concentrate incident solar radiation using a parabolic mirror, onto a long concentrator tube which is placed along the axis of the 5
length of the parabolic mirror. A Heat Transfer Fluid or HTF like oil or water is passed through the concentrator tube to absorb the heat from the concentrated solar radiation incident on the tube. This HTF is then used to produce steam to generate power using Rankine cycle or can be directly used in industrial processes requiring heat (IPH).
In order to ensure minimum heat losses due to convection and radiation from the tube, it is encased in a glass envelope and coated with a high absorptivity material or paint. The parabolic mirror system can be tracked in the east-west or north-south direction depending on its alignment to reduce cosine losses representing the loss associated with a surface not pointed directly at the sun’s rays.
Most commercial plants utilizing parabolic troughs are hybrids; fossil fuels are used during night hours, but the amount of fossil fuel used is limited, allowing the plant to qualify in the US as a renewable energy source. 6
. > -.'P
<------Mirror
------Absorber tube
— Field piping
Fig. 1: Basic diagram explaining working of parabolic trough solar concentrator (Courtesy: German Aerospace Center - DLR)
2.1.2. Solar Power Tower
A solar power tower is utilized to generate extremely temperature regions by concentrating solar radiation by using thousands of mirrors or heliostats on a single point located on a central receiver tower. These heliostats are tracked using a dual-axis tracking system which can concentrate the sunlight incident upon that particular heliostat depending on its position in the field with much accuracy. The generated high temperature region has a mesh of tubes containing a HTF, which absorbs the heat and transfers it to a boiler to produce steam which is used in a Rankine cycle to generate power. 7
Fig. 2: Solucar PS 10 (Andalusia, Spain) was the first solar thermal power plant based on tower in the world that generates electricity in a commercial way (Courtesy: Wikipedia)
2.1.3. Compact Linear Fresnel Reflectors (CLFR)
CLFRs use the principles of curved mirror trough systems, but with long parallel rows of lower cost flat mirrors. These modular reflectors focus the sun's energy onto elevated receivers, which consist of a system of tubes through which the HTF flows. The concentrated sunlight heats up the HTF, generating high pressure steam for direct use in power generation and industrial steam applications. 8
Fig. 3: Compact Fresnel Linear Reflector (Courtesy: AREVA)
2.1.4. Dish Stirling
A Dish Stirling or Dish Engine System consists of a stand-alone parabolic reflector that concentrates light onto a receiver positioned at the reflector's focal point. The reflector tracks the sun along two axes. The working fluid in the receiver is heated to 250-700 °C (480-1,300 °F) and then used by a Stirling engine to generate power. Parabolic-dish systems provide high solar-to-electric efficiency (between 31% and 32%), and their modular nature provides scalability. 9
Fig. 4: Dish Stirling System (Courtesy: German Aerospace Center - DLR / Ernsting)
2.2. Thermoelectricity
The thermoelectric effect is the direct conversion of temperature differences to electric voltage and vice versa. A thermoelectric device creates voltage when there is a different temperature on each side. Conversely, when a voltage is applied to it, it creates a temperature difference. At the atomic scale, an applied temperature gradient causes charge carriers in the material to diffuse from the hot side to the cold side. This effect can be used to generate electricity, measure temperature or change the temperature of objects. Because the direction of heating and cooling is determined by the polarity of the applied voltage, thermoelectric devices can be used as temperature controllers.
The term "thermoelectric effect" encompasses three separately identified effects: the Seebeck effect, Peltier effect, and Thomson effect. Thermoelectric power is generated 10
mainly due to Seebeck effect. It is observed when heat (or lack of heat) is applied to a junction of two dissimilar metals (or semiconductors) is directly converted into electricity, called “thermoelectricity”. At the hot junction, electrons move faster because of the heat being supplied, and slower at the colder junction which generates thermoelectricity. This can be enhanced by utilizing semiconductors, which have holes and electrons present in p-type and n-type semiconductors. Generally, the current magnitude has a proportional relationship with the temperature difference, (i.e., the more the temperature difference, the higher the current).
Heat Source
■■■■■■■■■■■■■
Fig. 5: Thermoelectricity generated in a semiconductor thermocouple due to Seebeck effect (Courtesy: Wikipedia archives)
These materials must have both high electrical conductivity (a) and low thermal conductivity (k) to be good thermoelectric materials. Having low thermal conductivity ensures that when one side is made hot, the other side stays cold, which helps to generate a large temperature gradient and voltage while in a temperature gradient. The measure of the magnitude of electrons’ flow in response to a temperature difference across that material is given by the Seebeck coefficient (5). The efficiency of a given material to produce a thermoelectric power is governed by its “figure of merit”, ZT: 11
S 2aT ZT = —— k
(i)
Where T is the absolute temperature.
For many years, the main three semiconductors known to have both low thermal conductivity and high ‘thermoelectric power factor’ (power factor = S 2a, used to determine usefulness of a material in a TEG. Materials with a high power factor are able to 'generate' more energy.) were bismuth telluride (Bi2Te3), lead telluride (PbTe), and silicon germanium (SiGe). These materials have very rare elements which make them very expensive compounds. Today, the thermal conductivity of semiconductors can be lowered without affecting their high electrical properties using nanotechnology. This can be achieved by creating nanoscale features such as particles, wires or interfaces in bulk semiconductor materials.
2.3. Thermoelectric Generator (TEG)
A thermoelectric generator (TEG) utilizes the temperature difference at its hot and cold side to generate electrical power. High temperature is usually achieved by utilizing a heat source such as hot exhaust flue in a boiler, automobile exhaust or solar radiation. Usually, the cold side of the TEG is exposed to the ambient, making it colder compared to the hot side. To achieve a better power output, sometimes a coolant or HTF is used to remove the heat conducted from the hot side to the cold side.
There are many challenges in designing a reliable TEG system that operates at high temperatures. Achieving high efficiency in the system requires extensive engineering design in order to balance between the heat flow through the modules and maximizing the temperature gradient across them. In addition, the system requires one to minimize the thermal losses due to the interfaces between materials at several places. 12
Thermoelectric generators have a variety of applications. Frequently, thermoelectric generators are used for low power remote applications or where bulkier but more efficient heat engines would not be feasible. Unlike heat engines, the solid state electrical components typically used to perform thermal to electric energy conversion have no moving parts. The thermal to electric energy conversion can be performed using components that require no maintenance, have inherently high reliability, and can be used to construct generators with long service free lifetimes. This makes thermoelectric generators well suited for equipment with low to modest power needs in remote uninhabited or inaccessible locations such as mountaintops, the vacuum of space, or the deep ocean.
Thermoelectric Generators are primarily used as remote and off-grid power generators for unmanned sites. They are the most reliable power generator in such situations as they can work day and night, perform under all weather conditions, and can work without battery backup. Although Solar Photovoltaic systems are also implemented in remote sites, Solar PV may not be a suitable solution where solar radiation is low, i.e. areas at higher latitudes with snow or no sunshine, areas with lots of cloud or tree canopy cover, dusty deserts, forests, etc. Many space probes, including the Mars Curiosity rover, generate electricity using a radioisotope thermoelectric generator whose heat source is a radioactive element. Cars and other automobiles produce waste heat (in the exhaust and in the cooling agents). Harvesting that heat energy, using a thermoelectric generator, can increase the fuel efficiency of the car. In addition to automobiles, waste heat is also generated in many other places, such as in industrial processes and in heating (wood stoves, outdoor boilers, cooking, oil and gas fields, pipelines, and remote communication towers). Microprocessors generate waste heat. Researchers have considered whether some of that energy could be recycled. 13
The efficiency of TEGs depend on the figure of merit (around unity) and temperature difference, as will be discussed in Chapter 3. Usually the efficiency lies between 5% to 8% [7]. This value can fluctuate a lot with the available temperature gradient.
— OUTPUT POWER
HEAT DISSIPATION
I l l f l l l M M M
GRAPHITE HEAT COATED FLOW C E P A M tC WAFER
EAT SOURCE
Fig. 6: Thermoelectric Generator (TEG) (Courtesy: www.tegpower.com)
2.4. Previous work done by researchers on STEGs
STEGs have always been a subject of interest for researchers. In recent years several innovations have been designed and tested, creating pathways for further modifications and research. 14
One such design is proposed by Kreamer et. al. [6], shown in Fig. 7, which utilizes thermal concentration of solar energy, but not using optics as previously suggested by Telkes [4]. Telkes suggested a method of optical concentration system to achieve a high temperature difference across a ZnSb alloy p-type material and Bi alloy n-type material. The design was not feasible due to involvement of a tracking system and low efficiency. Kreamer proposes a system that is fitted in a glass vacuum enclosure. The absorber plate with the selective absorber coating is placed on the top of the thermoelectric cell, while the selective absorber is facing the glass enclosure such that it is exposed to direct and diffused solar radiations. The thermoelectric elements used in this experiment are based on the nanostructured Bi2Te3 alloys [8]. Each of these elements is soldered to copper connector plates that are located at the bottom of the glass vacuum enclosure. These copper plates serve as the electrodes, heat spreader and the radiation shield. Heat spreader assists in cooling of the thermoelectric cell to maintain the temperature difference. According to Kreamer, depending on the thermoelectric material, the STEG could achieve an optimal hot side temperature of 165-200 G without any optical concentration which will lead to an efficiency of 5-6%. Kreamer has reported the peak efficiencies of 4.6% and 5.2% at solar radiation intensities of 1 kW/m2 and 1.5 kW/m2 for the thermoelectric cell used in the experiment. 15
Fig. 7: Schematic of the STEG proposed by Kraemer [6]
Another design proposed by Wei He et. al. in [9,10] work presented by He proposes the power generation and water heating system incorporating the thermoelectric generators with evacuated tube solar collectors as a heat source and the active cooling using the cold water jacket. To combat the problem of having high solar heat flux without involving an expensive tracking system, Wei He proposes a system with direct incorporation of thermoelectric generator with heat pipe type evacuated tube water collector which helps in converting the low heat flux to higher heat flux by having the larger evaporator area and smaller condenser area.
For the experimental testing of the proposed system, the commercially available thermoelectric generator of 40 mm length by 40 mm width by 4 mm thickness is used. According to the results presented in the paper, the thermoelectric generator reaches the maximum power value of 0.98W per thermoelectric generator at the solar radiation of 850 W/m2 and cooling water temperature of 303 K. Another test performed by the author with solar radiation of 780 W/m2 is reported in the literature where the temperature of 16
cooling water reaches 313 K and the power output is 0.78 W per thermoelectric generator cell.
insulation —
cooling water in copper channel rnrnrnrrrrIUaUUUUI enhancing heat transfer fin
thermoelectric
copper fin
heat pipe
outer glass tube inner glass tube
heat transfer fin of heat pipe
heat pipe
Fig. 8: Schematic of the integrated heat pipe type evacuated tube solar collector with direct incorporation of TEGs [9]
A research paper published by Miljkovic [11] literature presents the hybrid concentrated solar thermoelectric system using thermosiphon for passive heat transfer for various secondary thermal applications that require relatively medium to high temperature and high quality heat such as industrial process heating (IPH). The solar radiation is concentrated using a parabolic trough mirror, which then is incident upon the thermoelectric cells coated with selective surface powder. Thermoelectric generators are mounted around the thermosiphon that carries the remaining thermal energy to the condenser. Bismuth telluride, lead telluride and silicon germanium thermoelectric materials are considered in this research for power generation. This hybrid solar 17
thermoelectric system is investigated for temperature ranging from 300 to 1200 K and solar concentration of 1-100 sun (1 sun = 1000 W/m2). Evacuated tube helps to prevent thermal losses at the target due to convection and helps in increasing the hot side temperature of the thermoelectric generators. A two phase thermosiphon is inclined along length to facilitate the angle for gravity return of the working fluid from condenser back to the evaporator. Optimum working efficiencies with respective temperatures established by Miljkovic are 34.4% at condenser temperature of 500 K and solar concentration of 50 sun for the bismuth telluride thermoelectric generator and water copper thermosiphon is 48.1% at 776K and solar concentration of 100 sun for the lead telluride thermoelectric generator and mercury stainless steel thermosiphon.
Waste Heat Parabolic Condenser Section Concentrator Thermosyphon
Selective Absorber Vacuum Glass Thermoelectric Thermosyphon
Fig. 9: Schematic of concentrated solar thermoelectric system with thermoelectric generator attached around thermosiphon for carrying the heat to condenser to be used for some secondary application [11]. 18
3. Modeling and Calculations
3.1. Proposed Design
The objective of this thesis was to incorporate TEG into an evacuated solar concentrator tube and analyze its performance in terms of heat and power generation based upon the incoming solar radiation.
In order to provide least hindrance to the HTF, the TEG is arranged on the outside of the concentrator tube (along the curved surface area of the tube). The hot side of the TEG is exposed to the solar radiation coming through the glass envelope, which creates the high temperature required for thermoelectric power generation. This solar radiation is then conducted to the cold side of the TEG via conduction. The cold side of the TEG is in contact with the outer surface of the concentrator tube. The HTF flowing inside the concentrator tube, acts as a coolant, absorbing the heat rejected by the cold side of the TEG, which can then be utilized for power generation via Rankine cycle or industrial process heating. It should be noted that the use of the term “cold” is in reference to relative temperature in the TEG system, and that even the cold side of the element is at an elevated temperature with respect to ambient temperatures.
To reduce convection losses to the ambient, like most solar concentrator systems, the modified concentrator tube is enveloped by glass. The volume between the glass envelope and the concentrator tube is vacuum. This is to reduce any convection losses within the tube. In order to reduce radiation losses from the concentrator tube, the hot side of the TEG, which faces the inner surface of the glass envelope and receives the 19
solar radiation, is covered by a selective absorber coat of paint or material which has reduced emissivity and increased absorptivity.
Fig. 10: Proposed Model 20
3.2. Assumptions
In order to focus on the thermoelectric power generation and the heat transfer to the HTF, we assume that the current system has uniform incoming solar flux i.e., the concentrated solar flux is focused on the evacuated tube uniformly. In actual scenarios, due to the curvature of the mirrors, the flux received by the concentrator tube is non-uniform, with more solar radiation on the underside of the tube and less on the top. For simplification of the model it is assumed there is no change in temperature between the outside boundary wall of the tube and the cold side of the TEG and the HTF temperature is uniform across the cross section or averaged over the cross section. This is appropriate based upon the expectation of turbulent flow within the tube.
The model assumes that the speed of the HTF flow is constant regardless of the temperature. In order to more accurately assess the flow pattern in the concentrator tube, Computational Flow Dynamics (CFD) software might be required.
To accurately analyze the performance of the proposed design, radiative and convective losses from the concentrator tube to the atmosphere are considered. The losses considered are listed below:
• Radiation from the absorber surface to glass envelope • Radiation from the glass envelope to the sky • Convection losses from the glass envelope to the ambient air in the presence of wind 21
3.3. Heat Transfer Model
In order to analyze the performance of the proposed design, we divide the entire length of the tube into finite small elements of length dx along the HTF flow direction. We focus on an element at the length x along the axis from the origin or start of the concentrator tube and of length dx. At this position the temperature of the hot side and cold side of the TEG are TH(x) and Tc{x) respectively. The average HTF temperature is Tm(x). The hot side of the TEG element is being acted upon by a heat flux of qH{x) which is the net heat flux acting on the TEG module after accounting for losses. A part of this heat flux, qc(x) is what enters the HTF after passing through the TEG module and generating
thermoelectric power Pte 0*0 • t
Rh(x) = qc(x) + PTE(x)
(1)
qc(x) is the heat flux which reaches the HTF (in that element) due to convection between the cold side of the TEG and the HTF. Therefore:
qc(x) = hf (Tm(x))[Tc(x) - Tm(x)]
( 2)
Where, hf(Tm(x)) is the convection coefficient of the HTF at a temperature Tm(x) (also a function of temperature of the HTF).
Qnet(x) also results in an increase in the HTF temperature. Therefore: 22
rriCP((Tm(x)) ?c(*) = J/i Frnfr + Where, m = Mass flow rate of the HTF Cp((rm(x)) = Specific heat capacity of the HTF at fluid temperature Tm(x) dAy = Curved surface area of the element Equation (3) can be modified into, dA Tm(x + dx) = Tm(x) + qc(x) ■ X rhCP((Tm(x)) (4 ) n D d x Tm(x + dx) = Tm(x) + qc(x) — mCP((Tm(x)) (5) Where, D = Diameter of concentrator tube containing the HTF In a cylindrical hollow tube with fluid flowing along the axis of it, the convection coefficient will be calculated based on Reynolds number: ReD(7'Tn(x)), Nusselt number: NuD(Tm(_x)) and Prandtl number: Pr(Tm(x)). (6 ) 23 Re (T (x)) - t - n(Tm (*)) f7; From the Dittus-Boelter Equation: NuD(Tm(x)) = 0.023 ReD(r7n(x))°'8P r(rTn(x))0'4 The Nusselt number, thermal conductivity (k) will finally provide us with the convection coefficient: , /v , ^ nf V m \ x ) ) ~ ^ W Combining this finding with equation (2), we can obtain Tc(x) and hence the thermal heat gain by the system accrued over the length of the tube. Therefore: trc(x) \ = Tm(x)'r c \ + L hf {Tm(x)) (10) qH(x) can be expressed in terms of conduction across the TEG using the equation: Rh(x) = j (TH(pc) - Tc(x)) (U) Therefore, 24 Th(x) = Tc(x) + -^ X)~/ ( 12) Where, I Length of the TEG module along the radial direction k Thermal conductivity of the TEG module In order to calculate qH(x), we need to calculate the absorbed solar radiation by the concentrator tube and the losses in the concentrator tube. The concentrator tube is acted upon by solar radiation, which passes through the glass envelope, and loses heat to radiation to the glass envelope due to its high temperature. The effective incoming solar radiation (solar energy minus the optical losses) is absorbed by the glass envelope (qsoiGiass) and the absorber coating on the concentrator tube (qsoiAbs)• Some of that energy is conducted through the TEG module to the HTF by convection, remaining energy is radiated back to the glass envelope by radiation ( (<7GlassAmbConv) and to the sky by radiation ( qGiassskyRad)• 25 JSky ®SatAbs ^Arttb GLASS 1 GlassAm bConv ENVELOPE ^'GlassSJ* yRmd Fig. 11: Heat Transfer Diagram If energy balance equations are applied to all the surfaces: Qh ~ QsoLAbs ~ QAbsGlassRad (13) QsolGlass QAbsGlassRad ~ QdassAmbConv QGla.ssSk.yRad (14) Substituting (13) into (14), the energy balance for the glass envelope can be written as: QsolGlass "1" RsolAbs ~ Qh ~~ RdassAmbConv QciassSkyRad (15) 26 In this particular model, heat loss through via conduction through the concentrator support bracket is neglected. When calculating the amount of solar radiation incident on the glass envelope and the absorber coating, it is essential to account for optical inefficiencies that occur in parabolic trough system, such as [12]: • Shadowing (by support structure) • Tracking error • Geometry error (mirror alignment) • Clean mirror reflectance • Dirt on mirrors • Dirt on glass envelope Based on field tests conducted by NREL [12], such errors are accounted for approximately in this proposed model. Table 1: Estimates of Effective Optical Efficiency Terms £1 = Shadowing 0.974 s2 = Tracking Error 0.994 £3 = Geometry Error (mirror alignment) 0.98 p ci = Clean Mirror Reflectance 0.935 £4 = Dirt on Mirrors Reflectivity/pc; f 5 = Dirt on glass envelope (1 + e4)/2 f 6 = Unaccounted 0.96 * reflectivity is a user input (typically between 0.88 and 0.93) The solar flux absorbed by the glass envelope can be expressed as: 27 QsolGlass ~ QsolarVenv^env (16) With, Venv = £l £2s3£4£5£6Pcl (17) Where, Qsoiar = Solar flux incident on the tube rjenv = Effective optical efficiency at the glass envelope aenv = Absorptance of the glass envelope Similarly, the solar flux absorbed by the absorber coating can be expressed as: QsolAbs ~ QsolarVabs^abs (18) With, Vabs Venv^env (19) Where, Vabs = Effective optical efficiency at the absorber coating aabs ~ Absorptance of the absorber coating Tenv = Transmittance of the glass envelope 28 3.4. Thermal Losses The radiation heat transfer between the absorber and glass envelope ( qAbsGiassRad) at a distance x from the origin, is estimated with the following equation: [13]. fr(^(*)4-7c(*)4) QAbsGlassRadO0 — ^ 1 _|_ (1 ^£lass)^Abs^ &Abs &Glass^Glass (20) Where, Stefan-Boltzman constant (W/m2-K) Tg(x ) = Temperature of glass envelope ^Abs Emissivity of absorber coating £Glass Emissivity of glass envelope D.'Abs Diameter of absorber tube D Glass Diameter of glass envelope The expression can be simplified to: QAbsGLassRad(.x') ~ ( ^ ) 4 7’g C * ')4 ) (21) Where, ^ 1 | C1 jGlass}£Abs EAbs £GlassDGlass (22) 29 Due to the temperature difference between the glass envelope and the sky (atmosphere), there will be radiation losses. The radiation heat transfer between the glass envelope and the sky can be expressed as: QciassSkyRad ~ cr£Glass(Tc(.x)4 — ^Sky4) (23) Where, Tsky is the temperature of the sky, considered to be 8 ° C less than the ambient temperature [12]. As the glass envelope is exposed to the ambient air, there will be heat loss from the glass surface via convection. The convection heat transfer from the glass envelope to the atmosphere ((JdassAmbconv) is the largest source of heat loss, especially if there is a wind. From Newton’s law of cooling, we can express the heat loss as: QdassAmbConvi.~ ^■windiTd.^') ^amb) (24) Where, h wind is the convection coefficient for air at ambient temperature, Tamb . h-wind can be calculated by: Is , _ "'dir „ “ w ind ~ 7 i env u Glass (25) where, k air is the thermal conductance of air at ambient temperature and N u env is the average Nusselt number for the wind flow around the glass envelope. 30 If there is wind, the convection heat transfer from the glass envelope to the environment will be forced convection. The Nusselt number in this case is estimated with Zhukauskas’ correlation for external forced convection flow normal to an isothermal cylinder [13]. Nuenv = CReDaassmPralrn ( ^ - ) 1/4 ^ i Glass ( 26) Where, ReDGiass = Reynolds number at the glass envelope for wind speed at dwind Prair = Prandtl number for air at Tamb PrGlass = Prandtl number for air at TG(x) C, m and n are evaluated by: Table 2: Values of C and m for corresponding ]Reynolds numbers R en c m 1-40 0.75 0.4 40-1000 0.51 0.5 1000-200000 0.26 0.6 200000-1000000 0.076 0.7 And, n = 0.37, for Pr <=10; n = 0.36, for Pr >10 3.5. Thermoelectric Generator Performance The efficiency of a TEG can be expressed as [14]: 31 V l + ZT- 1 ! _ 7 c(x) Vte(x ) — (27) Where, rj (x) is the efficiency (local) of the TEG and ZT is the figure of merit of the TEG. Therefore, the power produced by the TEG element located at x distance from the origin along the axis can be calculated if Tc(x) and TH(x) are obtained from the above discussed heat transfer model. It can be expressed as: Pte(.x ) — VteM Rh (28) When integrated over the length of the tube, we can calculate the total power generated by the TEGs. 3.6. Model Parameters 3.6.1. Absorber and Mirror In order to achieve meaningful results, the dimensions of the proposed design are based on Schott PTR 70 HCEs (Heat Collection Elements). The Schott HCE has a 70 mm diameter 316LSS tube with a high solar absorptance Cermet coating inside a 125 mm diameter Pyrex® glass tube. The space between the metal and glass tube is evacuated to 32 minimize convection heat losses. An anti-reflection coating is applied to the inside and outside surfaces of the glass tube to increase transmittance through the glass. Schott claims their anti-reflective coating is more abrasion resistant than on existing HCEs, which should increase the lifetime of the coating when used in a solar plant [16]. Test results ran on Schott PTR 70 HCE on a LS-2 Collector from [15] are used as input values in this thesis. Fig. 12: Schott PTR 70 HCE installed on LS-2 Collector [15] 3.6.2. Heat Transferring Fluid Syltherm-800 is chosen as the HTF responsible for transferring heat from the TEG to the thermal load. This is the HTF used in the Schott PTR 70 HCE tests reported in in [15]. Values for specific heat capacity, density, viscosity and thermal conductivity for various temperatures were obtained from the Dow Chemicals’ Syltherm-800 Datasheet [17], and are used to calculate the Prandtl number and convection coefficients. The inlet 33 temperature of the HTF into the concentrator tube is assumed to be 100° C (373 K), which increases as it covers more length in the absorber tube. 3.6.3. Thermoelectric Material For the proposed design, a thermoelectric material was chosen suitable for power generation. To generate power, as seen in equation (27) and (28), it is important to choose a material with high figure of merit and ability to handle the temperature achieved by the hot and cold side of the TEG. Using UC Santa Barbara Material Research Laboratory’s extensive database of thermoelectric materials [18], a chalcogenide with the formula P60 985r0.27’e1Wa0A [19] was chosen. This thermoelectric material boasts an average figure of merit of 1.56 and thermal conductivity 1.03 W/mK. This material was chosen due to its high figure of merit and ability to withstand high temperatures (operating range: 700K). The thickness of the TEG is assumed to be 5 mm, same as other existing TEGs commercially available in the market. 34 UCSB O Mn oxide O ZnO, SrT#03 0 Co oxide O other oxide O cfathrate O 5kurterudite 0 half-Heusler O Zintl O chatcogenide 0 Si-Ge O s t lk t d e 700 600 500 I ...... "■ i.... L...... 400 : ...... r.. 300 C( 5 D > w S a 200 !.- .... *.- c Formula: Pb© saSro^Tei Nao i CP 100 Thermal conductivity (W/mK): 1.03 u Seebeck coefficient (pV/K): 263 Sfc 0 • * j ** i ZT: 1.56 o u -100 Temperature: 700 K j*: u Synthesis route: melting OJ -200 JO Final form: polycrystalline cu QJ -300 Author: Biswas 201 2 cn Structure: ICSD # 63099, 298K -400 ...... , ...... Comment -500 i.-...... ■ -600 1 1 ..... 10 Thermal conductivity (W/rrtK) Fig. 13: Thermoelectric material, Pb0 98Sr0 2Te1Na01 chosen from the UC Santa Barbara Material Research Laboratory’s database These values can now help in calculating the efficiency of the thermoelectric modules and the corresponding power generated. 35 3.6.4. Temperatures The ambient temperature is assumed to be 30 “C. Hence the sky temperature, which is 8 XI less than the ambient, is assumed to be 22 V. An average wind speed of 2 m/s is assumed to calculate convection losses from the glass envelope to the ambient air. As a boundary condition it is assumed that at the inlet (i.e. x = 0), Tc and Tm are equal. Hence: r c(0) = Tm(0) = 100 X or 373 K (29) This harmless assumption helps in reducing the number of variables and starting off the equation solving process, which will be discussed later in the thesis. 3.6.5. Energy Balance Equations qH(x) can also be expressed as per (13): k y (7h(JC) — Tq(x ')') RsolarVabs^abs ~ G^eff (Th 0 0 ) (30) Expanding equation (14), which is an energy balance for the glass envelope, for the element can be expressed as, /c RsolarVenva env + OsolarVabs^abs ~ ~J (Xh 0 0 ~ 00) = h-windO'c(*) — 1'amb) ^^GlassiXcO^^ — I'sky ) (31) Which can be arranged to the form, 36 ^ (T h (%) TC{X)) Solar(jlenv&env ~f" TJabs^abs') ^ivind(T c C*0 ^amb) ^^Glass(^G0 0 ^5fey ) f32> 3.6.6. Temperatures at the Origin At the origin i.e. x = 0 all the terms in equation (32) are known, except for TG (0) and r H(0). Tc(0) is taken to be 373 K (29). Y (Th (^') Tc ( 0 ) ) QsolarOlenv&env Vabs^abs') hwind(TQ(0') T'amb) ^ ^ G la ss ifc ( 0 ) — ^Sfcy ) (33) They can be evaluated through iteration of the above two equations. The RHS of equation (33) can be seen as a polynomial function of the variable Tc(0). f{Tc(0)) = -a eclassTc(0y - h w ind 7^(0) + G^GlassTsky + hwindTamb Qsolar^envaenv tlabs (34) Th(0) can be expressed as, Th(0) = l- /(rc(o)) + Tc{0) (35) Values of 7C(0) and TH(0) are to be found such that the equation (33) holds true at x = 0, y (Ttf(°)~ 7c(0)) = (36) According to equation (36), equation (33) can be written as, 37 (p{0) = (37) Values of 7C(0) and TH(0) need to be iterated in such a way that Starting with an initial value of 7^(0) = 304 K (slightly above ambient i.e. 303 K), multiple iterations can give us the values TG(0) and TH(0). Hence <7^(0), gc(0) and PTE(0) can be found, ? h ( 0 ) = QsolarVabs&abs ~ — Tq(0) ) (38) <7c(0) — 9w(0) — Pte (0) (39) Qc (0) — *7 h(0)( 1 — Vte(.®)) (40) , V i+ z r-i \/ rc(o)\ qc(o)-,„(o).(1- | — )) (41) Once the temperatures at the origin of the concentrating tube are established, each finite element can be analyzed. Progressively finding the fluid temperature in the next element, n D d x Tm(x + dx) = Tm(x) + qc(x) rnCP((Tm(x)) (42) Since the thickness of the element is very small (dx) the loop can harmlessly borrow the values of qc and hf from the previous element. Hence Tc(x + dx) can be derived using, 38 < k (* ) Tc(x + dx) = Tm(x + dx) + (43) And the loop can progress till x = L i.e. length of the tube, Refer Appendix B for a detailed look into the loop progression. 39 4. MATLAB Since the variation in the various HTF properties are known to us depending on the temperature, it is possible to generate polynomial functions which express these properties as a function of temperature which is Tm(x) for our case. For reference we use the datasheet provided by Dow for Syltherm-800 [Appendix A]. Using this data, we can find out the specific heat capacity and density, i.e. p{Tm{x)) , CP(Tm(x)) and match them with the corresponding temperature. If curve fit is applied in MATLAB, a polynomial can be obtained which can express p(Tm(x)), CP(Tm(x)) as a function of Tm(x). This polynomial then can be evaluated at different Tm(x) and then give us accurate specific heat capacities and densities. Similarly, using the data we can calculate Prandtl, Reynolds and Nusselt numbers for each corresponding temperature Tm (x). This would provide us corresponding values of the convection coefficient hf(Tm(x)) and hence obtain a polynomial expression for it too. MATLAB is utilized to solve equations (34,36,37) so as to estimate the surface temperatures at the origin by iterating through values of Tc at 0.01 K increments and solving the polynomial equation as per equation (37). The glass surface temperature at the origin leads to evaluating the remaining temperatures. All the equations discussed above are solved sequentially till a new value for TG (x) is obtained. At this point a simple for-loop in MATLAB processes the equations again to give us the all the temperatures and flux. Each element is assumed to be 10 cm long, and the loop runs 250 times, solving for 25 m of concentrator tube length. 40 Thermoelectric power obtained in the form of a flux (W/m2) is then converted into a polynomial of the second degree and integrated over the length of the tube to calculate total thermoelectric power generation, assuming that the modules are arranged in series. MATLAB codes used in this thesis are attached in the appendix [Appendix B]. 5. Results Simulations were run for different values of solar radiation i.e. qsoiar and different temperature profiles were obtained for Tm , Tc, TH and TG. qnet , heat loss flux, r]TE and PTE were also calculated. Graphs plotted below summarize the results obtained: Fluid Temperature Meters lOOOW/sq.m ------2000 W/sq.m 3000 W/sq.m 4000 W/sq.m —— 5000 W/sq.m Fig. 14: HTF fluid temperature versus length of the tube for various different values of solar insolation Fig. 15 Hot side TEG temperature versus length of the tube for various different values of values different various for tube the of length versus temperature TEG side Hot 15 Fig. Fig. 16: Cold side TEG temperature versus length of the tube for various different values different various for tube the of length versus temperature TEG side Cold 16: Fig. Kelvin lOOOW/sq.m lOOOW/sq.m ------2000W/sq.m 00Ws. 30 /qm 00Ws. 5000W/sq.m 4000W/sq.m 3000 W/sq.m 2000 W/sq.m Cold Side TEG Temperature TEG Side Cold Hot Side TEG Temperature TEG Side Hot of solar insolation solar of solar insolation solar ------3000W/sq.m Meters Meters ------4000W/sq.rn ------5.000W/sq.m 41 42 Glass Temperature Meters 1000 W/sq.m 2000 W/sq.m ------3000 W/sq.m 4000 W/sq.m 5000 W/sq.m Fig. 17: Glass envelope temperature versus length of the tube for various different values of solar insolation Q h Meters 1000 W/sq.m ------2000 W/sq.m 3000 W/sq.m 4000 W/sq.m------5000 W/sq.m Fig. 18: Heat incident by the hot side of the TEG versus length of the tube for various different values of solar insolation 43 Qc 3500 u 3000 0> i 2500 5 i 6 cn 2000 « 1500 a, i iooo ^ 500 0 0 10 Meters 1000 W/sq.m 2000 W/sq.m 3000 W/sq.m 4000 W/sq.ni 5000 W/sq.m Fig. 19: Heat transferred to the fluid by the cold side of the TEG versus length of the tube for various different values of solar insolation TEG Efficiency 0.8 *►> O-? g 0.6 ■3 0.5 £ 0.4 0.3 0.2 0.1 0 10 15 Meters 1000 W/sq.m ------2000 W/sq.m 3000 W/sq.m 4000 W/sq.m — —5000 W/sq.m Fig. 20: Thermoelectric efficiency of individual module versus length of the tube for various different values of solar insolation 44 TEG Power (flux) Meters — — 1000 W/sq.m------2000 W/sq.m —— 3000 W/sq.m 4000 W/sq.in 5000 W/sq.m Fig. 21: Thermoelectric power generated (flux) versus length of the tube for various different values of solar insolation 6. Conclusion The thesis investigates the feasibility of combining a parabolic trough solar thermal technology with Thermoelectric Generators (TEG) to produce heat and electric power. It also briefly discusses the work done by researchers in this field and the results achieved by them. The reader is informed about the issues that are faced by TEGs in general like low efficiency, inability to attain high temperature gradient and the steps researchers took to combat them. The thesis then discusses the proposed design and develops a heat transfer model using basic thermodynamic equations. The equations comprising of several dependent variables such as surface temperatures, density, Reynolds number etc. 45 are then solved using MATLAB to determine the performance of the proposed design for different values of solar insolation from 1 kW to 5 kW per square meter in increments of 1000 W. As seen in the results obtained via MATLAB simulation, the proposed design will not generate enough amount of electricity via the STEG cells to make it feasible. This can be attributed to the fact that even though a high temperature is achieved on the hot side of the TEG because of concentrating solar radiation, the HTF flowing in the concentrator tube is not cold enough to develop a respectable temperature gradient for the TEG to perform. Also, as can be seen in the results obtained, the temperature of the HTF rises along the length of the tube gradually decreasing the temperature gradient and leading to decreased TEG efficiency. The TEG almost becomes ineffective along the length of the tube. Although the heat being transferred to the HTF via solar radiation is not greatly reduced by the presence of TEG layer around the concentrating tube, the amount electricity generated is so small that the proposed design becomes unfeasible. In the future, if research leads to an inexpensive thermoelectric material which has a much higher figure of merit, the proposed design can show better outputs as compared to the current case. 7. References 1. Edward Weston. “Art of utilizing solar radiant energy” Patent: US 389125 A, 1888. 46 2. W.W. Coblentz “Thermal Generator” Patent: US 1077219 A, 1913. 3. K MeEnaney “Modeling of Solar Thermal Selective Surfaces and Thermoelectric Generators” Massachusetts Institute of Technology, 2010. 4. M. Telkes. “The efficiency of thermoelectric generators. I.” Journal of Applied Physics, 18(12):1116-1127, 1947. 5. Lauryn L. Baranowski, G. Jeffrey Snyder, Eric S. Toberer “Concentrated solar thermoelectric generators” Energy Environ. Sci., 2012, 5, 9055. 6. Kraemer D, Poudel B, Feng H-P, Caylor JC, Yu B, Yan X, et al. “High- performance flat-panel solar thermoelectric generators with high thermal concentration” Nature Materials 2011;10(7):532-8. 7. Thermoelectric Generator - Wikipedia https://en.wikipedia.org/wiki/Thermoelectric generator 8. Ashwine Date, Abhijit Date, Chris Dixon, Aliakbar Akbarzadeh “Progress of thermoelectric power generation systems: Prospect for small to medium scale power generation” Renewable and Sustainable Energy Reviews Vol. 33, 2014, Pages 371-381. 47 9. Wei He, Yuehong Su, Y.Q. Wang, S.B. Riffat, Jie Ji “A study on incorporation of thermoelectric modules with evacuated-tube heat-pipe solar collectors” Renewable Energy Vol. 37, Issue 1, January 2012, Pages 142-149. 10. Wei He, Yuehong Su, JinXin Hou, S.B. Riffat, Jie Ji “Parametrical analysis of the design and performance of a solar heat pipe thermoelectric generator unit” Applied Energy, Vol. 88, Issue 12, December 2011, Pages 5083-5089. 11. Nenad Miljkovic, Evelyn N. Wang “Modeling and optimization of hybrid solar thermoelectric systems with thermosyphons” Solar Energy Vol. 85, Issue 11, November 2011, Pages 2843-2855. 12. “Heat Transfer Analysis and Modeling of a Parabolic Trough Solar Receiver Implemented in Engineering Equation Solver” R. Forristall, October 2003 (NREL/TP-550-34169) 13. “Fundamentals of Heat and Mass Transfer”, 6th Ed., Frank Incropera et. al. 14. “Fundamentals of Renewable Energy Processes”, 2nd Ed., A.V. da Rosa. 15. “Final Test Results for the Schott HCE on a LS-2 Collector” Timothy A. Moss, Doug A. Brosseau, Ref. No. SAND2005-4034, Sandia National Laboratories, July 2005. 16. Schott PTR70 Datasheet http://tinyurl.com/piqvarh 17. Syltherm 800, Product Technical Data, Dow Chemicals http://tinvurl.com/o8ulfst 18. “High-performance bulk thermoelectrics with all-scale hierarchical architectures” Biswas et. al., September 2012. 19. UC Santa Barbara Material Research Laboratory: Energy Materials Datamining http://www.mrl. ucsb.edu:8080/datamine/thermoelectric.isp APPENDIX APPENDIX A Syltherm 800 Datasheet Specific T fc iiiw l V apm TemJ>. Heat Density Conductivity Vijcoalty Pressure °C kfihn' W /m K mPa»f k Pa -40 1.506 990.61 0.1463 51,05 0 0 “30 1.523 981.08 0.1444 35.45 0.0 -20 1.540 971.68 0.1425 25,86 0.0 -10 1.557 96237 0.1407 19.61 0.0 0 1.574 953.16 0.1388 15.33 0.0 10 1.591 944.04 01369 12.27 0.0 20 i,m 934.99 0.1350 10.03 0.0 30 1.625 926.00 0.1331 8.32 0.0 40 1.643 917.07 0.1312 7.00 0.1 50 1.660 908.18 0.1294 5.96 0.20 60 1.677 899.32 0.1275 5.12 0.42 70 1.694 890.49 0.1256 4.43 0.81 SO 1.711 881.68 0.1237 3,86 1.46 90 1.728 872.86 0.1218 3.39 2.47 too 1.745 864.05 0.1200 2.99 4 00 no 1.762 855.21 0.1181 2.65 6.22 120 i.779 84615 0.1162 2 16 9.30 130 1.796 837.46 0.1143 111 13.5 140 1.813 828.51 0,1124 1.89 19.0 150 t.830 819.51 0.1106 1.70 26.1 m I 847 810.45 01087 1.54 35.0 170 1.864 801.31 0.1068 1.39 46.0 tail 1.882 792.08 0.1049 1.26 59.5 190 1.899 782 76 0.1030 1.15 75,6 200 1.916 773.33 0.1012 1.05 94.6 210 1.933 763.78 0.0993 0.% 116.8 220 1.950 754.11 0.0974 0.88 142.4 230 1.967 744.30 0.0955 0.81 171.7 240 1.984 734.35 0.0936 0.74 204.8 250 2.001 724.24 0.0918 0,69 242.1 260 2.018 713.96 0.0899 0.63 283.6 270 2.035 703.51 0X3680 0.59 329.6 280 2.052 692 87 0.0861 0.54 380.2 290 2.069 682.03 0.0842 0.50 435.4 300 2.086 670.99 0.0824 0.47 495.5 m 2.104 659.73 0.0805 0.44 560.5 320 2 121 648 24 0.0786 0.41 6 v 5 330 2.138 63652 0.0767 0.38 705.6 340 2.155 624.55 0.0748 0.36 785.7 350 2.172 612 >3 0.0729 0.33 870.9 .360 2.189 599.83 0.0711 0.31 961.2 370 2,206 587.07 0.0692 0.29 1057 m 2.223 574.01 0.0673 0.28 1157 390 . 240 560.66 0.0654 0 26 1262 400 2.257 547..00 0,0635 0.25 1373 8.2. APPENDIX B MATLAB CODES 8.2.1. To obtain values of Syltherm 800 properties: 1. temp=[-4 0 0 40 80 120 160 200 240 280 320 360 400] 2. vis=[51.05 15.33 7 3.86 2.36 1.54 1.05 0.74 0.54 0.41 0.31 0.25] 3. rho=[990.61 953.16 917.07 881.68 846.35 810.45 773.33 734.35 692.87 648.24 599.83 547] 4. Cp = [1.506 1.574 1.643 1.711 1.779 1.847 1.916 1.98 2.052 2.121 2.189 2.257] 5. k = [0.14 63 0.1388 0.1312 0.1237 0.1162 0.1087 0.1012 0.0936 0.0861 0.0786 0.0711 0.0635] 6. pC_p=polyfit(temp,Cp,1); 7. p_rho=polyfit(temp,rho,1); 8. Pr=Cp.*vis./k 9. flow=0.00883 10. Dia_abs=0.07 11. CSA=0.25*pi*Dia_absA2 12. speed=flow/CSA 13. Re=rho*speed*Dia_abs./(vis*0.001) 14 . Nusselt=0.023.*Re.A0.8.*Pr.A0.4 15. h_f=Nusselt.*k./Dia_abs 16. pb=polyfit(temp,h_f, 2) 8.2.2. Calculating Temperatures at Origin using iteration: 1. sig= 5.67*10A-8; 2. k=l.03; 3. 1=0.005; 4. eps_g = 0.89; %Heat Loss Testing of Schott1s 2008 PTR70 Paraboli Trough Receiver 5. h_wind = 15.91; ^assumed constant throughout 6. n_env = 0.8; %NREL docu 7. alpha_env = 0.03; %PTR70 datasheet 8. eps_abs = 0.095; %PTR70 datasheet 9. t_env = 0.8 6; %NREL docu 10. n_abs = n_env.*t_env; %NREL docu 11. alpha_abs = 0.96; %NREL docu 12. T_sky = 295; %NREL docu 13. T_amb = 303; %NREL docu 14. qsolar = 5000; 15. Dia abs = 0.07; 51 16. Dia_g = 0.125; 17. eps_eff = 1/((1./eps_abs)+(((1- eps_g).*Dia_abs)./(eps_g.*Dia_g))); 18. g = [-sig.*eps_g 0 0 -h_wind qsolar.*(n_env.*alpha_env+n_abs.*alpha_abs)+h_wind.*T_amb+sig.*ep s_g.*T_skyA4]; 19. for i=l:1000 20. T_gx = 304+i/100; 21. phi = polyval(g,T_gx)/ 22. T_hx = (1./k).*phi+373; 23. epsilonO(i) = qsolar.*n_abs.*alpha_abs- sig.*eps_eff.*(T_hxA4-T_gxA4)-phi; 24. if epsilonO(i)>0.01 25. T_g0 = T_gx 26. T_h0 = T_hx 27. break 28. end 29. end 8.2.3. Calculating Temperatures along the length of the tube: 1. T_m = zeros(151,1); 2. T_c = zeros(151,1); 3. T_h = zeros(151,1); 4. T_g = zeros(151,1); 5. p_Cp = [0.0017 1.5743]; 6. p_hf = [0.0069 0.9443 142.2505]; 7. p_rho = [-0.9841 960.0584]; 8. p_speed = [0.0034 1.9762]; 9. sig= 5.67*10A-8; 10. deltax = 0.1; 11. ZT=1.56; 12. k=l.03; 13. 1=0.005; 14. eps_g = 0.89; %Heat Loss Testing of Schott’s 2008 PTR70 Parabolic Trough Receiver 15. h_wind = 15.91; %assumed constantthroughout 16. n_env = 0.8; %NREL docu 17. alpha_env = 0.03; %pyrex,change 18. eps_abs = 0.095; %PTR70 datasheet 19. t_env = 0.8 6; %NREL docu 20. n_abs = n_env.*t_env; %NREL docu 21. alpha_abs = 0.96; %NREL docu 22. T__sky = 295; %NREL docu 23. T_amb = 303; %NREL docu 24. T _ m (1,1)= 373; 25. T _ c (1,1)= 373; 26. T _ h (1,1)= T_h0; 27. T _ g (1,1)=T_g0; 28. Dia_abs = 0.07; 2 9. Dia_g = 0.125; 52 30. eps_eff = 1/((1./eps_abs)+(((1- eps_g) . *Dia_abs) . / (eps_g. *Dia_g) ) ) ; 31. for n=l:250 32. deltaT(n) = T_h(n,1)-T_c(n,1); 33. q_H(n) =qsolar.*n_abs.*alpha_abs- sig. *eps_eff. * (T_h (n, 1) A4-T_g (n,1)A4 ) ; 34. P_TE(n) = q_ H(n) . *(deltaT(n) ./T_h(n,l)) .*( ( (1 + ZT)A0.5- 1)./((1+ZT)A0.5+(T_c(n, 1)./T_h(n,l)))); 35. eff_TE(n) = 100.*(deltaT(n)./T_h(n,1)).*(((1+ZT)A0 .5- 1)./((1+ZT)A0 .5+(T_c(n,1)./T_h(n,1)))); 36. q_C(n) = q_H(n)-P_TE(n); 37. Cp(n) =polyval(p_Cp,T_m(n,1)); 38. speed(n) = polyval(p_speed,T_m(n,1)); 39. hf(n) = polyval(p_hf,T_m(n,1)); 40. rho(n) = polyval(p_rho,T_m(n,1)); 41. T_m(n+l,l)= T_m(n,l) + (pi.*Dia_abs.*q_C(n).*deltax)./(flow.*Cp(n)); 42. T_c(n+l,l) = T_m(n+1,1) + q_C(n).*(1/hf(n)); 43. g = [-sig.*eps_g 0 0 -h_wind qsolar . * (n_env. *alpha_env+n_abs . *alpha_abs ) +h_wind. *T_amb+sig. *ep s_g.*T_skyA4]/ 44 . for i=l:300 45. T_gx = T_g(n,l) + i/100; 46. phi = polyval(g,T gx)/ 47. T_hx = (l./k).*phi+T_c(n+l,1)/ 48. epsilon(i) = qsolar.*n abs.*alpha abs- sig.*eps_eff.* (T_hxA4-T gxA4)-phi; 49. if epsilon(i)>0.01 50. T_g(n+1,1) = T_gx; 51. T_h(n+1,1) = T_hx/ 52. break 53. end 54 . end 55. end 56. P_te = P_TE.1; 57. qc = q_C.1; 58. qh = q_H.1; 59. effTE = eff_TE.’; 60. deltat = deltaT.'; 61. v = 1:250; 62. pc = polyfit(v,P TE,2); 63. power func = @(x) p c (1,1)*x.A2+pc(1,2)*x+pc(1, 64 . PTE = pi*Dia_abs*integral(power func,0,25)