Validation, Optimization and Simulation of Solar Thermoelectric Generator Model

1 Validation, Optimization and Simulation of Solar Thermoelectric Generator Model By Ali Hamil Rakesh Krishnappa Harish Hadi Madkhali The Final Project of Thermoelectric I (ME 6590) College of Engineering and Applied Sciences Western Michigan University Prof. HoSung Lee August 19, 2015

2 Abstract In this project, a model of solar thermoelectric generator (STEG) is analyzed based on the concept of converting thermal energy into electricity. A recent paper [1] on solar thermoelectric generator reported a highest efficiency of 4.6%, in which the system consisted of a vacuum glass inside enclosure, flat panel (absorber), thermoelectric generator and water circulation for cold side. A validation was applied which was in good agreement with this paper. In our new design, a heat sink using air was added to the system instead of water circulation. Higher efficiency of 5.8% was obtained by applying Dr. Lee s theory of optimal design using dimensionless parameters. Finally, a numerical simulation using ANSYS software was created to compare with analytical solutions.

3 Acknowledgment We would like to express our appreciation to Prof. Lee who has given us this opportunity working in this project. This project would not be useful for us without his gaudiness. Good amount of experience has been gained during this semester. We are very fortunate taking ME 6590 (Thermoelectric I) class with a modest Professor like Dr. Lee. In addition, we are very thankful to Dr. Alla Alttar for his efforts helping us.

4 TABLE OF CONTENTS Topics Chapter 1 Introduction to Solar Thermoelectric Generator I. General II. III. Thermoelectric generators devices Solar Thermoelectric Generator Page No. 1 1 2 2 IV. Recent works Chapter 2 Analytical Part I. Validation of A Model II. New Design 4 8 10 III. Optimizing the New Design Chapter 3 Numerical part 13 Chapter 4 Comparisons, Discussions & Conclusion 16 References 18 Appendices 19

5 1.1 General Chapter 1 Introduction Due to the raising in energy prices, growing in the demand of energy, and increasing in environmental pollution, researchers have been working toward developing the phenomena of generating electrical power depending on thermal process which is called thermoelectric effect. Fossil burning of fuel in energy systems has led to environmental problems such as climate change, acid rain and gases emissions. Thermoelectric generator is a solid state device that converts thermal energy into electricity depending on Seebeck effect between its two layers. A hundred years ago, thermoelectric devices were not sufficient in technology due to their low efficiencies and the massive designs. However, now days all thermoelectric applications is considered as a solution for human activities of burning fuel. 1.2 Thermoelectric Devices At present, thermoelectric generators have been widely used because of their advantages of reliability such as in space or for terrestrial uses. Thermoelectric generators devices based on heat sources are classified into two parts, waste recovery energy and renewable energy systems. Waste recovery systems use the waste heat of combustion systems to recover power and most common applications are in power plant and in automobiles. These systems are considered as large scale size. However, there is a small scale size such in space probe and satellites called radioisotope thermoelectric generators (RTG). Renewable or clean energy systems are the second applications that use the nature sources such as the solar, geothermal, and ocean to generator electrical power.

6 1.3 Solar Thermoelectric Generator Solar thermoelectric generator represents a new technique of using solar energy as a way of generating electricity. There are two methods of using solar energy which are photovoltaic and solar thermal processes. Photovoltaic technology uses flat panels on the building, houses and farms. This technology has wider use than solar thermal process due to its amount of power that can be produced. On other hand, thermal process technique has grown quickly in last ten years because of its ability to store solar energy and generator power even though no light sun especially in nights or due to clouds. Many benefits of using STEGs have been clearly noticed which are life time stabilities, no vibration, no moving parts, low scale systems. 1.4 Recent Papers In order to carry out this project, some technical research papers have been referred to inculcate the basic idea of design and efficiencies achieved in solar thermoelectric generators in the past years. In 1954, Maria Telkes reported the first significant experimental STEG efficiency of 3.35%, in which a concentrating optical lens of 50 times was used in order to increase the incident solar flux and achieved a temperature difference of 247 0 C across a thermoelectric elements made of zinc antimony (ZnSb) and bismuth antimony (BiSb). However this efficiency was insufficient for commercial and domestic purposes. Also, the system was not cost effective due to the use of optical concentrators, which required tracking device. In 2011, Daniel Kraemer [1] demonstrated a promising flat-panel solar thermal energy to electric power conversion method, based on Seeback effect and high thermal concentration without any optical concentrators. STEG model consists of flat panel absorber inside vacuum glass, TEG module and circulation of pumping water for cold side as shown in Fig (1). The developed STEG reached a peak efficiency of 4.6%. This was a major breakthrough and was

7 achieved using a new design. This approach consisted of a highly solar-absorbing surface that converts the solar radiation into heat and thermally concentrates onto the thermoelectric elements by means of lateral conduction. Figure (1) In 2015 Sue & Chen [2] investigated a new model of STEG consists of solar collector, Nano structures of thermoelectric generator (TEG), and heat sink as shown in Fig (2). Solar collector has two parts, optical lens and selective absorber which they are in evacuated enclosure to prevent convective and conductive losses. Main reason of using solar collector is to create large amount of thermal concentration. TEG with inhomogeneous doping has a pair of p& n - type material using Silicon based quantum. This paper reported a high efficiency of 14.8% of STEG. Figure (2) Figure (2)

8 Chapter 2 Analytical Part 2.1 Model Validation First step in this project was validating Kraemer s model of STEG. This Model that was validated in this project was tested experimentally by Kraemer et al.[1], see Fig (1). The basic parts of the model are: 1. Glass vacuum enclosure in order to eliminate the convection losses. 2. Thermoelectric element; the thermocouple material for both (p-type) and (n-type) is Bismuth Telluride (Bi2Te3). Therefore, specifying the material properties (, Seebeck coefficient (α), electrical resistivity (ρ), and thermal conductivity (k)) of Bi2Te3 was from chart.(see APPENDIX) for nanostructure and at average temperature of (100 ), α = 426 V/K, ρ = 2.2 Ωm, k = 1.87 W/mK 3. Wavelength selective solar absorber: The absorber has high absorptivity (αa = 0.95) towards short-wave incident solar radiation but low emissivity at long-wave reradiated radiation from the surface to the surroundings. The dimensions of the thermo-element (p-type and n-type) are 1.35 X 1.35 X 1.65 mm 3. After specifying the materials properties and dimensions of thermocouple, defining each element in Kramer s model is the second task. C th = A a A e Where Cth is the thermal concentration, Aa is the area of the absorber that is equal to 874.8 mm 2, and Ae the cross-sectional area of the thermoelectric elements. The corresponding thermal concentration (Cth) of the STEG used for 1000 W/m 2 at AM1.5G conditions is 299. The

9 temperature of the cold side is 20 ). The transmissivity (τg) of the cover glass is 0.94 and ZTaver =1 2.2 The Basic Equations of Solar Thermoelectric Generator: I. The Ideal Equations of Thermoelectric Generator (TEG): Figure (3): Schematic of heat balances across a thermoelectric couple The figure above shows a simple schematic of heat balances across a pair of thermoelectric elements. The Ideal Equations describe the heat transfer rates across the junctions of the thermoelectric couple. Qh represents the hot side heat transfer rate that occurs at the hot junction with the higher temperature Th. Qc is the cold side heat transfer rate that occurs at the cold junction with the lower temperature Tc. Therefore, the hot and the cold side heat transfer rate can be represented by the following equations: Q h = αt h I 1 2 I2 ρl e A e Q c = αt c I + 1 2 I2 ρl e A e + A ek L e (T h T c ) (1) + A ek L e (T h T c ) (2)

10 Where I is the electrical current, A e & L e are the cross-sectional area and length of thermoelectric elements (p-type & n- type) respectively, α, ρ and k are the Seebeck coefficient, electrical resistivity and thermal resistance respectively. As mentioned before, theses equations are ideal; they are due to assumptions: A. Thomson effects are negligible B. Steady state conditions. C. Material properties are constant and evaluated at the mean operating temperature; means uniform properties at any temperature. D. No convection and radiation losses between the junctions E. No contact resistances at the interfaces of the thermoelectric. II. STEG System Equations: It can be obtained hot heat transfer junction from Q h = Q solar Q Irr,amb Q Irr,plate Since, Q solar = A a τ g α a q i (3) Q Irr,amb = A a ε a σ sb (T 4 h T 4 ) (4) Q Irr,plate = A a ε e σ sb (T 4 h T 4 c ) (5) So, hot heat transfer junction can be written as: Q h = A a [τ g α a q i ε a σ sb (T h 4 T 4 ) + ε e σ sb (T h 4 T c 4 )] (6) Where Q solar is the solar power absorbed by the absorber though passing the glass cover, Q Irr,amb is the solar irradiation between absorber top surface and the surroundings, Q Irr,plate is

11 the solar irradiation between the absorber bottom and the base of heat sink at the cold side, T, T h & T c are the temperatures of the ambient, hot junction and cold junction respectively, A a is the absorber surface area, τ g is the transmissivity of the cover glass, α a is the absorptivity of the absorber, q i is the solar flux of 1,000 W/m 2 at AM1.5G conditions, ε a is the emissivity of the absorber to the ambient air, ε e is the effective emissivity between the bottom of the absorber and the base of the cold side heat sin and σ sb is the Stefan-Boltzmann constant. For the cold side, it can be written cold heat transfer rate as; Where, R th,c is the thermal resistance. Q c = (T c T ) R th,c (7) 2.3 Validation Results: Validation results were obtained by applying equations (1, 2, 6 &7) based on Mathcad program. Figures ( 4) & (5) show good agreement with Kreamer s results. Figure (4) Efficiency versus Current

12 Figure (5) Efficiency versus Current 2.4 New Design In this Model, heat sink in the clod side is used instead of the water circulation as shown in Fig (6). Using forced convection for the cooling side in order to maintain the cold temperature at a specific value needs more energy for pumping the water. The Heat sink is a great alternative process here because it is natural convection; no pumping for the fluid. Not only, the benefits of using the heat sink in this model consumes energy, but also the efficiency of the solar thermoelectric generator has been raised after applying the optimizing theory that it is provided by Dr. Lee. Same input data that were given from Kraemer s paper is used in this design. However, for the cold heat sink side, the convective heat transfer coefficient h c for natural air typically ranges from about 5 to 25 W m 2 K 1.

13 Figure (6) The new proposed design uses the same thermoelectric material and dimensions. In order to make the system as cost effective, a cold side heat sink with natural air convection is used. The convective heat transfer coefficient h c for natural air typically ranges from about 5 to 25 W m 2 K 1. Assuming that the heat sink has 8 fins on a base area of 2 6 = 12 cm 2. The profile length is 2 cm and height of 6 cm for each fin. Both sides of a fin are exposed to the cooling fluid i.e. air. The thickness of each fin is 0.25 cm thick and has a spacing of 0.25 cm as well. The total surface area available for cooling is computed as A c = 8 [2(2 + 0.25)6 + 2 0.25] = 220 cm 2 = 0.022 m 2. Also, the design of the fins has an efficiency η c of 80%, the value for H c = η c h c A c = 0.8 0.022 5 = 0.088 W K 1. The heat sink thermal resistance R th,c = 11.364 K W 1 is obtained where R th,c = (H c ) 1

14 2.5 New Design Results before Optimization Figure (7) shows the efficiency and power output versus current for the new model without optimization. 2.6 Optimizing the New Model Figure (7) Using the optimization theory that is provided by Dr. Lee for the thermoelectric generator, the dimensionless parameters of the solar thermoelectric generator can be derived. Defining dimensionless parameters: T h = T h T (8) T c = T h T (9)

15 R r = R L R (10) ZT = α2 ρk T (11) N k = n ( A e L e ) kr th,c (12) From equations (1,2, 6,7, 8, 9, 10, 11 &12), we get: A a R th,c N k T [τ g α a q i ε a σ sb [(T h T ) 4 T 4 ] ε e σ sb [(T h T ) 4 (T c T ) 4 ]] = ZT (T h T c )T h (R r +1) ZT (T h T c ) 2 2(R r +1) 2 + (T h T c ) (13) T c 1 N k = ZT (T h T c )T c + ZT (T h T c ) 2 + (T (R r +1) 2(R r +1) 2 h T c ) (14) By using Mathcad software, we solved the above two equations, and then got: T h = f(n k, R r, A a, ZT ) T c = f(n k, R r, A a, ZT ) 2.7 Optimizing Results Figures (8) & (9) represent the results of optimization of new model. Similarly, the Kraemer s model has been optimized as shown in Fig. (10).

16 Figure (8) Figure (9) Figure (10)

17 Chapter 3 Numerical Part 3.1 Basic Approach Attaining a good agreement with Kraemer s papers, designing a new model that featured with cold heat sink instead of the water pump and optimizing new model have attracted us to simulate the new model. In fact, this part is the challenging task in this project. The net rate of solar energy is obtained analytically then applied directly to the absorber plate. Figures (11) & (12) show the geometry and mesh respectively. Figure (11) Figure (12)

18 3.2 Numerical Results Figure (13) shows the junction temperatures (Th, Tc ). Figure (13) 3.3 Accurate Approach There is a proper way to simulate this system that would give much accurate results. This way needs to divide the system into three main parts and connect them for transferring the data. These parts are solar fluent, Thermoelectric and heat sink fluent. Meanwhile, this way has not been used in this project due to there are many missing inputs which makes this option much complicated. Analysis fluent of radiation systems has two ways as in following; I. Solar ray tracing; it is highly efficient and practical means of applying solar loads as a heat source in the energy equation. The input data that are required for the solar ray tracing

19 algorithm are sun direction vector, direct solar irradiation, diffuse solar irradiation, spectral fraction, direct and IR absorptivity (opaque wall), direct and IR absorptivity and transmissivity (semi-transparent wall), diffuse hemispherical absorptivity and transmissivity (semi-transparent wall), quad tree refinement factor, scattering fraction, and ground reflectivity. II. Discrete Ordinates Irradiation (DO); it is available to supply outside beam direction and intensity parameters directly to the DO model. In this option, the irradiation flux is applied directly to semi-transparent walls as a boundary condition, so the radiative heat transfer is derived from the solution of the DO transfer equation. This option does not compute the heat fluxes and apply them as heat sources to the energy equation. The inputs that are required in this option are total irradiation, beam direction, beam width, and diffuse fraction. Solar load model includes a solar calculator utility that can be used to construct the sun s location in the sky for a given time of day, date, and position. Also, it can be used for modeling steady and unsteady flows. Global position, starting date and time, grid orientation, solar irradiation method, and sunshine factor are the inputs needed for the solar calculator.

20 Chapter 4 Comparisons, Discussions & Conclusion 4.1 Comparisons Table 1: Comparison of results obtained. Parameters Kraemer et al. s Design Optimum Kraemer et al. s Design New Design before optimization Optimized New Design A a 874.8 mm 2 874.8 mm 2 874.8 mm 2 874.8 mm 2 T h 162.46 C 162.50 C 166.48 C 185.40 C T c 20 C 20.23 C 25.34 C 25.92 C η STEG 4.6% 4.7% 4.5% 5.37% W 46.2 mw 46.2 mw 34.2 mw 55.61 mw Rr 1.62 1.6 1.53 1.62 Similar input conditions: τ g = 0.94, α a = 0.95, ε a = 0.125, T = 20 C From the numerical results, Th = 156.92 C, Tc = 39.06 C 4.2 Discussions The dimensions of the thermoelectric elements to be 1.35 1.35 1.65 mm 3 and the material to be nanostructured bismuth telluride. Kraemer s et al. design did not consist any heat sinks at the cold side. Instead used a cold water circulation, making the system cost to high. The system accounted an overall efficiency of 4.6% and power output of 46.2mW.

21 The new design is optimized with the help of dimensional analysi to obtain a higher efficiency. The optimized design shows 5.37% overall efficiency and is possible when the correct thermoelectric element geometry and load resistance are used so that the optimum values of N k and R r are met. Also, the power output of 55.61 mw is obtained with respect to optimum values of N k and R r, which is higher than Kraemer s power output The bottom line is, the optimized model has more efficiency than Kraemer et al. model. These maximum values are achieved with just the natural air cooling, making the optimized model to be more efficient and cost effective. 4.3 Conclusion The Kraemer s work is a breakthrough since it has experimental results demonstrate its analytical analysis. This work validates Kraemer s results. The obtained values in this project are in good agreement with Kraemer values. Also, here it is confirmed that Kraemer s results are optimized values. The proposed new design gives higher efficiency and power output than Kraemer s work. These higher values are achieved through applying Dr. Lee theory of optimal design.

22 References 1. Kraemer, Daniel, Bed Poudel, Hsien-Ping Feng, J. Christopher Caylor, Bo Yu, Xiao Yan, Yi Ma, et al. 2011. High-performance flat-panel solar thermoelectric generators with high thermal concentration. Nature materials 10, (7): 532-538 2. Su, Shanhe, and Jincan Chen. "Simulation Investigation of High-Efficiency Solar Thermoelectric Generators With Inhomogeneously Doped Nanomaterials." EEE TRANSACTIONS ON INDUSTRIAL ELEC 62, no. 6 (June 2015) 3. Lee, HoSung. "Optimal Design of Thermoelectric Devices with Dimensional Analysis." Applied Energy (February 14, 2013) 4. Lee, HoSung. Thermal Design Heat Sinks, Thermoelectrics, Heat Pipes, Compact Heat Exchangers, and Solar Cells. Hoboken, New Jersey: JOHN WILEY & SONS, INC, 2010 5. Yu, Xiao Yan, et al. 2008. High-thermoelectric performance of nanostructured bismuth antimony telluride bulk alloys. Science 320, (5876): 634-638 6. Kraemer, Daniel, Kenneth McEnaney, Matteo Chiesa, and Gang Chen. 2012. Modeling and optimization of solar thermoelectric generators for terrestrial applications. Solar Energy 86, (5): 1338-1350

Appendices 23