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ScienceDirect Energy Procedia 75 (2015) 639 – 644

The 7th International Conference on Applied Energy – ICAE2015

Study on thermoelectric-hydraulic performance of longitudinal vortex generators in a large-scale thermoelectric power generator Ting Ma1,2, Jaideep Pandit2, Srinath V. Ekkad2, Scott T. Huxtable2, Samruddhi Deshpande2, Qiuwang Wang1,* 1

Key Laboratory of Thermo-Fluid Science and Engineering, Ministry of Education, School of Energy and Power Engineering, Xi'an Jiaotong University, Xi’an, Shaanxi 710049, P.R. China 2 Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA 24061, USA

Abstract In this paper, the effect of longitudinal vortex generators (LVGs) on the performance of a large-scale thermoelectric power generator (TEG) with a plate-fin heat exchanger is investigated. The fluid-thermal-electric multi-physics coupled model for the TEG is established on the COMSOL® platform, in which the Seebeck, Peltier, Thomson, and Joule heating effects are taken into account. The equivalent thermal-electrical properties of the TE module are used in the numerical simulation. The results indicate that the LVGs could produce complex transverse vortices in the cross section downstream from the LVGs, thus enhancing the heat transfer and electric performances of the TEG compared with a TEG without LVGs. © 2015 Published by Elsevier Ltd. This © 2015The TheAuthors. Authors. Published by Elsevier Ltd.is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Selection and/or peer-review under responsibility of ICAE Peer-review under responsibility of Applied Energy Innovation Institute

Keywords: Thermoelectric power generator; Longitudinal vortex generator; Equivalent thermal-electrical properties; heat transfer enhancement; plate-fin heat exchanger

1. Introduction As a solid-state energy converter, a thermoelectric material can directly convert thermal energy into electrical energy without additional power generation devices. Many automotive manufacturers are exploring thermoelectric power generators (TEGs) to convert some of the waste heat from the exhaust gas into useful electric power. However, the efficiency of TEGs is still poor so considerable research efforts have focused on improving the efficiency of thermoelectric materials. However, the heat transfer

* Corresponding author. Tel.: +86-029-82665539; Fax: +86-029-82665539. E-mail address: [email protected].

1876-6102 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of Applied Energy Innovation Institute doi:10.1016/j.egypro.2015.07.475

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Ting Ma et al. / Energy Procedia 75 (2015) 639 – 644

performance of the heat exchangers also plays an important role on the total efficiency of TEGs. Recently, for the purpose of enhancing the heat transfer and efficiency of TEGs, Lesage et al. [1] and Amaral et al. [2] applied turbulating inserts into the fluid channel in a liquid-to-liquid thermoelectric generator, while Pandit et al. [3] examined three-dimensional partial pin fin arrays on the hot-side walls in a gas-to-liquid thermoelectric generator. In our previous work, the feasibility of using longitudinal vortex generators (LVGs) to improve heat transfer in a small-scale integrated thermoelectric device was studied [4]. It was found that the heat input, net power and thermal conversion efficiency performance of the thermoelectric generators with LVGs could be enhanced by 29%-38%, 90%-104% and 31%-36%, respectively, compared to smooth flow channel. In large-scale TEGs, plate-fin heat exchangers are widely used. Thus, in this study, the effect of LVGs on the performance of large-scale TEGs with plate-fin heat exchanger is examined. Nomenclature A Cross sectional area for a TE leg, m2 I Electric current, A l Length of a TE leg, m k Thermal conductivity, W/(m·K) N Number of a TE leg T Temperature, K Į Seebeck coefficient, V/K ȡ Electrical resistivity, ȍ·m Subscripts E Equivalent thermal-electrical properties for a TE module i The ith TE leg 2. Physical model description As shown in Fig.1, the TE module is composed of a ceramic substrate, conductive copper, couples of P-type and N-type legs, conductive copper and another ceramic substrate from top to bottom. The bottom and top surfaces of TE modules are attached to the cold-side and hot-side plates, respectively. Because the coolant flows in the cold side, the temperature of the bottom surface can be assumed as a constant. On the hot side, a plate fin heat exchanger is usually used to enhance the heat. In order to further improve the heat transfer performance and thus increase the power output, LVGs are proposed to be mounted on the plate-fin channel. The main purpose of this paper is to study the effect of LVGs on the performance of a TEG. The size of the hot-side rectangular channel is 20 mm (width) × 10 mm (height) × 138.56 mm (length), while the thickness of hot-side and cold plates is 1 mm. The thickness of fins is 1.5 mm, and the LVGs are 5 mm (length) × 1 mm (width) × 10 mm (height) with an inclined angle of 45°. The longitudinal pitch and transverse pitch of the LVGs are 34.64 mm and 4.22 mm, respectively. The assembled TE module has a square cross section of 40 mm × 40 mm with a height of 4.2 mm, which consists of 127 couples of p-type and n-type semiconductor legs (Bi2Te3). There are three TE modules laid between the hot-side and coldside plates. The thickness of the ceramic and copper layers are 0.7 mm and 0.6 mm, respectively. The inlet and outlet of the hot-side channel are extended to be 5 times the hydraulic diameter of the hot-side channel to support uniform flow for the inlet and to suppress backflow at the outlet. The inlet velocity of the hot-side gas is 2 m/s with a temperature of 400 °C. The temperature of the cold side is 90 °C.

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Fig. 1. Physical model of TEG with LVGs.

3. Numerical model It is difficult to simulate all 127 couples of the semiconductor legs in detail. However, the thermal resistance of these semiconductor legs is connected in parallel, while the electrical resistance is in series. We obtain the following equations (1)-(3) according to the heat flux equilibrium between the TE module and semiconductor legs caused by the Peltier effect, heat conduction and Joule heating. N

α ETI = ¦ α iTI

(1)

i =1

kE A

N ΔT ΔT · § = ¦ ¨ ki Ai ¸ l l ¹ i =1 ©

(2)

N § l l · = ¦ ¨¨ I ρ i ¸¸ A i=1 © Ai ¹ (3) Here, the thermal-electrical properties of the semiconductor legs are assumed to be temperatureindependent. Thus the equivalent thermal-electrical properties of the TE module can be derived from those of the semiconductor legs according to the following equations (4)-(5):

I ρE

α E = Nα i

(4)

k E = ki

(5)

ρ E = N ρi

(6) A fluid-thermal-electric multi-physics coupled model was established in the COMSOL4.4 platform. The Seebeck, Peltier, Thomson, and Joule heating effects are considered in the TE modules. The flow in the hot-side channel is considered as 3D, laminar, incompressible, and steady. The physical properties of the hot gas are assumed as constant. ®

4. Code Validation The fluid-thermal-electric multi-physics coupled model for the TEG was validated with the results of Reddy et al. [5], which showed that the maximum relative deviations were less than 6%. However, in this

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validation the detailed TE legs were simulated. Therefore, the method of equivalent physical properties for the TE module should be further validated. Figure 2 shows that comparison of the present study with the experimental data in Ref. [6]. The averaged relative errors between the present study and the experimental results in Ref. [6] are 9.5% for ǻT=200 K and 15.9% for ǻT=100 K. The good agreement validates the present numerical method. Experimental result for ΔT=200 K in Ref. [6] Present result for ΔT=200 K Experimental result for ΔT=100 K in Ref. [6] Present result for ΔT=100 K

1.2

1.0

Voltage (V)

0.8

0.6

0.4

0.2

0.0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Current (A)

Fig. 2. Validation of the method of using equivalent physical properties for the TE module.

5. Results and discussion Figure 3 shows the velocity and voltage distributions of the TEG without LVGs. Because the channel is smooth, the fluid flows straight along the channel and the thermal boundary layer forms on the top surface of hot plate. The voltage produced by the TE modules from the left inlet side to the right outlet side decreases because the temperature difference decreases along the streamwise direction as the hot fluid cools. The open circuit voltage in this case is 4.82 V, and the heat input is 24.23 W. When the LVGs are attached to the top surface of the hot plate, the fluid flow is disturbed and the two pairs of vortices are formed downstream from every LVG, as shown in Fig.4. The maximum velocity increases due to the smaller cross section in the channel with LVGs. Therefore, the heat input is increased to 37.42 W and the open circuit voltage in this case is increased to 7.27 V.

Fig. 3. Velocity and voltage distributions of the TEG without LVGs.


Fig. 4. Velocity and voltage distributions of the TEG with LVGs.

6. Conclusion The plate-fin heat exchanger is widely used in large-scale TEGs as a heat sink. In this paper, we establish a fluid-thermal-electric multi-physics coupled model for the gas-to-liquid TEG on the COMSOL® platform. The Seebeck, Peltier, and Thomson effects along with Joule heating are considered in the TE modules. In order to simplify the numerical model of the large-scale TEG, the equivalent thermal-electrical properties of the TE module are used to replace the specific thermal-electrical properties of the TE legs. This numerical method is validated by comparing results with experimental data in the open literature. The comparison of velocity and voltage distributions of the TEG with and without LVGs indicates that the LVGs could produce complex vortices in the cross section downstream the LVGs, thus enhancing the heat transfer performance and electric performance of the TEG. Under the same operating conditions, the heat input and open circuit voltage of the TEG with LVGs are increased by 54% and 51%, respectively, compared to a TEG without LVGs. Acknowledgements This material is based upon work supported by the U.S. National Science Foundation and Department of Energy through the NSF/DOE Joint Thermoelectric Partnership (Grant No. CBET-1048708), and the National Natural Science Foundation of China (Grant No. 51306139). References [1] Lesage FJ, Sempels ÉV, Lalande-Bertrand N. A study on heat transfer enhancement using flow channel inserts for thermoelectric power generation. Energy Conversion and Management 2013;75:532-541. [2] Amaral C, Brandão C, Sempels ÉV, Lesage FJ. Net thermoelectric generator power output using inner channel geometries with alternating flow impeding panels. Applied Thermal Engineering 2014;65:94-101. [3] Pandit J, Thompson M, Ekkad SV, Huxtable ST. Effect of pin fin to channel height ratio and pin fin geometry on heat transfer performance for flow in rectangular channels. International Journal of Heat and Mass Transfer 2014;77:359-368.

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[4] Ma T, Pandit J, Ekkad SV, Huxtable ST, Wang QW. Simulation of thermoelectric-hydraulic performance of a thermoelectric power generator with longitudinal vortex generators. Energy 2014. (Submitted) [5] Reddy BVK, Barry M, Li J, Chyu MK. Three Dimensional Multiphysics Coupled Field Analysis of an Integrated Thermoelectric Device. Numerical Heat Transfer, Part A: Applications: An International Journal of Computation and Methodology 2012;62:933-947. [6] Jang JY, Tsai YC. Optimization of thermoelectric generator module spacing and spreader thickness used in a waste heat recovery system. Applied Thermal Engineering 2013;51:677-689.

Ting Ma is an assistant professor at School of Energy and Power Engineering, Xi’an Jiaotong University. He received his Ph.D. in engineering thermophysics from Xi’an Jiaotong University in 2012. He is a visiting scholar at the Mechanical Engineering, Virginia Tech from March 2014 to February, 2015. His research includes thermoelectric power generator, heat transfer enhancement at high temperature/high pressure conditions. Qiu-Wang Wang is a professor in School of Energy and Power Engineering, Xi’an Jiaotong University. He received his Ph.D. in engineering thermophysics from Xi’an Jiaotong University in 1996. He then joined the faculty of the university and took the professor post in 2001. His main research interests include Computational Fluid Dynamics and Numerical Heat Transfer, heat transfer enhancement, transport phenomena in porous media, compact heat exchangers, building energy savings, indoor air quality, etc. He has also been authors or co-authors of 4 books and more than 100 journal papers. He has obtained 16 China Invent Patents and 2 US Patents.