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Effect of geometric dimensions on thermoelectric and mechanical performance for Mg2Si-based thermoelectric unicouple
Materials Science in Semiconductor Processing 17 (2014) 21–26
Contents lists available at ScienceDirect
Materials Science in Semiconductor Processing journal homepage: www.elsevier.com/locate/mssp
Effect of geometric dimensions on thermoelectric and mechanical performance for Mg2Si-based thermoelectric unicouple Yu Mu a, Gang Chen a, Rui Yu a, Guodong Li a, Pengcheng Zhai b,n, Peng Li b a
Department of Engineering Structure and Mechanics, Wuhan University of Technology, Wuhan 430070, China State Key Laboratory of Advanced Technology of Materials Synthesis and Processing, Wuhan University of Technology, Wuhan 430070, China b
a r t i c l e i n f o
abstract
Available online 4 September 2013
The generating efficiency of thermoelectric generation (TEG) depends not only on the thermoelectric (TE) performance of TE device, but also on its mechanical performance. And choosing suitable TE materials and geometric dimension can improve the working performance of TE device. Mg2Si is one of the most promising TE materials in the medium temperature range, and Mg2Si-based TE devices have broad application prospects. In this paper, a three-dimensional finite model of the Mg2Si-based TE unicouple used for recovering vehicle exhaust waste heat is constructed for the performance analysis. The TE performance and mechanical performance of the Mg2Si-based TE unicouple under the influence of different geometric dimensions are investigated, respectively. The curves of the output power, the power conversion efficiency and the thermal stress distribution varying with different geometric dimensions are discussed in detail. The calculated result would be helpful for further understanding of the TE and mechanical properties of the Mg2Si-based TE unicouple, and it can also provide guidance for further strength check and optimum geometric design of TE unicouples in general. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Mg2Si TE unicouple TE performance Mechanical performance Finite element method
1. Introduction TE device is the core component of TEG, which can convert thermal energy into electric energy via the Seebeck effect. As environment problems and energy crisis have turned increasingly serious, TE device has drawn wider and wider international attention, and improving the generating efficiency of TE device becomes the primary task to promote its commercial application [1–4]. Up to now, many researchers have done a lot to improve the TE performance of the TE device. Using the ANSYS software, Xiao et al. [5] optimized the TE performance of the single-stage TE unicouples by choosing the bismuth telluride as a low-temperature material and skutterudite as
n
Corresponding author. Tel.: þ86 13971443060. E-mail address: [email protected] (P. Zhai).
1369-8001/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.mssp.2013.08.009
a medium-temperature TE material. When the temperature difference ΔT between the hot side and cold side reached 473 K, the maximum output power and conversion efficiency of the bismuth telluride-based TE unicouple was 0.0279 W, 10.82%. Similarly, for the skutterudite-based TE unicouple, when ΔT reached 773 K, the maximum output power and conversion efficiency was 0.1009 W, 9.24%. Niu et al. [6] carried out an experimental study on the influence of the boundary conditions on the maximum output power and conversion efficiency of a low-temperature TEG. The result revealed that the effect of hot and cold fluid inlet temperatures (Tfh, Tfc) was most obvious. The maximum output power and conversion efficiency could reach 146.5 W and 4.4%, when Tfh ¼423 K and Tfc ¼303 K. Wang et al. [7] optimized and designed the length of and fin-to-fin spacing of the heat fin, and the TE performance of the TEG was improved. The output power density was increased by 88.7% after optimization.
22
Y. Mu et al. / Materials Science in Semiconductor Processing 17 (2014) 21–26
However, in practical application, the TE device serves in a high temperature environment, and the mismatch of the coefficients of thermal expansion (CTE) of various component materials will produce thermal stresses. This thermal stress will cause cracks between material layers, leading to serious failure of the TE device. Huang et al. [8] detailed the analysis of the thermal stresses (existing in the layered structure and induced by the temperature difference) via a non-coupled thermal elastic theory. Their results revealed that the shear stress was proportional to the temperature gradient and increased with the increasing heterogeneity in the CTE of the materials. In order to minimize the CTE mismatch between the electrode and the CoSb3 material, Zhao et al. [9] adopted the W–Cu alloy of different alloy compositions as the electrode to connect with the CoSb3 material. The thermal stress distribution of the TE element was obtained by the finite element method. The result indicated that the W80Cu20 was the optimal electrode material, and the maximum thermal stress appeared at the zone close to the CoSb3/electrode interface. Al-Merbati et al. [10] studied the influence of the geometric dimension of TE legs on the thermal stress of TE unicouple. When the ratio RA of the cross sectional area of the top side of leg (AH) to the bottom side (AL) was 0.5, 1, 2, the maximum thermal stress was 1.12 GPa, 0.969 GPa, 0.912 GPa, respectively. According to the above work, choosing suitable TE materials and optimizing geometric dimension can improve the working performance of TE devices. Mg2Si has been regarded as a potential TE material which is widely applied in middle-temperature range (500–900 K) [11–14]. Wang et al. [15] combined the first-principles calculations and the empirical models to interpret and predict the TE performance of the Mg2Si-based TE model. Their result promised the broad application prospect of the Mg2Si-based TE
Fig. 1. Finite element model of the TE unicouple.
devices in the future. In this study, the Mg2Si-based TE unicouple used for recovering the vehicle exhaust waste heat is investigated. The temperature range of the vehicle exhaust is 380 K–773 K, and the temperature-dependent material properties are taken into consideration, such as the Seebeck coefficient, thermal conductivity, and electrical conductivity. During the calculation, a three-dimensional finite model of the Mg2Si-based TE unicouple is constructed for the performance analysis. The TE performance and mechanical performance of the Mg2Si-based TE unicouple under the influences of different geometric dimensions are investigated, respectively. The output power, power conversion efficiency and maximum thermal stress of the TE unicouple are chosen as the indices of the TE performance and mechanical performance. The curves of performance varying with different geometric dimensions are obtained, which is wished to provide guidance for further strength check and optimum geometric design of TE unicouples. 2. Computational model and method The structure of the Mg2Si-based TE unicouple is shown in Fig. 1, the cross-section shape of the TE legs is chosen to be square. The initial width of the p- and n-legs is 2.5 mm, and the length is 3.0 mm. Each leg is separated by a distance of 1.0 mm and soldered to the Mo–Cu electrodes with the welding strips. The thicknesses of the ceramic plates, the Mo–Cu electrodes, and the welding strips are 0.7, 0.25 and 0.1 mm, respectively. According to the results of Choi et al. [16], the Mo-Cu electrodes with different alloy compositions have different CTEs (Mo:Cu vol%¼ 90:10, 80:20, 70:30, 60:40, and 50:50, the thermal expansion coefficients are 6.59 10 6 K 1, 7.65 10 6 K 1, 8.5 10 6 K 1, 9.87 10 6 K 1, 11.21 10 6 K 1). As the CTE of the Mg2Si is determined to be 7.5 10 6 K 1, so the 80:20 composition is chose as the electrode material, as the CTE is close to that measured for Mg2Si. The selection of TE materials directly affects the performance of the generator. The TE materials Mg2Si0.6Ge0.4(Ga0.8%) [17] and Mg2Si0.3Sn0.7 [18] are used as the p- and n-type TE legs, respectively. The material properties used in this work are listed in Table 1 [16–19], where ρ, E and υ are the density, Young's modulus and Poisson's coefficient. Since the TEG is usually operated under large temperature changes, the material properties of the TE materials such as shown in Figs. 2–4, the Seebeck coefficient α, thermal conductivity λ, and electrical conductivity s vary with temperature, and these variations are incorporated into the simulations. On the cold side, the effect of the heat convection is considered. The realistic coolant temperature is forced to
Table 1 Material properties. Material
λ (W/m K)
s (S/m)
E (GPa)
ν
CTE (10 6 K 1)
Ceramic plate [19] Mo–Cu electrode [16] Ti foil [16] p-Type Mg2Si0.6Ge0.4.Ga0.8%) [17] Between 300 K to 800 K n-Type Mg2Si0.3Sn0.7 [18] between 300 K to 800 K
35 167 11.8 1.6 2.3 2.3 2.7
2.5 1010 2.3 107 5.3 105 5.5 103 1 104 6.4 104 1.7 105
380 210 70 120
0.26 0.31 0.37 0.16
4.89–6.03 7.65 9.7 7.5
Y. Mu et al. / Materials Science in Semiconductor Processing 17 (2014) 21–26
23
mounted on a substrate and kept in close contact with the cooling water tank to achieve good thermal exchange. The performance of the TE unicouple is evaluated by the output power and the power conversion efficiency. The output power is defined as follows, P out ¼ I 2 RL
ð1Þ
where I is the load current and RL is the load resistance. The heat input to the TE unicouple is calculated as [21] Q in ¼ 2qA
Fig. 2. Seebeck coefficient and electrical conductivity of the p-type TE materials.
ð2Þ
where q and A is the input heat flux density and the area of the TE leg, respectively. In this case, the power conversion efficiency can be obtained by, η ¼ P out =Q in
ð3Þ
In operation, the heat losses mainly contain convection loss and radiation loss. Convection heat loss includes the loss between the surface of the generator and the ambient air. Radiation heat loss is the radiation of the surface to the ambient. Since the main work of this paper is to study the TE and mechanical performances of the TE unicouple under ideal conditions, the heat losses due to convection and radiation are not taken into account. 3. Results and discussion 3.1. Thermoelectric performance of Mg2Si-basd TE unicouple
Fig. 3. Seebeck coefficient and electrical conductivity of the n-type TE materials.
Fig. 4. Thermal conductivity of the TE materials.
remain at 60 1C, and the heat convection coefficient is 1000 W km 2 [20]. On the hot side, the second boundary condition is carried out, and the input heat flux density is assumed to be 100,000 W m 2 in this study. The displacement boundary conditions are imposed as follows. The hot side is the free end, while the cold side of the model is
In this paper, the influence of the interfacial thermal resistance and electrical resistance on the output power and power conversion efficiency is not considered. As the present work is currently in the design stage, which mainly focuses on the effects of geometric dimensions on the TE performance and mechanical performance. The contact interface is just considered as in perfect contact. The contact effect will be investigated through the experiment in our future study, when an optimum geometric dimension of the TE unicouple is obtained. The effect of geometric dimensions on TE and mechanical performances of TE unicouple is significant. In this section, two main geometric-dimension factors of the TE unicouple are discussed, i.e., the length and width of leg. Besides, the effect of the thickness of the ceramic (H1), Mo–Cu electrode (H2) and welding strip (H3) on the mechanical properties are also investigated. The curves of output power and power conversion efficiency of Mg2Si-based TE unicouple with varied length L and width W of legs can be obtained by using the finite element analysis software ANSYS. During the calculation, the variation scopes of L and W are from 1 mm to 7 mm. As Fig. 5 shows, the hot side temperature (Th) linearly increases along with the length L of leg, while the cold side temperature (Tc) decreases slightly. The temperature difference (Th Tc) between the two sides increases from 57 K to 403 K. As the temperature difference (Th Tc) directly influences the TE performance, a detailed discussion is done to show the output power and the power conversion efficiency of the TE unicouple with the varied length. From Fig. 6, it can be seen the output power and the power conversion efficiency increasing linearly with the increasing length L
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Y. Mu et al. / Materials Science in Semiconductor Processing 17 (2014) 21–26
Fig. 8. TE performance versus the width (W) of leg. Fig. 5. Temperature versus the length (L) of leg.
Fig. 6. TE performance versus the length (L) of leg. Fig. 9. Maximum first principal stress of the TE legs versus the length (L) of leg.
side temperature (Tc) maintains 432 K, and the temperature difference (Th Tc) between the two sides decreases from 210 K to 150 K. The Fig. 8 indicates that the output power increases nonlinearly along with W. When the leg width is small, the output power increases slowly. The output power increases quickly with the increasing W, and when the W increases to 7 mm, the output power reaches 189 mW. In contrast, the power conversion efficiency declines nonlinearly along with the increasing W. When the W increases from 1 mm to 7 mm, the power conversion efficiency declines from 2.64% to 1.84%, a decreases of 30%. Therefore, in order to achieve better TE performance, the longer leg length and the shorter leg width should be desired during the practical design and fabrication. Fig. 7. Temperature versus the width (W) of leg.
3.2. Mechanical performance of Mg2Si-based TE unicouple of leg. As the L increases from 1 mm to 7 mm, the output power increases from 10 mW to 70 mW. Similarly, the power conversion efficiency increases from 0.65% to 4.6%. The results of Figs. 5 and 6 indicate that the temperature difference (Th Tc) between the two sides keeps increasing along with L, which makes the output power and the power conversion efficiency increase significantly. As is shown in Fig. 7, the hot side temperature (Th) decreases slightly with the width W of the leg, while the cold
The good mechanical performance of Mg2Si-based TE unicouple, especially at high temperature, is also important for the effective operation of TEG. There are some previous researches demonstrating that high thermal stresses and cracking occurred at the layer between the TE materials and the electrode [9,10]. Since the Mg2Sibased TE materials belong to the brittle materials and have a high serving temperature, the TE legs may damage easily.
Y. Mu et al. / Materials Science in Semiconductor Processing 17 (2014) 21–26
Fig. 10. Distribution of the maximum first principal stress in the TE legs at L ¼7 mm.
Fig. 11. Maximum first principal stress in the TE legs versus the width (W) of leg.
In this study, the maximum first principal stress in the TE legs under the influence of the geometric dimensions is studied in detail. During the investigation, a thermal elastoplastic stress analysis of the Mg2Si-based TE model is carried out. The Mo–Cu alloy and welding strip are considered to be elastoplastic materials and the other materials are assumed to be linear elastic materials. Fig. 9 shows the maximum first principal stress of the TE legs as a function of the L. It can be found that the maximum first principal stress increases significantly along with the increasing L. As is illustrated, the large temperature difference of the model and the different CTEs between different materials will induce higher thermal stress. When the length L of the leg is 1 mm, the maximum first principal stress reaches 48 MPa, and the corresponding temperature difference is 57 K. When L¼ 7 mm, the maximum first principal stress reaches 90 MPa, which increases to two times bigger than the value of L¼1 mm. And the corresponding temperature difference is 403 K. Fig. 10 shows the distribution of the maximum first principal stress at L¼7 mm. As depicted on the hot side, the lower compress stress locates on the central area, and the higher tensile stress locates along the boundaries. Because the CTE of the welding strip is different from that of the TE materials, the corresponding deformations of different materials are inconsistent under the action of high
25
Fig. 12. Distribution of the maximum first principal stress in the TE legs at W¼ 7 mm.
Fig. 13. Maximum first principal stress in the TE legs versus the thickness (H2) of the electrode.
temperature-dependent load. And the inconsistent deformations would induce the different stress status. It can be also seen that the peak value of the maximum first tensile stress located on the inside corners of the TE leg is 90 MPa, and the high stress zone just takes up a small area, while most of the other tensile stress area is lower than 28 MPa. Besides, most of the TE leg area is subjected to the compressive stress, and the maximum value is about 22 MPa. Fig. 11 is the curve of the maximum first principal stress of the TE legs versus the W. As shown in the figure, the maximum first principal stress increases drastically over the W growth firstly, and then the rate of increase slows down after W¼4 mm. When W increases from 1 mm to 7 mm, the maximum first principal stress of the TE legs increases from 30 MPa to 83 MPa. The distribution of the first principal stress at W¼7 mm is also displayed in Fig. 12. It can be observed that there is compressive stress zone inside the TE legs, and the value is lower than 15 MPa, while the areas nearby the interfaces of TE unicouple and welding strips are subjected to the tensile stress, and the larger values occur along the boundary of the legs. Besides, the maximum first principal stresses of the TE legs under the influences of the thickness of the ceramic (H1), Mo-Cu electrode (H2) and welding strip (H3) are also investigated. The results show that the maximum first principal stress changes slightly with the different thickness
26
Y. Mu et al. / Materials Science in Semiconductor Processing 17 (2014) 21–26
of the ceramic and the welding strip,whereas the thickness of the Mo–Cu electrode has a greater impact upon the value of the maximum first principal stress. In the calculation, the change range of the thicknesses of the Mo–Cu electrode is assumed to be from 0.1 mm to 0.4 mm. Fig. 13 shows the curve of the maximum first principal stress versus the thickness of the Mo–Cu electrode. It can be observed that the maximum first principal stress increases quickly at first and then slows down with the thickness growth of the Mo– Cu electrode. The high level tensile stress is mainly located along the boundary of the legs of the hot side, while the compressive stress areas are located on the central regions of the legs. And the peak values of the tensile stress and the compressive stress reach 67 MPa and 12 MPa respectively, when the thickness of the electrode layer is 0.4 mm. Consequently, the results reveal that the impact of length and width of the TE leg on the maximum first principal stress of the TE material is prominent. Among the ceramic, copper electrode and welding strip, the thickness of the copper electrode has greater effect on the maximum first principal stress of the TE materials. The calculated results indicate that the tensile thermal stress is very high when the L or W reaches the limitation value 7 mm. 4. Conclusions The three-dimensional model of Mg2Si-based TE unicouple is discussed by using the finite element method. The results of the temperature difference (Th Tc), the output power, the conversion efficiency, and the thermal stress in view of the geometric dimensions are as follows: 1) The temperature difference (Th Tc), the output power and the power conversion efficiency increases significantly with the increasing L. When L increases to 7 mm, the output power and the power conversion efficiency are 70 mW and 4.6%, respectively. And for the impact of W, the output power increases greatly with the increasing W. When W increases to 7 mm, the output power reaches 189 mW. However, the temperature difference (Th Tc) and the power conversion efficiency decrease slightly with the increasing W. 2) The maximum first principal stress of TE legs increases nonlinearly along with the length and width growth of the leg. Interestingly, the maximum first principal stress increases drastically over the W growth firstly, and then increases slowly after the leg width W¼3 mm. The Mo–Cu electrode has greater effect on the maximum first principal stress than the ceramic, or the welding strip. Our study is a fundamental study, which is meant to contribute to a better understanding of the influence of the
geometric dimensions on the TE and mechanical properties. The results are wished to be of help to further strength check and optimum geometric design of TE unicouples.
Acknowledgments This work is financially supported by the National Program on Key Basic Research Project (973 Program no. 2013CB632505), National Natural Science Foundation of China (No. 51272198), National High-tech R&D Program of China (863 Program no. 2012AA051104), the Fundamental Research Funds for the Central Universities (No. 2012-Ia036) and the Fundamental Research Funds for the Central Universities (2013-ZY-120). Reference [1] L.G. Chen, J. Li, F.R. Sun, C. Wu, Applied Energy 82 (2005) 300–312. [2] X.L. Gou, H. Xiao, S.W. Yang, Applied Energy 87 (2010) 3131–3136. [3] D.G. Zhao, X.Y. Li, L. He, W. Jiang, L.D. Chen, Intermetallics 17 (2009) 136–141. [4] W.H. Chen, C.Y. Liao, C.I. Hung, W.L. Huang, Energy 45 (2012) 874–881. [5] J.S. Xiao, T.Q. Yang, P. Li, P.C. Zhai, Q.J. Zhang, Applied Energy 93 (2012) 33–38. [6] X. Niu, J.L. Yu, S.Z. Wang, Journal of Power Sources 188 (2009) 621–626. [7] C.C. Wang, C.I. Hung, W.H. Chen, Energy 39 (2012) 236–245. [8] M.J. Huang, P.K. Chou, M.C. Lin, Sensors and Actuators A: Physical 126 (2006) 122–128. [9] D.G. Zhao, H.R. Geng, X.Y. Teng, Journal of Alloys and Compounds 517 (2012) 198–203. [10] A.S. Al-Merbati, B.S. Yilbas, A.Z. Sahin, Applied Thermal Engineering 50 (2013) 683–692. [11] Q. Zhang, J. He, J. Zhu, S.N. Zhang, X.B. Zhao, T.M. Tritt, Applied Physics Letters 93 (2008) 102109. [12] G.S. Nolas, D. Wang, M. Beekman, Physical Review B. 76 (2007) 235204. [13] T. Dasgupta, C. Stiewe, R. Hassdorf, A.J. Zhou, L. Boettcher, E. Mueller, Physical Review B. 83 (2011) 235207. [14] W. Liu, X.J. Tan, K. Yin, H.J. Liu, X.F. Tang, J. Shi, Q.J. Zhang, C. Uher, Physical Review Letters 108 (2012) 166601. [15] H.F. Wang, W.G. Chu, H. Jin, Computational Materials Science 60 (2012) 224–230. [16] S.M. Choi, K.H. Kim, S.M. Jeong, H.S. Choi, Y.S. Lim, W.S. Seo, I.H. Kim, Journal of Electronic Materials 41 (2012) 1004–1010. [17] H. Ihou-Mouko, C. Mercier, J. Tobola, G. Pont, H. Scherrer, Journal of Alloys and Compounds 509 (2011) 6503–6508. [18] W. Liu, X.J. Tan, K. Yin, H.J. Liu, X.F. Tang, J. Shi, Q.J. Zhang, C. Uher, Physical Review Letters 108 (2012) 1666601. [19] S. Turenne, Th. Clin, D. Vasilevskiy, R.A. Masut, Journal of Electronic Materials 39 (2010) 1926–1933. [20] P. Li, L.L. Cai, P.C. Zhai, X.F. Tang, Q.G. Zhang, M. Niino, Journal of Electronic Materials 39 (2010) 1522–1530. [21] R.Y. Nuwayhid, A. Shihadeh, N. Ghaddar, Energy Conversion and Management 46 (2005) 1631–1643.
Contents lists available at ScienceDirect
Materials Science in Semiconductor Processing journal homepage: www.elsevier.com/locate/mssp
Effect of geometric dimensions on thermoelectric and mechanical performance for Mg2Si-based thermoelectric unicouple Yu Mu a, Gang Chen a, Rui Yu a, Guodong Li a, Pengcheng Zhai b,n, Peng Li b a
Department of Engineering Structure and Mechanics, Wuhan University of Technology, Wuhan 430070, China State Key Laboratory of Advanced Technology of Materials Synthesis and Processing, Wuhan University of Technology, Wuhan 430070, China b
a r t i c l e i n f o
abstract
Available online 4 September 2013
The generating efficiency of thermoelectric generation (TEG) depends not only on the thermoelectric (TE) performance of TE device, but also on its mechanical performance. And choosing suitable TE materials and geometric dimension can improve the working performance of TE device. Mg2Si is one of the most promising TE materials in the medium temperature range, and Mg2Si-based TE devices have broad application prospects. In this paper, a three-dimensional finite model of the Mg2Si-based TE unicouple used for recovering vehicle exhaust waste heat is constructed for the performance analysis. The TE performance and mechanical performance of the Mg2Si-based TE unicouple under the influence of different geometric dimensions are investigated, respectively. The curves of the output power, the power conversion efficiency and the thermal stress distribution varying with different geometric dimensions are discussed in detail. The calculated result would be helpful for further understanding of the TE and mechanical properties of the Mg2Si-based TE unicouple, and it can also provide guidance for further strength check and optimum geometric design of TE unicouples in general. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Mg2Si TE unicouple TE performance Mechanical performance Finite element method
1. Introduction TE device is the core component of TEG, which can convert thermal energy into electric energy via the Seebeck effect. As environment problems and energy crisis have turned increasingly serious, TE device has drawn wider and wider international attention, and improving the generating efficiency of TE device becomes the primary task to promote its commercial application [1–4]. Up to now, many researchers have done a lot to improve the TE performance of the TE device. Using the ANSYS software, Xiao et al. [5] optimized the TE performance of the single-stage TE unicouples by choosing the bismuth telluride as a low-temperature material and skutterudite as
n
Corresponding author. Tel.: þ86 13971443060. E-mail address: [email protected] (P. Zhai).
1369-8001/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.mssp.2013.08.009
a medium-temperature TE material. When the temperature difference ΔT between the hot side and cold side reached 473 K, the maximum output power and conversion efficiency of the bismuth telluride-based TE unicouple was 0.0279 W, 10.82%. Similarly, for the skutterudite-based TE unicouple, when ΔT reached 773 K, the maximum output power and conversion efficiency was 0.1009 W, 9.24%. Niu et al. [6] carried out an experimental study on the influence of the boundary conditions on the maximum output power and conversion efficiency of a low-temperature TEG. The result revealed that the effect of hot and cold fluid inlet temperatures (Tfh, Tfc) was most obvious. The maximum output power and conversion efficiency could reach 146.5 W and 4.4%, when Tfh ¼423 K and Tfc ¼303 K. Wang et al. [7] optimized and designed the length of and fin-to-fin spacing of the heat fin, and the TE performance of the TEG was improved. The output power density was increased by 88.7% after optimization.
22
Y. Mu et al. / Materials Science in Semiconductor Processing 17 (2014) 21–26
However, in practical application, the TE device serves in a high temperature environment, and the mismatch of the coefficients of thermal expansion (CTE) of various component materials will produce thermal stresses. This thermal stress will cause cracks between material layers, leading to serious failure of the TE device. Huang et al. [8] detailed the analysis of the thermal stresses (existing in the layered structure and induced by the temperature difference) via a non-coupled thermal elastic theory. Their results revealed that the shear stress was proportional to the temperature gradient and increased with the increasing heterogeneity in the CTE of the materials. In order to minimize the CTE mismatch between the electrode and the CoSb3 material, Zhao et al. [9] adopted the W–Cu alloy of different alloy compositions as the electrode to connect with the CoSb3 material. The thermal stress distribution of the TE element was obtained by the finite element method. The result indicated that the W80Cu20 was the optimal electrode material, and the maximum thermal stress appeared at the zone close to the CoSb3/electrode interface. Al-Merbati et al. [10] studied the influence of the geometric dimension of TE legs on the thermal stress of TE unicouple. When the ratio RA of the cross sectional area of the top side of leg (AH) to the bottom side (AL) was 0.5, 1, 2, the maximum thermal stress was 1.12 GPa, 0.969 GPa, 0.912 GPa, respectively. According to the above work, choosing suitable TE materials and optimizing geometric dimension can improve the working performance of TE devices. Mg2Si has been regarded as a potential TE material which is widely applied in middle-temperature range (500–900 K) [11–14]. Wang et al. [15] combined the first-principles calculations and the empirical models to interpret and predict the TE performance of the Mg2Si-based TE model. Their result promised the broad application prospect of the Mg2Si-based TE
Fig. 1. Finite element model of the TE unicouple.
devices in the future. In this study, the Mg2Si-based TE unicouple used for recovering the vehicle exhaust waste heat is investigated. The temperature range of the vehicle exhaust is 380 K–773 K, and the temperature-dependent material properties are taken into consideration, such as the Seebeck coefficient, thermal conductivity, and electrical conductivity. During the calculation, a three-dimensional finite model of the Mg2Si-based TE unicouple is constructed for the performance analysis. The TE performance and mechanical performance of the Mg2Si-based TE unicouple under the influences of different geometric dimensions are investigated, respectively. The output power, power conversion efficiency and maximum thermal stress of the TE unicouple are chosen as the indices of the TE performance and mechanical performance. The curves of performance varying with different geometric dimensions are obtained, which is wished to provide guidance for further strength check and optimum geometric design of TE unicouples. 2. Computational model and method The structure of the Mg2Si-based TE unicouple is shown in Fig. 1, the cross-section shape of the TE legs is chosen to be square. The initial width of the p- and n-legs is 2.5 mm, and the length is 3.0 mm. Each leg is separated by a distance of 1.0 mm and soldered to the Mo–Cu electrodes with the welding strips. The thicknesses of the ceramic plates, the Mo–Cu electrodes, and the welding strips are 0.7, 0.25 and 0.1 mm, respectively. According to the results of Choi et al. [16], the Mo-Cu electrodes with different alloy compositions have different CTEs (Mo:Cu vol%¼ 90:10, 80:20, 70:30, 60:40, and 50:50, the thermal expansion coefficients are 6.59 10 6 K 1, 7.65 10 6 K 1, 8.5 10 6 K 1, 9.87 10 6 K 1, 11.21 10 6 K 1). As the CTE of the Mg2Si is determined to be 7.5 10 6 K 1, so the 80:20 composition is chose as the electrode material, as the CTE is close to that measured for Mg2Si. The selection of TE materials directly affects the performance of the generator. The TE materials Mg2Si0.6Ge0.4(Ga0.8%) [17] and Mg2Si0.3Sn0.7 [18] are used as the p- and n-type TE legs, respectively. The material properties used in this work are listed in Table 1 [16–19], where ρ, E and υ are the density, Young's modulus and Poisson's coefficient. Since the TEG is usually operated under large temperature changes, the material properties of the TE materials such as shown in Figs. 2–4, the Seebeck coefficient α, thermal conductivity λ, and electrical conductivity s vary with temperature, and these variations are incorporated into the simulations. On the cold side, the effect of the heat convection is considered. The realistic coolant temperature is forced to
Table 1 Material properties. Material
λ (W/m K)
s (S/m)
E (GPa)
ν
CTE (10 6 K 1)
Ceramic plate [19] Mo–Cu electrode [16] Ti foil [16] p-Type Mg2Si0.6Ge0.4.Ga0.8%) [17] Between 300 K to 800 K n-Type Mg2Si0.3Sn0.7 [18] between 300 K to 800 K
35 167 11.8 1.6 2.3 2.3 2.7
2.5 1010 2.3 107 5.3 105 5.5 103 1 104 6.4 104 1.7 105
380 210 70 120
0.26 0.31 0.37 0.16
4.89–6.03 7.65 9.7 7.5
Y. Mu et al. / Materials Science in Semiconductor Processing 17 (2014) 21–26
23
mounted on a substrate and kept in close contact with the cooling water tank to achieve good thermal exchange. The performance of the TE unicouple is evaluated by the output power and the power conversion efficiency. The output power is defined as follows, P out ¼ I 2 RL
ð1Þ
where I is the load current and RL is the load resistance. The heat input to the TE unicouple is calculated as [21] Q in ¼ 2qA
Fig. 2. Seebeck coefficient and electrical conductivity of the p-type TE materials.
ð2Þ
where q and A is the input heat flux density and the area of the TE leg, respectively. In this case, the power conversion efficiency can be obtained by, η ¼ P out =Q in
ð3Þ
In operation, the heat losses mainly contain convection loss and radiation loss. Convection heat loss includes the loss between the surface of the generator and the ambient air. Radiation heat loss is the radiation of the surface to the ambient. Since the main work of this paper is to study the TE and mechanical performances of the TE unicouple under ideal conditions, the heat losses due to convection and radiation are not taken into account. 3. Results and discussion 3.1. Thermoelectric performance of Mg2Si-basd TE unicouple
Fig. 3. Seebeck coefficient and electrical conductivity of the n-type TE materials.
Fig. 4. Thermal conductivity of the TE materials.
remain at 60 1C, and the heat convection coefficient is 1000 W km 2 [20]. On the hot side, the second boundary condition is carried out, and the input heat flux density is assumed to be 100,000 W m 2 in this study. The displacement boundary conditions are imposed as follows. The hot side is the free end, while the cold side of the model is
In this paper, the influence of the interfacial thermal resistance and electrical resistance on the output power and power conversion efficiency is not considered. As the present work is currently in the design stage, which mainly focuses on the effects of geometric dimensions on the TE performance and mechanical performance. The contact interface is just considered as in perfect contact. The contact effect will be investigated through the experiment in our future study, when an optimum geometric dimension of the TE unicouple is obtained. The effect of geometric dimensions on TE and mechanical performances of TE unicouple is significant. In this section, two main geometric-dimension factors of the TE unicouple are discussed, i.e., the length and width of leg. Besides, the effect of the thickness of the ceramic (H1), Mo–Cu electrode (H2) and welding strip (H3) on the mechanical properties are also investigated. The curves of output power and power conversion efficiency of Mg2Si-based TE unicouple with varied length L and width W of legs can be obtained by using the finite element analysis software ANSYS. During the calculation, the variation scopes of L and W are from 1 mm to 7 mm. As Fig. 5 shows, the hot side temperature (Th) linearly increases along with the length L of leg, while the cold side temperature (Tc) decreases slightly. The temperature difference (Th Tc) between the two sides increases from 57 K to 403 K. As the temperature difference (Th Tc) directly influences the TE performance, a detailed discussion is done to show the output power and the power conversion efficiency of the TE unicouple with the varied length. From Fig. 6, it can be seen the output power and the power conversion efficiency increasing linearly with the increasing length L
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Fig. 8. TE performance versus the width (W) of leg. Fig. 5. Temperature versus the length (L) of leg.
Fig. 6. TE performance versus the length (L) of leg. Fig. 9. Maximum first principal stress of the TE legs versus the length (L) of leg.
side temperature (Tc) maintains 432 K, and the temperature difference (Th Tc) between the two sides decreases from 210 K to 150 K. The Fig. 8 indicates that the output power increases nonlinearly along with W. When the leg width is small, the output power increases slowly. The output power increases quickly with the increasing W, and when the W increases to 7 mm, the output power reaches 189 mW. In contrast, the power conversion efficiency declines nonlinearly along with the increasing W. When the W increases from 1 mm to 7 mm, the power conversion efficiency declines from 2.64% to 1.84%, a decreases of 30%. Therefore, in order to achieve better TE performance, the longer leg length and the shorter leg width should be desired during the practical design and fabrication. Fig. 7. Temperature versus the width (W) of leg.
3.2. Mechanical performance of Mg2Si-based TE unicouple of leg. As the L increases from 1 mm to 7 mm, the output power increases from 10 mW to 70 mW. Similarly, the power conversion efficiency increases from 0.65% to 4.6%. The results of Figs. 5 and 6 indicate that the temperature difference (Th Tc) between the two sides keeps increasing along with L, which makes the output power and the power conversion efficiency increase significantly. As is shown in Fig. 7, the hot side temperature (Th) decreases slightly with the width W of the leg, while the cold
The good mechanical performance of Mg2Si-based TE unicouple, especially at high temperature, is also important for the effective operation of TEG. There are some previous researches demonstrating that high thermal stresses and cracking occurred at the layer between the TE materials and the electrode [9,10]. Since the Mg2Sibased TE materials belong to the brittle materials and have a high serving temperature, the TE legs may damage easily.
Y. Mu et al. / Materials Science in Semiconductor Processing 17 (2014) 21–26
Fig. 10. Distribution of the maximum first principal stress in the TE legs at L ¼7 mm.
Fig. 11. Maximum first principal stress in the TE legs versus the width (W) of leg.
In this study, the maximum first principal stress in the TE legs under the influence of the geometric dimensions is studied in detail. During the investigation, a thermal elastoplastic stress analysis of the Mg2Si-based TE model is carried out. The Mo–Cu alloy and welding strip are considered to be elastoplastic materials and the other materials are assumed to be linear elastic materials. Fig. 9 shows the maximum first principal stress of the TE legs as a function of the L. It can be found that the maximum first principal stress increases significantly along with the increasing L. As is illustrated, the large temperature difference of the model and the different CTEs between different materials will induce higher thermal stress. When the length L of the leg is 1 mm, the maximum first principal stress reaches 48 MPa, and the corresponding temperature difference is 57 K. When L¼ 7 mm, the maximum first principal stress reaches 90 MPa, which increases to two times bigger than the value of L¼1 mm. And the corresponding temperature difference is 403 K. Fig. 10 shows the distribution of the maximum first principal stress at L¼7 mm. As depicted on the hot side, the lower compress stress locates on the central area, and the higher tensile stress locates along the boundaries. Because the CTE of the welding strip is different from that of the TE materials, the corresponding deformations of different materials are inconsistent under the action of high
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Fig. 12. Distribution of the maximum first principal stress in the TE legs at W¼ 7 mm.
Fig. 13. Maximum first principal stress in the TE legs versus the thickness (H2) of the electrode.
temperature-dependent load. And the inconsistent deformations would induce the different stress status. It can be also seen that the peak value of the maximum first tensile stress located on the inside corners of the TE leg is 90 MPa, and the high stress zone just takes up a small area, while most of the other tensile stress area is lower than 28 MPa. Besides, most of the TE leg area is subjected to the compressive stress, and the maximum value is about 22 MPa. Fig. 11 is the curve of the maximum first principal stress of the TE legs versus the W. As shown in the figure, the maximum first principal stress increases drastically over the W growth firstly, and then the rate of increase slows down after W¼4 mm. When W increases from 1 mm to 7 mm, the maximum first principal stress of the TE legs increases from 30 MPa to 83 MPa. The distribution of the first principal stress at W¼7 mm is also displayed in Fig. 12. It can be observed that there is compressive stress zone inside the TE legs, and the value is lower than 15 MPa, while the areas nearby the interfaces of TE unicouple and welding strips are subjected to the tensile stress, and the larger values occur along the boundary of the legs. Besides, the maximum first principal stresses of the TE legs under the influences of the thickness of the ceramic (H1), Mo-Cu electrode (H2) and welding strip (H3) are also investigated. The results show that the maximum first principal stress changes slightly with the different thickness
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of the ceramic and the welding strip,whereas the thickness of the Mo–Cu electrode has a greater impact upon the value of the maximum first principal stress. In the calculation, the change range of the thicknesses of the Mo–Cu electrode is assumed to be from 0.1 mm to 0.4 mm. Fig. 13 shows the curve of the maximum first principal stress versus the thickness of the Mo–Cu electrode. It can be observed that the maximum first principal stress increases quickly at first and then slows down with the thickness growth of the Mo– Cu electrode. The high level tensile stress is mainly located along the boundary of the legs of the hot side, while the compressive stress areas are located on the central regions of the legs. And the peak values of the tensile stress and the compressive stress reach 67 MPa and 12 MPa respectively, when the thickness of the electrode layer is 0.4 mm. Consequently, the results reveal that the impact of length and width of the TE leg on the maximum first principal stress of the TE material is prominent. Among the ceramic, copper electrode and welding strip, the thickness of the copper electrode has greater effect on the maximum first principal stress of the TE materials. The calculated results indicate that the tensile thermal stress is very high when the L or W reaches the limitation value 7 mm. 4. Conclusions The three-dimensional model of Mg2Si-based TE unicouple is discussed by using the finite element method. The results of the temperature difference (Th Tc), the output power, the conversion efficiency, and the thermal stress in view of the geometric dimensions are as follows: 1) The temperature difference (Th Tc), the output power and the power conversion efficiency increases significantly with the increasing L. When L increases to 7 mm, the output power and the power conversion efficiency are 70 mW and 4.6%, respectively. And for the impact of W, the output power increases greatly with the increasing W. When W increases to 7 mm, the output power reaches 189 mW. However, the temperature difference (Th Tc) and the power conversion efficiency decrease slightly with the increasing W. 2) The maximum first principal stress of TE legs increases nonlinearly along with the length and width growth of the leg. Interestingly, the maximum first principal stress increases drastically over the W growth firstly, and then increases slowly after the leg width W¼3 mm. The Mo–Cu electrode has greater effect on the maximum first principal stress than the ceramic, or the welding strip. Our study is a fundamental study, which is meant to contribute to a better understanding of the influence of the
geometric dimensions on the TE and mechanical properties. The results are wished to be of help to further strength check and optimum geometric design of TE unicouples.
Acknowledgments This work is financially supported by the National Program on Key Basic Research Project (973 Program no. 2013CB632505), National Natural Science Foundation of China (No. 51272198), National High-tech R&D Program of China (863 Program no. 2012AA051104), the Fundamental Research Funds for the Central Universities (No. 2012-Ia036) and the Fundamental Research Funds for the Central Universities (2013-ZY-120). Reference [1] L.G. Chen, J. Li, F.R. Sun, C. Wu, Applied Energy 82 (2005) 300–312. [2] X.L. Gou, H. Xiao, S.W. Yang, Applied Energy 87 (2010) 3131–3136. [3] D.G. Zhao, X.Y. Li, L. He, W. Jiang, L.D. Chen, Intermetallics 17 (2009) 136–141. [4] W.H. Chen, C.Y. Liao, C.I. Hung, W.L. Huang, Energy 45 (2012) 874–881. [5] J.S. Xiao, T.Q. Yang, P. Li, P.C. Zhai, Q.J. Zhang, Applied Energy 93 (2012) 33–38. [6] X. Niu, J.L. Yu, S.Z. Wang, Journal of Power Sources 188 (2009) 621–626. [7] C.C. Wang, C.I. Hung, W.H. Chen, Energy 39 (2012) 236–245. [8] M.J. Huang, P.K. Chou, M.C. Lin, Sensors and Actuators A: Physical 126 (2006) 122–128. [9] D.G. Zhao, H.R. Geng, X.Y. Teng, Journal of Alloys and Compounds 517 (2012) 198–203. [10] A.S. Al-Merbati, B.S. Yilbas, A.Z. Sahin, Applied Thermal Engineering 50 (2013) 683–692. [11] Q. Zhang, J. He, J. Zhu, S.N. Zhang, X.B. Zhao, T.M. Tritt, Applied Physics Letters 93 (2008) 102109. [12] G.S. Nolas, D. Wang, M. Beekman, Physical Review B. 76 (2007) 235204. [13] T. Dasgupta, C. Stiewe, R. Hassdorf, A.J. Zhou, L. Boettcher, E. Mueller, Physical Review B. 83 (2011) 235207. [14] W. Liu, X.J. Tan, K. Yin, H.J. Liu, X.F. Tang, J. Shi, Q.J. Zhang, C. Uher, Physical Review Letters 108 (2012) 166601. [15] H.F. Wang, W.G. Chu, H. Jin, Computational Materials Science 60 (2012) 224–230. [16] S.M. Choi, K.H. Kim, S.M. Jeong, H.S. Choi, Y.S. Lim, W.S. Seo, I.H. Kim, Journal of Electronic Materials 41 (2012) 1004–1010. [17] H. Ihou-Mouko, C. Mercier, J. Tobola, G. Pont, H. Scherrer, Journal of Alloys and Compounds 509 (2011) 6503–6508. [18] W. Liu, X.J. Tan, K. Yin, H.J. Liu, X.F. Tang, J. Shi, Q.J. Zhang, C. Uher, Physical Review Letters 108 (2012) 1666601. [19] S. Turenne, Th. Clin, D. Vasilevskiy, R.A. Masut, Journal of Electronic Materials 39 (2010) 1926–1933. [20] P. Li, L.L. Cai, P.C. Zhai, X.F. Tang, Q.G. Zhang, M. Niino, Journal of Electronic Materials 39 (2010) 1522–1530. [21] R.Y. Nuwayhid, A. Shihadeh, N. Ghaddar, Energy Conversion and Management 46 (2005) 1631–1643.