本研究以均質化的熱流固耦合物理模型為基礎，建立了一套完整的模擬優化技術，利用多孔隙材質中的熱流耦合分析，將高雷諾數與具有鰭片頂端間隙的三維散熱片陣列冷卻流道降階為二維模型，以大幅提升模擬計算效率，同時保留關鍵的三維資訊，包括鰭片高度對鰭片熱傳效率與流場、流阻的影響，以及鰭片基板、鰭片與工作流體之間的溫差以及高度軸向(z軸)上的流速與溫度分佈。此大幅修正改良完成的均質化模型，與拓撲優化結合，針對一組電動車用的IGBT功率控制模組的鰭片陣列冷卻流道，進行模擬優化分析。此模組包含逆變器(Invertor)控制晶片組、發電機(Generator)控制晶片組與冷卻流道三個主要的部件。Invertor段與Generator段的冷卻流道、鰭片陣列幾何尺寸以及晶片熱源排列方式相似，主要差異為鰭片尖端與流道壁面間的間隙高度。三維熱流固耦合模擬結果顯示，由於Invertor及Generator兩段冷卻流道中的鰭片尖端與流道壁面間的間隙高度差異，且Invertor位於冷卻流道的上游，Generator位於下游，在總體流體壓降及熱傳上表現出不同的特徵。Invertor段的由於間隙高度較小，流阻(壓降)較高，但是也因為鰭片陣列區域有較多且溫度較低的冷卻流體進入，熱傳表現較佳。Generator的流道間隙較大，因此流阻低，但也因此造成流入鰭片陣列區的冷卻流體比例較低，進而導致鰭片陣列熱傳效能不佳，晶片溫度明顯較上游的Invertor 高。
為了優化IGBT鰭片陣列冷卻流道的設計，本研究將均質化模型與拓撲優化結合。首先驗證本研究修正的均質化模型，在高雷諾數以及具有鰭片端面與流道底部間隙的條件下，確實可在合理的誤差範圍內計算出模組流體壓降與基板溫度分佈，同時大幅度地將模擬計算時間由原先的4.5小時縮短至不到1分鐘即可完成。此均質化模型的高效率、準確性以及三維速度與溫度分佈的優點，使其可以實際應用於散熱鰭片陣列冷卻模組的設計優化分析。在進行鰭片陣列的優化時，分別針對Invertor與Generator以三種不同的熱傳對流阻優化權重進行分析。結果顯示，在適當的優化權重設定下，可以同時取得熱傳效能提升以及流阻降低的雙贏(win-win)優化設計。由於IGBT模組的體積與晶片電路佈置(layout)限制，即使在偏向增強熱傳效能的優化權重下，優化結果也以流體壓降的改善較為明顯。同時，由於原始設計中，在主要熱源區的鰭片效率尚未達到上限，因此模組的熱傳優化趨勢呈現建議加長熱源區的鰭片。然而Invertor段的鰭片增長設計空間僅有0.5 mm，Generator段的設計空間則有3 mm。所以本研究優先選擇Generator段，開放鰭片長度可以在容許空間範圍內雙向增減。此外，為了加速優化分析，本研究嘗試以設計者的思維介入，根據初步模擬所得到的模組熱傳與流阻表現，提出「中央快速通道」與「川流快速通道」兩種改良版本的鰭片陣列冷卻流道設計，經過均質化模型掃頻分析各種快速通道組合的熱表現因子(Thermal Performance Factor)，決定最佳的初始流道設計，再進入第二階段的鰭片拓撲優化。以Generator段的模擬結果為例，原始設計的流體壓降與基板最大溫度分別為1.94 kPa與82.2℃，將之進行均質化拓撲優化，在整體性能最佳的設計下，壓降與基板最高溫度分別改善至0.99 kPa與78.1℃。以川流快速通道模型最為初始設計進行拓撲優化，在偏向熱傳增強的權重設定下，優化設計的壓降與基板最高溫度分別為2.39 kPa與76.9℃。
最後，本研究將均質化模擬與優化技術嘗試應用於另外一個散熱系統優化重要的設計分析主題：接觸與介面熱阻的分析。系統中的接觸與介面熱阻分佈，通常難以量測，但卻對於熱傳網路有關鍵性的影響。透過與實驗數據的比對，利用均質化模擬的高效率與保留三維熱傳資訊的特性，快速取得一個熱傳系統中的介面接觸熱阻分佈。經由穩態與暫態模擬和實驗量測所得晶片溫升的比對，驗證此介面接觸熱阻分佈分析技術具備良好的有效性與準確性。

In this study, an effective and efficient thermal-fluid-structure modeling and optimization technology was successfully developed based on a modified homogenized model. This homogenized simulation and optimization technique was used to rapidly evaluate and modify a 3D pin-fin heat sink array in a cooling channel. The core of the homogenized model is a coupled thermal-fluid-structure analysis of heat flow in porous materials using integral-average values of velocity and temperature profiles in the z direction. In this way, the pin-fin array flow channel is reduced to a 2D model, which greatly improves the simulation calculation efficiency while retaining key 3D information, including the effect of the fin height on the heat transfer efficiency of the fin, the flow field, and the flow resistance, as well as the substrate. The temperature differences between the fluid and the pin fin is included, i.e. the pin fin and the surrounding coolant is considered at non-thermally equilibrium, which is more realistic comparing to the general thermal-equilibrium assumption for convective heat transfer in porous media. The flow velocity and temperature distribution along the height (z-axis) of the pin-fin and channel are imbedded in the homogenized model. The greatly revised homogenized model is combined with topology optimization to optimize a pin-fin array cooling channel of an Insulated Gate Bipolar Transistor (IGBT) power control module that is used for electric vehicles. This module includes three main components: Invertor control chip assembly, Generator control chip assembly, and cooling channel with pin-fin array. The original design parameters for the Invertor and Generator sections are similar except the gap between the fin tips and the channel wall. Due to this gap height difference and fact that the Invertor is located upstream of the cooling channel to the Generator, the overall flow pressure drop and the heat transfer performance showed different characteristics. The Invertor section has a higher flow resistance (pressure drop) due to the smaller gap height. However, because more amount of coolant enters the pin-fin array region, the heat transfer performance in the Invertor section is better than that in the Generator section. The generator has a larger flow channel gap, so the flow resistance is low, but the proportion of coolant flowing into the pin-fin array region is also low, resulting in poor heat transfer performance of the pin-fin array module, and the chip temperature is significantly higher than that of the upstream Invertor. Therefore, it is essential to optimized this cooling module to improve and ensure good thermal management of the power module. To reach this goal, first, the homogenized model from the literature was revised for the conditions of high Reynolds number and the gap between the pin-fin tip to the wall of the channel. The revised homogenized model module was validated with the 3D simulation results and experimental data. The results showed that the fluid pressure drop, the lateral temperature distribution of the fluid, pin-fin, and the substrate can be obtained with a reasonably good accuracy. More importantly, the homogenized model significantly reduces the simulation time from 4.5 hours to less than 1 minute. The high efficiency, accuracy, and the advantages of the preserved three-dimensional velocity and temperature distribution characteristics of this homogenized model make it practical for the design optimization analysis. During optimizing the pin-fin array, three different heat transfer versus flow resistance optimization weights were used for the analysis of the Invertor and the Generator respectively. The results show that, with appropriate optimization weight settings, a win-win optimization design can be achieved simultaneously with improved heat transfer performance and reduced flow resistance. Due to the limitation of the size of the IGBT module and the layout of the chip circuit, even under the optimization weight that favors enhancing the heat transfer performance, the optimization result is more obvious in the improvement of the fluid pressure drop. At the same time, since the efficiency of the fins in the main heat source region has not yet reached the upper limit in the original design, the heat transfer optimization trend of the module shows that it is recommended to lengthen the fins. However, the design space for the fin height of the Invertor section is only 0.5 mm, and the design space of the Generator section is 3 mm. Therefore, the Generator section was selected to be optimized first in this study. In addition, in order to speed up the optimization analysis, two improved designs of the cooling channel with "Central Avenue" and "Cross-flow Paths" are proposed for replacing the original standard design of the pin-fin array channel. In this regard, the thermal performance factor (TPF) was analyzed by sweeping of various fast track combinations by using the homogenized model. The combination of the fast track with the best TPF was then determined and used for the second stage topology optimization of the pin-fin array. Taking the results of the Generator section as an example, the original design of the fluid pressure drop and the maximum temperature of the substrate are 1.94 kPa and 82.2°C, respectively. The homogenized-topology optimized design carried out directly from the original design showed the pressure drop and the maximum temperature of the substrate are improved to 0.99 kPa and 78.1℃, respectively. The homogenized-topological optimization was also carried out for the fast-track design with the best performance model as the initial design. Under the weight setting favoring heat transfer enhancement, the pressure drop and the maximum temperature of the substrate in the optimized design are 2.39 kPa and 76.9 °C, respectively.
Finally, the homogenized topological optimization technique was applied on the analysis of contact and interfacial thermal resistances, which has a critical impact on the heat transfer network. Through the comparison with the experimental data, the homogenized topological simulation was used to quickly obtain the interfacial contact thermal resistance distribution in this IGBT heat transfer system. Through the comparison of the chip temperature rise obtained by steady-state and transient simulation and experimental measurement, it is verified that this interface contact thermal resistance distribution analysis technology has good accuracy.

[1] S. Ozguc, L. Pan, J. A. Weibel, “Topology optimization of microchannel heat sinks using a homogenization approach”, International Journal of Heat and Mass Transfer, vol. 169, 120896, 2021.
[2] T. Van Oevelen, “Optimal heat sink design for liquid cooling of electronics”, Katholieke Universiteit Leuven, Ph.D. dissertation, 2014.
[3] J. Kim, D. H. Kim, W. Lee, S. Lee, J. Hong, “A novel interconnect design for thermal management of a commercial-scale planar solid oxide fuel cell stack”, Energy Conversion and Management, vol. 246, 114682, 2021.
[4] L. Jin, J. Tian, S. Gao, P. Xie, M. Akbarzadeh, T. Kalogiannis, M. Berecibar, Y. Lan, D. Hu, Y. Ding, G. Qiao,, "A novel hybrid thermal management approach towards high-voltage battery pack for electric vehicles.", Energy Conversion and Management, vol. 247, 114676, 2021.
[5] M. Shi, X. Yu, Y. Tan, X. Wang, X. Zhang, J. Li, “Thermal performance of insulated gate bipolar transistor module using microchannel cooling base plate”, Applied Thermal Engineering, vol. 201, 117718, 2022.
[6] M. Ehrhardt, "An introduction to fluid-porous interface coupling", Progress in Computational Physics, vol. 2, pp. 3-12, 2010.
[7] G. S. Beavers, D. D. Joseph, “Boundary conditions at a naturally permeable wall”, Journal of Fluid Mechanics, vol. 30, pp. 197-207, 1967.
[8] P. G. Saffman, “On the boundary condition at the interface of a porous medium”, Study in Applied Mathematics, vol. 50, pp. 93-101, 1971.
[9] D. Martínez-Maradiaga, A. Damonte, A. Manzo, J. H. K. Haertel, K. Engelbrecht, “Design and testing of topology optimized heat sinks for a tablet”, International Journal of Heat and Mass Transfer. vol. 142, 118429, 2019.
[10] J. C. Ward, “Turbulent flow in porous media”, Journal of the Hydraulics Division, vol. 90, pp. 1-2, 1964.
[11] P. H. Forchheimer, “Wasserbewegung durch boden”, Zeitschrift des Vereins Deutscher Ingenieure, vol. 45, pp. 1782-1788, 1901.
[12] A. A. Zukauskas, “Convective heat transfer in cross flow”, in S. Kakac, R. K. Shah, and W. Aung, eds., Handbook of Single-Phase Convective Heat Transfer, Chapter 6, Wiley, New York, 1987.
[13] R. Yang, R. Xiong, W. Shen, X. Lin, “Extreme learning machine-based thermal model for lithium-ion batteries of electric vehicles under external short circuit”, Engineering, vol. 7, p.395–405, 2021.
[14] T. M. Liou, C. C. Chen, C. S. Wang, E. S. Wang, “Thermal-fluidic correlations for turbulent flow in a serpentine heat exchanger with novel wing-shaped turbulators”, International Journal of Heat and Mass Transfer, vol. 160, 120220, 2020.
[15] C. Chen, J. T. Teng, C. H. Cheng, S. Jin, S. Huang, C. Liu, M. T. Lee, H. H. Pan, R. Greif, “A study on fluid flow and heat transfer in rectangular microchannels with various longitudinal vortex generator”, International Journal of Heat and Mass Transfer, vol. 69, pp. 203-214, 2014.
[16] J. Ma, Y. Sun, S. Zhang, J. Li, S. Li, “Experimental study on the performance of vehicle integrated thermal management system for pure electric vehicles”, Energy Conversion and Management, vol. 253, 115183, 2022.
[17] J. Lee, S. Ki, D. Seo, J. Kim, Y. Nam, “Liquid cooling module incorporating a metal foam and fin hybrid structure for high power insulated gate bipolar transistors (IGBT)”, Applied Thermal Engineering, vol. 173, 115230, 2020.
[18] IEA, “Global Electric Vehicle Outlook 2022”, 2022.
[19] C. H. Chen, C. C. Wang, “A novel trapezoid fin pattern applicable for air-cooled heat sink”, Heat and Madd Transfer, vol. 51, pp. 1631-1637, 2015.
[20] B. Wang, L. Zhou, Y. Zhang, K. Wang, X. Du and P. Sun, "Active Junction Temperature Control of IGBT Based on Adjusting the Turn-off Trajectory," in IEEE Transactions on Power Electronics, vol. 33, no. 7, pp. 5811-5823, 2018.
[21] L. L. Li, X. B. Zhang, M. L. Tseng, M. Lim, Y. Han, “Sustainable energy saving: A junction temperature numerical calculation method for power insulated gate bipolar transistor module”, Journal of Cleaner Production, vol. 185, pp. 198-210, 2018.
[22] L. L. Li, J. D. Chang, K. J. Wu, M. L. Tseng, Z. G. Li, “Assessing electric vehicle inverter to reduce energy consumption: using insulated gate bipolar transistor module to prevent the power loss and junction temperature”, Journal of Cleaner Production, vol. 224, pp. 60-71, 2019.
[23] S. Yang, A. Bryant, P. Mawby, D. Xiang, L. Ran, P. Tavner, ”An industry-based survey of reliability in power electronic converters”, IEEE Transactions on Industry Applications, pp. 1441-1451, 2011.
[24] U. Choi, F. Blaabjerg, K. Lee, “Study and handling methods of power IGBT module failures in power electronic converter systems”, IEEE Transactions on Power Electronics, vol. 30, pp. 2517-2533, 2015.
[25] J. H. Ryu, D. H. Choi, S. J. Kim, “Three-dimensional numerical optimization of a manifold microchannel heat sink”, International Journal of Heat and Mass Transfer, vol. 46, pp. 1553-1562, 2003.
[26] T. Y. Lee, “Design optimization of an integrated liquid-cooled IGBT power module using CFD technique”, IEEE Transactions on Components and Packaging Technologies, vol. 23, pp. 55-60, 2000.
[27] A. Bhunia, C. L. Chen, “Jet impingement cooling of an inverter module in the harsh environment of a hybrid vehicle”, ASME Summer Heat Transfer Conference, San Francisco, United States, pp.561-567, 2005.
[28] A. S. Bahman, F. Blaabjerg, “Optimization tool for direct water cooling system of high power IGBT modules”, 2016 18th European Conference on Power Electronics and Appllication, Karlsruhe, Germany, pp. 1-10, 2016.
[29] M. Wong, I. Owen, C. J. Sutcliffe, A. Puri, “Convective heat transfer and pressure losses across novel heat sinks fabricated by selective laser melting”, International Journal of Heat and Mass Transfer, vol. 52, pp. 281-288, 2009.
[30] S. Zeng, B. Kanargi, P. S. Lee, “Experimental and numerical investigation of a mini channel forced air heat sink designed by topology optimized”, International Journal of Heat and Mass Transfer, vol. 121, pp. 663-679, 2018.