Thermofluid modeling for concurrent size-topology optimization of heat sinks for planar motors
ZHAO Jiaqi, ZHANG Ming, ZHU Yu, CHENG Rong, LI Xin, WANG Leijie, HU Chuxiong
Beijing Key Laboratory of Precision/Ultra-precision Manufacturing Equipments and Control, State Key Laboratory of Tribology, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China
Abstract：The thermal-hydraulics of water-cooled heat sinks for planar motors were analyzed using a thermofluid model of a heat sink to concurrently optimize the heat sink size and topology. The three-layer thermofluid model of the heat sink included the coupled flow and heat transfer effects between the cover plates and the fluid-solid mixing channel including the influence of the flow channel thickness on the thermal-hydraulics. The model used a porosity model to describe the channel topology and a continuous-adjoint structural optimization model for the geometric variables related to the channel topology and thickness in a concurrent size-topology optimization scheme. Various numerical examples show the accuracy and efficiency of the three-layer thermofluid model and the size-topology optimization scheme. The three-layer model uses 10% less calculational time than full 3D models while still accurately predicting the temperature distribution. The optimized heat sinks have unique topologies with up to 30.82% better heat transfer than baseline designs. This concurrent approach is efficient and obtains designs that are competitive with discrete optimization approach results.
[1] MOORE A L, SHI L. Emerging challenges and materials for thermal management of electronics[J]. Materials Today, 2014, 17(4):163-174. [2] 袁丁. 多自由度无铁芯永磁式平面电机的建模与设计方法研究[D]. 北京:清华大学, 2019.YUAN D. Modeling and design method for multi-DOF ironless permanent magnet planar motor[D]. Beijing:Tsinghua University, 2019. (in Chinese) [3] 曹家勇, 朱煜, 汪劲松, 等. 平面电动机设计、控制与应用技术综述[J]. 电工技术学报, 2005, 20(4):1-8.CAO J Y, ZHU Y, WANG J S, et al. Survey of the state of the art in planar motor technology[J]. Transactions of China Electrotechnical Society, 2005, 20(4):1-8. (in Chinese) [4] ZHANG M, XU Q M, CHENG R, et al. Radiator optimization design for planar motors based on parametric components[J]. Journal of Beijing Institute of Technology, 2020, 29(2):222-231. [5] AHMED H E, SALMAN B H, KHERBEET A S, et al. Optimization of thermal design of heat sinks:A review[J]. International Journal of Heat and Mass Transfer, 2018, 118:129-153. [6] WANG L K, MANGLIK R M, SUNDÉN B. Plate heat exchangers:Design, applications and performance[M]. Boston:WIT Press, 2007. [7] DEDE E M. Multiphysics topology optimization of heat transfer and fluid flow systems[C]//Proceedings of the COMSOL Conference. Boston, USA:COMSOL, 2009. [8] ALEXANDERSEN J, ANDREASEN C S. A review of topology optimisation for fluid-based problems[J]. Fluids, 2020, 5(1):29. [9] DBOUK T. A review about the engineering design of optimal heat transfer systems using topology optimization[J]. Applied Thermal Engineering, 2017, 112:841-854. [10] HAERTEL J H K, ENGELBRECHT K, LAZAROV B S, et al. Topology optimization of a pseudo 3D thermofluid heat sink model[J]. International Journal of Heat and Mass Transfer, 2018, 121:1073-1088. [11] ZENG T, WANG H, YANG M Z, et al. Topology optimization of heat sinks for instantaneous chip cooling using a transient pseudo-3D thermofluid model[J]. International Journal of Heat and Mass Transfer, 2020, 154:119681. [12] YAN S N, WANG F W, HONG J, et al. Topology optimization of microchannel heat sinks using a two-layer model[J]. International Journal of Heat and Mass Transfer, 2019, 143:118462. [13] ZENG S, KANARGI B, LEE P S. Experimental and numerical investigation of a mini channel forced air heat sink designed by topology optimization[J]. International Journal of Heat and Mass Transfer, 2018, 121:663-679. [14] ZHAO J Q, ZHANG M, ZHU Y, et al. Topology optimization of planar cooling channels using a three-layer thermofluid model in fully developed laminar flow problems[J]. Structural and Multidisciplinary Optimization, 2021, 63(6):2789-2809. [15] ZHAO J Q, ZHANG M, ZHU Y, et al. Concurrent optimization of the internal flow channel, inlets, and outlets in forced convection heat sinks[J]. Structural and Multidisciplinary Optimization, 2021, 63(1):121-136. [16] ZHAO J Q, ZHANG M, ZHU Y, et al. Concurrent optimization of additive manufacturing fabricated lattice structures for natural frequencies[J]. International Journal of Mechanical Sciences, 2019, 163:105153. [17] WELTY J R, WICKS C E, WILSON R E, et al. Fundamentals of momentum, heat, and mass transfer[M]. 5th ed. Hoboken:John Wiley & Sons, 2008. [18] LAZAROV B S, SIGMUND O. Filters in topology optimization based on Helmholtz-type differential equations[J]. International Journal for Numerical Methods in Engineering, 2011, 86(6):765-781. [19] WANG F W, LAZAROV B S, SIGMUND O. On projection methods, convergence and robust formulations in topology optimization[J]. Structural and Multidisciplinary Optimization, 2011, 43(6):767-784. [20] SVANBERG K. The method of moving asymptotes-a new method for structural optimization[J]. International Journal for Numerical Methods in Engineering, 1987, 24(2):359-373.
2022, Vol. 62 
