Topology optimization of a pseudo 3D thermofluid heat sink model

Abstract

This paper investigates the application of density-based topology optimization to the design of air-cooled forced convection heat sinks. To reduce the computational burden that is associated with a full 3D optimization, a pseudo 3D optimization model comprising a 2D modeled conducting metal base layer and a thermally coupled 2D modeled thermofluid design layer is used. Symmetry conditions perpendicular to the flow direction are applied to generate periodic heat sink designs. The optimization objective is to minimize the heat sink heat transfer resistance for a fixed pressure drop over the heat sink and a fixed heat production rate in the base plate. Optimized designs are presented and the resulting fin geometry is discussed from a thermal engineering point of view and compared to fin shapes resulting from a pressure drop minimization objective. Parametric studies are conducted to analyze the influence of the pressure drop on the heat sink heat transfer resistance. To quantify the influence of the assumptions made in the pseudo 3D optimization model, validation simulations with a body-fitted mesh in 2D and 3D are conducted. A good agreement between optimization model and validation simulations is found, confirming the physical validity of the utilized optimization model. Two topology optimized designs are exemplarily benchmarked against a size optimized parallel fin heat sink and an up to 13.6% lower thermal resistance is found to be realized by the topology optimization.

Topology optimization of heat sinks for instantaneous chip cooling using a transient pseudo-3D thermofluid model

“…As disrobed in Ref. [41], one part of the heat production is absorbed by the fins in the channel layer. The other part of heat production causes a rise of temperature of the base plate.…”

“…Obviously, the value of the heat convection coefficient in the pseudo-3D model has a great influence on the accuracy of the model, which means that it will determine whether the pseudo-3D model could replace the full 3D model accurately during the simulation and optimization procedure. [41]. However, Zeng et al provided detailed derivation processes in [42], which is used as a reference in this work.…”

“…The choice of 4 initial designs in Fig. 12 relies on several reasons: Firstly, the comparison of uniform and non-uniform density distribution need to be made; Secondly, because the design domain and the model is axisymmetric, the density layouts selected in this section are axisymmetric as well; Lastly, the layout of rounds that represent cylinder heat sink fins in full 3D model, in Initial design 2-4 refers to the layout of initial designs of model a in [48] to compare the performance of different layout directions and fins number.…”

“…Therefore, many researchers are exploring simplified 2D approximations of the full 3D problems, giving a cheaper computational cost with acceptable. A pseudo-3D thermofluid model was first proposed by Haertel et al [41] coupling a solid thermal base layer to a fluid-solid cross-sectional flow layer.…”

A “poor man’s” approach to topology optimization of natural convection problems

“…Topology optimization has been extended to passive and reactive transport problems (Thellner, 2005;Andreasen et al, 2009;Okkels and Bruus, 2007). Topology optimization of conjugate heat transfer problems is an active research area, starting with the work by Dede (2009) and Yoon (2010a), and with many works being published the last few years (Koga et al, 2013;Marck et al, 2013;Haertel et al, 2015;Yaji et al, 2016;Laniewski-Wollk and Rokicki, 2016;Haertel and Nellis, 2017;Zeng et al, 2018;Haertel et al, 2018;Dugast et al, 2018;Subramaniam et al, 2018;Yaji et al, 2018;Dilgen et al, 2018).…”