Simultaneous topology optimization of two hydraulically interconnected porous flow layers in cold plates

Abstract

Cold plate topology optimization is a focus area of research in thermal management, often approached with simplified two-dimensional models to maintain the low computational costs needed for iterative design. However, embracing higher dimensionality in optimization can yield significant performance enhancements, as exemplified by cold plate architectures like manifolded microchannels. In this study, we present a novel 2.5D topology optimization framework tailored to two-flow-layer manifold cold plates, leveraging the homogenization approach to topology optimization. Under this framework, multiple stacked flow layers are simultaneously optimized within a 2D stack while considering local mass and energy exchange between them, enabling the design of intricate 3D flow geometries with the computational efficiency of 2D simulations. The mass and energy exchange between the layers is governed by the optimizable inter-layer flow resistance. This approach is demonstrated for a test case with two coupled flow layers between enclosing solid substrates heated from their external surfaces. The homogenization approach is used to define the local design variables in these layers based on the physical porosity of microstructures (viz., square pin-fins) and the inter-layer coupling within computational cells. A multi-objective cost function, encompassing total pressure drop and thermal resistance, guides the optimization of the microstructure distribution in each layer, resulting in a Pareto front of designs illustrating the balance between these two competing objectives. Full-scale, high-fidelity 3D flow simulations were performed on the topology-optimized two-flow-layer cold plate to validate results from the homogenized 2D simulations. The calculated flow fields showed good agreement between low-cost 2D simulations and high-fidelity 3D simulations, demonstrating the accuracy of the approach. The study provides valuable insights into the topology optimization of multi-layer cold plates, highlighting the potential for enhanced performance via higher dimensionality, as well as manufacturability through the homogenization approach.