Validity of the quasi-2D optimal variable density lattice for effective liquid cooling based on Darcy–Forchheimer theory

Abstract

In this study, we investigate the validity of variable-lattice-density optimization based on the Darcy–Forchheimer theory for an effective liquid-cooling quasi-2D structure including experimental verification. The unit lattice features a simple cylinder shape, and its size distribution is optimized. Considering its anisotropy, we regard Darcy’s permeability, Forchheimer’s drag coefficient, and the effective thermal conductivity as tensors and calculate these effective properties using the representative-volume-element method. Two types of optimizations are performed, i.e., minimizing the surface temperature and maximizing the flow rate, using the gradient method. We examine the results using three methods: an approximate simulation based on the Brinkman–Forchheimer equation, a detailed simulation based on the Navier–Stokes equation, and an experiment. We focus primarily on the exact measurement of planar temperature distribution using thermocouples. The proposed methodology exhibits high accuracy in regions with a certain flow level, although the error can be significant in low-flow regions.