Topology optimization of microstructures considering multi-scale thermo-fluid problems

Abstract

Thermo-fluid multi-scale topology optimization problems are typically solved using the finite element method (FEM); however, they inherently involve high computational cost and large memory consumption. Moreover, accurate resolution of thermo-fluid phenomena requires high-resolution discretization, which further increases the computational burden. This study presents a multi-scale topology optimization framework for thermo-fluid problems based on computational homogenization. Unlike conventional approaches that assume a predefined microstructure or optimize only its geometric parameters, the proposed method determines the microstructural topology to enhance macroscopic performance. The objective function is defined as the convective heat flux to maximize heat exchange between the fluid and solid phases, while pressure loss is imposed as a constraint. To reduce the computational cost of microscopic analyses, the homogenized thermal conductivity and permeability tensors of the microstructure are efficiently evaluated using a fast Fourier transform (FFT)-based computational homogenization method. Compared with FEM-based microscopic solvers, the FFT-based approach offers improved memory efficiency and computational speed, particularly for high-resolution discretizations. At the macroscopic scale, the thermal advection–diffusion equation and Darcy’s law are solved using the FEM, and the sensitivities of the objective and constraint functions are derived using the continuous adjoint method. The effectiveness and robustness of the proposed framework are demonstrated through numerical examples, confirming its potential as an efficient and accurate approach for multi-scale thermo-fluid topology optimization.