Three-dimensional topology optimization of natural convection using double multiple-relaxation-time lattice Boltzmann method

Abstract

A topology optimization method based on the double multiple-relaxation-time (MRT) lattice Boltzmann method and level-set method is developed for 3D natural convection heat transfer with the adjoint double MRT model rigorously derived. The double MRT model with better numerical stability enables the optimization at higher Grashof number (Gr) and larger thermal conductivity ratio. Besides, the model is well-suited for large-scale 3D optimization problems since the ideal linear scaling can be nearly achieved for the whole optimization solution. The forward and optimization models are validated individually by typical problems with relative errors as 2 % and 5 % respectively. Physically reasonable heat sink designs in the shape of “thermal tree” or “thermal flower” are obtained, which can outperform the convectional pin fin and rectangular straight fin with at least 17.8 % lower temperature with Gr ranging from 5.9 × 103 to 1.6 × 106, mainly owing to better organization of fluid flow. Parametric studies find that increasing Gr or decreasing the thermal conductivity ratio results in more contracted heat sinks, while decreasing the penalty factor or increasing the spatial resolution leads to smoother design surface. Anisotropic regularization provides more flexibility in shape control, and adding more solid will enrich the structural details.