Topology optimization of convective heat transfer by the lattice Boltzmann method

Abstract

Topology optimization (TO) is a dependable approach to obtain innovative designs with improved performance. This study presents a TO method based on the adjoint lattice Boltzmann method (ALBM) and the level set method which is developed for both one‐way coupled and two‐way coupled convective heat transfer problems. The adjoint lattice Boltzmann model for fully coupled natural convection system is derived, and the coupled solution strategy is applied in the ALBM. The forward model is validated by the finite element simulation, while the adjoint model and the sensitivity expression is validated by a finite difference check, and the whole TO method is validated by a typical pure fluid flow optimization problem given in the literature. The validated TO method is then applied to enhance the heat transfer of forced convection in a two‐dimensional open chamber, and the Pareto frontier of the bi‐objective optimization is further presented and the effects of the blockages at the inlet and outlet on the overall performance are revealed. Finally, the two‐dimensional natural convection process in a closed cavity is optimized, in which the effective heat transfer coefficient can be increased to 3.96 ∼ 6.11 times of that without the optimized design when the Grashof number ranges from 1.7 to 4.2 × 105. Moreover, effects of Grashof number, porosity limitation and solid thermal diffusivity on the optimization results are analyzed in detail. Physically reasonable designs are obtained for both forced convection and natural convection systems under various parameter settings, demonstrating the effectiveness and robustness of the presented TO method.

Topology optimization using the lattice Boltzmann method for unsteady natural convection problems

“…Hence, the adjoint problem can be solved by a completely explicit scheme without any matrix operations. This method has been applied to pressure drop minimization problems (Yaji et al 2014;Xie et al 2021), convection problems (Yaji et al 2016;Dugast et al 2018;Luo et al 2022), chemical transport problems (Dugast et al 2020), and unsteady flow problems (Chen et al 2017;Yaji et al 2018;Nguyen et al 2020). Besides, there is another way to formulate the adjoint problem using the LBM, in which the original discrete equation-lattice Boltzmann equation-is used for deriving the discrete adjoint equation (Tekitek et al 2006).…”