Multifidelity Topology Design for Turbulent Heat Transfer Problems Using a Darcy Flow Model Incorporating Pseudo-Boundary Layer

Abstract Topology optimization (TO) for turbulent heat transfer problems is a significant challenge due to the complexity of the physical model, especially near-wall flow modeling. To address this challenge, the Darcy flow model has been used as a low-fidelity (LF) model. It assumes a linear relationship between the pressure gradient and velocity but neglects key physical effects. Therefore, there is no guarantee that optimized designs achieve the desired performance. To overcome this limitation, we propose a modified Darcy flow model incorporating a pseudo-boundary layer, which introduces an artificial near-wall velocity gradient to mimic viscous effects. By integrating artificial boundary layer effects, the proposed flow model suppresses the formation of inappropriate optimized structures, such as excessive branching and narrow flow channels, thereby facilitating the generation of high-performance design solutions even under turbulent conditions. The optimization framework is configured based on the multifidelity topology design (MFTD) using the proposed flow model in its LF optimization. The LF optimization performs TO under various pseudo-boundary layer thickness conditions and generates diverse design solutions. Subsequently, high-fidelity (HF) evaluation selects the best design solution based on turbulence model-based evaluations, identifying practically effective designs. The effectiveness of the proposed approach is demonstrated through TO for 2D and 3D turbulent heat transfer problems. The results highlight that incorporating the pseudo-boundary layer into the Darcy flow model enables the generation of effective design solutions for turbulent heat transfer problems.