Mechanisms of turbulence effects on sensitivity analysis and optimization performance in fluid-thermal coupled topology optimization

Topology optimization has become a promising technique for the design of heat exchange devices. However, the application of topology optimization in turbulence flow coupled with the heat transfer process remains scarce mainly hindered by the critical step of sensitivity analysis. In this study, a continuous adjoint-based sensitivity analysis framework is developed for multi-objective topology optimization problems, and the information about turbulence effects on flow and heat transfer processes is incorporated into sensitivity analysis results by differentiating the turbulence viscosity within the diffusion terms. The developed framework is then applied to two topology optimization problems. The results reveal the mechanism of turbulence effects on sensitivity deviations, which are observed in both low and high Reynolds number flow regimes. Through the analysis of the backpropagation pathway of the thermal objective function gradient, it is revealed that the differentiation of the convective heat transfer term plays a dominant role in driving the formation of multi-branch cooling structures. Compared to the frozen turbulence assumption, the optimized heat sink structure considering turbulence effects demonstrates improved performance, with reductions of 3.84 % in flow losses, 2.61 % in mean temperature, and 3.34 % in maximum temperature rise.