Topology optimization of heat sink in turbulent natural convection using k-ω turbulent model

The geometric structure of two-dimensional (2-D) heat sinks cooled by turbulent natural convection is optimized using a density-based topology optimization approach. The governing equations are the coupled equations of the k-ω turbulent equation, which is one type of the Reynolds-Averaged Navier-Stokes (RANS) equations, and the thermal convection-diffusion equation based on the Bousinessq approximation. In order to facilitate topology optimization, we make some modifications to the original governing equations to control the fluid/solid distribution by introducing a material density as the design variable. Specifically, several penalization terms are added to the original k-ω turbulent model for immersing the solid material, and the thermophysical properties are interpolated to obtain a generalized thermal equation suitable for both the fluid and solid materials. During the optimization process, the design variable is updated according to the gradient information obtained through adjoint-based sensitivity analysis. In numerical examples, the effects of the Grashof number and the solid thermal conductivity on optimal configurations are, respectively, investigated for two types of heat sinks. The numerical results indicate that the Grashof numbers and the solid thermal conductivity can significantly affect the optimal results; the flow channels will become narrower to accommodate the flow and heat transfer conditions with the increase of the Grashof number; and the design characteristics and heat transfer performance vary greatly for increasing the solid thermal conductivity when the conductivity is low, while at the case of high conductivity, this variation slows down obviously.