Topology optimization for shallow-flow channel design using depth-integrated model

A topology optimization method is proposed for the design of shallow-flow channels based on quasi-three-dimensional flow models of laminar and turbulent flows. The models for laminar flow and turbulent flow are derived from the Navier– Stokes equations and the Reynolds-Averaged Navier–Stokes (RANS) equations, respectively, by integrating along the direction of channel thickness. The thickness is employed as the design variable in the topology optimization. The design variables are updated using a time-dependent diffusion equation with a design sensitivity which is calculated by a discrete adjoint approach. Numerical examples for minimizing dissipation energy or variance of flow velocity magnitude using the topology optimization demonstrates that the proposed method is capable of finding optimal solutions that satisfy the KKT conditions. In the former example, the design domain was clearly divided into domains where the thickness was either near the upper limit or near the lower limit. However, in the latter example, the thickness was at an intermediate level in almost the whole the design domain. The distribution of the thickness varied depending on the Reynolds number in both examples.