Topology optimization for turbulent flow with Spalart–Allmaras model

Abstract

In this research, a new finite element (FE) based topology optimization (TO) for turbulent flow was developed using the Spalart–Allmaras (S–A) equation, which is one of the Reynolds-Averaged Navier–Stokes (RANS) equations. Despite many innovative works on the subject of fluidic TO, it is rare to consider the influence of turbulent flow in TO. To consider the effect of complex turbulent fluid motion, this research considered the S–A model developed mainly for aerodynamic flows. For a successful TO, one primary issue is modification of the S–A turbulent model to account for topological evolution during the optimization process. To address this issue, we proposed the addition of penalization terms to the original governing equations. To show the validity of the present approach and the effect of turbulent flow on optimal layouts, some two dimensional benchmark designs studied for laminar flow were reconsidered. By considering the effect of turbulent flow, the eddy viscosity values were increased at some local regions due to the Boussinesq hypothesis, and naturally optimal layouts affected by the spatially varying viscosity were obtained in turbulent flow. It was also found that the balance between the inertia force and the viscosity force plays an important role in topological designs.