Topology Optimization Method Applying Wall Law on Immersed Boundary in an Incompressible Viscous Flow

Abstract

This paper describes a level set-based topology optimization method for steady state Navier-Stokes flow. In this method, turbulence flow is also considered during optimization processes. For steady state fluid mechanics, RANS (Reynolds Averaged Navier-Stokes) model is one of famous model for analyzing turbulence flow and is applied to solve fluid field such as velocity and pressure in proposed method. It is also important for turbulence flow to consider wall law in boundary of optmized structure. We utilize immersed boundary method to treat wall low during optimization process. For Sensitivity analysis, topological sensitivity is applied in this method. The level set function updating scheme uses a reaction-dffusion equation. As a result, we can solve optimization problem with high Reynolds number flow. Example is shown in this paper. The effectiveness of this method is discussed.