Topology Optimization of Hydrodynamic Body Shape for Drag Reduction in Low Reynolds Number Based on Variable Density Method

Abstract

This paper presents a variable density topology optimization method to numerically investigate the optimal drag-reduction shape of objects in the two-dimensional and three-dimensional flows with steady incompressible external flow conditions, taking into account material volume constraints. By introducing the porous media model, the artificial Darcy friction is added to the Navier-Stokes equation to characterize the influence of materials on the fluid. Material density is applied to implement material interpolation. By transforming the boundary integral form of viscous dissipative expression of drag into the volume integral of artificial Darcy friction and convection term, we solve the problem of drag expression on the implicit interface corresponding to the structure. The continuous adjoint method is used to analyze gradient information for iteratively solving topology optimization problems. We obtain the relevant topology optimization structures of the minimum drag shapes, investigate the effect of the low Reynolds number on the drag force corresponding to two objective functions and discuss the mechanism of drag reduction by a hydrodynamic body shape.

Keywords

• variable density method
• topology optimization
• drag reduction
• porous medium model
• adjoint analysis