On the Calculation of the Brinkman Penalization Term in Density-Based Topology Optimization of Fluid-Dependent Problems

Abstract

In topology optimization of fluid-dependent problems, there is a need to interpolate within the design domain between fluid and solid in a continuous fashion. In density-based methods, the concept of inverse permeability as of a volumetric force is utilized to enforce zero fluid velocity in non-fluid regions. This volumetric force consists of a scalar term multiplied by fluid velocity. This scalar term takes a value between two limits as determined by a convex interpolation function. The maximum inverse permeability limit is typically chosen through a trial and error analysis of the initial form of the optimization problem; such that the fields resolved resemble those obtained through an analysis of a pure fluid domain with a body-fitted mesh. In this work, we investigate the dependency of the maximum inverse permeability limit on mesh size and flow conditions through analyzing the Navier-Stokes equation in its strong and discretized finite element forms.