An efficient topology optimization method for steady gas flows in all flow regimes

TL;DR

This paper introduces a unified, efficient topology optimization method for steady gas flows applicable across all flow regimes, from continuum to free-molecular, using a modified fictitious porosity model within gas-kinetic theory.

Contribution

It develops a novel fictitious porosity model and numerical schemes that work effectively across all flow regimes, enabling comprehensive topology optimization of gas flow systems.

Findings

Successfully optimized airfoil designs across various flow regimes.

Demonstrated high efficiency and accuracy of the method.

Validated the approach with multiple flow condition cases.

Abstract

An efficient topology optimization method applicable to both continuum and rarefied gas flows is proposed in the framework of gas-kinetic theory. The areas of gas and solid are marked by the material density, based on which a fictitious porosity model is used to reflect the effect of the solid on the gas and mimic the diffuse boundary condition on the gas-solid interface. The formula of this fictitious porosity model is modified to make the model work well in all flow regimes, i.e., from the continuum to free-molecular flow regimes. To find the optimized material density, a gradient-based optimizer is adopted and the design sensitivity is obtained by the continuous adjoint method. To solve the primal kinetic equation and the corresponding adjoint equation, the numerical schemes efficient and accurate in all flow regimes are constructed. Several airfoil optimization problems are solved to demonstrate the good performance and high efficiency of the present topology optimization method, covering the flow conditions from continuum to rarefied, and from subsonic to supersonic.