Topology optimization method with finite elements based on the k-epsilon turbulence model

Abstract

A new finite element (FE) based topology optimization (TO) for turbulent flow was developed using the k - epsilon turbulent model, which is one of the Reynolds-Averaged Navier-Stokes (RANS) equations. Despite many innovative works on the subject of fluidic TO, it remains important to consider the impact of turbulent flow in TO. To consider the effect of complex turbulent fluid motion, this study considered the k - epsilon turbulent finite element model. To conduct a successful TO, the modification of the k - epsilon turbulent model to account for the topology evolutions during an optimization process is important. Correspondingly, to account for these effects, we proposed the addition of penalization terms to the original k - epsilon turbulent model. To validate the present approach and the effect of turbulent flow on optimized layouts, various two-dimensional designs were optimized by minimizing the turbulent kinetic or the turbulent dissipation energies. Numerical optimization results showed that it is possible to conduct the topology optimization for turbulent flow.