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

• Published in: Computer methods in applied mechanics and engineering 2020-04, Vol.361, p.112784, Article 112784
• Main Author: Yoon, Gil Ho
• Format: Article
• Language: English
• Subjects: [formula omitted] turbulent model; Computational fluid dynamics; Finite element method; Fluid flow; K-epsilon turbulence model; Mathematical models; Optimization; RANS model; Topology optimization; Turbulence models; Turbulent flow
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2019.112784

A new finite element (FE) based topology optimization (TO) for turbulent flow was developed using the k−ε 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−ε turbulent finite element model. To conduct a successful TO, the modification of the k−ε 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−ε 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. •Structures considering turbulent flow are optimized.•The k−ε equations are modified for topology optimization.•The k−ε turbulent model is solved by the finite element method.•The turbulent kinetic energy and the energy dissipation are considered.