Topology Optimization of Turbulent Flows

The aim of this work is to present a fast and viable approach for taking into account turbulence in topology optimization of complex fluid flow systems, without resorting to any simplifying assumptions in the derivation of discrete adjoints. Topology optimization is an iterative gradient-based design process which minimizes an objective and satisfies a set of selected design constraints by distributing material in a design domain. The gradients are obtained using adjoint sensitivity analysis which requires solutions of a forward state problem and an additional adjoint problem. In the presented article the forward solver is based on finite volume discretized Reynolds-averaged Navier–Stokes equations coupled with either one- or two-equation turbulence closure models, and the adjoint solver is obtained via automatic differentiation. The presented approach is demonstrated on the optimization of several 2D and 3D examples including a detailed comparison to designs and sensitivities obtained with different turbulence models and under a frozen turbulence assumption. The results demonstrate the importance of exact sensitivity analysis and open new possibilities for the design of large scale multiphysics problems involving turbulent flows.