Level Set-based Topology Optimization of Turbulent Flows
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Predicting fluid flows and designing fluid devices is key in various engineering domains. For different applications such as mixing, mass and heat transfer, it can be beneficial to operate at higher flow rates in the turbulent regime. Better control of the flow and higher performance of fluid devices can be achieved by optimizing their layouts. In this work, we propose a level set-based topology optimization framework for the design of fluid devices operating in the turbulent regime [1]. The proposed framework relies on the level set method and an immersed boundary technique, here the extended finite ele- ment method. This combination allows for an accurate description of the geometry and the physics across fluid/solid interfaces and alleviates the need to generate conforming meshes as the design is updated. The geometry of fluid devices is represented by one or several level set functions. Turbulent flows are predicted using the Reynolds Averaged Navier-Stokes equations stabilized by the Streamline Upwind Petrov-Galerkin and the Pressure-Stabilizing Petrov-Galerkin formulations. The turbulence is introduced using a one-equation model, here the Spalart-Allmaras model [2]. To allow for the immersion of fluid/solid interfaces into fixed background meshes, a generalized enrichment strat- egy is used to extend standard finite element approximations [3]. Boundary conditions are imposed weakly via Nitsche’s method and a face-oriented ghost stabilization is used to mitigate numerical instabilities related to the generation of small integration subre- gions. Gradient-based algorithms are used to solve the optimization problems and the required sensitivities, accounting for the dependence of the design criteria and the resid- ual equations on the turbulence variable, are computed through the adjoint method. The capabilities of the proposed optimization framework are illustrated with two-dimensional designs of turbulent fluid systems for minimum power dissipation.