Topology optimization for stationary fluid-structure interaction problems with turbulent flow

Topology optimization methods face serious challenges when applied to structural design with fluid-structure interaction (FSI) loads, specially for high Reynolds fluid flow. This paper devises an explicit boundary method that employs separate analysis and optimization grids in FSI systems. A geometry file is created after extracting a smooth contour from a set of binary design variables that defines the structural design. The FSI problem can then be modeled with accurate physics and explicitly defined regions. The Finite Element Method is used to solve the fluid and structural domains. This is the first work to consider a turbulent flow in the fluid-structure topology optimization framework. The fluid flow is solved considering the $k-\varepsilon$ turbulence model including standard wall functions at the fluid and fluid-structure boundaries. The structure is considered to be linearly elastic. Semi-automatic differentiation is employed to compute sensitivities and an optimization problem using binary design variables is solved via sequential integer linear programming. The fluid loading is linearly interpolated in order to provide the sensitivities of the fluid flow on the fluid-structure interfaces. Results show that the proposed methodology is able to provide structural designs with smooth boundaries considering loads from low and high Reynolds flow.