Topology optimization for 3D fluid diode design considering wall-connected structures

Abstract This paper proposes a density-based topology optimization method for the three-dimensional design of fluid diodes considering wall-connected structures based on the fictitious physical modeling approach. The optimum design problem of fluid diodes is formulated as maximizing the energy dissipation in the reverse flow subject to the upper bound constraint of the energy dissipation in the forward flow. A fictitious physical model and a geometric constraint are constructed to detect and restrict the “floating” solid domains, which are not connected to the outer boundaries. The sensitivities of cost functions are derived and computed based on the continuous adjoint method. The finite volume method is employed to discretize the governing and adjoint equations to mitigate the huge computational costs of three-dimensional fluid analysis. Numerical investigations are presented to validate the fictitious physical model and the geometric constraint for excluding “floating” islands. Finally, topology optimization for fluid diodes with and without the geometric constraint is performed, and the result demonstrates that the proposed method is capable of generating fluid diodes with wall connectivity, while maintaining a good functional performance.