The continuous adjoint cut-cell method for shape optimization in cavitating flows

Abstract

A continuous adjoint formulation for shape optimization in steady-state, cavitating flows is developed. A Transport Equation-based mixture model, extended with the Kunz cavitation model, is implemented to incorporate phase transition due to cavitation and for which the adjoint equations are derived. Flow and adjoint equations are discretized on 2D Cartesian meshes with cut-cells. In the cut-cell method, Cartesian cells intersected by the solid boundaries are reshaped by discarding their solid part, resulting in cells with an arbitrary number of sides. Emphasis is laid on the accurate computation of geometric sensitivities at the cut-cells, required by the adjoint method to compute the objective gradient. The sensitivity derivatives obtained via the adjoint method are compared with finite differences for the purpose of validation. The proposed adjoint formulation is assessed by performing three shape optimizations with two different objectives, namely cavitation suppression and hydrofoil lift maximization over isolated hydrofoils.