Prediction Model for Partially Cavitating Hydrofoils based on Sensitivity Derivatives

Abstract

. Much work has been done over the past years to obtain a better understanding of cavitation, as well as to predict and alleviate its effects on performance. Particularly, lifting-surface sheet cavitation is addressed in various works as a free-streamline problem. Typically, a potential solver is used in conjunction with a geometric criterion to determine the shape of the cavity, whereas an iterative scheme is employed to locate the cavity surface. In this work we reformulate the problem of steady partially cavitating two-dimensional hydrofoils in a shape-optimization setup. The sensitivities required for the gradient-based optimization algorithm are derived using the continuous adjoint method. The objective function is formulated based on the assumption that the pressure on the cavity is constant and is evaluated using a source-vorticity BEM solver, whereas the control points of the B-spline cavity parametrization serve as design variables. The proposed numerical scheme is validated and found to predict well both the cavity shape and the cavitation number. Moreover, the benefits of using the adjoint method to predict the sensitivity derivatives are highlighted in a selected study case.