Application of the Wu model for solving the inverse problem of designing supercavitating hydrofoils

In the paper, we solve the problem of designing a hydrofoil in the supercavitation regime simulated by the Wu model. The distributions of velocities along the wetted part of the hydrofoil and the cavitation number are assumed to be given. We derive formulas that allow one to express the lift and drag forces in terms of integral functionals of the initial data. Thus, the formulas generalize the Kutta-Zhukovskii theorem on the lift force of a profile in continuous flow for the case of supercavitational flow. The shape of the hydrofoil is restored by the methods of inverse boundary value problems. It has been rigorously proven that for lifting profiles, the lift-to-drag ratio increases monotonically with increasing cavitation numbers.