Supercavitating three-dimensional hydrofoil analysis by viscous lifting-line approach

A new viscous lifting-line method for three-dimensional supercavitating hydrofoils is presented. The method is designed to allow for the strong nonlinear hydrodynamic characteristic of two-dimensional supercavitating sections. These nonlinearities, manifesting as sudden variation of the sectional lift-curve slope, are included in the numerical model by the introduction of variable positions of the collocation points where the body boundary condition is enforced. The nonlinear hydrodynamic performance of the two-dimensional sections is predicted via multiphase Navier-Stokes computations. An iterative algorithm is necessary to converge on the three-dimensional hydrofoil performance measured in terms of lift and drag forces. The convergence properties of the method are verified, and it is validated via a systematic series of experiments on a three-dimensional hydrofoil, considering a wide range of angle of attack and cavitation numbers, which comprise very different cavitation regimes on both the front and the rear sides of the hydrofoil. Results of the viscous lifting-line model are compared with both experimental measurements in the cavitation tunnel and high-fidelity three-dimensional unsteady Reynolds-averaged Navier-Stokes computations. Findings of the validation study suggest that the proposed viscous lifting-line method can be applied toward predicting the hydrodynamic performance of three-dimensional hydrofoils in fully wet, partially cavitating, and supercavitating regimes and for planform aspect ratios that are as low as 1.