Unsteady Cavitating Flow around a Hydrofoil Simulated Using the Partially-Averaged Navier-Stokes Model

Numerical simulations of unsteady cavitating flow around a NACA66-mod hydrofoil were performed using the partially-averaged Navier-Stokes method with different values of the resolution control parameters (f(k) = 1.0-0.2, f(epsilon) = 1). With decreasing f(k), the predicted cavitating flow becomes unsteady as the time-averaged turbulent viscosity at the rear part of the attached cavity is gradually reduced. For f(k) = 0.9 and 0.8, the cavity becomes unstable and its length dramatically expands and shrinks, but the calculation fails to predict the vapor cloud shedding behavior observed experimentally. With smaller f(k) less than 0.7, the cloud shedding behavior is simulated numerically and the predicted cavity shedding frequency increases. With f(k) = 0.2, the whole cavitating flow evolution can be reasonably reproduced including the cavity growth/destabilization observed previously. The re-entrant flow along the suction surface of the hydrofoil is the main trigger to cause the vapor cloud shedding. The wall pressure along the hydrofoil surface oscillates greatly due to the dynamic cavity shedding. Comparing the simulations and experiments, it is confirmed that for the PANS method, resolution control parameters of f(k) = 0.2 and f(epsilon) = 1 are recommended for numerical simulations of unsteady cavitating flows. Thus, the present study shows that the PANS method is an effective approach for predicting unsteady cavitating flow over hydrofoils.