A modified SST k-? turbulence model to predict the steady and unsteady sheet cavitation on 2D and 3D hydrofoils

Abstract

The paper presents a study of using a modified SST (Shear-Stress Transport) k-? model with a multi-phase mixture flow RANS solver to predict the steady and unsteady cavitating flows around 2D and 3D hydrofoils. Based on Reboud et al [6] s idea of modifying turbulent viscosity for a RNG k-­ model, a modification is applied to a SST k-? model in the present work. The cavitation is modeled by Schnerr-Sauer s cavitation model [16]. First, results of 2D NACA0015 foil at two cavitation numbers, ? =1.6 (stable sheet cavitation) and ?=1.0 (unsteady with shedding) are compared for different grids and with available experiment data. Then, the problem of the standard SST model in predicting unsteady cavitation is discussed. Finally the results for a 3D twisted hydrofoil are compared with the experiment by Foeth and Terwisga [3]. It is found that with the modified SST k-? model the RANS solver is able to predict the essential features like development of re-entrant jets, the pinch-off, the shedding of vortex and cloud cavities for the 2D NACA0015 foil at ? =1.0. For the case at ? =1.6, the model predicts a high frequency fluctuating sheet cavity with minor shedding at its closure. Compared with the standard SST model, the global quantities like lift, drag, and shedding frequency predicted by the modified model are closer to the experimental data, although considerable discrepancy with the experiment data is noted for the unsteady case at ? =1.0. In addition, a special type of secondary cavities, developed downstream an upstream-moving collapse cavity and termed as vortex group cavitation by Bark et al [1], appears to be observable in the simulation at this condition. The existence of this type of cavity has been reconfirmed in a recent experiment in the SSPA s cavitation tunnel.