Numerical analysis of unsteady cavitating turbulent flow and shedding horse shoe vortex structure around a twisted hydrofoil
Abstract Cavitating turbulent flow around hydrofoils was simulated using the Partially Averaged Navier Stokes (PANS) method and a mass transfer cavitation model with the maximum density ratio r l r v ,clip effect between the liquid and the vapor. The predicted cavity length and thickness of stable cavities as well as the pressure distribution along the suction surface of a NACA66(MOD) hydrofoil compare well with experimental data when using the actual maximum density ratio r l r v ,clip 43391) at room temperature. The unsteady cavitation patterns and their evolution around a Delft twisted hydrofoil were then simulated. The numerical results indicate that the cavity volume fluctuates dramatically as the cavitating flow develops with cavity growth, destabilization, and collapse. The predicted three dimensional cavity structures due to the variation of attack angle in the span wise direction and the shedding cycle as well as its frequency agree fairly well with experimental observations. The distinct side lobes of the attached cavity and the shedding U shaped horse shoe vortex are well captured. Furthermore, it is shown that the shedding horse shoe vortex includes a primary U shaped vapor cloud and two secondary U shaped vapor clouds originating from the primary shedding at the cavity center and the secondary shedding at both cavity sides. The primary shedding is related to the collision of a radially diverging re entrant jet and the attached cavity surface, while the secondary shedding is due to the collision of side entrant jets and the radially diverging re entrant jet. The local flow fields show that the interaction between the circulating flow and the shedding vapor cloud may be the main mechanism producing the cavitating horse shoe vortex. Two side views described by iso surfaces of the vapor volume fraction for a 10% vapor volume, and a non dimensional Q criterion equal to 200 are used to illustrate the formation, roll up and transport of the shedding horse shoe vortex. The predicted height of the shedding horse shoe vortex increases as the vortex moves downstream. It is shown that the shape of the horse shoe vortex for the non dimensional Q criterion is more complicated than that of the 10% vapor fraction iso surface and is more consistent with the experiments. Further, though the time averaged lift coefficient predicted by the PANS calculation is about 12% lower than the experimental value, it is better than other predictions based on RANS solvers.