Numerical simulation of unsteady three-dimensional sheet cavitation

Abstract

The shedding of a sheet cavity is governed by the direction and momentum of re-entrant and side-entrant jets and their impingement on the free surface of the cavity. Therefore, for an accurate prediction of the shedding of the sheet cavity it is important to predict the re-entrant and side-entrant jets accurately. It appears that these jets are inertia driven suggesting that a numerical method based on the Euler equations is able to capture the phenomena associated with unsteady sheet cavitation. Due to the dynamics of sheet cavitation, strong pressure pulses are generated, originating from the collapse of shed vapor structures. To be able to predict the dynamics of the pressure waves the fluid is considered as a compressible medium by adopting appropriate equations of state for the liquid phase, the two-phase mixture and the vapor phase of the fluid. In this paper a computational method for solving the compressible unsteady Euler equations on unstructured grids is employed to predict the structure and dynamics of threedimensional unsteady sheet cavitation occurring on stationary hydrofoils, placed in a steady uniform flow. In the two-phase flow region an equilibrium cavitation model is employed, which assumes local thermodynamic and mechanical equilibrium. In this model the phase transition does not depend on empirical constants to be specified. The three-dimensional unsteady cavitating flow about a three-dimensional hydrofoil (Twist11) is calculated. It is shown that the formation of the re-entrant flow and a cavitating horseshoe vortex are captured by the present numerical method. The calculated results agree reasonably well with experimental observations. Furthermore, it is demonstrated that the collapse of the shed vapor structures and the resulting high pressure pulses are captured in the numerical simulations.