Numerical investigation of three-dimensional cloud cavitation with special emphasis on collapse induced shock dynamics

The aim of the present investigation is to model and analyze compressible three-dimensional (3D) cavitating liquid flows with special emphasis on the detection of shock formation and propagation. We recently developed the conservative finite volume method CATUM (Cavitation Technische Universitat Munchen), which enables us to simulate unsteady 3D liquid flows with phase transition at all Mach numbers. The compressible formulation of the governing equations together with the thermodynamic closure relations are solved by a modified Riemann approach by using time steps down to nanoseconds. This high temporal resolution is necessary to resolve the wave dynamics that leads to acoustic cavitation as well as to detect regions of instantaneous high pressure loads. The proposed two-phase model based on the integral average properties of thermodynamic quantities is first validated against the solution of the Rayleigh-Plesset equation for the collapse of a single bubble. The computational fluid dynamics tool CATUM is then applied to the numerical simulation of the highly unsteady two-phase flow around a 3D twisted hydrofoil. This specific hydrofoil allows a detailed study of sheet and cloud cavitation structures related to 3D shock dynamics emerging from collapsing vapor regions. The time dependent development of vapor clouds, their shedding mechanism, and the resulting unsteady variation of lift and drag are discussed in detail. We identify instantaneous local pressure peaks of the order of 100 bar, which are thought to be responsible for the erosive damage of the surface of the hydrofoil. (c) 2008 American Institute of Physics.