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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 Universität München), 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 100bar, which are thought to be responsible for the erosive damage of the surface of the hydrofoil.

New instabilites of unsteady transonic flows with non-equilibrium phase transition are presented including unsymmetric flow patterns with moving oblique shock systems in supersonic nozzles with perfectly symmetric shapes. The phenomena were first detected when performing experiments in our supersonic wind tunnel with atmospheric supply and could be perfectly reproduced by numerical simulations based on the Euler equations, i.e. neglecting the viscosity of the fluid. The formation of the liquid phase is modelled using the classical nucleation theory for the steady state together with the Hertz–Knudsen droplet growth law and yields qualitatively and quantitatively excellent agreement with experiments in the unsteady flow regime with high-frequency oscillations including the unstable transient change of the structure from symmetric to unsymmetric flow.For engineering applications the sudden increase or decrease of the frequency by a factor 2 or more and of the pressure amplitude at the bifurcation limits is of immediate practical interest, e.g. for flutter excitation of turbomachinery blading.

This paper presents a numerical approach f o r a cavitation model that bases on a combination of the Volume-of-Fluid technique with a model predicting the growth and collapse process of bubbles. T h e caviiation model is applied f o r the simulation of caviiating nozzle flows and caviiating flow over a NACA 0015 hydrofoil and showed it's capability to resolve characterisiic e$ecis of cavitation such as the cyclic formation of the cavitation cloud, the formation of the re-entrant j e t and the local occurrence of hydrodynamic pressure peaks due t o bubble cloud collapse.