Riemann techniques for the simulation of compressible liquid flows with phase-transition at all Mach numbers - Shock and wave dynamics in cavitating 3-D micro and macro systems

We investigate numerical flux functions for the inviscid flux components of the 3-D time-dependent balance laws of mass, momentum and energy. Special emphasis is put on the suitability of these fluxes to simulate compressible low speed liquid flows as well as to simulate liquid flows with phase transition. It is demonstrated that the classical approaches based on exact or approximate solutions of the Riemann problem between adjacent cells do not lead to uniformly consistent flux functions with respect to multidimensional low Mach number flow. Therefore, we introduce a uniformly consistent numerical flux function and perform a series of steady and unsteady simulations of pure liquid flow and cavitating liquid flow. We demonstrate the applicability of the proposed CFD-Tool CATUM to resolve wave dynamics and to predict the evolution of cavitation structures inside a 3-D multi-hole injector. Finally, we investigate the 3-D time dependent cavitating flow around a prismatic body. Here we point out the suitability of our CFD-Tool to predict erosive shock loads of collapsing vapor clouds.