DNS and LES of two-phase flows with cavitation
  We report on recent progress in the physical and numerical modeling of compressible two-phase flows that involve phase transition between the liquid and gaseous state of the fluid.   The high-speed dynamics of cavitation bubbles is studied in well-resolved simulations (DNS) with a sharp-interface numerical model on a micro scale. The underlying assumption of the employed evaporation/condensation model is that phase change occurs in thermal non-equilibrium and that the associated timescale is larger than that of the wave dynamics. Results for the collapse of a spherical vapor bubble close to a solid wall are discussed for three different bubble-wall configurations. The major challenge for such numerical investigations is to accurately reproduce the dynamics of the interface between liquid and vapor during the entire collapse process, including the high-speed dynamics of the late stages, where compressibility of both phases plays a decisive role.   Direct interface resolving simulations are intractable for real world technical applications such as turbulent flows involving cavitation clouds with millions of vapor bubbles and a wide range of time and length scales. For this reason, we developed a coarse grained model for large-eddy simulation (LES) of turbulent two-phase flows with cavitation. In LES, vapor bubbles constitute sub-grid scales that have to be modeled accordingly. On the grid scale, we solve the compressible Navier-Stokes equations for a homogeneous mixture of liquid and vapor. For deriving an appropriate equation of state, we assume that the characteristic time scale of phase change is much smaller than the numerical time step and that phase change is isentropic and in mechanical equilibrium at the saturation pressure. This macroscopic model is applied to realistic technical problems and to more generic flows to study the mutual interaction of turbulence and cavitation. 
Stefan Hickel
physics.flu-dyn physics.comp-ph