Single-phase and modified turbulence models for simulation of unsteady cavitating flows

The aim of this research is to provide a physical complete and numerical efficient simulation method to predict developed cavitation in hydrodynamic turbomachinery as well as in micro fluid dynamic applications, e.g. in high pressure injection nozzles of combustion engines. Cavitating two-phase flows are always very unstable, highly unsteady, 3-D and turbulent. To understand cavitation dynamics and its interaction with viscous effects like boundary layers and separation, we introduce the single-phase turbulence k - ω model of Wilcox without modifications with respect to dispersed structures of bubbly liquids, which overestimates viscous effects in the transitional regime between the vapor and liquid phase and tends to suppress typical cavitation instabilities. Consequently our further approach consists of modifications of the single-phase Wilcox model to account for the strong nonlinear variation of the turbulent viscosity μt, depending on the local void fraction α. The key issue of all numerical methods for simulation of cavitating flows is the treatment of the sudden density change of the fluid, in cold water up to 40.000:1, embedded in a global incompressible liquid flow. Here the two-phase fluid is modeled as dispersed mixture of an incompressible liquid and tiny vapor bubbles which grow or collapse, accordingly to the local static pressure and their convective transport. Therefore, the standard VOF method for capturing distinct interfaces without phase transition, e.g. free surface flow or single bubbles, is extended to include phase transition of dispersed mixtures. For simulation of bubble dynamics we apply the Rayleigh equation, which is completed by an energy balance to account for thermal effects, if hot water or if technical fluids others than water, e.g. refrigerants, with high vapor densities are considered. By using our CFD tool CAVKA we present examples of cavitating flow around hydrofoils and through single hole injection nozzles. Comparing Euler and single-phase turbulence simulations, results based on the inviscid approach are closer to experiments, which indicates an interesting option to reduce computational time. (orig.)