| A comprehensive computational methodology is developed for turbulent cavitating flows. The ensemble-averaged Navier-Stokes equations, along with a volume fraction transport equation, are employed. The flow field is computed in both phases with the vapor pressure recovered inside the cavity via a mass transfer model. The two-equation k-ϵ model is adopted for turbulence closure. Based on the mean flow variables, both steady-state and transient computations are conducted. To ensure stable and convergent computations, unified incompressible-compressible pressure-based algorithms for steady and time dependent computations are presented, with the large density ratio at the phase boundary handled via pressure-density coupling schemes. While no temperature effect is considered, the resulting pressure-correction equation shares common features with that of high-speed flows, exhibiting a convective-diffusive nature instead of only a diffusive type. To address the empiricism in existing cavitation models, an analysis of the mass and momentum conservation at a phase change boundary is conducted and a new transport equation-based interfacial dynamics cavitation model is developed. The new model eliminates the empirical parameters in existing models by introducing interfacial velocity terms. The computational capability has been applied to axisymmetric projectiles and a planar hydrofoil for steady-state simulation, and to convergent-divergent nozzles for both steady-state and time-dependent simulation. The steady-state results indicate that comparable pressure distribution predictions are yielded by all the cavitation models considered. The vorticity dynamics in the closure region is detailed and it is shown that the baroclinic vorticity generation is important for the turbulence production in the cavity closure region. To account for the two-phase mixture effect, the implications of the speed of sound definition in cavitating flows are investigated. The interplay of cavitation number, pressure gradient and cavitation model has been probed to assess the time-dependency of the cavitation dynamics. The computational methodology has demonstrated capabilities to predict both qualitative and quantitative features of the turbulent cavitating flow. |
