Partially Averaged Navier-Stokes method for time-dependent turbulent cavitating flows

Cavitation typically occurs when the fluid pressure is lower than the vapor pressure in a local thermodynamic state, and the flow is frequently unsteady and turbulent. The Reynolds-Averaged Navier-Stokes (RANS) approach has been popular for turbulent flow computations. The most widely used ones, such as the standard k − ɛ model, have well-recognized deficiencies when treating time dependent flow field. To identify ways to improve the predictive capability of the current RANS-based engineering turbulence closures, conditional averaging is adopted for the Navier-Stokes equation, and one more parameter, based on the filter size, is introduced into the k − ɛ model. In the Partially Averaged Navier-Stokes (PANS) model, the filter width is mainly controlled by the ratio of unresolved-to-total kinetic energy f1. This model is assessed in unsteady cavitating flows over a Clark-Y hydrofoil. From the experimental validations regarding the forces, frequencies, cavity visualizations and velocity distributions, the PANS model is shown to improve the predictive capability considerably, in comparison to the standard k − ɛ model, and also, it is observed the value of f1 in the PANS model has substantial influence on the predicting result. As the filter width f1 is decreased, the PANS model can effectively reduce the eddy viscosity near the closure region which can significantly influence the capture of the detach cavity, and this model can reproduce the time-averaged velocity quantitatively around the hydrofoil.