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 - ε 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 - ε 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 - ε 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 f ₁ 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.