Partially Averaged Navier-Stokes method based on k-ω model for simulating unsteady cavitating flows

Abstract

The turbulence closure is significant to unsteady cavitating flow computations as the flow is frequently time-dependent accompanied with multiple scales of vortex. A turbulence bridging model named as PANS (Partially-averaged Navier-Stokes) purported for any filter-width is developed recently. The model filter width is controlled through two parameters: the unresolved-to-total ratios of kinetic energy f_k and dissipation rate f_ω. In the present paper, the PANS method based on k-ω model is used to simulate unsteady cavitating flows over a Clark-y hydrofoil. The main objective of this work is to present the characteristics of PANS k-ω model and evaluate it depending on experimental data. The PANS k-ω model is implemented with various filter parameters (f_k=0.2~1, f_ω =1/f_k). The comparisons with the experimental data show that with the decrease of the filter parameter f_k, the PANS model can reasonably predict the time evolution process of cavity shapes and lift force fluctuating in time. As the PANS model with smaller f_k can overcome the over-prediction of turbulent kinetic energy with original k-ω model, the time-averaged eddy viscosity at the rear of attached cavity decreases and more levels of physical turbulent fluctuations are resolved. What's more, it is found that the value of ω in the free stream significantly affects the numerical results such as time-averaged cavity and fluctuations of the lift coefficient. With decreasing f_k, the sensitivity of ω-equation on free stream becomes much weaker.