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A nonlinear Partially-Averaged Navier–Stokes model with near-wall correction is developed for separated turbulent flow simulations. The periodic hills flow is simulated to validate the new model and the results are compared with the standard $k-𝜀$ model, MPANS model, MSST PNAS model, standard $k-𝜀$ PANS model, and experimental/LES results. It is found that the new model shows better performance in the prediction of both mean velocity and turbulent statistics compared to the other models. From the prediction of the near-wall friction coefficient of periodic hills flow, the new model shows good resolution in the near-wall region by considering the near-wall damping function to turbulent viscosity, gradient production term, and turbulence scale correction term for the near-wall region. From the analysis of anisotropy-invariant and sub-filtered stress (SFS), it can be found that the nonlinear term is necessary for prediction accuracy improvement in turbulent flow simulation with strong separation.

In this paper, we describe the use of a new nonlinear partially-averaged Navier–Stokes (PANS) model with near-wall correction for simulating the cavitating flow around a Clark-Y hydrofoil. For comparison, the standard $k$–$𝜀$ PANS model is also used. The results demonstrate that compared to $k$–$𝜀$ PANS and experiment, the new PANS model shows better performance for cavitation flow, including time-averaged velocity, root mean square (rms) velocity and cavity shedding processing. Through the calculation of the lift and drag coefficient at $\sigma =0.8$ and $\sigma =2.0$, it can be concluded that the cavitation will decrease the lift and increase the drag of the hydrofoil, resulting in a decrease of the lift-to-drag ratio. From the analysis of different terms in both the turbulent kinetic energy (TKE) and dissipation rate transport equations of the cloud cavitation, it is found that the production term and the dissipation term are dominant in the turbulent transport, and they are mainly distributed in the vapor–liquid interface and the trailing edge of the hydrofoil.

The Partially Averaged Navier–Stokes (PANS) method is assessed with various values of the control parameters ($f_k=0.3$–1.0, $f_{𝜀}=1.0$) by performing unsteady cavitating flows around a NACA0015 hydrofoil in a surrogate fluid of fluoroketone. Available experimental data of the cavity evolution and pressure are utilized to validate and evaluate the computational method. The results show that decreasing the control parameter $f_k$ can help to avoid the overestimations of the turbulence viscosity near the rear region of the cavity and can resolve more scales turbulence structure. The control parameter $f_k=0.4$ yields good predictions on cavitation shedding dynamics behavior and pressure distribution. Furthermore, the temperature around the hydrofoil undergoes a strong evolution that is contributed by the local evaporation and condensation processes. Interestingly, there are significant unsteady characteristics along the chordwise and spanwise directions of the hydrofoil. Finally, the thermal effect on cavitating flows is associated with the physical properties of fluid media. Evaporative cooling effects are more pronounced at high temperature and subsequently suppress the intensity of cavitation.