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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.

In order to investigate the turbulence-induced acoustic characteristics of hydrofoils, the flow and sound field for a model NH-15-18-1 asymmetric hydrofoil were calculated based on the mixed method of large eddy simulation (LES) with Lighthill analogy theory. Unsteady fluid turbulent stress source around the hydrofoil were selected as the inducements of quadrupole sound. The average velocity along the mainstream direction was calculated for different Reynolds numbers $(Re)$. Compared to experimental measurements, good agreement was seen over a range of $Re$. The results showed that the larger the $Re$, the larger the vortex intensity, the shorter the vortex initial shedding position to the leading edge of the hydrofoil, and the higher the vortex shedding frequency $(f_s)$. The maximum sound pressure level (SPL) of the hydrofoil was located at the trailing edge and wake of the hydrofoil, which coincided with the velocity curl $(\omega )$ distribution of the flow field. The maximum SPL of the sound field was consistent with the location of the vortex shedding. There were quadratic positive correlations between the total sound pressure level (TSPL) and the maximum value of the vortex intensity $({\mathrm{\Gamma }}_{max})$ and velocity curl, which verified that shedding and diffusion of vortices are the fundamental cause of the generation of the quadrupole source noise.

Unsteady cavitating turbulent flow around a NACA66 hydrofoil was simulated using a mass transfer cavitation model and a modified filter-based turbulence model in this paper. The modified filter-based turbulence model can accurately predict the pressure coefficient in midplane and shedding frequency of the unsteady cloud cavitation than standard $\kappa$–$𝜀$ model and filter-based turbulence model. The time evolution of transient cavitation cloud structure predicted by the three-turbulence model was compared. The result which was predicted by the modified filter-based turbulence model is in good agreement with the experimental results. The time evolution of re-entrant jet had been analyzed. The instantaneous wall-pressure evolution on the suction surface (SS) predicted by the modified filter-based turbulence model had been analyzed. The cavitation-vortex interaction had been analyzed in this study. The different effects on the cavitation-vortex interaction of the vortex stretching term, vortex dilatation term and baroclinic torque term in the transport equation of vorticity had been discussed.

Cavitating flows around a hydrofoil are simulated in this work by using a transport equation-based model. It is shown that the original Launder-Spalding k-ε model significantly over-predicts the viscosities. The viscosity-corrected models can simulate better the cavitation characteristics including the shedding process.