Numerical simulation of the transient cavitating turbulent flows around the Clark-Y hydrofoil using modified partially averaged Navier-Stokes method

This paper presents the implementation and assessment of a modified Partially averaged Navier-Stokes (PANS) turbulence model which can successfully predict the transient cavitating turbulent flows. The proposed model treats the standard k-e model as the parent model, and its main distinctive features are to (1) formulate the unresolved-to-total kinetic energy ratio (f_k) based on the local grid size as well as turbulence length scale, and (2) vary the f_k-field both in space and time. Numerical simulation used the modified PANS model for the sheet/cloud cavitating flows around a three-dimensional Clark-Y hydrofoil. The available experimental data and calculations of the standard k-e model, the f_k = 0.8 PANS model, the f_k = 0.5 PANS model are also provided for comparisons. The results show that the modified PANS model accurately captures the transient cavitation features as observed in experiments, namely, the attached sheet cavity grows in the flow direction until to a maximum length and then it breaks into a highly turbulent cloud cavity with three-dimensional structures in nature. Time-averaged drag/lift coefficients together with the streamwise velocity profiles predicted by the proposed model are in good agreement with the experimental data, and improvements are shown when compared with results of the standard k-e model, the f_k = 0.8 PANS model and the f_k = 0.5 PANS model. Overall, the modified PANS model shows its encouraging capability of predicting the transient cavitating turbulent flows.