LES investigation of the tip vortex cavitating flow with special emphasis on the interaction between cavitation and vorticity by a modified cavitation model

Cavitation within the tip vortex (TV) flow remains a challenging issue in the design of high-speed and low-noise hydraulic machinery. In this paper, the TV cavitating flow around an elliptical hydrofoil is calculated by using large eddy simulation (LES) combined with a modified Schnerr-Sauer (S-S) cavitation model. The original S-S cavitation model is modified by taking into account the typical effect of vortex flow. The partial pressure term which can describe the vortex quantitatively and qualitatively is confirmed as ρ_m ω_x² r_c² , and is considered into the R-P equation of the modified S-S cavitation model. Comparison between the numerical and experimental results shows good agreement in the form and evolution of cavities, including attached cavities (AC) and tip vortex cavities (TVC). The vorticity transport equation is utilized to investigate the dynamic mechanisms of the vortex development around the TVC. Further analyses indicate that cavitation in the TV flow influences the pressure in the core of the cavity and the local flow patterns. Typical vortex structures in the TV cavitating flow include TV, secondary vortex (SV) and wake vortex (WV). The direction and magnitude of the rotation effect can be described by axial vorticity which is drawn on the iso-surface of Q = 1 × 10⁵ s⁻². The development of the TV cavitating flow can be divided into two stages: Stage I, the development and fusion of TV, SV, stage II, the dissipation of SV. The stretching term dominates the evolution of TV, and the dilatation term is the main reason in the mergence process of SV.