The mechanisms of air-driven growth of tip vortex cavity

Tip vortex cavitation (TVC) is a critical phenomenon in propeller and turbine machinery. While much of the existing research on TVC has focused on its inception, the mechanisms driving its continuous growth remain under-explored. In this study, we propose a comprehensive theoretical model that integrates both gas diffusion and free nuclei entrainment to better understand the slow growth of tip vortex cavity. The efficacy of this model is validated by comparing its predicted temporal evolution of cavity size with experimental data, under both nuclei-depleted and large nuclei-injection conditions. Additionally, the model is used to further examine the individual effects of nuclei content and size on tip vortex cavity growth. Results reveal that, in sub-saturated nuclei flow, two critical equilibrium values for cavity size are identified: one determined by the balance of dissolved gases inside the cavity and the surrounding fluid, and the other by the balance between dissolved gases inside the cavity and the surrounding gas nuclei. The cavity stability size gradually shifts from the first to the second critical value as the gas nuclei content increases. However, since the model does not consider the destabilization mechanism of the cavity, the cavity may destabilize before reaching the second critical value. Meanwhile, the cavity growth rate increases significantly with increasing gas nuclei size. This work not only provides a comprehensive explanation for the experimental observations, but also provides new insights into the hysteresis phenomenon observed in TVC.