Mechanisms for diffusion-driven growth of cavitating wing-tip vortices

Following their inception, vortex cavities emanating from stationary wing tips in cavitation tunnels are often observed to grow. These effects are usually attributed to the free and dissolved non-condensable gases in the liquid. However, a detailed mechanism for the cavity's growth is not known. Consequently, the repeatability of vortex cavitation in different flow facilities is generally poor. The main aim of our work is to highlight the contribution of dissolved gases to the cavity's growth, hence addressing water-quality influence in nuclei-depleted conditions. A model is provided for a steady-state diffusion-driven mechanism that transports dissolved gases from the surrounding liquid into the vortex cavitation through a diffusion layer located outside its interface. The model results show that the cavity grows uncontrollably when the dissolved gas concentration in the liquid is saturated or oversaturated relative to its saturation level at ambient pressure conditions (c_∞/c_sat≥1). In addition, it is shown that stable cavity sizes can be achieved when the c_∞/c_sat<1. The predictions in the range 1.04≤c_∞/c_sat≤1.33 are compared with experimental data and infer either of the two geometries for the diffusion layer: (i) a 5μm thin film approximated by a hollow cylinder around the cavity, or (ii) one that evolves like a boundary layer along the axis of the cavity. For the latter modeling approach, the observed length of the cavity was much larger than that required to match with the experimental data, skewing a preference to the thin-film assumption. In the undersaturated regime (c_∞/c_sat=0.14 & 0.39), the proposed model has a qualitative agreement with the data of Briançon-Marjollet and Merle (1996).