Effects of model size and free stream nuclei on tip vortex cavitation inception scaling

Because of the complexity of the flow field in a trailing vortex, prediction of tip vortex cavitation inception on a hydrofoil or a propeller still relies heavily on model tests and application of cavitation scaling. Experiments indicate that the major parameters influencing tip vortex cavitation inception are fluid viscosity (Reynolds number) and free stream nuclei (Weber number). A scaling method based on these two parameters has been developed in this paper. Size effects on circulation, vortex cores thickness and pressure distributions in a full-scale trailing vortex are predicted from model data based on a Reynolds scale similarity flow solution. Nuclei effect on tip vortex cavitation inception is obtained from cavitation scaling and expressed in a term called G. For prescribed pressure fields in the trailing vortex, a modified Rayleigh-Plesset bubble equation is used to evaluate effects of free stream bubbles on cavitation inception. Bubble radius history and acoustic pressure are computed for various initial bubble sizes and different release locations into the vortex core. A method based on the acoustic pressure sigma gradient is introduced to define cavitation inception. The values of G at cavitation inception are obtained. Depending on the ratio of initial bubble sizes between model and full-scale waters, the nuclei effect on tip vortex cavitation inception can be greater, equal or less than one.