Dynamic and diffusive growth of microbubbles near a two-dimensional hydrofoil

A technique for predicting the bubble growth along a two-dimensional hydrofoil with traveling bubble cavitation is presented. The method is based on the dynamic response of ambient microbubbles to the flow field and the subsequent diffusion of dissolved air into the flow field cavities. The bubble growth model is divided into three components, including the prediction of 1) the hydrofoil surface pressure distribution, 2) the ambient microbubble response to the pressure distribution, and 3) the diffusive mass flow rate. The hydrofoil velocity and pressure field is determined by two-dimensional thin airfoil theory. The microbubble response to the pressure field is given by the Rayleigh-Plesset equation with the addition of a mass diffusion term. The diffusion of dissolved gasses into the cavitation bubbles is determined by a solution to the steady-state diffusion equation under spherically symmetric convective flow. Results are given for the bubble wake of a NACA 66-006 ( meanline) hydrofoil with traveling bubble cavitation. The effect of the relative velocity of the cavitation bubbles with respect to the surrounding water is investigated as well as the significance of the mass diffusion term in the Rayleigh-Plesset equation.