A Finite Element Model of Unsteady Cavitating Fluid Flow around a Hydrofoil

The present study deals with the unsteady dynamics of cavitation around the NACA 0015 hydrofoil in a channel. A finite element model is proposed to solve the governing equations of momentum and mass conservation. Turbulent flows around the hydrofoil are described by the Prandtl-Kolmogorov model. The cavitation phenomenon is modeled through a mixture model involving liquid and vapor flows and the Zwart-Gerber-Belamri (ZGB) model is considered to evaluate the transport of the water vapor fraction. The variational finite element model formulation includes the mixing of the characteristic method and the finite element. Also, at the open sides of the channel flow, an open boundary condition is imposed. Numerical experiments are performed for cavitation numbers 0.8 and 0.4. The presented model predicts the essential features of unsteady cavitating flows, the generation of vapor cavities, the time-dependent oscillations of the variables and the presence of vortical flow structures associated to vapor volume concentrations during the shedding process.