A hybrid multi-scale model for cavitating flows

Cavitating flows possess large vapor cavities that can be represented on a computational grid alongside small bubbles that cannot be similarly resolved. We develop a compressible multiscale model where the resolved mixture of liquid and large-scale vapor is governed by the compressible Navier Stokes equations and the sub-grid vapor bubbles are tracked in a Lagrangian sense. For the subgrid bubbles, a novel ‘kR-RP’ equation is developed by integrating the spherical momentum equation from the bubble surface (r = R) to a finite distance (r = kR, k - constant parameter). The variable k allows the bubble to consistently respond to a local external pressure rather than the pressure at infinite distance. The classic RP variants (e.g. Keller-Miksis, original RP equation) are recovered when k and c approach infinity. We demonstrate the hybrid model’s insensitivity to the value of k, and its ability to capture inter-bubble interactions among sub-grid bubbles, and between resolved and sub-grid bubbles.