Numerical simulation of tip vortex cavitation using a multiscale method

Abstract

We propose a multiscale Euler–Lagrange method to simulate tip vortex cavitation (TVC), accurately modelling bubble dynamics at the macroscopic Eulerian scale. The method employs mapping strategies using a Gaussian kernel function and topological relationships to represent momentum and mass transfer between the Eulerian and Lagrangian frames. We investigate the effects of nuclei content and spatial distribution on TVC inception induced by an elliptical foil, comparing the predicted cavitation inception indices with experimental data, wetted flow simulations, and conventional Euler cavitation simulations. Our results demonstrate that the model yields cavitation inception indices that closely align with experimental observations. Additionally, our simulations reveal a direct correlation between the index and location of TVC inception with both the content and spatial distribution of nuclei. We also examine the temporal evolution of a single nucleus injected at the same position under different cavitation numbers to elucidate the mechanism of TVC inception. We observe two distinct outcomes for nucleus evolution. At higher ambient pressures, only localised elongated cavities move downstream and eventually collapse, a phenomenon not captured by traditional Euler simulations or hybrid Euler–Lagrange methods. When pressure is sufficiently low, a nucleus captured downstream of the minimum pressure location can progress upstream and trigger sustained TVC by connecting to the downstream cavity. This research offers a promising methodology for a deeper understanding of TVC inception and highlights the significant role of nuclei in this process.