On the Numerical Study of Bubbly Wakes Generated by Ventilated Cavity Using Population Balance Approach

Abstract

In this study, an Eulerian–Eulerian two-fluid model integrated with the population balance approach based on Multiple-Size-Group (MUSIG) model was proposed to simulate on the gas leakage bubbly wake of a ventilated cavitation problem. Three selected flow conditions with Froude number ranging from 20 to 29 have been selected for investigation. Predicted void fraction and bubble velocity profiles were validated against the experimental measurements in the high-speed water tunnel of Schauer (2003) and Wosnik (2005). Sensitivity studies on the mesh resolution and three different turbulence closures were first carried out. In comparison with experimental data, the shear stress transport (SST) turbulence model was found to be the best candidate in modelling the re-circulation motions within the cavity wake region. To consider the neighbouring effect of closely packed bubbles, an empirical equation was proposed to correlate the turbulent dispersion coefficient to the local gas void fraction. Based on the proposed empirical equation, the turbulent dispersion coefficient reduces to 0.1 when local gas void fraction is higher than 60%. In general, numerical predictions were in satisfactory agreement with the experimental data. Some discrepancies have nonetheless been found between the numerical and experimental results. The lack of exact gas leakage mechanism remains an outstanding challenge in determining the actual gas leakage rate and initial bubble size from the continuous cavity. Further effort should be also focused on combing free-surface tracking model with the present population balance approach to investigate the complex vortex structure and interaction between ventilated cavity and discrete leakage bubbles.