VEnt: An air entrainment model for turbulent free surface flows

We present a model for bubble entrainment caused by the interaction of turbulence with a free surface. The model improves over the mechanistic bubble entrainment model of Castro et al. ["A mechanistic model of bubble entrainment in turbulent free surface flows," Int. J. Multiphase Flow 86, 35 (2016)] by replacing the original vortex/free surface interaction model with the model derived from direct numerical simulations introduced by Hendrickson et al. ["Modelling entrainment volume due to surface-parallel vortex interactions with an air-water interface," J. Fluid. Mech. 938, A12 (2022)]. Implementation of the Hendrickson model for vortex/free surface interaction requires determining vortex number densities and velocities derived from simple models using a full turbulence spectrum that is dependent upon the local turbulent kinetic energy and dissipation. The resulting model has no adjustable constants and is applicable to high Reynolds number methodologies where the small-scale turbulence is not resolved but these scales can be characterized. We validate the model prediction of void fraction and bubble size distribution in the wake of a full-scale ship transom flow using both Reynolds Averaged Navier-Stokes (RANS) and hybrid RANS/Large Eddy Simulation approaches. We also present the model performance for the challenging problem of a full-scale ship executing a turning maneuver in irregular waves, indicating that the newly developed entrainment model is robust and performs satisfactorily for realistic full-scale problems.