A consistent mass-momentum flux computation method for the simulation of plunging jet

In the present study, a robust and conservative numerical scheme is proposed to simulate the violent two-phase flows with high-density ratios. In this method, the mass conservation equation and the momentum equation are solved in a consistent manner. The tangent of hyperbola for interface capturing scheme is extended for the computation of the mass flux by which the sharpness and conservation property of density field is preserved. Compared with other recently proposed methods, no geometrical computation is involved in deriving the mass flux and the spurious velocity in the interfacial region can be completely avoided. To improve the computational efficiency, the present method is implemented on a parallel block-structured adaptive mesh refinement method with a staggered layout of variables. High-fidelity numerical simulation of plunging jet through the liquid surface is performed. A bubble detection algorithm is developed to track bubbles generated in air entrainment process. The evolution of the bubble cloud, air concentration, bubble-size, and bubble-velocity distributions are predicted and compared quantitatively with the experiment. Numerical results show the air entrainment and penetration depth are highly correlated with the upstream disturbance. The growing interfacial roughness of the jet yields more entrained air in the final stage of jet impingement. It is found that when the initial perturbation is introduced, the overall size of the equivalent bubble radius will expand, and the penetration depth of the bubble cloud will decrease, while a larger volume of air is entrained.