Phase field lattice Boltzmann model for air-water two phase flows

Two phase flows occur in different forms with liquid and gas in general, among which, the interaction of the flow of air and water is a common scenario. However, modeling the two phase flow still remains a challenge due to the large density ratio between them and different space-time scales involved in the flow regimes. In the present work, the lattice Boltzmann (LB) model capable of handling large density ratio (1000) and high Reynolds number (104) simultaneously is proposed. The present model consists of two sets of LB equations, one for the flow field in terms of normalized pressure-velocity formulation and the other for the solution of the conservative Allen-Cahn equation to capture the interface. The numerical tests such as stationary drop, bubble coalescence, and capillary wave decay have been performed, and the results exhibit excellent mass conservation property. The capability of the present model to handle complex scenarios has been tested through test cases, for example, rise of an air bubble, splash of a water droplet on a wet bed, and Rayleigh-Taylor instability. In all test cases, the simulation results agree well with the available reference data. Finally, as an application of the present model, the breaking of a deep water wave with high Reynolds number (104) is simulated. The plunging breaker with wave overturning and the generation of secondary jet and splashes are well described by the present LB model. The evolution of wave energy dissipation during and after breaking is in agreement with the reference data.