Direct Numerical Simulation of Two-phase Flows with Application to Air Layer Drag Reduction

An accurate and robust numerical method has been developed to simulate turbulent two-phase flows. The phase interface is tracked by the level-set method to capture frequent topological changes due to breaking or merging. Because of the broad-band characteristics of length scales in two-phase flow, a Lagrangian drop breakup model has been developed, which is coupled to the level-set method. In this approach, small subgrid droplets produced from resolved ligaments are then transferred from the levelset representation to the Lagrangian particles. The further secondary atomization is handled by a stochastic breakup model. When pinching-o↵ of ligaments is not resolved on the level-set grid, a capillary breakup model is used to predict the drop size distribution from the pinching o↵ and inserted as Lagrangian drops. This method improves the mass conservation as well as reducing the computational cost. For a high-fidelity simulation of two-phase flow, a new numerical algorithm has been developed to improve the robustness of the numerical method. The conservative formulation of Navier-Stokes equations is solved with a density correction term in the present method. The density flux terms are calculated from the level-set field for accuracy. In addition, a constant coe cient Poisson system is solved for pressure to satisfy the continuity equation in the fractional-step method. In order to show the capability of the method as an e cient tool in the breakup process, the atomization of a round liquid jet surrounded by a coaxial gas is considered. The numerical results are consistent with the observed breakup mechanisms in