Conservative, Consistent All-Mach Method to Simulate Liquid Atomization in Supersonic Flows

Abstract

Atomization of bulk liquids subjected to a supersonic flow is essential to applications such as liquid fuel injection in supersonic propulsion systems. Since high-level details are often difficult to measure in experiments, numerical simulation is an important alternative to shed light on the unclear physics. A detailed numerical simulation (DNS) of liquid atomization in supersonic flows will need to rigorously resolve the shock waves, the interfaces, and the interaction between the two. In the present study, a new simulation framework for compressible multiphase flows is proposed. The geometric volume-of-fluid (VOF) method is employed to advect the sharp interfaces. The convection fluxes of density, momentum, and energy are computed based on the VOF flux, to achieve an important mass-momentum-energy consistence. To suppress spurious oscillations near shocks, numerical diffusion is introduced in single-phase regions away from the interface. The contribution of pressure is incorporated using a projection method, so that the method can be used for flows of all Mach numbers. Different compressible interfacial multiphase flow problems, including the two-phase shocktube, Richtmyer-Meshkov instability (RMI), and shock-drop interaction have been used to test the present method. The linear singlemode RMI with finite Weber and Reynolds numbers are simulated. The simulation results agree very well with the linear stability theory, which clearly affirms the capability of the present method in capturing the viscous and capillary effects on shock-interface interaction.