Simulating droplet aerobreakup with a low-dissipation diffuse interface method

Abstract

This thesis aims to present a novel low-dissipation flux vector splitting numerical method for simulating multiphase flows, particularly regarding applications of droplet aerobreakup. Airborne particulates present a hazard for flight vehicles traveling at supersonic and hypersonic velocities, demonstrated by early experimental works. When predicting the damage from particulate impact, numerical simulations of damage modeling are improved by having accurate geometries of the droplet at the time of impact. Solid particulates undergo little deformation, but liquid particulates, such as rain or ice particles, have much more dynamic behavior. Therefore, an accurate model for simulating the interaction of liquid droplets with shocks is necessary. This thesis presents a simulation method built on the diffuse interface representation of multiphase flows in a finite volume framework. The fluxes across the cell faces are constructed through a multiphase extension of the modified Steger-Warming flux vector splitting scheme. This flux scheme, normally split into positive and negative flux components, is rearranged such that the flux is split into advection and diffusion components. The dissipative portion of the flux is then limited by numerical switches to apply only in discontinuous regions of the flow, namely at shocks and material interfaces, to ensure numerical stability. The unrestricted diffusion of the material interface is limited through the implementation of a multidimensional formulation of an interface sharpening scheme. Finally, surface tension is incorporated through a continuum surface force model to allow for more realistic comparison of the results with real world flow conditions. The method is validated by simulating common cases in one and two dimensions. This method is then applied to more complex cases involving droplet aerobreakup in two and three dimensions.