Numerical modeling of atomization in compressible flow
The study of atomization in supersonic combustors is critical in designing efficient and high performance scramjets and ensuring reliable ignition in their complex startup conditions. Numerical methods incorporating surface tension effects have largely focused on the incompressible regime as most atomization applications occur at low Mach numbers. Simulating surface tension effects in compressible flow requires robust numerical methods that can handle discontinuities caused by both material interfaces and shocks. In this work, a shock and interface capturing finite volume scheme is developed to solve the compressible multicomponent Navier-Stokes equations with capillary forces. Shock capturing is performed with a Harten-Lax-van Leer-Contact (HLLC) Riemann solver modified to account for the surface tension induced pressure jump across the gas-liquid interface. Interface capturing is performed with a diffuse interface model. The solver utilizes a total variation diminishing (TVD) third-order accurate Runge-Kutta method for time-marching and second-order accurate TVD spatial reconstruction. To prevent numerical smearing of the material interface, an interface compression/sharpening scheme is required. A PDE-based compression scheme is implemented and with developments to account for surface tension effects. The approach is successfully used to model liquid atomization problems but is not discretely conservative. To address this, a Tangent of Hyperbola for INterface Capturing (THINC) interface reconstruction scheme is investigated with developments to account for the phasic densities in the context of the five equation model. The resulting solver can account for the effects of compressibility, surface tension, and molecular diffusion in interfacial flows. One and two-dimensional benchmark problems demonstrate the desirable interface sharpening and conservation properties of the approach. Two and three-dimensional examples of primary atomization of a liquid jet in a Mach 2 crossflow and secondary atomization of a liquid droplet after its interaction with a shockwave demonstrate the robustness of the method. The dependence of Weber and Mach number on the breakup characteristics of cylindrical liquid columns are then investigated with a series of numerical experiments. A range of Weber numbers is considered for two different shock-droplet interactions consisting of either subsonic or supersonic post-shock conditions. In the subsonic case, a number of different breakup modes are observed with a strong dependence on the Weber number and provide good correlation with experimental observations. Droplets at lower Weber numbers exhibit lower drag coefficients with implications for point particle type atomization models. In the supersonic case, less variation of the drag coefficient as a function of Weber number is observed.