<p>Compressible interfacial multiphase flows (CIMS) are challenging for numerical simulation. This is particularly true when shock interaction with sharp interfaces is involved. For small-scale CIMS problems where the surface tension is important to the interfacial dynamics, such as aerobreakup of small droplets in supersonic flows, the sharp interface and the corresponding curvature must be calculated rigorously. In the present study, a new numerical approach is developed to resolve CIMS with shock-interface interaction. The interface is captured using a mass-momentum-energy consistent volume-of-fluid (VOF) method. The advection fluxes for the conservative variables, including the mass, momentum, and energy for each phase are computed consistently with the VOF fluxes. To suppress spurious oscillations near shocks, numerical diffusion is introduced based on the Kurganov-Tadmor central scheme in the region away from the interface. The contribution of pressure is incorporated using the projection method and is obtained by solving the Poisson-Helmholtz pressure equation, which allows the method to handle flows with all Mach numbers. The capability of the present method in resolving shock-interface interaction is tested by a series of benchmark problems, including the single-phase and multiphase shocktubes, shock-bubble and shock-droplet interactions, and Richtmyer-Meshkov instability (RMI). The simulation results are validated against theories, experiments, and other simulations, and excellent agreement has been achieved. In particular, the simulation results for the linear single-mode Richtmyer-Meshkov instabilities for finite Weber and Reynolds numbers are shown to agree very well with the linear stability theory, which affirms the capability of the present method in capturing shock-interface interaction when the viscous and capillary effects are present.&nbsp;<br>
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A Mass-Momentum-Energy Consistent Volume-of-Fluid Method for Direct Numerical Simulation of Compressible Interfacial Multiphase Flows

Paper Proceedings: https://asmedigitalcollection.asme.org/FEDSM/FEDSM2021/volume/85284

ASME 2021 Fluids Engineering Division Summer Meeting (FEDSM2021)

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