A pressure-based unified solver for low Mach compressible two-phase flows

In this study, a low Mach, pressure-based solver is developed for simulation of compressible two-phase flows. The two-dimensional solver developed on collocated grids in a finite volume framework adopts a unified formulation to efficiently handle different combinations of the two phases, including the cases where compressible and incompressible phases coexist. The pressure-based solver is coupled to a sharp interface capturing approach based on the coupled level set and volume of fluid method, which can accurately account for surface tension. The energy equation considered in the framework also accounts for dissipative effects due to viscosity and heat conduction. A variety of representative test cases of increasing complexity are considered to evaluate the performance of the solver in simulating compressibility effects while accurately resolving the interface. The results for Rayleigh-Taylor instability exhibit equivalent performance in both incompressible and low Mach regimes, while accounting for thermal effects arising due to compressibility. An isothermal bubble compression case due to a velocity field shows excellent agreement with existing results. The numerical results of bubble oscillations immersed in an incompressible liquid validated with one-dimensional and two-dimensional Rayleigh-Plesset model at different density ratios depict the ability of the unified approach to handle pressure waves effectively. This is further demonstrated by simulating bubble expansion inside an incompressible fluid due to decaying pressure.