A semi implicit compressible solver for two-phase flows of real fluids

The development of numerical solvers able to simulate compressible two-phase flows is still a great challenge in computational fluid dynamics. The interaction between acoustic waves and interfaces is of major concern for several engineering and biomedical applications, among which atomization in combustion chambers, cavitation problems, underwater explosions and bubble shock interactions. For instance, there are experimental evidences that acoustic waves can have an important effect on the atomization process, and this could have a great impact on combustion. However, usual approaches for DNS of primary atomization are based on incompressible solvers and therefore are not able to capture the propagation of acoustic waves and therefore cannot be used to simulate such phenomena. The numerical problem associated with the simulation of compressible two- phase flows is challenging, mostly because of the huge spatial variations of the speed of sound and the corresponding low Mach number in the liquid phase. In the present work, a numerical solver able to study subsonic compressible two-phase flows is presented. The solver is based on a complete formulation of the Navier-Stokes equations with real fluid equations of state, which are solved with a semi-implicit projection method. It is shown that the solver can handle a large range of compressible subsonic flows, both for a single phase or for two phases, as the flow induced by free convection, a bubble expansion in isothermal or isentropic conditions, and interaction between acoustic waves and liquid-gas interfaces. Eventually, attention will be given to the simulation of a water droplet in air, under the excitation of a stationary acoustic wave. It is also shown that the solver exhibits equivalent performances as an incompressible solver in configurations where compressible effects have no effects