Simulation of the Kelvin–Helmholtz instability using a multi-liquid moving particle semi-implicit method

In general, multi-fluid multi-interface problems are more complicated than single-phase problems and therefore require sophisticated and robust algorithm development. In this study, a moving particle semi-implicit (MPS) method based on the Lagrangian approach was extended to a multi-phase system with multiple interfaces. Accordingly, several new particle interaction models, including self-buoyancy-correction, surface tension, and interface boundary condition models, were introduced. Representative multi-liquid MPS sloshing simulation results were compared with corresponding experimental results with three liquids. The results agree well for both global behaviors and the much smaller-scale interfacial instability phenomenon called the Kelvin–Helmholtz instability (KHI). The validated multi-phase MPS method was subsequently applied to the classical Poiseuille problem of two fluids flowing with different velocities between two parallel plates The KHI is triggered when the destabilizing effect of a shear across an interface with a sufficient relative velocity overcomes the stabilizing effect of gravity and surface tension. Both viscosity and surface tension tend to limit the growth of KHIs when they are over certain values. For many possible combinations of density ratios and surface tensions producing the same Richardson-number, the body-force component plays a much more important role than the surface-tension component if the interfacial wave number is not very high.