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Turbulent mixing of multi-phase flows is of great interests in many research fields. In this talk, I will present results from turbulence simulations of two-phase flows. We use a hybrid particle level set method (Enright et al., 2003) to capture the interface in the turbulent flows. Based on the phase-field model, we propose a simple way to calculate the surface tension force from the re-initialized level set function. >From direct numerical simulations, we find quantities such as the number of drops and the total circumference of the drops to scale with the surface tension at the statistical equilibrium state. In addition we report evidence for self-similar probability distribution of drop size in turbulent mixing. If time allows, I will also present an algorithm to enforce volume conservation in level set methods using ``help" from volume of fluid methods.

This is a collaboration with J. Ferziger, N. Mansour, F. Ham and M. Herrmann.