Jump conditions for filtered quantities at an under-resolved discontinuous interface. Part 1: Theoretical development

Abstract In this paper, we study turbulent two-phase flow. We consider the level of description where only the large scales of turbulence and the large deformations of bubbles are explicitly described: • the small scale of turbulence are not represented and we are close to the Large Eddy Simulation concept, • the mean geometry of each bubble is explicitly described but the small deformations of the bubbles are not represented. The bubble interface is still supposed to be infinitely thin ( i.e. interfaces are supposed to be under-resolved and discontinuous). At this level of description, there is no reason that the well known jump conditions are still valid. Using a two-step methodology, we determine the jump conditions for filtered quantities ( i.e. local mean velocity and pressure) at the under-resolved discontinuous interface ( i.e. small deformations of the interface are not represented). In particular, we express the velocity of the under-resolved discontinuous interface as a function of the filtered velocity, a scale similarity hypothesis and the time evolution of the interface mean curvature.

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