Jump conditions for filtered quantities at an under-resolved discontinuous interface. Part 2: A priori tests

In order to study and validate the jump conditions established in part 1, we realize a priori tests thanks to the data of a 3D Direct Numerical Simulation (DNS) of a strongly deformable bubble in a spatially decaying turbulence. The complex interactions between interface and turbulence are fully resolved. An explicit filtering of the DNS has been employed to evaluate the filtered quantities and to check the potential of the models for two-phase flows in the Interface and Subgrid Scales (ISS) modeling case proposed in part 1. The ISS concept is our proposal of a two-phase equivalent for the one-phase Large Eddy Simulation (LES) modeling case with sharp-interfaces. In this concept, bubbles remain bigger than the mesh size. Due to the impossibility to define a filter equivalent to the matched asymptotic expansions, we only test the modeling of the equivalent interface transport (the momentum jump conditions are not tested in this article, but will deserve additional results in a posteriori tests). Because the closure of the transport equation of the under-resolved discontinuous interface requires more modeling assumptions than the closure of the momentum equation, we think that the most relevant test has been done. The a priori tests realized show excellent agreement between the ISS models and the real contributions.