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On the modeling of separated and disperse phase flows: derivation of well-posed and physically relevant diffuse interface models

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Florence Drui (ECP et Maison de la simulation)

With the aim of simulating the transition from separated-phase to disperse-phase flows, in atomization configurations for instance, we are interested in this work in compressible two-fluid models that can be used for the simulation of interfacial flows through the diffuse-interface approach. Such models are moreover studied in a context of disperse phase flows, such as bubbly flows, where their derivation based on averaging techniques are now well-developed.
We present another way of deriving these two-fluid models, based on a variational principle, whose advantage is to choose a priori the physical scales of description for the system. Attention is paid, on a one hand, to the well-posedness of such equations and, on the other hand, to the physical meaning of the relaxation parameters that have been introduced so as to satisfy the second principle of thermodynamics. We have physically identified these parameters thanks to comparisons with reference models and experiments on bubbly flows. The two-fluid models show thus a good ability for describing separated-phases as well as disperse phase flows, and some leads are given for a unification with spray models. We also present first numerical results using these models and associated finite volume numerical recipes: 1D tests of acoustic wave propagation as well as 2D and 3D AMR simulations of interfacial flows.