A simple turbulent two-fluid model

We present in this paper a simple turbulent two-phase flow model using the two-fluid approach. The model, which relies on the classical ensemble averaging, allows the computation of unsteady flows including shock waves, rarefaction waves, and contact discontinuities. It requires the definition of adequate source terms and interfacial quantities. The hyperbolic turbulent two-fluid model is such that unique jump conditions hold within each field. Closure laws for the interfacial velocity and the interfacial pressure comply with a physically relevant entropy inequality. Moreover, source terms that account for mass, momentum and energy interfacial transfer are in agreement with the entropy inequality. Particular attention is also given to the jump conditions when assuming a perfect gas equation of state within each phase; this enables us to recover expected bounds on the mean density through shock waves.