Mathematical modelling of multi-phase flow using entropy symmetrization

Jet atomizations play a crucial role in many applications such as in cryogenic combustion chambers. Since direct numerical simulations of these two-phase flows in engine real configurations are still out of reach, predictive numerical tools must be developed using reduced-order models with sound mathematics properties. The contribution of this paper is three-fold. First, we introduce a new formalism to symmetrize non-conservative systems using entropic variables by extending Mock-Godunov theory and apply it to the Baer-Nunziato model. This new theory broaches new leads to obtain an original Eulerian diffuse interface model describing various mixture disequilibrium level based on an a consolidated mixture thermodynamic. Second, to cope with the strong discontinuities encountered in jet atomization, a robust and accurate numerical method using multi-slope MUSCL technique is applied to the various levels of the diffuse interface models. Third, relying on the previous two points, simulations of a jet atomization in a cryogenic combustion chamber in subcritical conditions are presented using diffuse interface models with thermal and velocity disequilibria coupled to an Eulerian kinetic-based moment method.