A homogeneous model for compressible three-phase flows involving heat and mass transfer.

A homogeneous model is proposed in order to deal with the simulation of fast transient three-phase ows involving heat and mass transfer. The model accounts for the full thermodynamical disequilibrium between the three phases in terms of pressure, temperature and Gibbs enthalpy. The heat and mass transfer between the phases is modeled in agreement with the second law of thermodynamics, which ensures a stable return to the thermodynamical equilibrium. The set of partial differential equations associated with this model is based on the Euler set of equations supplemented by a complex pressure law, and by six scalar-equations that allow to account for the thermodynamical disequilibrium. It therefore inherits a simple wave structure and possesses important mathematical properties such as: hyperbolicity, unique shock definition through Rankine-Hugoniot relations, positivity of the mixture fractions. Hence the computation of approximated solutions is possible using classical algorithms, which is illustrated by an example of simulation of a steam-explosion.