A multiphase model for fluid-particle flows with added mass and phase change

In our prior work, a kinetic-based model for fluid-particle flows with added mass was derived (Fox et al., 2020) and successfully validated for non-reacting cases without mass transfer (Boniou and Fox, 2023). In this work, the multiphase model is extended to allow for the added-mass phase to have a different temperature and density than the particle and bulk-fluid phases, and to account for mass transfer from the particle phase to the added-mass phase. For this purpose, mass and energy transfer between particles and their added mass, and the added-mass and bulk-fluid phases are included. As before, the particle-phase density rho(p) is assumed constant, but now the added-mass density rho(a) is allowed to differ from the bulk-fluid density rho(f). These densities are coupled through the assumption that their pressures are equal, i.e., p(a) = p(f), and determined by a fluid-phase equation of state. Since mass transfer will change the particle volume, an additional balance equation for the particle number density N-d is required to complete the multiphase model. The computational algorithm for the extended model is tested using sublimation and condensation of carbon-dioxide particles interacting with a strong shock wave.