A Hyperbolic Eulerian Model for Dilute Two-Phase Suspensions

Conventional modeling of two-phase dilute suspensions is achieved with the Euler equations for the gas phase and gas dynamics pressureless equations for the dispersed phase, the two systems being coupled by various relaxation terms. The gas phase equations form a hyperbolic system but the particle phase corresponds to a hyperbolic degenerated one. Numerical difficulties are thus present when dealing with the dilute phase system. In the present work, we consider the addition of turbulent effects in both phases in a thermodynamically consistent way. It results in two strictly hyperbolic systems describing phase’s dynamics. Another important feature is that the new model has improved physical capabilities. It is able, for example, to predict particle dispersion, while the conventional approach fails. These features are highlighted on several test problems involving particles jets dispersion and are compared against experimental data. With the help of a single parameter (a turbulent viscosity), excellent agreement is obtained for various experimental configurations studied by different authors