A compressible two-phase model for dispersed particle flows with application from dense to dilute regimes

Abstract

Multiphase flows are present in many important fields ranging from multiphase explosions to chemical processing. An important subset of multiphase flow applications involves dispersed materials, such as particles, droplets, and bubbles. This work presents an Eulerian–Eulerian model for multiphase flows containing dispersed particles surrounded by a continuous media such as air or water. Following a large body of multiphase literature, the driving force for particle acceleration is modeled as a direct function of both the continuous-phase pressure gradient and the gradient of intergranular stress existing within the particle phase. While the application of these two components of driving force is well accepted in much of the literature, other models exist in which the particle-phase pressure gradient itself drives particle motion. The multiphase model treats all phases as compressible and is derived to ensure adherence to the 2nd Law of Thermodynamics. The governing equations are presented and discussed, and a characteristic analysis shows the model to be hyperbolic, with a degeneracy in the case that the intergranular stress, which is modeled as a configuration pressure, is zero. Finally, results from a two sample problems involving shock-induced particle dispersion are presented. The results agree well with experimental measurements, providing initial confidence in the proposed model.