Two-fluid modeling of cratering in a particle bed by a subsonic turbulent jet

Abstract

The Two-Fluid Method is capable of modeling large-scale (i.e., lab scale or larger) multiphase (particle-fluid) flows by treating both the fluid and particle phase as interpenetrating continua and solving mass and momentum balances for each phase. To solve for the flow of the solids phase the momentum balance requires constitutive relations in the form of normal and shear stresses – i.e., pressures and viscosities. However, the stresses that account for frictional contacts in dense particle systems, and are relevant to this work, are empirically based. A study of the effects of adjusting the frictional model formulation (the empirical parameters of the model), by changing the overall frictional stress magnitude and the relative magnitude of the frictional viscosity to the frictional pressure, on the behavior of the bed is presented here. It was found that the magnitude of the frictional viscosity relative to the frictional pressure affects the crater growth prediction almost as much as the magnitude of the overall frictional stress. Additionally, a frictional model formulation is validated for sand particles, and predictions are compared with existing experimental data for the crater formation of a sand bed under a vertical, impinging jet of gas (Metzger et al. J Areo Eng (2008) v22, p24–32). In the low jet velocity regime (subsonic, turbulent jet), the model predicts the salient features previously measured for the growth rate of the crater of time, the profile of the crater, and the response of the crater to turning the jet off. In the high jet velocity regime (compressible, near sonic jet flow) the prediction agrees qualitatively with prior experimental observations.