Ejecta from Granular-Medium Cratering by a Supersonic Jet Entering a Continuum Atmosphere

High-fidelity three-dimensional numerical simulations are analyzed to investigate cratering on a granular bed of particles due to a supersonic multi-species fluid jet. In the simulations, the volume-averaged two-phase equations are solved with a multi-species large-eddy simulation formulation for the fluid and a kinetic-theory-based model for the particle bed. The simulations vary according to the ratio of the jet-to-ambient-fluid density (and pressure) and the ambient density. The characteristics of the jets and crater are different according to the cross-sectional shape, which is determined by the jet/ambient density ratio: a conical shape is observed when the ratio is near unity, and a parabolic shape occurs when this ratio is large. Craters are characterized by their diameter, an upper depth, and a lower depth, with the difference between the two depths accounting for the granular medium compaction zone. The variation of the crater diameter timewise evolution is evaluated, and the evolution of the ratio between the upper or lower crater depths and the crater diameter is examined. Joint probability density functions of the Mach number based either on the fluid velocity or the relative velocity between the fluid and particles show that a large portion of the granular medium is dominated by subsonic conditions. The azimuthally averaged ejecta's radial variation is inspected, and joint probability density functions elucidate the regions where gravity effects are important.