Cratering in a Granular Bed due to an Impinging Supersonic Jet Penetrating a Planetary Atmosphere in the Continuum Regime

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 jet density. The characteristics of the jets and crater are examined and they are found to be 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 close to unity, and a parabolic shape occurs when this ratio is large. The variation of the crater diameter time-wise evolution is evaluated, and the time-wise evolution of the ratio between the upper or lower crater depths and the crater diameter are also examined. The azimuthally averaged ejecta radial variation is inspected, and joint probability density functions elucidate the regions where gravity effects are important, and the Mach number regime in different parts of the flow.