Hyperbolic high-fidelity simulations of cratering on a particle bed induced by a turbulent supersonic plume

A recently proposed hyperbolic granular model (Balakrishnan and Bellan, 2024) has been used to investigate the problem of supersonic-jet induced cratering on a solid-particle bed. This model relies upon the concept of added mass and a fluid-mediated particle pressure to render the system of equations hyperbolic. The jet is modeled using Large Eddy Simulation (LES) and the solid phase is modeled in an Eulerian framework using a Kinetic-Theory-based model modified for dense particle collections. The formulation also incorporates pseudo- turbulent kinetic energy (PTKE) which has been shown to modify a flow field laden with particles. The results explore the influence of the jet-to-ambient fluid density ratio, of the ambient fluid density, and of PTKE. A detailed analysis of the local and time-wise evolution of the added mass is presented through quantification of convection, added mass source and velocity-difference contributions. A quantitative assessment of the PTKE equation shows that while production is mostly effective at the crater base and walls, the dissipation and source term, both of which are also effective in the ejecta, nearly balance each other. The influence of the PTKE is mostly observed in the dilute particle regions (soil/gas interface and ejecta), with no effect on the macroscopic length scales of the flow. Both the jet-to-ambient fluid density ratio and the ambient fluid density affect the macroscopic crater features through entertainment into the jet that is determined by the former, and through the density of the fluid entrained, determined by the latter. This complex interaction governs the evolution of the crater diameter, visible top-view depth, and lower depth of the compacted region.