Added-Mass and Pseudo-Turbulent Kinetic Energy Effects on Ejecta During Jet-Induced Cratering in a Soil

Simulations from a three-dimensional hyperbolic granular flow model are analyzed to understand the impact of two model features on the interaction between a supersonic, turbulent jet with a granular bed. Specifically, the roles of added mass and pseudo-turbulent kinetic energy (PTKE) on the cratering process are investigated. The fluid-phase equations conform to the large-eddy simulation formulation, and the solid-phase equations are based on the kinetic theory. Azimuthally-averaged quantities and their root mean square are investigated to elucidate the roles of added mass and PTKE on the ejecta. Additionally, correlations are analyzed to determine the potential locations where the added mass or PTKE might be important. The momentum flux and solid particle kinetic energy flux are examined to understand how entities in the path of these ejecta may be affected, depending on the inclusion of the added-mass and PTKE models. Finally, joint probability density functions are evaluated for pairs of variables to better understand the relationships between them. The results show that neither the added mass nor the PTKE influence the crater shape and morphology, but the jet-to-ambient density and the ambient density influence the crater dynamics; these modeling features also influence the ejecta radial distribution, which is practically independent of the PTKE. Whereas the ejecta distribution is strongly correlated with the added mass, PTKE strongly affects the kinetic energy of the ejecta.