Sensitivity to added mass closure models on predictions of supersonic jet-induced cratering in a particle bed

A recent formulation of supersonic-plume impingement on a granular bed has been shown to have the desirable property of being hyperbolic, thus permitting the physical propagation of pressure waves. This property stemmed from the inclusion of a model for the added mass and a fluid-mediated particle pressure. The present study is devoted to exploring the sensitivity of the results to added-mass models that is pivotal to ensuring hyperbolicity of the equations. Several added-mass models are explored and first evaluated with available shock tube experimental data. The effect of added-mass models on the spatial multidimensional dynamics of supersonic jet-induced cratering in particle beds is then investigated. Particularly, cratering dynamics, ejecta formation and dispersion, and other aspects crucial to avoiding potential disasters during spacecraft controlled landing on planetary bodies are comparatively assessed to understand the range of predictions corresponding to the added mass models. Crucially, several aspects of the results are examined to identify experimental results that would discriminate among models for the purpose of only retaining the model encapsulating the correct physics.