A Multi-Species Modeling Framework for Describing Supersonic-Jet Induced Cratering in a Granular Bed: Cratering on Titan Case Study

Abstract

The dynamics of cratering caused by a multi-component supersonic jet due to its interaction with the granular soil on the surface of Titan is investigated using a two-phase model and numerical simulations. Both fluid and particles are mathematically described in an Eulerian framework. The fluid is modeled using multi-species Large Eddy Simulation accounting for the details of diffusion among species, and the solid phase is described by a Kinetic-Theory-based model. The general framework is that of a recent model that successfully predicted specific details of Mars/Earth cratering observed by the Mars Science Laboratory (Balakrishnan and Bellan, International Journal of Multiphase Flow, 99, 1–29, 2018), however the distinctive differences between the present and previous model allows new physics to be uncovered that is peculiar to cratering in the presence of a dense atmosphere. Unsteady, three-dimensional simulations are performed to elucidate the morphological features of the crater and the dynamics of its evolution with time. Parametric variations of the initial conditions are conducted to understand the effect of the surface evenness, jet Mach number, particle size in the granular bed, jet composition, and the inter-granular stress coefficient. The new observation of crater-in-a-crater formation at early times is discussed and explained; this phenomenon is transient and the subsequent consumption of the inner crater by the surrounding crater walls is explained in detail. The jet exhibits complex morphological features revealed by vorticity and helicity analysis. The primary-crater walls display ripples along their surface that are traced to the interaction with the dense jet fluid which, having reached the crater bottom, changes direction to exit the crater using the spaces unoccupied by the jet and rubs the crater walls. Detailed analyses of the particle volume fraction and the particle momentum revealed the detailed morphology of the craters and the ejections from the craters, and related them to the initial conditions. A larger jet Mach number results in increased erosion due to the higher momentum content of the jet. A smaller increase in the jet momentum obtained by increasing the jet-fluid molar mass jet results in a crater that is more angled at the top, this feature being due to the increased jet expansion rate. The inter-granular stress coefficient does not affect the large-scale features of the crater, but does affect the peak compaction values. Species diffusion is investigated and it is found that both regular and uphill diffusion occur, the latter being primarily concentrated in the vicinity of the jet and the depths of the crater. The presented detailed formulation and numerical methodology for investigating supersonic jet-induced cratering on granular soil are sufficiently robust to accommodate plume-induced cratering on a variety of planetary bodies having an atmosphere.

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