Predicting Regolith Erosion during a Lunar Landing: Role of Continuous Size Distribution

When a rocket lands on the Moon, the exhaust plume causes the lunar regolith (soil) to be ejected in all directions. Such high-speed ejection poses a threat to nearby equipment and structures. As a step toward better understanding the ejection process and mitigating the corresponding destruction, the discrete element method (DEM) is used to investigate the erosion flux of soil with a (continuous) lognormal distribution of particle size. The results show that the erosion flux increases relative to a monodisperse (single particle size) case with the same Sauter mean diameter due to an increase in the erosion flux of large particles and a reduction in that of small particles. The physical underpinnings of this counterintuitive behavior involve the interaction between small and large particles, particularly through collisions and static packing. Namely, the faster-moving smaller particles preferentially transfer momentum via collision to larger particles from a lower vertical position, causing an increase in large-particle flux and vice versa for small particles. Polydisperse mixtures also pack tighter than monodisperse mixtures, thereby increasing the erosion flux of both species by increasing the bulk density of the soil and the eroding material. Finally, to facilitate the use of kinetic-theory-based continuum models for this application, the discretization of continuous distributions is explored (e.g., representing a Gaussian distribution with a discrete approximation, e.g., particles of five different sizes). Two techniques are considered: the method of matching moments and a new method known as volumetric discretization. For the parameter space studied here, the volumetric discretization performs better when comparing the erosion flux of the continuous and discretized distributions.