Prediction of Regolith Ejection During Extraterrestrial Landings

Closeout Summary: The ejection of regolith upon landing of a spacecraft on an extraterrestrial body can present many challenges, including danger to surrounding hardware. The understanding of this ejection is limited and so the overall objective of this work is to understand and predict the transport of ejected regolith, with a special emphasis on the role of collisions and polydispersity. This knowledge will then be incorporated into a predictive tool that can be used by NASA engineers to design systems to mitigate the effects of regolith ejection. This objective will be accomplished by a combination of simulations using the Discrete Element Method (DEM), which treats particles as discrete entities using Newton’s equations, and a continuum model, which uses averaged flow variables to describe particle motion as a continuum (similar to how the Navier-Stokes equations are used to describe the motion of a molecular fluid). DEM will first be used to examine the role of collisions, which are absent from previous models for regolith ejection. The DEM, along with experiments, will be used to validate the continuum model. After validation, the continuum model can be transferred to NASA engineers as a predictive tool. This result is crucial for the future of space exploration. Due to increasing computational cost with number of particle species, it is impractical to use a continuum model to simulate a true continuous size distribution. Murray et al. developed and validated a technique to discretize a continuous distribution by matching the arithmetic moments of the distribution using a discrete number of particle sizes [25]. However, they only compared scalar transport properties for the continuous PSD in DEM and the discretized PSD in the continuum model. However, such an analysis is insufficient because other important physics are at play in many systems, such as gas-solid interactions for the lunar system of interest. In order to expand upon their work, a comparison of the continuous and discretized PSDs is done using the near-field DEM model from above. In order to accomplish this, the continuous PSDs used above are discretized according to the method of matching moments used by Murray et al. [25]. Additional considerations are taken to consider the truncation of the continuous PSDs. However, when examining the total erosion flux, we found that the erosion flux in the case of the discretized PSD is lower than that of the truncated continuous PSD. After careful consideration, we found this is due to underrepresentation of the smallest particles in the continuous PSD, which leads to a decrease in the erosion flux. The above issues led to the development of a new discretization method. In this new method, the continuous PSD is broken into bins of equal volume. Each bin is then assigned a size based on the arithmetic mean of the bin with the corresponding volume weights being equal for each size. Bins of equal number and surface area, along with a sauter-mean diameter (representing equivalent volume to area ratio), were also considered. After verifying this discretization is equivalent to the continuous PSD in the limit of increasing sizes, the erosion simulations were redone, with results shown in Figure 14. As S increases, the erosion flux becomes very similar to that of the continuous PSD, shown in Figure 8. A value of S=10 appears to yield a sufficiently good match in the erosion flux and is small enough to be practical in a continuum model. As a final validation of the continuum model for use in simulating the blowing of lunar reglith during a rocket landing, a far-field simulation will be compared against available Apollo landing data, as well as any available experimental data. The continuum simulation will be significantly larger than the simulations used in the comparison with the DEM model above, with distances on the order of 10 or possibly 100m from impingement (DEM domain is order 0.1cm). In order to appropriately simulate erosion from the surface, the erosion flux will be calculated at several distances from impingement, up to the distance at which no erosion takes place due to gas forces being too small (~3-4m from impingement). These calculated erosion fluxes will then be used to fit a function for the erosion flux as a function of distance from impingement. This function can then be used as the boundary condition at the surface. The bulk solids density and horizontal velocity of particles as they erode will be handled in a similar manner. Minor, straightforward modifications to MFIX will be necessary to use these functions as boundary conditions. In addition, the decision to use a true three-dimensional domain or an psuedo-two-dimensional (periodic in horizontal dimension perpendicular to flow) domain will be made based on computational cost. The challenge with using a pseudo-two-dimensional domain is that as particles travel further from the impingement point, they should spread out in the radial direction, which reduces the solids bulk density. However, modifications can be made to the code to account for this if necessary. Upon completion of determining the appropriate boundary conditions, the continuum model will be used to run a full-scale simulation of the ejection of lunar regolith during a rocket landing. The results from this simulation can then be compared against what is currently known from previous Apollo landings. Namely, Metzger et al. reported an ejection angle and particle density of the ejecting cloud [37]. The ejection angle reported was generally below 3 degrees and a particle density of 108 particles/m3. However, this data likely represents mostly small particles, which have the largest optical density, due to their high area/mass ratio. Similar data can be extracted from the proposed simulations and will be compared against this data. In addition, the physical characterization of the Surveyor III lander, which was sandblasted by the Apollo 12 landing, can be used as a rough validation. Namely, the Surveyor III showed signs of both scouring by small particles and pitting by larger particles, but was likely not within the main spray of soil. The proposed simulations will provide particle flux across a particular surface of a variety of particle sizes, which can demonstrate that both small and large particles could have potentially collided with the Surveyor III.