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Author Archive

Simulation of Rocket Plume Impingement and Dust Dispersal on the Lunar Surface

  • Contours of dust number density for 2 micron sized grains when particle collisions are neglected (left) and accounted for (right).  Note the dust layer is much thicker when grain - grain collisions are included.
  • Contours of horizontal velocity for a 1 m tall fence locations 10, 15, and 20 m from the landing site.
  • Contours of gas number density for various hovering altitudes.
  • Contours of static pressure when a realistic nozzle geometry (left) is simulated  compared to an assumed uniform flow at the exit plane of the nozzle.
  • Contours of horizontal velocity for a 1 m tall fence locations 10, 15, and 20 m from the landing site.
  • Contours of gas number density for various hovering altitudes.
  • Contours of gas number density for various hovering altitudes.
  • Contours of horizontal velocity for a 1 m tall fence locations 10, 15, and 20 m from the landing site.
  • Far field calculations for the gas and dust number densities caused from a lander hovering 5 m above the surface.
  • Gas number density and dust profiles for a four nozzle configuration where the engines are symmetrically placed 1.5 m from the axis of symmetry.
  • Number density contours from the continuum solver, DPLR.  The hybrid interface is indicated by the dashed line.
  • Macroscopic properties at the nozzle exit plane.

When a rocket lands on the Moon the engine exhaust plume will strike the lunar surface and disturb and disperse dust and larger debris. For any pre-existing structures (or residents) that plume of particulate ejecta represents a significant safety hazard. The scattered particles may penetrate weak surfaces, get stuck in mechanical systems, or coat solar panels, thermal radiators or optical systems. Such debris/dust may be difficult or impossible to clear from surfaces because of electrostatic attractions and the highly adhesive properties of lunar soil.  The dust also abrades optical surfaces and space suits, gets into joints, damages seals, and was considered by astronauts John Young and Gene Cernan to be among the most important obstacles to normal lunar operations. Moreover, since there is negligible background atmosphere on the moon, the range of particulate trajectories is very large. Knowledge of the high velocity dust spray will be necessary when making engineering design decisions.  However, it is difficult to examine this experimentally because of the difficulties associated with firing rocket engines into a dust bed while maintaining vacuum in a low gravity environment. Therefore, we examine this problem using the direct simulation Monte Carlo (DSMC) method.

The main objective of this work is to model and characterize the dust sprays that arise during various lunar landing scenarios.  The specific landing scenarios modeled in this work include: axisymmetric hover, landing on an inclined surface, and multiple nozzle configurations.  We parametrically study the effects that the hovering altitude and engine thrust have on the erosion profiles and the resulting dust sprays.  In a multiple engine configuration, we examine the plume-plume interactions and the effects that it has on trenching and dust spray behavior. In addition, high velocity dust sprays are likely unavoidable and can be detrimental to sensitive structures at a nearby lunar outpost.  Various mitigation techniques, such as a fence, have been proposed to shield nearby structures from the dust spray.  To assess the effectiveness of such a fence, the interaction between the high velocity dust spray with the fence is also studied.  To accomplish these tasks, we first model the plume flow field using a hybrid continuum–DSMC solver that is computationally efficient in the continuum near field and also accurate as the flow transitions towards rarefied and free molecular flow.  The surface stresses are computed and used to determine the dust erosion rate.  A two–phase flow model is then used to determine the trajectories of the entrained dust grains.  Once entrained into the flow, the effects of dust particle collisions are also studied.  This work will aid in the design of future lunar landers by describing how the dust sprays respond for different weight landers and engine configurations.  The high velocity dust sprays may be unavoidable without a pre-established landing platform.  Mitigation structures, such as a fence or berm, may be necessary to protect any establishments on the moon.  Our models can aid in the design of such a fence by predicting the impingement stresses and how the dust spray will respond.

 

LCROSS

  • Temperature of four grains each with different initial radius. These plots used the updated energy balance equation applied to the updated LCROSS code.
  • This is a schematic drawing of the LCROSS plume. The Shepherding Spacraft is labeled “S-S/C” on the top of the diagram. The spike and cone components of the plume are labeled as such. δ_s and δ_c are the spike and cone angles with respect to the vertical.
  • Sample run showing the optical depth of the plume as seen from the lunar south pole.
  • Diagram of some of the regolith physics included in the model
  • Radiance vs time plot for LCROSS plume
  • Radius plot for multiple LCROSS simulations. The Color Lines show a two species simulation with two grain species: pure ice and pure dirt. The different colors indicate the fraction of total ice mass that is initially in the spike component of the plume. The black line shows a one species simulation with one grain species: pure dirt core with a thin ice coating.

In 2009, the Lunar Crater Observation and Sensing Satellite (LCROSS) impacted the Moon to determine the existence of water ice in permanently shadowed lunar craters. The upper stage of the satellite struck the Cabeus crater near the lunar south pole, creating a large plume. The satellite flew through that plume collecting data before striking the Moon as well. Here at UT we are modeling the impact using a free molecular dynamics code to model the evolution of the plume. The code tracks the lunar ice covered regolith grains as they undergo radiative heat transfer and sublimate their water in the sunlight. Ionization and photo-dissociation of the water is also modeled, as well as “thermal hopping” due to adsorbtion and re-emission from the lunar surface. The spectral radiance of the plume as detected by the SSC as it descended is computed by using a single-scattering approximation.

Current work includes modeling additional physics of the regolith grains, incorporating separate pure regolith and pure ice species, adding dirty ice grains with variable ice to regolith ratios, modeling plume opacity as a function of wavelength, and generating spectra along lines of sight. These improvements will allow us to better understand the properties of the ice and dust particles and their interactions within the plume. This knowledge will help to assess conditions within permanently shadowed regions on the Moon.

PAPER II Submitted to Phys. of Fluids

Stephani, K., Goldstein, D., and Varghese, P., PAPER II Submitted to Phys. of Fluids.

Generation of a Hybrid DSMC/Navier-Stokes Solution via a Surface Reservoir Approach

Stephani, K., Goldstein, D., and Varghese, P., “Generation of a Hybrid DSMC/Navier-Stokes Solution via a Surface Reservoir Approach” to appear in J. Comp. Phys..

Sensitivity analysis for DSMC simulations of high-temperature air chemistry

Strand, J. and Goldstein, D. “Sensitivity analysis for DSMC simulations of high-temperature air chemistry,” submitted to J. Comp. Phys..

Unsteady flows in Io’s atmosphere caused by condensation and sublimation during and after eclipse: Numerical study based on a model Boltzmann equation

Kosuge, S., Aoki, K., Inoue, T., Goldstein, D. Varghese, P., “Unsteady flows in Io’s atmosphere caused by condensation and sublimation during and after eclipse: Numerical study based on a model Boltzmann equation”, submitted to Icarus.

HST/STIS Observations of Io’s Emission Spectrum in Jupiter Shadow: Probing Io’s Jupiter-facing eclipse Atmosphere

Trafton, L., Moore, C., Goldstein, D. Varghese, P. “HST/STIS Observations of Io’s Emission Spectrum in Jupiter Shadow: Probing Io’s Jupiter-facing eclipse AtmosphereIcarus 2012, 220(2) 1121-1140.

Discrete Velocity Gas Dynamics

  • Time variation of entropy and number of collisions, note logarithmic scale for collisions.
  • Comparison of the moments of the B-K-W distribution for relaxation with and without the interpolation scheme. The interpolation scheme allows for any post-collision velocity to be used while still maintaining conservation of mass, momentum, and energy.
  • Instantaneous snap shots of the instantaneous density and temperature profiles obtained by the variance reduction method (symbols) compared to time averaged DSMC solutions. The right axis shows the number of sampled collisions in the variance reduction method.
  • Slice of the Bobylev-Krook-Wu distribution function at z = 0. The B-K-W distribution is the only known analytic solution to the Boltzmann equation. It is used for verification of the code after changes have been made.
  • Instantaneous snap shots of the instantaneous density and temperature profiles obtained by the variance reduction method (symbols) compared to time averaged DSMC solutions. The right axis shows the number of sampled collisions in the variance reduction method.
  • Relaxation of the 4th, 6th, 8th, and 10th moments of the distribution function.
  • Slices of the BKW distribution at different times. The square symbols are from the variance reduction method and the triangles are without variance reduction.
  • Discrete representation of the Bobylev-Krook-Wu distribution along z = 0. The grid spacing is uniform and the spacing is β = 0.7. The B-K-W distribution is the only known analytic solution to the Boltzmann equation. It is used for verification of the code after changes have been made.
  • Instantaneous snap shots of the instantaneous density and temperature profiles obtained by the variance reduction method (symbols) compared to time averaged DSMC solutions. The right axis shows the number of sampled collisions in the variance reduction method.
  • The figure shows a comparison of our discrete velocity method with Direct Simulation Monte Carlo using the variable hard sphere collision model. A VHS parameter of ω = 0.78 was used (the value for N-2).  The two methods show good agreement in shock thickness when using the variable hard sphere model. It should also be noted how the discrete velocity solution produces smooth results.
  • The figure shows the relaxation of the Maxwellian distribution with an initial translational temperature and no initial rotational temperature. Internal energy is exchanged through the Larsen-Borgnakke model for rotational energy. The relaxation rate is Zr = 5, which controls the number of inelastic collisions (collisions that exchange energy) to elastic collisions (no internal energy exchange).

The Navier-Stokes (continuum) equations fail to accurately represent a flow when the characteristic length scale for macroscopic gradients is on the same order as the mean free path of the molecules in a gas, and the Boltzmann equation is needed. It remove the continuum constraint and models the gas on a microscopic level through interactions and convection of individual molecules. Such conditions may occur in micro- and nano-scale devices, shocks, satellite attitude control thruster plumes, around satellites in low-earth orbit, and during hypersonic re-entry.

A standard method for modeling a flow on the microscopic level is called Direct Simulation Monte Carlo (DSMC) where individual particles representing a set number of real molecules are tracked. The method is successful under a wide variety of flow conditions, but it has a number of difficulties with complex and transient flows, stochastic noise, trace species, and high level internal energy states.

One of the primary goals of this research is to address the concerns with DSMC through the development of an accurate and efficient discrete velocity method for solving the Boltzmann equation. The evolution of a flow is modeled through the collisions and motion of variable mass quasi-particles defined as delta functions on a truncated, discrete velocity domain. The work is an extension of a previous method developed by Aaron Morris, Philip Varghese, and David Goldstein for a single, monatomic species solved on a uniformly spaced velocity grid. The collision integral was computed using a variance reduced stochastic model where the deviation from equilibrium was calculated and operated upon. This method produces fast, smooth solutions of near-equilibrium flows. A 2D representation of the discrete velocity distribution function can be seen in a relaxation of the Bobylev-Krook-Wu distribution (the only analytic, time dependent solution to the Boltzmann equation). Notice that the quasi-particles change size due to collisions but remain at fixed velocity locations (bkw_converted).

Improvements to the method in the current research include:

  • Improved collision cross-section models such as variable hard sphere (VHS) and variable soft sphere (VSS).
  • Diffuse boundary conditions. Transient solutions to couette flow at Kn=0.1 display an application of the boundary condition.
  • Simple realignment of velocity grid lines into non-uniform grids.
  • Multiple species. Specifically trace species and species with large molecular mass ratios.
  • Quantized rotational and vibrational energy. The evolution of vibrational levels is easily tracked during flow simulations. For instance, in a homogeneous relaxation of kinetic and vibrational temperature (levels), results show smooth instantaneous solutions to vibrational distributions down to O(10E-6) density fraction values. Good resolution of high energy states will be important to future work on chemistry and ionization.

A variance reduced form of each of the improvements has been developed in order to maintain the computational benefits of the method. Each of the improvements allow for more complex or more accurate flow simulations by either expanding the physical complexity of the model or by providing more efficient computations. Some of the major benefits of the method are accurate and smooth representation of rare but important particles such as highly energetic trace species, high energy vibrational states, or the very low densities found at the front of an expansion into vacuum:

vacuum

Funding for this research was provided by NASA and the NSF.

DSMC simulation of plasma bombardment on Io’s sublimated and sputtered atmosphere

Moore, C.,Walker, A., Goldstein, D., Varghese, P., Trafton, L., Parsons, N., Levin, D., “DSMC simulation of plasma bombardment on Io’s sublimated and sputtered atmosphere”, AIAA paper 2012-0560 presented at the AIAA ASM, Nashville, Jan. 2012.

Investigation of turbulent wedge spreading mechanism with comparison to turbulent spots

Chu, J. and Goldstein, D., “Investigation of turbulent wedge spreading mechanism with comparison to turbulent spots”, AIAA paper 2012-0751 presented at the AIAA ASM, Nashville, Jan. 2012.