Browsing by Subject "engineering, aerospace"
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Item Conservative Deterministic Spectral Boltzmann Solver Near The Grazing Collisions Limit(2012-07) Haack, J. R.; Gamba, I. M.; Haack, Jeffrey R.; Gamba, Irene M.We present new results building on the conservative deterministic spectral method for the space homogeneous Boltzmann equation developed by Gamba and Tharkabhushaman. This approach is a two-step process that acts on the weak form of the Boltzmann equation, and uses the machinery of the Fourier transform to reformulate the collisional integral into a weighted convolution in Fourier space. A constrained optimization problem is solved to preserve the mass, momentum, and energy of the resulting distribution. Within this framework we have extended the formulation to the case of more general case of collision operators with anisotropic scattering mechanisms, which requires a new formulation of the convolution weights. We also derive the grazing collisions limit for the method, and show that it is consistent with the Fokker-Planck-Landau equations as the grazing collisions parameter goes to zero.Item Far Field Deposition Of Scoured Regolith Resulting From Lunar Landings(2012) Morris, A. B.; Goldstein, D. B.; Varghese, P. L.; Trafton, L. M.; Morris, A. B.; Goldstein, D. B.; Varghese, P.L.; Trafton, L.M.As a lunar lander approaches a dusty surface, the plume from the descent engine impinges on the ground, entraining loose regolith into a high velocity dust spray. Without the inhibition of a background atmosphere, the entrained regolith can travel many kilometers from the landing site. In this work, we simulate the flow field from the throat of the descent engine nozzle to where the dust grains impact the surface many kilometers away. The near field is either continuum or marginally rarefied and is simulated via a loosely coupled hybrid DSMC - Navier Stokes (DPLR) solver. Regions of two-phase and polydisperse granular flows are solved via DSMC. The far field deposition is obtained by using a staged calculation, where the first stages are in the near field where the flow is quasi-steady and the outer stages are unsteady. A realistic landing trajectory is approximated by a set of discrete hovering altitudes which range from 20m to 3m. The dust and gas motions are fully coupled using an interaction model that conserves mass, momentum, and energy statistically and inelastic collisions between dust particles are also accounted for. Simulations of a 4 engine configuration are also examined, and the erosion rates as well as near field particle fluxes are discussed.Item High Performance Computing With A Conservative Spectral Boltzmann Solver(2012-07) Haack, J. R.; Gamba, I. M.; Haack, Jeffrey R.; Gamba, Irene M.We present new results building on the conservative deterministic spectral method for the space inhomogeneous Boltzmann equation developed by Gamba and Tharkabhushaman. This approach is a two-step process that acts on the weak form of the Boltzmann equation, and uses the machinery of the Fourier transform to reformulate the collisional integral into a weighted convolution in Fourier space. A constrained optimization problem is solved to preserve the mass, momentum, and energy of the resulting distribution. We extend this method to second order accuracy in space and time, and explore how to leverage the structure of the collisional formulation for high performance computing environments. The locality in space of the collisional term provides a straightforward memory decomposition, and we perform some initial scaling tests on high performance computing resources. We also use the improved computational power of this method to investigate a boundary-layer generated shock problem that cannot be described by classical hydrodynamics.Item Improvement Of A Discrete Velocity Boltzmann Equation Solver With Arbitrary Post-Collision Velocities(2009-12) Morris, A. B.; Varghese, P. L.; Goldstein, D. B.; Morris, A. B.; Varghese, P. L.; Goldstein, D. B.We present a discrete velocity scheme which solves the Boltzmann equation and show numerical results for homogeneous relaxation problems. Although direct simulation of the Boltzmann equation can be efficient for transient problems, computational costs have restricted its use. A velocity interpolation algorithm enables us to select post-collision velocity pairs not restricted to those that lie precisely on the grid. This allows efficient evaluation of the replenishing part of the collision integral with reasonable accuracy. In previous work [1] the scheme was demonstrated with the depleting terms evaluated exactly, which made the method of O(N(2)) where N is the number of grid points in the velocity space. In order to reduce the computational cost, we have developed an acceptance-rejection scheme to enable more efficient evaluation of the depleting term. We show that the total collision integral can be evaluated accurately in combination with the mapping scheme for the replenishing term. To improve our scheme, we study the error and computational time associated with the number of depleting and replenishing points. We predict the correct relaxation rate for the Bobylev-Krook-Wu distribution and obtain exact conservation of mass, momentum, and energy. Comparisons between computed and reference solutions are shown as well, demonstrating the correct relaxation rate and dependence of error on parameters in the computational scheme.Item Io'S Atmospheric Freeze-Out Dynamics In The Presence Of A Non-Condensable Species(2009-12) Moore, C. H.; Goldstein, D. B.; Varghese, P. L.; Trafton, L. M.; Stewart, B. D.; Walker, A. C.; Moore, C. H.; Goldstein, D. B.; Varghese, P. L.; Trafton, L. M.; Stewart, B. D.; Walker, A. C.One dimensional direct simulation Monte Carlo (DSMC) simulations are used to examine the effect of a trace non-condensable species on the freeze-out dynamics of Io's sulfur dioxide sublimation atmosphere during eclipse and egress. Due to finite ballistic times, essentially no collapse occurs during the first 10 minutes of eclipse at altitudes above similar to 100 km, and hence immediately after ingress auroral emission morphology above 100 km should resemble that of the immediate pre-eclipse state. In the absence of a non-condensable species the sublimation SO2 atmosphere will freeze-out (collapse) during eclipse as the surface temperature drops. However, rapid collapse is prevented by the presence of even a small amount of a perfect non-condensable species due to the formation of a static diffusion layer several mean free paths thick near the surface. The higher the non-condensable mole fraction, the longer the collapse time. The effect of a weakly condensable gas species (non-zero sticking/reaction coefficient) was examined since real gas species may not be perfectly non-condensable at realistic surface temperatures. It is found that even a small sticking coefficient dramatically reduces the effect of the diffusion layer on the dynamics. If the sticking coefficient of the non-condensable exceeds similar to 0.25 the collapse dynamics are effectively the same as if there was no non-condensable present. This sensitivity results because the loss of non-condensable to the surface reduces the effective diffusion layer size and the formation of an effective diffusion layer requires that the layer be stationary which does not occur if the surface is a sink. As the surface temperature increases during egress from eclipse the sublimating SO2 gas pushes the non-condensable diffusion layer up to higher altitudes once it becomes dense enough to be collisional. This vertical species stratification should alter the auroral emissions after egress.Item Modeling Io'S Sublimation-Driven Atmosphere: Gas Dynamics And Radiation Emission(2009-12) Walker, A. C.; Gratiy, S. L.; Levin, D. A.; Goldstein, D. B.; Varghese, P. L.; Trafton, L. M.; Moore, C. H.; Stewart, B.; Walker, A. C.; Goldstein, D. B.; Varghese, P. L.; Trafton, L. M.; Moore, C. H.; Stewart, B.Io's sublimation-driven atmosphere is modeled using the direct simulation Monte Carlo method. These rarefied gas dynamics simulations improve upon earlier models by using a three-dimensional domain encompassing the entire planet computed in parallel. The effects of plasma impact heating, planetary rotation, and inhomogeneous surface frost are investigated. Circumplanetary flow is predicted to develop from the warm subsolar region toward the colder night-side. The non-equilibrium thermal structure of the atmosphere, including vibrational and rotational temperatures, is also presented. Io's rotation leads to an asymmetric surface temperature distribution which is found to strengthen circumplanetary flow near the dusk terminator. Plasma heating is found to significantly inflate the atmosphere on both day- and night-sides. The plasma energy flux also causes high temperatures at high altitudes but permits relatively cooler temperatures at low altitudes near the dense subsolar point due to plasma energy depletion. To validate the atmospheric model, a radiative transfer model was developed utilizing the backward Monte Carlo method. The model allows the calculation of the atmospheric radiation from emitting/absorbing and scattering gas using an arbitrary scattering law and art arbitrary surface reflectivity. The model calculates the spectra in the v, vibrational band of SO(2) which are then compared to the observational data.Item Modeling The Vapor And Dust Dynamics Due To The Impact Of The Lcross Spacecraft On The Moon(2009-12) Goldstein, D. B.; Summy, D.; Colaprete, A.; Varghese, P. L.; Trafton, L. M.; Goldstein, D. B.; Summy, D.The implications of possibly large volatile reservoirs on the Moon are significant for the future of manned activity there and for space science and exploration in general. In autumn of 2008 NASA will launch the LCROSS mission to impact two spacecraft into a permanently shadowed crater-a cold trap - at the south pole of the Moon. The lead spacecraft will excavate its own several meter crater. The process will be observed by the following smaller vehicle and by orbiting and Earth-based instruments in hopes of observing the release of volatiles-predominantly water -- from the lunar soil. The following vehicle will then impact as well. We examine the plausible vapor dynamics following the impacts and concentrate on the observability of the gas from Earth or lunar orbit. In the free-molecular computational model of the vapor motion, water and OH molecules move ballistically, have a temperature-dependent surface residence time, and are subject to photo-dissociation and ionization losses. Sunlight shadowing, separation of the vapor from the dust grains, dust thermodynamics and different impact plume models are considered.Item A Novel Discrete Velocity Method For Solving The Boltzmann Equation Including Internal Energy And Non-Uniform Grids In Velocity Space(2012) Clarke, P.; Varghese, P.; Goldstein, D.; Morris, A.; Bauman, P.; Hegermiller, D.; Clarke, P.; Varghese, P.; Goldstein, D; Morris, A.; Bauman, P.; Hergermiller, D.The discrete velocity method has been extended to include inelastic collisions with rotational-translational energy exchange. A single value of rotational energy per unit mass is assigned to every velocity in the velocity domain and inelastic collisions are modeled using the Larsen-Borgnakke method. The discrete velocity version of energy exchange is used to simulate both a homogeneous relaxation of a distribution with non-equilibrium rotational and translational temperatures and a 1D shock with rotational energy modes. The method has also been modified to allow for non-uniform grids in velocity space. Non-uniform grids permit computational effort to be focused on specific areas of interest within the velocity distribution function. The Bobylev-Krook-Wu solution to the Boltzmann equation (the only analytic solution known) is used to compare a non-uniform grid with a uniform grid.