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NASA NTRS1986

Consistent transport coefficients in astrophysics

A consistent theory for dealing with transport phenomena in stellar atmospheres starting with the kinetic equations and introducing three cases (LTE, partial LTE, and non-LTE) was developed. The consistent hydrodynamical equations were presented for partial-LTE, the transport coefficients defined, and a method shown to calculate them. The method is based on the numerical solution of kinetic equations considering Landau, Boltzmann, and Focker-Planck collision terms. Finally a set of results for the transport coefficients derived for a partially ionized hydrogen gas with radiation was shown, considering ionization and recombination as well as elastic collisions. The results obtained imply major changes is some types of theoretical model calculations and can resolve some important current problems concerning energy and mass balance in the solar atmosphere. It is shown that energy balance in the lower solar transition region can be fully explained by means of radiation losses and conductive flux.

Fontenla, Juan M.↗

NASA NTRS2012

Numerical Simulation of Rocket Exhaust Interaction with Lunar Soil

This technology development originated from the need to assess the debris threat resulting from soil material erosion induced by landing spacecraft rocket plume impingement on extraterrestrial planetary surfaces. The impact of soil debris was observed to be highly detrimental during NASA s Apollo lunar missions and will pose a threat for any future landings on the Moon, Mars, and other exploration targets. The innovation developed under this program provides a simulation tool that combines modeling of the diverse disciplines of rocket plume impingement gas dynamics, granular soil material liberation, and soil debris particle kinetics into one unified simulation system. The Unified Flow Solver (UFS) developed by CFDRC enabled the efficient, seamless simulation of mixed continuum and rarefied rocket plume flow utilizing a novel direct numerical simulation technique of the Boltzmann gas dynamics equation. The characteristics of the soil granular material response and modeling of the erosion and liberation processes were enabled through novel first principle-based granular mechanics models developed by the University of Florida specifically for the highly irregularly shaped and cohesive lunar regolith material. These tools were integrated into a unique simulation system that accounts for all relevant physics aspects: (1) Modeling of spacecraft rocket plume impingement flow under lunar vacuum environment resulting in a mixed continuum and rarefied flow; (2) Modeling of lunar soil characteristics to capture soil-specific effects of particle size and shape composition, soil layer cohesion and granular flow physics; and (3) Accurate tracking of soil-borne debris particles beginning with aerodynamically driven motion inside the plume to purely ballistic motion in lunar far field conditions. In the earlier project phase of this innovation, the capabilities of the UFS for mixed continuum and rarefied flow situations were validated and demonstrated for lunar lander rocket plume flow impingement under lunar vacuum conditions. Applications and improvements to the granular flow simulation tools contributed by the University of Florida were tested against Earth environment experimental results. Requirements for developing, validating, and demonstrating this solution environment were clearly identified, and an effective second phase execution plan was devised. In this phase, the physics models were refined and fully integrated into a production-oriented simulation tool set. Three-dimensional simulations of Apollo Lunar Excursion Module (LEM) and Altair landers (including full-scale lander geometry) established the practical applicability of the UFS simulation approach and its advanced performance level for large-scale realistic problems.

Liever, Peter↗

NASA NTRS2012

Motion Imagery and Robotics Application (MIRA): Standards-Based Robotics

Martinez, Lindolfo↗

NASA NTRS1996

Fluid Creep Effects on Near-Wall Solute Transport for Non-Isothermal Ampoules

There is a growing practical and theoretical interest in developing accurate macroscopic modelling for flows arising in chemical or physical vapor transport (VT) crystal growth experiments, including those conducted in reduced gravity environments. Rosner was the first person to point out that previously neglected rarefield gas dynamics phenomena (Stefan and bouyancy-driven flows) become rather important sources of convection. In particular, the combination of rarefaction and strong gradients of temperature (and/or concentration) tangential to the side-walls of the ampoule induces convective flows known as thermal (and concentration) 'creep' respectively. His order-of-magnitude estimates revealed that thermal creep effects can be non-negligible even at normal gravitational levels. On the macroscopic level, the bulk fluid mechanics can be adequately described by the familiar macroscopic equations as long as the boundary conditions are modified to account for the integrated effect of kinetic boundary layers adjacent to solid boundaries. Motivated by the growing importance of these phenomena, we have embarked on a series of computational studies to elucidate these fundamental creep-induced effects for a rarefied gas in simple, two-dimensional confined geometries. However, unlike previous related studies, we resort to a microscopic description of the gas, mathematically expressed by the Boltzmann integro-differential equation. We employ the direct simulation Monte Carlo (DSMC) method of Bird, the theoretical foundations and several practical applications. In the case of thermally induced flows, the no-time counter method of Bird is used, as implemented for a hard-sphere gas. The scheme has been also extended to account for realistic molecular interaction models, an extension necessary if the diffusion physics underlying concentration creep are to be captured.

Papadopoulos, Dimitrios↗

NASA NTRS1968

Slip coefficient of a gas.

Slip coefficient of gas calculated from linearized Boltzmann-Bhatnagar-Gross-Krook equation for slip velocity problem

Huang, A. B.↗

NASA NTRS1993

Burnett solutions along the stagnation line of a cooled cylinder in low-density hypersonic flows

The Burnett equations in the cylindrical coordinate system have been applied to the hypersonic flow over a cylinder in low density environments. Through a local similarity transformation, the Burnett equations are degenerated into nonlinear third-order ordinary differential equations which are only valid along the stagnation line. These equations are solved by the multi-staged Runge-Kutta integration technique. Steady state solutions are asymptotically reached by the time-marching procedure. A newly-developed computer code is used to solve both the Navier-Stokes and the Burnett equations within the shock layer. The computed heat transfer coefficients are consistent with wind-tunnel and STS flight data. Comparisons with the DSMC solutions and the Boltzmann solutions show that the Burnett equations are more appropriate as the governing equations than the Navier-Stokes equations in the transitional flow regime.

Liaw, G. S.↗

NASA NTRS1980

A gravitational kinetic theory for planetesimals

An analytical theory is developed for the velocity evolution of nonaccreting planetesimal populations, based on the Boltzmann and Fokker-Planck equations. Adapting Shkarofsky's calculation of plasma viscosities, the rate of increase in random velocities due to gravitational encounters between planetesimals of equal mass is found to be one-third to one-half Safronov's result. Comparison with Wetherill's numerical experiments suggests that the Fokker-Planck equation underestimates the effectiveness of encounters and that Safronov's value is approximately correct. For populations of nonuniform sizes, the Fokker-Planck equation indicates an efficient redistribution of energy from the largest bodies to the smaller ones. By conserving angular momentum, the rate of radial spreading of orbits is also derived.

Stewart, G. R.↗

NASA NTRS1988

Charged-particle transport in one dimension

A numerical solution to high-energy charged-particle transport is found by evaluation of the integral equations obtained by inverting the Boltzmann differential operator. An algorithm has been written for either continuous or discrete spectra at the boundary, which allows efficient and accurate evaluation of this rather complicated problem. Present results are compared with analytic solutions based on the perturbation theory.

NASA Discipline Radiation Health↗

NASA NTRS1974

The Boltzmann- and the Klimontovich formalisms with reference to turbulence resolution

The Navier-Stokes equation expressed in terms of Klimontovich microscopic density is compared with the conventional one based on the Boltzmann formalism. Their difference is described by the two-point BBGKY equation. An implication is given that the averaging procedure from the Klimontovich to the Boltzmann formalism wipes out not only thermal agitation, but also a certain hydrodynamic turbulence. This is substantiated by agreement with measurements due to Schubauer and Klebanoff.

Tsuge, S.↗

NASA NTRS1983

Expansion of a multi-ion plasma into a vacuum

A numerical investigation of the expansion of a plasma with two ion species into a vacuum is presented. A set of Vlasov equations describe the ion behavior and the electrostatic potential is modelled by the Poisson equation. Electrons are assumed to follow Boltzmann's law. A plasma with H(+) and O(+) ions is considered, with the ions forming various combinations. Hydrodynamic calculations are performed for ions and electrons at equal temperatures, and for the presence of hot electrons. Self-similarity is shown to be valid where charge neutrality is dominant. An absence of significant quantities of ion-acoustic oscillations were observed.

Singh, N.↗

NASA NTRS1993

Boost-phase discrimination research

The final report describes the combined work of the Computational Chemistry and Aerothermodynamics branches within the Thermosciences Division at NASA Ames Research Center directed at understanding the signatures of shock-heated air. Considerable progress was made in determining accurate transition probabilities for the important band systems of NO that account for much of the emission in the ultraviolet region. Research carried out under this project showed that in order to reproduce the observed radiation from the bow shock region of missiles in their boost phase it is necessary to include the Burnett terms in the constituent equation, account for the non-Boltzmann energy distribution, correctly model the NO formation and rotational excitation process, and use accurate transition probabilities for the NO band systems. This work resulted in significant improvements in the computer code NEQAIR that models both the radiation and fluid dynamics in the shock region.

Langhoff, Stephen R.↗

NASA NTRS1998

A Unified Theory of Non-Ideal Gas Lattice Boltzmann Models

A non-ideal gas lattice Boltzmann model is directly derived, in an a priori fashion, from the Enskog equation for dense gases. The model is rigorously obtained by a systematic procedure to discretize the Enskog equation (in the presence of an external force) in both phase space and time. The lattice Boltzmann model derived here is thermodynamically consistent and is free of the defects which exist in previous lattice Boltzmann models for non-ideal gases. The existing lattice Boltzmann models for non-ideal gases are analyzed and compared with the model derived here.

Luo, Li-Shi↗

NASA NTRS2017

Lattice Boltzmann and Navier-Stokes Cartesian CFD Approaches for Airframe Noise Predictions

Lattice Boltzmann (LB) and compressible Navier-Stokes (NS) equations based computational fluid dynamics (CFD) approaches are compared for simulating airframe noise. Both LB and NS CFD approaches are implemented within the Launch Ascent and Vehicle Aerodynamics (LAVA) framework. Both schemes utilize the same underlying Cartesian structured mesh paradigm with provision for local adaptive grid refinement and sub-cycling in time. We choose a prototypical massively separated, wake-dominated flow ideally suited for Cartesian-grid based approaches in this study - The partially-dressed, cavity-closed nose landing gear (PDCC-NLG) noise problem from AIAA's Benchmark problems for Airframe Noise Computations (BANC) series of workshops. The relative accuracy and computational efficiency of the two approaches are systematically compared. Detailed comments are made on the potential held by LB to significantly reduce time-to-solution for a desired level of accuracy within the context of modeling airframes noise from first principles.

Airframe Noise Prediction↗

NASA NTRS1992

Lattice Boltzmann model for compressible fluids

A lattice Boltzmann model is derived which simulates compressible fluids. By choosing the parameters of the equilibrium distribution appropriately, the sound speed (which may be set arbitrarily low), bulk viscosity, and kinematic viscosity can be selected. This model simulates compressible flows and can include shocks. With a proper rescaling and zero-sound speed, this model simulates Burgers's equation. The viscosity determined by a Chapman-Enskog expansion compares well with that measured form simulations. The exact solutions of Burgers's equation on the unit circle are compared to solutions of lattice Boltzmann model finding reasonable agreement.

Alexander, F. J.↗

NASA NTRS2008

Non-Boltzmann Modeling for Air Shock-Layer Radiation at Lunar-Return Conditions

This paper investigates the non-Boltzmann modeling of the radiating atomic and molecular electronic states present in lunar-return shock-layers. The Master Equation is derived for a general atom or molecule while accounting for a variety of excitation and de-excitation mechanisms. A new set of electronic-impact excitation rates is compiled for N, O, and N2+, which are the main radiating species for most lunar-return shock-layers. Based on these new rates, a novel approach of curve-fitting the non-Boltzmann populations of the radiating atomic and molecular states is developed. This new approach provides a simple and accurate method for calculating the atomic and molecular non-Boltzmann populations while avoiding the matrix inversion procedure required for the detailed solution of the Master Equation. The radiative flux values predicted by the present detailed non-Boltzmann model and the approximate curve-fitting approach are shown to agree within 5% for the Fire 1634 s case.

Johnston, Christopher O.↗

NASA NTRS1979

Calculation of radiative properties of nonequilibrium hydrogen plasma

A computer program called NEQRAP is described that calculates the radiative properties of nonequilibrium ionized hydrogen. From the given electron temperature, electron density, and atom density values (which do not necessarily satisfy the equilibrium relationship) and intensities of incident radiation, the non-Boltzmann populations of electronic states are computed by solving the equation of quasi-steady-state population distribution. Emission and absorption coefficients are determined as functions of wavelength by invoking the principle of detailed balance between the upper and lower states of each radiative transition. Radiative transport through the medium is computed assuming a one-dimensional uniform slab. The rate of ionic reaction is also computed. When used on a sample case, the program shows that there is a large difference between the calculated intensities of radiation emitted by a bulk of equilibrium and nonequilibrium hydrogen. The accuracy of the program is estimated to be better than 10%.

Park, C.↗

NASA NTRS1986

Temporal features of the refilling of a plasmaspheric flux tube

The refilling of plasmaspheric flux tubes was studied by assuming that the protonosphere provides an ionospheric boundary where the H(+) density can be assumed; the supersonic flow in the flux tube is driven by the depletion of the plasma from the flux tube, while the base density and pressure in the protonosphere remain constant. The time-dependent continuity and momentum equations for the H(+) ions were solved. The electron gas was assumed to obey the Boltzmann law, and the proton gas was assumed to be isothermal. In agreement with the postulate of Banks et al. (1971), it was found that an important feature of the refilling is the formation of a shock pair at the equator; as the shocks propagate toward the ionosphere, the refilling occurs. Depending on the density at the ionospheric boundaries, a fair agreement was found between the refilling rates obtained for L = 6.6 and those from the GEOS 2 observations.

Singh, Nagendra↗

NASA NTRS2011

Gas Flux and Density Surrounding a Cylindrical Aperture in the Free Molecular Flow Regime

The equations for rigorously calculating the particle flux and density surrounding a cylindrical aperture in the free molecular flow regime are developed and presented. The fundamental equations for particle flux and density from a reservoir and a diffusely reflecting surface will initially be developed. Assumptions will include a Maxwell-Boltzmann speed distribution, equal particle and wall temperatures, and a linear flux distribution along the cylindrical aperture walls. With this information, the equations for axial flux and density surrounding a cylindrical aperture will be developed. The cylindrical aperture will be divided into multiple volumes and regions to rigorously determine the surrounding axial flux and density, and appropriate limits of integration will be determined. The results of these equations will then be evaluated. The linear wall flux distribution assumption will be assessed. The axial flux and density surrounding a cylindrical aperture with a thickness-to-radius ratio of 1.25 will be presented. Finally, the equations determined in this study will be verified using multiple methods.

Soulas, George C.↗