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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

The generalized diffusion-convection equation

Starting from the Boltzmann equation, a transport equation is derived for energetic particles in a moving magnetized plasma in which the scattering centers that keep the particles quasi-isotropic are moving with a velocity that is not necessarily the same as that of the plasma. The scattering is characterized by three very loose constraints: (1) there is a rest frame for each scatterer in which the particles scatter elastically; (2) in this frame the scattering will not disturb an isotropic distribution; and (3) the momentum transfer in an average collision may be described by a tensor operating on the particles original momentum. Since the strength of the scattering is not specified, the derivation should be as valid for plasma microturbulence as for hard-sphere scattering. The results show clearly which phenomena are responsible for tying the particles to the plasma in the transport equation.

Jones, Frank C.↗
DOE OSTI2024

Semi-Lagrangian nodal discontinuous Galerkin method for the BGK model

In this work, we propose a semi-Lagrangian (SL) nodal discontinuous Galerkin (DG) solver for the BGK equation. The BGK model was introduced by Bhatnagar, Gross, and Krook [1] as a relaxation model for the fundamental Boltzmann equation [5], which describes the kinetic dynamic of rarefied gases with a probability distribution function. The challenges of designing efficient numerical schemes for the Boltzmann equation mainly come from its high dimensionality and complicated nonlinear collision operator. The BGK model gains interests since it has much lower computational cost, due to the relatively simple structure of the relaxation operator in replacement of the collision operator, while simultaneously preserving several important physical properties, such as macroscopic quantities and dissipation of entropy.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1973

Equations for the kinetic modeling of supersonically flowing electrically excited lasers

The equations for the kinetic modeling of a supersonically flowing electrically excited laser system are presented. The work focuses on the use of diatomic gases, in particular carbon monoxide mixtures. The equations presented include the vibrational rate equation which describes the vibrational population distribution, the electron, ion and electronic level rate equations, the gasdynamic equations for an ionized gas in the presence of an applied electric field, and the free electron Boltzmann equation including flow and gradient coupling terms. The model developed accounts for vibration-vibration collisions, vibration-translation collisions, electron-molecule inelastic excitation and superelastic de-excitation collisions, charge particle collisions, ionization and three body recombination collisions, elastic collisions, and radiative decay, all of which take place in such a system. A simplified form of the free electron Boltzmann equation is developed and discussed with emphasis placed on its coupling with the supersonic flow. A brief description of a possible solution procedure for the set of coupled equations is then discussed.

Lind, R. C.↗
NASA NTRS1991

Transport methods and interactions for space radiations

A review of the program in space radiation protection at the Langley Research Center is given. The relevant Boltzmann equations are given with a discussion of approximation procedures for space applications. The interaction coefficients are related to solution of the many-body Schroedinger equation with nuclear and electromagnetic forces. Various solution techniques are discussed to obtain relevant interaction cross sections with extensive comparison with experiments. Solution techniques for the Boltzmann equations are discussed in detail. Transport computer code validation is discussed through analytical benchmarking, comparison with other codes, comparison with laboratory experiments and measurements in space. Applications to lunar and Mars missions are discussed.

Wilson, John W.↗
NASA NTRS2003

Large-Eddy/Lattice Boltzmann Simulations of Micro-blowing Strategies for Subsonic and Supersonic Drag Control

This report summarizes the progress made in the first 8 to 9 months of this research. The Lattice Boltzmann Equation (LBE) methodology for Large-eddy Simulations (LES) of microblowing has been validated using a jet-in-crossflow test configuration. In this study, the flow intake is also simulated to allow the interaction to occur naturally. The Lattice Boltzmann Equation Large-eddy Simulations (LBELES) approach is capable of capturing not only the flow features associated with the flow, such as hairpin vortices and recirculation behind the jet, but also is able to show better agreement with experiments when compared to previous RANS predictions. The LBELES is shown to be computationally very efficient and therefore, a viable method for simulating the injection process. Two strategies have been developed to simulate multi-hole injection process as in the experiment. In order to allow natural interaction between the injected fluid and the primary stream, the flow intakes for all the holes have to be simulated. The LBE method is computationally efficient but is still 3D in nature and therefore, there may be some computational penalty. In order to study a large number or holes, a new 1D subgrid model has been developed that will simulate a reduced form of the Navier-Stokes equation in these holes.

Menon, Suresh↗
NASA NTRSDate not supplied

Simulating Underexpanded Jets in Martian and Lunar Environments

As part of the Game Changing Development (GCD) Program, funded by NASA’s Space Technology Mission Directorate (STMD), the development of simulation capability for the prediction of extra-terrestrial Plume Surface Interaction (PSI) environments has been undertaken by the Fluid Dynamics Branch at NASA/MSFC. The GCD PSI Project, planned to be accomplished over a four year period, contains a Predictive Simulation Capability (PSC) Element focused on creating simulation capability for the reliable and accurate prediction of PSI in Martian (~650 Pa) and Lunar (vacuum) ambient environments. In addition to the PSC Element, the PSI Project also contains a companion Ground Testing Element for development of focused datasets for validation of predictive capability as well as a Flight-focused Instrumentation Element. This paper describes the activities and accomplishments in the past year for the Prediction of Plume Flow in low pressure environments component of the PSI Project. While the Loci/Chem Computational fluid dynamics (CFD) application has been validated and used extensively for simulating launch environments in atmospheric conditions, use of this tool for simulating supersonic plumes at Mars-like ambient pressure requires further validation. CFD simulations of underexpanded jets have been performed using Loci/Chem for Mars-like conditions to predict several metrics for steady laminar, turbulent, and impinging plumes. The CFD results are compared with an experimental data set for low Reynolds number plumes at these conditions in order to evaluate the current capability of the Loci/Chem tool for these types of environments. The CFD validation results to date show reasonable agreement with the experimental data across all of the metrics of interest for the configurations considered. The Loci/Chem-Boltzmann CFD application is a hybrid continuum/rarefied flow solver which extends modeling capabilities to very low pressure environments such as those on the Moon. The Loci/Chem-Boltzmann solver uses a gradient-based continuum breakdown criterion to restrict solution of the computationally expensive Boltzmann equation to only a subset of the domain, while using the Navier-Stokes equations elsewhere. This CFD application is under active development, and current efforts toward establishing production ready capability for evaluating Lunar plume surface interactions are well under way. Initial simulations of an Apollo LEM indicate that several regions of the flow require solving the Boltzmann equations due to extreme rarefaction. Early simulations are promising, indicating reasonable overall computational time for a full 3D human scale lander simulation.

Thomas Shurtz↗
NASA NTRSDate not supplied

Simulating Underexpanded Plumes in Martian and Lunar Environments

While the Loci/Chem Computational fluid dynamics (CFD) application has been validated and used extensively for simulating launch environments in atmospheric conditions, use of this tool for simulating supersonic plumes at much lower ambient pressure requires further validation. Simulations of underexpanded plumes have been performed using Loci/Chem at Martian pressure to predict several metrics for laminar, turbulent, and impinging plumes. The CFD results are compared with an experimental data set for low Reynolds number plumes at these conditions in order to evaluate the current capability of the Loci/Chem tool for these types of environments. The CFD validation results to date show reasonable agreement with the experimental data across all the metrics of interest for the configurations considered. The Loci/Chem-Boltzmann tool is a hybrid continuum/rarefied flow solver which extends modeling capabilities to very low-pressure environments such as those on the Moon. The Loci/Chem-Boltzmann solver uses a gradient-based continuum breakdown criterion to restrict solution of the computationally expensive Boltzmann equation to only a subset of the domain, while using the Navier-Stokes equations elsewhere. This CFD application is under active development, and current efforts toward establishing production ready capability for evaluating Lunar plume surface interactions are well under way. Initial simulations of an Apollo Lunar excursion module indicate that several regions of the flow require solving the Boltzmann equations due to extreme rarefaction. Early simulations are promising, indicating reasonable overall computational time for a full 3D human scale lander simulation.

Plume Surface Interaction↗
NASA NTRS2002

Multiple-Relaxation-Time Lattice Boltzmann Models in 3D

This article provides a concise exposition of the multiple-relaxation-time lattice Boltzmann equation, with examples of fifteen-velocity and nineteen-velocity models in three dimensions. Simulation of a diagonally lid-driven cavity flow in three dimensions at Re=500 and 2000 is performed. The results clearly demonstrate the superior numerical stability of the multiple-relaxation-time lattice Boltzmann equation over the popular lattice Bhatnagar-Gross-Krook equation.

dHumieres, Dominique↗
NASA NTRS1993

Computer modeling of pulsed CO2 lasers for lidar applications

The object of this effort is to develop code to enable the accurate prediction of the performance of pulsed transversely excited (TE) CO2 lasers prior to their construction. This is of particular benefit to the NASA Laser Atmospheric Wind Sounder (LAWS) project. A benefit of the completed code is that although developed specifically for the pulsed CO2 laser much of the code can be modified to model other laser systems of interest to the lidar community. A Boltzmann equation solver has been developed which enables the electron excitation rates for the vibrational levels of CO2 and N2, together with the electron ionization and attachment coefficients to be determined for any CO2 laser gas mixture consisting of a combination of CO2, N2, CO, He and CO. The validity of the model has been verified by comparison with published material. The results from the Boltzmann equation solver have been used as input to the laser kinetics code which is currently under development. A numerical code to model the laser induced medium perturbation (LIMP) arising from the relaxation of the lower laser level has been developed and used to determine the effect of LIMP on the frequency spectrum of the LAWS laser output pulse. The enclosed figures show representative results for a laser operating at 0.5 atm. with a discharge cross-section of 4.5 cm to produce a 20 J pulse with aFWHM of 3.1 microns. The first four plots show the temporal evolution of the laser pulse power, energy evolution, LIMP frequency chirp and electric field magnitude. The electric field magnitude is taken by beating the calculated complex electric field and beating it with a local oscillator signal. The remaining two figures show the power spectrum and energy distribution in the pulse as a function of the varying pulse frequency. The LIMP theory has been compared with experimental data from the NOAA Windvan Lidar and has been found to be in good agreement.

Spiers, Gary D.↗
NASA NTRS2000

An Improved Neutron Transport Algorithm for Space Radiation

A low-energy neutron transport algorithm for use in space radiation protection is developed. The algorithm is based upon a multigroup analysis of the straight-ahead Boltzmann equation by using a mean value theorem for integrals. This analysis is accomplished by solving a realistic but simplified neutron transport test problem. The test problem is analyzed by using numerical and analytical procedures to obtain an accurate solution within specified error bounds. Results from the test problem are then used for determining mean values associated with rescattering terms that are associated with a multigroup solution of the straight-ahead Boltzmann equation. The algorithm is then coupled to the Langley HZETRN code through the evaporation source term. Evaluation of the neutron fluence generated by the solar particle event of February 23, 1956, for a water and an aluminum-water shield-target configuration is then compared with LAHET and MCNPX Monte Carlo code calculations for the same shield-target configuration. The algorithm developed showed a great improvement in results over the unmodified HZETRN solution. In addition, a two-directional solution of the evaporation source showed even further improvement of the fluence near the front of the water target where diffusion from the front surface is important.

Heinbockel, John H.↗
NASA NTRS2001

Development of an Innovative Algorithm for Aerodynamics-Structure Interaction Using Lattice Boltzmann Method

The lattice Boltzmann equation (LBE) is a kinetic formulation which offers an alternative computational method capable of solving fluid dynamics for various systems. Major advantages of the method are owing to the fact that the solution for the particle distribution functions is explicit, easy to implement, and the algorithm is natural to parallelize. In this final report, we summarize the works accomplished in the past three years. Since most works have been published, the technical details can be found in the literature. Brief summary will be provided in this report. In this project, a second-order accurate treatment of boundary condition in the LBE method is developed for a curved boundary and tested successfully in various 2-D and 3-D configurations. To evaluate the aerodynamic force on a body in the context of LBE method, several force evaluation schemes have been investigated. A simple momentum exchange method is shown to give reliable and accurate values for the force on a body in both 2-D and 3-D cases. Various 3-D LBE models have been assessed in terms of efficiency, accuracy, and robustness. In general, accurate 3-D results can be obtained using LBE methods. The 3-D 19-bit model is found to be the best one among the 15-bit, 19-bit, and 27-bit LBE models. To achieve desired grid resolution and to accommodate the far field boundary conditions in aerodynamics computations, a multi-block LBE method is developed by dividing the flow field into various blocks each having constant lattice spacing. Substantial contribution to the LBE method is also made through the development of a new, generalized lattice Boltzmann equation constructed in the moment space in order to improve the computational stability, detailed theoretical analysis on the stability, dispersion, and dissipation characteristics of the LBE method, and computational studies of high Reynolds number flows with singular gradients. Finally, a finite difference-based lattice Boltzmann method is developed for inviscid compressible flows.

Mei, Ren-Wei↗
NASA NTRS1976

A study of turbulent flow between parallel plates by a statistical method

Turbulent Couette flow between parallel plates was studied from a statistical mechanics approach utilizing a model equation, similar to the Boltzmann equation of kinetic theory, which was proposed by Lundgren from the velocity distribution of fluid elements. Solutions to this equation are obtained numerically, employing the discrete ordinate method and finite differences. Two types of boundary conditions on the distribution function are considered, and the results of the calculations are compared to available experimental data. The research establishes that Lundgren's equation provides a very good description of turbulence for the flow situation considered and that it offers an analytical tool for further study of more complex turbulent flows. The present work also indicates that modelling of the boundary conditions is an area where further study is required.

Srinivasan, R.↗
NASA NTRS1989

The diffusion approximation and transport theory for cosmic rays in relativistic flows

Equations describing the transport of cosmic rays in relativistic flows in the diffusion approximation are obtained. The analysis is based on the zeroth, first, and second differential moment equations of the relativistic Boltzmann equation with a BGK collision term. A perturbation solution of the moment equations in the diffusion approximation yields both the co-moving frame particle current and viscous stresses. The resultant cosmic-ray continuity equation contains three readily recognized energy change terms: the adiabatic energy change term; the viscous shear energy change term; and a term proportional to the scalar product of the acceleration vector of the scattering frame and the heat flux.

Webb, G. M.↗