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Results for “Boltzmann Theory”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 37 records · Page 2
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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 NTRS1986

A second-order accurate kinetic-theory-based method for inviscid compressible flows

An upwind method for the numerical solution of the Euler equations is presented. This method, called the kinetic numerical method (KNM), is based on the fact that the Euler equations are moments of the Boltzmann equation of the kinetic theory of gases when the distribution function is Maxwellian. The KNM consists of two phases, the convection phase and the collision phase. The method is unconditionally stable and explicit. It is highly vectorizable and can be easily made total variation diminishing for the distribution function by a suitable choice of the interpolation strategy. The method is applied to a one-dimensional shock-propagation problem and to a two-dimensional shock-reflection problem.

Deshpande, Suresh M.↗
NASA NTRS1986

On the Maxwellian distribution, symmetric form, and entropy conservation for the Euler equations

The Euler equations of gas dynamics have some very interesting properties in that the flux vector is a homogeneous function of the unknowns and the equations can be cast in symmetric hyperbolic form and satisfy the entropy conservation. The Euler equations are the moments of the Boltzmann equation of the kinetic theory of gases when the velocity distribution function is a Maxwellian. The present paper shows the relationship between the symmetrizability and the Maxwellian velocity distribution. The entropy conservation is in terms of the H-function, which is a slight modification of the H-function first introduced by Boltzmann in his famous H-theorem. In view of the H-theorem, it is suggested that the development of total H-diminishing (THD) numerical methods may be more profitable than the usual total variation diminishing (TVD) methods for obtaining wiggle-free solutions.

Deshpande, S. M.↗
NASA NTRS1971

Brownian motion from Boltzmann's equation.

Two apparently disparate lines of inquiry in kinetic theory are shown to be equivalent: (1) Brownian motion as treated by the (stochastic) Langevin equation and Fokker-Planck equation; and (2) Boltzmann's equation. The method is to derive the kinetic equation for Brownian motion from the Boltzmann equation for a two-component neutral gas by a simultaneous expansion in the density and mass ratios.

Montgomery, D.↗
NASA NTRS1996

A viscoelastic higher-order beam finite element

A viscoelastic internal variable constitutive theory is applied to a higher-order elastic beam theory and finite element formulation. The behavior of the viscous material in the beam is approximately modeled as a Maxwell solid. The finite element formulation requires additional sets of nodal variables for each relaxation time constant needed by the Maxwell solid. Recent developments in modeling viscoelastic material behavior with strain variables that are conjugate to the elastic strain measures are combined with advances in modeling through-the-thickness stresses and strains in thick beams. The result is a viscous thick-beam finite element that possesses superior characteristics for transient analysis since its nodal viscous forces are not linearly dependent an the nodal velocities, which is the case when damping matrices are used. Instead, the nodal viscous forces are directly dependent on the material's relaxation spectrum and the history of the nodal variables through a differential form of the constitutive law for a Maxwell solid. The thick beam quasistatic analysis is explored herein as a first step towards developing more complex viscoelastic models for thick plates and shells, and for dynamic analyses. The internal variable constitutive theory is derived directly from the Boltzmann superposition theorem. The mechanical strains and the conjugate internal strains are shown to be related through a system of first-order, ordinary differential equations. The total time-dependent stress is the superposition of its elastic and viscous components. Equations of motion for the solid are derived from the virtual work principle using the total time-dependent stress. Numerical examples for the problems of relaxation, creep, and cyclic creep are carried out for a beam made from an orthotropic Maxwell solid.

Johnson, Arthur R.↗
NASA NTRS1975

Theory of photoelectron thermalization and transport in the ionosphere

A new theoretical approach for calculating the equilibrium photoelectron flux energy and pitch angle distribution in the ionosphere is presented. Photoelectron transport, secondary electron production, and energy degradation by the excitation of the discrete energy states of the neutral atmospheric constituents and by continuous energy transfer to the ambient thermal electron gas are included in a manner consistent with the Boltzmann equation which constitutes the foundation of the theory. A difference equation, suitable for numerical solution, is given, and a numerical method for the solution of this equation is discussed in detail.

Mantas, G. P.↗
NASA NTRS1996

Electrical double layers at the oil/water interface

This review presents the historical development and current status of the theory of the electrical double layer at a liquid/liquid interface. It gives rigorous thermodynamic definitions of all basic concepts related to liquid interfaces and to the electrical double layer. The difference between the surface of a solid electrode and the interface of two immiscible electrolyte solutions (ITIES) is analyzed in connection to their electrical properties. The most important classical relationships for the electrical double layer are presented and critically discussed. The generalized adsorption isotherm is derived. After a short review of the classical Gouy-Chapman and Verwey-Niessen models, more recent developments of the double layer theory are presented. These include effects of variable dielectric permittivity, nonlocal electrostatics, hydration forces, the modified Poisson-Boltzmann equation and the ion-dipole plasma. The relative merits of different theories are estimated by comparing them with computer simulation of the ITIES and electrical double layer. Special attention is given to the structure of ITIES and its variation due to adsorption of ions and amphiphilic molecules.

Non-NASA Center↗
NASA NTRS1993

Dust-acoustic double layers - Ion inertial effects

Space and astrophysical plasmas often comprise a number of massive ion components in addition to a tenuous, negatively charged dust component and an electron component. Stationary electrostatic double layers in a dusty plasma are investigated in a model treating the ion components as Boltzmann-distributed (inertialess) fluids. On comparison with the inertialess theory, one finds considerably reduced double layer existence parameter regimes. Significantly, highly nonlinear double layers are ruled out when ion inertia is incorporated. However, in the restricted parameter regimes in which the inertial theory predicts double layers for small ion/dust mass ratios (about 10 exp -15-10 exp -8) there is good qualitative agreement with inertialess theory. The reasons for these, and other discrepancies and similarities, are discussed.

Mace, Richard L.↗
NASA NTRS1982

Kinetic theory in astrophysics and cosmology

Results associated with exact solution of the Einstein-Boltzmann and Einstein-Maxwell-Boltzmann equations are presented. The generalization of Ehler's killing vector approach for the distribution function to charged particles is considered.

Ray, J. R.↗
NASA NTRS1974

Rarefied gas dynamics; Proceedings of the Eighth International Symposium, Stanford University, Stanford, Calif., July 10-14, 1972

Recent studies in the theory of rarefied gases (kinetic theory, shock structure, molecular forces and interactions, evaporation and condensation, expansions and jets, flow past bodies, gas-solid interactions) are presented along with descriptions of numerous experiments in these areas. Some of the topics covered include: singular limits of solutions of Boltzmann's equations, the Boltzmann and Klimontovich formalisms with reference to turbulent resolution, higher-order kinetic theory for the Lorentz gas, intermolecular potentials from shock structure experiments, cooling of particles in aerosol beams, hypersonic-subsonic transition in spherically symmetric expanding flows, absolute velocity measurements in a rarefied gas flow by an ion time-of-flight technique, the product distribution of gas-solid reactions from absolute rate theory, and relaxation of a gas with internal degrees of freedom. Individual items are announced in this issue.

Karamcheti, K.↗
NASA NTRS1982

Electrical characterization of Hg(1-x)Cd(x)Te alloys

Theoretical models are described for calculations of charge-carrier concentrations, Fermi energy, and conduction electron mobility as functions of x, temperature, and ionized and neutral defect concentrations of Hg(1-x)Cd(x)Te alloys. Measurements are reported of electron concentration and electron mobility from 5-300 K for alloys with x values of between 0.17 and 0.30. The electrical data are in reasonable agreement with theory, and were analyzed to obtain estimates of donor and acceptor state concentrations. The electron mobilities are calculated in terms of a microscopic theory of electrical conduction derived from the solution of the Boltzmann equation for the perturbed steady-state electron distribution function, and they show that longitudinal optical-phonon and charged and neutral defect scattering are the dominant mobility-limiting mechanisms.

Lehoczky, S. L.↗
NASA NTRS1993

Assessment of three numerical methods for the computation of a low-density plume flow

Results from three numerical methods including one based on the Navier-Stokes equations, one based on kinetic theory using the DSMC method, and one based on the Boltzmann equation with a Krook-type collision term are compared to each other and to experimental data for a model problem of heated nitrogen flow in a conical nozzle expanding into a vacuum. The problem simulates flow in a resistojet, a low-thrust, electrothermal rocket. The continuum method is applied to both the internal flow and near-field plume. The DSMC and Boltzmann methods are applied primarily to the plume. Experimental measurements of Pitot pressure and flow angle, taken with an apparatus that duplicates the model nozzle flow, are used in the comparisons.

Penko, Paul F.↗