摘要:

We consider the Boltzmann transport equation for point test particles in a background of polyatomic field particles in thermal equilibrium, under the action of an external constant force field, and in the Lorentz gas limit. The internal degrees of freedom of field particles are described by a discrete set of quantum energy levels. The asymptotic limit when elastic scattering becomes dominant is performed by means of a first order Chapman-Enskog expansion, after discussing the main properties of the collision operator. For the proper hydrodynamic quantity (a partial energy-dependent density) the limiting equation is a suitable drift-diffusion approximation, with additional inelastic scattering terms linking together different energies. ©2001 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.1407545

出版商:AIP    

年代:1901

数据来源: AIP

摘要:

Rarefied gas dynamics has traditionally been founded on the dilute gas assumption, which presupposes that the densities are so low that only binary collisions and single-body gas surface interactions occur. However, expressions for many-body collision rates and for many-body gas surface interaction (GSI) rates seem to suggest that at lower heights the dilute gas assumption is not valid. In particular, in the pure rarefied regime, two-body GSIs and some three-body interactions occur whereas, in the transition regime into continuum flow, four body collisions and four-body GSIs occur. In this paper I derive expressions for the collision rate for two-, three-and four-body encounters and then I generalize the result to any number of interacting bodies. I calculate collision rate ratios for the higher order interactions relative to the two-body result. By equating these ratios to unity I determine under what densities and temperatures a high order collision rate is comparable to the binary collision rate. I show that the frequencies of high order collisions are more sensitive to density and temperature variations than does the frequency of binary collisions. In fact, the higher the order of the collision the greater the sensitivity. This means that as the density and temperature decrease towards low values binary collisions predominate (higher order collisions diminish much faster). As the conditions increase towards high values high order collisions catch up with and supersede binary collisions (higher order collisions increase much faster). The expressions allow us to determine what conditions are safe to ignore high order collisions and what conditions necessitate their introduction in Direct Simulation Monte Carlo computations. The collision rate expressions are also useful in chemical kinetics. ©2001 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.1407546

出版商:AIP    

年代:1901

数据来源: AIP

摘要:

Although rarefied gas dynamics has traditionally stood on the dilute gas assumption, which supposes that the densities are so low that only binary collisions and single-body gas surface interactions occur, expressions for many-body collision rates and for many-body gas surface interaction (GSI) rates seem to suggest that at lower heights the dilute gas assumption is not valid. In particular, in the pure rarefied regime, two-body GSIs and some three-body interactions occur whereas, in the transition regime into continuum flow, four body collisions and four-body GSIs occur. In this paper I formulate anHtheorem for many-body collisions involving atoms. This exercise constitutes the final stage of constructing reciprocity proofs for many body collisions. The first two stages were pursued during the formulation of the many body collision models. They involved demonstrating that reciprocity models for monatomic many-body collisions satisfy detailed balance at equilibrium as well as symmetry with respect to the forward and inverse processes. I begin by deriving the Boltzmann equation for monatomic gases undergoing many body collisions. This leads to the formulation of an elastic collision integral. All these descriptions are carried out in the single-particle phase space of the gas. I formulate the properties of the elastic collision integral and then I use these to formulate anHtheorem for reciprocity-based many body collisions. Equilibrium distributions are derived from the approach. AnHtheorem proof for reciprocity models demonstrates that these models will drive a gas towards equilibrium when used in DSMC computations. ©2001 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.1407547

出版商:AIP    

年代:1901

数据来源: AIP

摘要:

Evaluation of the short-time expansion coefficients of a transient transport characteristics is a difficult problem; it is difficult to go beyond order two or three in the conventional analytical method. The present paper proposes a systematic way of evaluating the short-time expansion coefficients by using a matrix representation of the Boltzmann operator. The theory is an extension of a previous one so as to take account of the effects of the inelastic collision important in molecular gases. Good results of energy relaxation in a model gas are presented. ©2001 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.1407548

出版商:AIP    

年代:1901

数据来源: AIP

摘要:

©2001 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.1407549

出版商:AIP    

年代:1901

数据来源: AIP

摘要:

Group analysis developed especially for differential equations allows systematic study of solutions of the full Boltzmann kinetic equation. The study is connected with the admitted Lie group of infinitesimal transformations. Group classification of admitted group gives all representations of essentially different invariant solutions. Usually the group classification is quite difficult to do: it requires the application of special methods developed in group analysis. The lucky fact for the Boltzmann equation is that this equation and the system of gas dynamics equations admit isomorphic Lie groups. It allows using results of the group classification obtained for the gas dynamics equations. In this report the representations of all invariant solutions of the full Boltzmann equation and its Fourier representation when they are reduced to the equations with one or two independent variables were constructed. ©2001 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.1407550

出版商:AIP    

年代:1901

数据来源: AIP

摘要:

It has now been firmly established from both theoretical calculations and observations, that the exospheres of the terrestrial planets have extended coronae of translational energetic oxygen atoms. The current model generally accepted as the source of these hot atoms is the dissociative recombination ofO2+,that is,O2++e−→O*+O*where the productO*atoms are translationally energetic. The determination of the extent of this population of superthermal atoms is an important endeavor. The present paper considers a simple model based on the Boltzmann equation for the energy and altitude dependence of the oxygen atom distribution function. The density and temperature distributions are determined with this distribution. ©2001 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.1407551

出版商:AIP    

年代:1901

数据来源: AIP

摘要:

The asymptotic behavior of the cylindrical Couette flow problem for a rarefied rotating gas with evaporation and condensation is studied when the state of equilibrium is perturbed by the following small thermodynamic forces: (i) the pressure difference of the evaporating gas; (ii) the angular velocity difference of the cylinders; and (iii) the temperature difference of the cylinders. The problem is solved by using the hydrodynamic equations that follow from the balance equations of mass, momentum and energy of a viscous heat conducting rarefied gas. The hydrodynamic equations are solved analytically by considering slip and jump boundary conditions. The fields of density, velocity, temperature, heat flux vector and viscous stress tensor are calculated as functions of the Knudsen number for each thermodynamic force and for different values of the angular velocity. The asymptotic behavior of these fields are compared with those obtained from the kinetic equation. ©2001 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.1407552

出版商:AIP    

年代:1901

数据来源: AIP

摘要:

This is the continuation of the effort to utilize a kinetic molecular model approach to the problem of turbulence oriented computation of compressible flow. The Boltzmann equation is employed in its integral form with the BGK model of the collision term. This time, we compute a periodic compressible flow inside a unit cube from a random velocity field having an energy spectrum of isotropic type, uniform density and temperature. Results show the development of many small shock waves like structures along with vortex or eddy shocklets scattered in the entire flow field. While the energy spectrum does not change much in its pattern with time, as should be the case, some quantities like density distribution changes quickly to a turbulent state from its initial uniform one. Some geometric properties of computed flow field are derived from its velocity deformation tensor. ©2001 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.1407553

出版商:AIP    

年代:1901

数据来源: AIP

摘要:

A convex body, with high thermal conductivity, is immersed in a nonuniformly flowing gas. The body is small compared to the mean free path, which in turn is small compared to the macroscopic length scale of the gas. The equilibrium temperatureTwof the body is calculated. For an axially symmetric body in a simply shearing gas of temperatureTone obtains the equilibrium temperatureTwT=1+&bgr;a8 pxyp&hthinsp;sin2&hthinsp;&thgr;&hthinsp;sin(2&Jgr;).(this is for the case that the body is at rest with respect to the gas). &thgr;, &Jgr; are polar angles of the axis of the body (zis the polar axis).ais a geometric shape factor of the body (which vanishes for a sphere) and &bgr; depends on the Sonine coefficients. &bgr; takes the value 1 if only the lowest order Sonine term is retained.pis the pressure andpxy(the non-vanishing component of) the viscous pressure tensor. ©2001 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.1407554

出版商:AIP    

年代:1901

数据来源: AIP