Rarefied Gas Dynamics

MSN.81. W. C. Schieve and 1. Prigogine, The role of subdynamics in kinetic theory, in Rarefied Gas Dynamics, Academic Press, San Erancisco, 1974, pp. 19-35. 

When Bernie Shizgal arrived at UBC in 1970, his research interests were in applications of kinetic theory to nonequilibrium effects in reactive systems. He subsequently applied kinetic theory methods to the study of electron relaxation in atomic and molecular moderators,46 hot atom chemistry, nucleation,47 rarefied gas dynamics,48 gaseous electronics, and other physical systems. An important area of research has been the kinetic theory description of the high altitude portion of planetary atmospheres, and the escape of atmospheric species.49 An outgrowth of these kinetic theory applications was the development of a spectral method for the solution of differential and integral equations referred to as the quadrature discretization method (QDM), which has been used with considerable success in statistical, quantum, and fluid dynamics.50... 

D. T. Lyons, Proc. 19th Int. Symp. Rarefied Gas Dynamics, Eds. J. K. Harvey tind R. G. Lord (Oxford University Press, Oxford, 1995), p. 1408. 

G. E. Caledonia, Laboratory Simulations of Energetic Atom Interactions Occurring in Low Earth Orbit, Rarefied Gas Dynamics — Space-Related Studies Proceedings of the 16th International Symposium on Rarefied Gas Dynamics, held in Pasadena, CA, 10-16 July 1988, Progress in Astronautics and Aeronautics, Vol. 116, Eds. E. P. Muntz, D. P. Weaver and D. H. Campbell (AIAA, Washington, D.C., 1989) pp. 129-142. 

R. C. Tennyson, Atomic-Oxygen and its Effects on Materials in Space, Rarefied Gas Dynamics Technical Papers from the Proceedings of the 18th International Symposium on Rarefied Gas Dynamics, held in Vancouver, B.C., Canada, 26-30 July 1992, Progress in Astronautics cind Aeronautics, Exls. B. D. Shizgad and D. P. Weaver (AIAA, Washington, D.C., 1992) pp. 461-477. 

The local value of Knudsen number determines the degree of rarefaction and the degree of validity of the continuum model in a particular flow. The different Knudsen number regimes depicted in Fig. 2 have been determined empirically and are therefore only approximate for a particular flow geometry. The pioneering experiments in rarefied gas dynamics were conducted by Knudsen in 1909 [24]. 

M. K. Kogan, Rarefied Gas Dynamics, Plenum Press, New York, 1959. 

Kogan MN (1969) Rarefied Gas Dynamics. Trilling L ed translated from... 

Cercignani, C. 2000 Rarefied Gas Dynamics. Cambridge Cambridge University Press. 

Talbot, L. 1981 Thermophoresis - a review, in 12th International Symposium on Rarefied Gas Dynamics, New York (NY) American Institute of Aeronautics and Astronautics, pp. 467 88. 

One of the earliest particle-based schemes is the Direct Simulation Monte Carlo (DSMC) method of Bird [126]. In DSMC simulations, particle positions and velocities are continuous variables. The system is divided into cells and pairs of particles in a cell are chosen for collision at times that are determined from a suitable distribution. This method has seen wide use, especially in the rarefied gas dynamics community where complex fluid flows can be simulated. 

At low pressures (or more precisely at high values of the Knudsen number Kn > 0.2) the continuum approximation can no longer be used, and rarefied gas dynamics has to be invoked for plasma flow. For practical plasma reactors, this becomes necessary at pressures below 10 mtorr. 

J. P. Hartnett, A Survey of Thermal Accommodation Coefficients, Rarefied Gas Dynamics, L. Talbot ed., pp. 1-28, Academic Press, New York, 1961. 

J. Gspann and H. Vollmer, in Rarefied Gas Dynamics, edited by K. Karam-cheti (Academic, New York, 1974) p. 261. 

Ashkenas, J. Sherman, F. S. "Proceedings of the 4th International Symposium on Rarefied Gas Dynamics", 1966 deLeevw,... 

Fain, D.E., Brown, W.K., Neonisotopeseparation by gaseousdif-fusion transport in the transition flow regime with regular geometries, 1976 20 p 10. in International Symposium on Rarefied Gas Dynamics, Aspen, CO, July 18, 1976, https //inis.iaea. org/search/search. aspx orig q=source "CONF-760710-6 , accessed on October 2014. 

A typical magnitude of the mean free path i in equilibrium air under the standard conditions is about 5 10 m. Thus, if a channel has a cross-sectional size a in the range from 10 to 10 m, then the Knudsen number Kn = tja is not so small in order to use the approach based on continuum mechanics. In this case, gas flows must be considered on the kinetic level, i.e., the methods of rarefied gas dynamics based on the Boltzmann equation [1-3] must be used. The advantage of the kinetic approach is that it is applicable for any value of the Knudsen number, namely, for very small values (Kn [Pg.1269]

Sharipov F (2012) Benchmark problems in rarefied gas dynamics. Vacuum 86 1697-1700... 

The main parameter determining the gas rarefaction is the Knudsen number Kn = Ha, where I is the mean free path of fluid molecules and a is a typical dimension of gas flow. If the Knudsen number is sufficiently small, say Kn < 10 , the Navier-Stokes equations are applied to calculate gas flows. For intermediate and high values of the Knudsen number, the Navier-Stokes equations break down, and the implementation of rarefied gas dynamics methods is necessary. In practical calculations usually the rarefaction parameter defined as the inverse Knudsen number, i.e.. 

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