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Results for “KNUDSEN NUMBER”

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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All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

General equations for the motions of ice crystals and water drops in gravitational and electric fields

General equations for the Reynolds number of a variety of types of ice crystals and water drops are given in terms of the Davies, Bond, and Knudsen numbers. The equations are in terms of the basic physical parameters of the system and are valid for calculating velocities in gravitational and electric fields over a very wide range of sizes and atmospheric conditions. The equations are asymptotically matched at the bottom and top of the size spectrum, useful when checking large computer codes. A numerical system for specifying the dimensional properties of ice crystals is introduced. Within the limits imposed by such variables as particle density, which have large deviations, the accuracy of velocities appears to be within 10 percent over the entire range of sizes of interest.

Nisbet, John S.↗
NASA NTRS1987

Computational fluid dynamics near the continuum limit

Two dimensional Navier-Stokes equations for a perfect gas are solved for hypersonic flow over a flat plate at Reynolds numbers ranging from continuum to the free molecule flow. In the transition flow regime, new slip boundary conditions are introduced, which reduce to the well-known slip conditions of Maxwell at small Knudsen numbers and yield the correct shear stress and heat transfer in the limiting case of free molecule flow. Comparison of the computed results with the existing experimental data and Monte Carlo calculations indicates that the continuum Navier-Stokes equations give surprisingly realistic results throughout the transition flow regime, when the new slip boundary conditions are used.

Maccormack, Robert W.↗
NASA NTRS1971

Dynamic upper atmospheric force model on stabilized vehicles for a high-precision trajectory computer program

The upper atmosphere model draws heavily on the behavior of the earth's upper atmosphere which exhibits cyclic as well as irregular variations in density profile, temperature, pressure, and composition in unison with solar activities as deduced from the more recent land-based and satellite observations. The lift and drag model is designed specifically for inertially stabilized vehicles of the Mariner class, with possible extension to gravity gradient stabilized vehicles of the GEOS class. The model considers operation in the free molecular flow regimes with large Knudsen numbers. The vehicle is considered a composite structure with basic components having well-defined shapes, each with its own surface characteristics in terms of temperature, reflectivity, and accommodation of free stream molecules. The model takes into account both the calculation of precise aerodynamic force coefficients in terms of expansion of modified Bessel functions in speed ratios and angle of attack, and approximate force coefficients when the speed ratios approach infinity. Other considerations include specular and diffused reflectivity, shielding, and shadow effects.

Khatib, A. R.↗
NASA NTRS1972

Kinetic theory analysis of rarefied gas flow through finite length slots

An analytic study is made of the flow a rarefied monatomic gas through a two dimensional slot. The parameters of the problem are the ratios of downstream to upstream pressures, the Knudsen number at the high pressure end (based on slot half width) and the length to slot half width ratio. A moment method of solution is used by assuming a discontinuous distribution function consisting of four Maxwellians split equally in angular space. Numerical solutions are obtained for the resulting equations. The characteristics of the transition regime are portrayed. The solutions in the free molecule limit are systematically lower than the results obtained in that limit by more accurate numerical methods.

Raghuraman, P.↗
NASA NTRS1974

A study of dynamical behavior of space environment

Studies have covered a wide range of problems in the space environment, such as the problems of the dynamical behavior of the thermosphere, hydromagnetic wave propagation in the ionosphere, and interplanetary space environment. The theories used to analyze these problems range from a continuum theory of magnetohydrodynamics to the kinetic theory of free molecular flow. This is because the problems encountered covered the entire range of the Knudsen number (i.e., the ratio of mean free path to the characteristic length). Significant results are summarized.

Wu, S. T.↗
NASA NTRS1975

Propagation of acoustic modes in the transitional ionosphere

Continuum theory is unsatisfactory for describing wave propagation in the transitional ionosphere, since the mean free path is of the same order as the characteristic length (i.e., Knudsen number in this region is of the order of unity). Therefore a transition model in which isotropic electrons behave as a fluid while the ions are governed by the kinetic equation modified by ion-electron collision effects is proposed to study acoustic wave propagation in the upper atmosphere in the altitude region from 500 to 2000 km. The results show that the dissipation of acoustic waves by electrons is through the viscous and thermal conduction effects, and the dissipation of acoustic waves by ions is through Landau damping. Comparisons of the characteristics of acoustic mode propagation and wave dissipation mechanisms in the collision-dominated, transitional from collisional to collisionless, and collisionless media are also discussed.

Hung, R. J.↗
NASA NTRS1976

Environmental dynamics at orbital altitudes

The work reported involved the improvement of aerodynamic theory for free molecular and transition flow regimes. The improved theory was applied to interpretation of the dynamic response of objects traveling through the atmosphere. Satellite drag analysis includes analysis methods, atmospheric super rotation effects, and satellite lift effects on orbital dynamics. Transition flow regimes were studied with falling sphere data and errors resulting in inferred atmospheric parameters from falling sphere techniques. Improved drag coefficients reveal considerable error in previous falling sphere data. The drag coefficient has been studied for the entire spectrum of Knudsen Number and speed ratio, with particular emphasis on the theory of the very low-speed ratio regime.

Karr, G. R.↗
NASA NTRS1977

Kinetic theory analysis of rarefied gas flow through finite length slots

A kinetic-theory analysis is made of the flow of a rarefied monatomic gas through a two-dimensional slot connecting two reservoirs. Numerical solutions are obtained by the moment and discrete-ordinate methods. The former method portrays the transition-regime characteristics well but has limitations in the free-molecule regime. The latter method gives accurate results in the free-molecule and slip regimes and bolsters confidence in the accuracy of the transition-regime results. The numerical solution for the mass flux through the slot agrees well with an approximate analytical solution of the moment equations for length-to-width ratios from 6 to 0.5, pressure ratios from 0.8 to 0.1, and Knudsen numbers from 5 to 0.5.

Raghuraman, P.↗
NASA NTRS1979

Fermi liquid viscosity in a finite geometry

Forced flow of a Fermi liquid is studied for a cell geometry consisting of two planes with a separation on the order of mean free path. An approximate transport equation is used to derive an integral equation for the velocity profile, which is solved numerically. Results for the total flux through the cell, which determines the dissipation, are given as a function of the Knudsen number N (ratio of cell thickness to mean free path). Effects of specular reflection at the boundaries are considered. It is found that the dissipation has a minimum at N approximately equal to 1/2, and behaves linearly for N greater than or equal to 3. Implications for present experimentation are discussed.

Jaffe, J. E.↗
NASA NTRS1979

Fermi liquid viscosity in a finite geometry

Forced flow of a Fermi liquid is studied for a cell geometry consisting of two planes with a separation on the order of the mean free path. An approximate transport equation is used to derive an integral equation for the velocity profile, which is solved numerically. Results for the total flux through the cell, which determines the dissipation, are given as a function of the Knudsen number kappa (ratio of cell thickness to mean free path). Effects of specular reflection at the boundaries are considered. It is found that the dissipation has a minimum at kappa of 1/2, and behaves linearly for kappa not less than 3. Implications for present experimentation are discussed.

Jaffe, J. E.↗
NASA NTRS1981

Evacuation-induced pressure differentials in multilayer insulation systems

The pressure differentials induced across three types of multilayer insulation systems during evacuation have been measured and compared with values predicted using an idealized parallel plate geometric model. The systems tested were double-aluminized Mylar with a Tissuglas or silk net spacer and crinkled single-aluminized Mylar. Test samples were circular. The influence of purge gas type, layer density, sample diameter, and temperature was systematically investigated. The experimental approach was to measure the absolute pressure history and corresponding pressure differential induced across the insulation during evacuation. The measured pressure differentials were nondimensionalized and compared with those predicted by the parallel plate model as a function of Knudsen number. It was concluded that the parallel plate model is adequate for making engineering analyses. The influence of all parameters, except layer density, is well represented by the model. Representation of the influence of layer density is less satisfactory, but can be improved by modification of the flat plate model to allow for the more obvious practical nonidealities, such as crinkling, or the presence of a net spacer.

Glassford, A. P. M.↗
NASA NTRS1982

Heat loss and drag of spherical drop tube samples

Analysis techniques for three aspects of the performance of the NASA/MSFC 32 meter drop tube are considered. Heat loss through the support wire in a pendant drop sample, temperature history of a drop falling through the drop tube when the tube is filled with helium gas at various pressures, and drag and resulting g-levels experienced by a drop falling through the tube when the tube is filled with helium gas at various pressures are addressed. The developed methods apply to systems with sufficiently small Knudsen numbers for which continuum theory may be applied. Sample results are presented, using niobium drops, to indicate the magnitudes of the effects. Helium gas at one atmosphere pressure can approximately double the amount of possible undercooling but it results in an apparent gravity levels of up to 0.1 g.

Wallace, D. B.↗
NASA NTRS1981

Insights into the gas dynamics in galaxies via a particle model

Techniques of rarefied gas dynamics are applied to the astrophysical problem of gas flow in disk galaxies. Historically, studies of the interstellar gas dynamics in spiral galaxies have assumed the medium could be regarded as both isothermal and continuous. However, it now appears that the gaseous interstellar medium may be better idealized as a rarefied gas or discrete system of interacting particles. Principal evidence for this is that the galaxies themselves exhibit a degree of disorder and raggedness that is characteristic of a rarefied gaseous system with a Knudsen number of approximately 0.02-0.2. In this paper a particle model for gas flow in a spiral galaxy is developed and some implications of the results are discussed. The results are compared to an analytical inviscid calculation to gain further physical insight.

Levinson, F. H.↗
NASA NTRS1983

The collapse of the local, Spitzer-Haerm formulation and a global-local generalization for heat flow in an inhomogeneous, fully ionized plasma

The breakdown of the classical (CBES) field aligned transport relations for electrons in an inhomogeneous, fully ionized plasma as a mathematical issue of radius of convergence is addressed, the finite Knudsen number conditions when CBES results are accurate is presented and a global-local (GL) way to describe the results of Coulomb physics moderated conduction that is more nearly appropriate for astrophysical plasmas are defined. This paper shows the relationship to and points of departure of the present work from the CBES approach. The CBES heat law in current use is shown to be an especially restrictive special case of the new, more general GL result. A preliminary evaluation of the dimensionless heat function, using analytic formulas, shows that the dimensionless heat function profiles versus density of the type necessary for a conduction supported high speed solar wind appear possible.

Scudder, J. D.↗