Showing papers on "Knudsen number published in 1969"

Rarefied Gas Dynamics

Abstract: Rarefied gas dynamics is concerned with flows at such low density that the molecular mean free path is not negligible. Under these conditions, the gas no longer behaves as a continuum. Important modifications in aerodynamic and heat transfer characteristics occur which are ascribable to the basic molecular structure of the gas.

Axially Symmetric Expansion of a Monatomic Gas from an Orifice into a Vacuum

Abstract: The problem of the steady axially symmetric expansion of a monatomic gas from an orifice into a vacuum is considered. The reservoir conditions are such that the local Knudsen number is initially small. It is noted that the near continuum solution, valid near the orifice, is not uniformly valid far downstream where the local mean free path may be comparable with some characteristic length. A valid solution of Boltzmann's equation, for Maxwell molecules, is deduced for this far field core region. Near the gas‐vacuum front, predicted by the equilibrium solution, this expansion procedure also breaks down. It is shown that a further scaling of the variables in Boltzmann's equation, consistent with this limit, can be found and the corresponding moment equations deduced. However, in contrast to the behavior in the core, these equations no longer form a closed set.

Mean Free Path Effect in Spiral-Grooved Thrust Bearings

Abstract: : The objective of the paper is to study the effect of the mean-free path on the steady-state performance characteristics of a spiral-grooved thrust bearing operating in extremely thin film and/or low ambient pressure environments. Numerical results for the most popular three versions of the spiral-grooved designs are presented. These results reveal that the effect of slip boundary conditions could contribute substantial reduction in performance. Helium is the worst gas lubricant in this sense because of its high Knudsen number. The slip-flow corrected results check well with recently published experimental data. (Author)

Nearly Free Flow through an Orifice

Abstract: In the case of steady flow out of an orifice into an originally evacuated half‐space, a method is given for obtaining the first correction to free flow for the net outflow through the orifice for the class of collision functions B(θ, V) cut off or made regular near θ = π/2. An explicit computation is described for hard‐sphere molecules and the resultant fractional correction is 1 + 0.145/K where K is the Knudsen number. The coefficient 0.145 is about 30% lower than the current best data for argon.

Sound Velocity and Absorption in Low‐Pressure Gases Confined to Tubes of Circular Cross Section

Abstract: The propagation constant for sound waves propagated through gases confined to tubes is shown to be a function of the specific heat of the gas, a “Reynolds” number, a “Knudsen” number, and the momentum and energy accommodation coefficients of the surface. A numerical solution for the propagation constant agrees with room‐temperature velocity and absorption measurements in Ar and N2 assuming a momentum accommodation coefficient of 1 and an energy accommodation coefficient of 0.9. No effort was made to clean the tube‐wall surface, and no difference could be detected in a stainless steel and a brass tube. The method offers considerable promise for measuring energy‐accommodation coefficients. [Work supported by the Office of Naval Research.]

The drag of a cylinder in the transition region

Abstract: The equation for the drag of a cylinder the size of which is comparable with the mean free path of the gas molecules is derived under the assumptions of diffuse reflection and full accommodation and with the use of the concept of the “molecular layer.” The thickness of the “molecular layer” was determined from the asymptotic reduction of the derived equation to the corresponding equation in the range of small Knudsen numbers. The derived equation is analyzed and checked against the experimental data.

Experimental Determination of Thermal Accommodation Coefficients

Abstract: The free molecule flow regime of rarefied gas dynamics and heat transfer is of considerable Interest In any situation dealing with a highly rarefied atmosphere. Free molecule flow occurs when the Knudsen number Kn, is greater than about 3 where Kn = λ/L is the ratio of the mean free path λ to the characteristic length of the system L [1,2]. In a free molecule flow situation collisions between gas molecules are negligible when compared with collisions between gas molecules and the solid surfaces. Hence, a molecule may be considered to travel from one wall to the other without suffering a collision in between.

Flows at Small Knudsen Numbers

Abstract: It was shown in Chapter III (see §§3.6–3.8) that, at internal points of the flow, the Hilbert—Enskog— Chapman expansion gives a solution which converges asymptotically to a solution of the Boltzmann equation for Knudsen numbers tending to zero. However, for an arbitrarily small Knudsen number, there is a region near the boundary in which that series is not a solution of the Boltzmann equation. As we saw in §§3.6–3.8 (and this will be proved again in a somewhat different manner below), the thickness of that region, called the Knudsen layer, is of the order of the mean free path λ.

The Linearized Boltzmann Equation

Abstract: The Hilbert and Chapman-Enskog methods are perturbation procedures for solving the Boltzmann equation on the basis of the assumption of a small Knudsen number ; other procedures based on the assumption of a large Knudsen number will briefly be described later (Chapter VIII, Section 3). The above two procedures are valid in the so-called near-continuum (or slip) regime (Kn → 0) and in nearly-free regime (Kn → ∞). They are both based upon a specific assumption on the order of magnitude of the Knudsen number. Accordingly, the intermediate regime (the so-called transition region) remains untouched by the above procedures because it cannot be described in terms of either a higher-order continuum theory or of small corrections to a picture of essentially noninteracting particles. A treatment of the transition regime requires the full use of the Boltzmann equation (or, at least, sufficiently accurate models of the latter). As a consequence, if we want to investigate the transition regime, we have either to give up the idea of using perturbation methods, or look for some other parameter, different from the Knudsen number, to be regarded as small under suitable conditions.

Relaxation of the uniform Knudsen gas coupled to a thermal bath

Abstract: The possibility of a reduced macroscopic description of the Knudsen gas coupled to a thermal bath (by analogy with the hydrodynamical description of an isolated rarefied gas) is discussed.A study o...

Solution of the Boltzmann Equation for Degenerate Flows

Abstract: Because of the complex structure of the collision integral, only a small number of exact solutions of the Boltzmann equation have been obtained at the present time. In spite of the fact that a large proportion of those solutions describe highly artificial situations, they are very valuable as standard solutions for confirmation of approximate methods of calculation, as well as giving valuable information on the qualitative behavior of solutions of the Boltzmann equation.

Experimental cylinder drag data for hypersonic, rarefied flow.

Abstract: A FREE-FLIGHT technique has recently been used in the AEDC-VKF Tunnel L to obtain drag data for cylinders normal to the flow. (Tunnel L is an arc-heated, continuous, low-density facility using nitrogen as the test gas. Flow properties are given in Table 1 for the two different nozzles used in the present tests.) The technique, which has previously been used to obtain data for spheres,1 has provided cylinder data over the range of Knudsen numbers 0.135 < Knmtd < 18.4.