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Cylindrical Couette Flow in a Rarefied Gas According to Grad's Equations

Ai, Daniel Kwoh-i (1960) Cylindrical Couette Flow in a Rarefied Gas According to Grad's Equations. Hypersonic Research Project Memorandum, 56. California Institute of Technology , Pasadena, CA. (Unpublished) http://resolver.caltech.edu/CaltechAUTHORS:20151104-154821570

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Abstract

Grad's thirteen moment method is applied to the problem of the shear flow and heat conduction between two concentric, rotating cylinders of infinite length. In order to concentrate on the effects of curvature the problem is linearized by requiring that the Mach number is small compared with unity, and that the temperature difference between the two cylinders is small compared with the mean temperature. The solutions of the linearized Grad equations show a qualitatively correct transition of the cylinder drag from free-molecule flow to the classical Navier-Stokes regime. However the magnitude of the curvature effect on the drag in rarefied flow is not given correctly, because Grad's distribution function ignores the wedge-like domains of influence of the two cylinders. The solution obtained for the heat transfer rate is physically unrealistic in the free-molecule flow limit, and this result is produced by a cross-coupling between the normal stresses and the radial heat flux imposed by Grad's distribution function. In this simple problem the difficulty can be eliminated by taking the normal stresses to be identically zero and employing a truncated moment method. However, in general this device cannot be utilized in problems involving curved solid boundaries, or when dissipation is considered. One concludes that the choice of the distribution function to be employed in Maxwell's moment equations is dictated by the requirements imposed in the limiting case of highly rarefied gas flows, as well as in the Navier-Stokes regime.


Item Type:Report or Paper (Technical Report)
Additional Information:Army Ordnance Contract No. DA-04-495-Ord-1960.
Group:Hypersonic Research Project
Funders:
Funding AgencyGrant Number
U.S. Army Office of OrdnanceDA-04-495-Ord-1960
Record Number:CaltechAUTHORS:20151104-154821570
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20151104-154821570
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:61860
Collection:CaltechAUTHORS
Deposited By: Kristin Buxton
Deposited On:05 Nov 2015 02:40
Last Modified:05 Nov 2015 02:40

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