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A kinetic theory description for external spherical flows with arbitrary Knudsen number by a moment method


Brinker, Gary Duane (1969) A kinetic theory description for external spherical flows with arbitrary Knudsen number by a moment method. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/B115-B274.


The Maxwell integral equations of transfer are applied to a series of problems involving flows of arbitrary density gases about spheres. As suggested by Lees a two sided Maxwellian-like weighting function containing a number of free parameters is utilized and a sufficient number of partial differential moment equations is used to determine these parameters. Maxwell's inverse fifth-power force law is used to simplify the evaluation of the collision integrals appearing in the moment equations. All flow quantities are then determined by integration of the weighting function which results from the solution of the differential moment system. Three problems are treated: the heat-flux from a slightly heated sphere at rest in an infinite gas; the velocity field and drag of a slowly moving sphere in an unbounded space; the velocity field and drag torque on a slowly rotating sphere. Solutions to the third problem are found to both first and second-order in surface Mach number with the secondary centrifugal fan motion being of particular interest. Singular aspects of the moment method are encountered in the last two problems and an asymptotic study of these difficulties leads to a formal criterion for a "well posed" moment system. The previously unanswered question of just how many moments must be used in a specific problem is now clarified to a great extent.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Engineering
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Engineering and Applied Science
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Lees, Lester
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 March 1969
Funding AgencyGrant Number
Army Research OfficeUNSPECIFIED
Advanced Research Projects AgencyDA-31-124-ARO(D)-33
Alfred P. Sloan FoundationUNSPECIFIED
Record Number:CaltechTHESIS:01112016-132852787
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9368
Deposited On:11 Jan 2016 23:03
Last Modified:09 Nov 2022 19:20

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