Citation
Narasimha, Roddam (1961) Some flow problems in rarefied gas dynamics. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd11042003095050
Abstract
This thesis discusses three rather loosely connected problems in free molecule and nearly free molecule flow. First the expansion of a gas cloud into perfect vacuum is considered on the basis of the collisionless Boltzmann equation, and it is shown that if the initial distribution is an isothermal Maxwellian, the density obeys a diffusion equation with a diffusion coefficient proportional to the time. This leads to the description of the free expansion of symmetric clouds in terms of a thick 'diffusion front' traveling at the initial isothermal speed of sound. The expansion of asymmetric clouds and the flow due to sources and jets are also studied.
Second, a method of iteration proposed by Willis for calculating nearly free molecular flow is extended to general unsteady flows; it is then applied to the flow through an orifice to show that the correction to the mass flow is of the first order in the inverse Knudsen number. The coefficient, estimated by making some reasonable assumptions about the threedimensional nature of the flow, is found to agree quite well with Liepmann's measurements.
Finally a physical basis is suggested for Krook's collision model used in the above calculations. Several consequences of the model are then derived, including the important one that, in the NavierStokes limit, the model implies a Stokesian gas with a Prandtl number of unity. The value to be given to the parameter in the model is also discussed at some length.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Degree Grantor:  California Institute of Technology 
Division:  Engineering and Applied Science 
Major Option:  Aeronautics 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  1 January 1961 
Record Number:  CaltechETD:etd11042003095050 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd11042003095050 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  4400 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  04 Nov 2003 
Last Modified:  26 Dec 2012 03:08 
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