Some Flow Problems in Rarefied Gas Dynamics

Citation

Narasimha, Roddam (1961) Some Flow Problems in Rarefied Gas Dynamics. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/1S8T-QA38. https://resolver.caltech.edu/CaltechETD:etd-11042003-095050

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 collision-less 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 three-dimensional 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 Navier-Stokes 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.

Thesis Files