Momentum Transport in Rarefied Gases.
Abstract
The study of nonuniform rarefied gas flow under different geometries and boundary conditions is fundamental to problems in a variety of systems. This dissertation investigates problems of viscous flow or momentum transport in the thin regions (Knudsen layers) close to the boundaries where rarefied gas flows must be described by the Boltzmann equation (Kinetic Theory). The problems of planar slip flow and planar Poiseuille flow for rigid spheres are examined by solving the linearized Boltzmann equation using the discrete ordinates (S_{rm N} ) method. The slip flow or halfspace problem of rarefied gas flow is considered and use of the S_ {rm N} (discrete ordinates) algorithm outlined. Accurate numerical results for the velocity slip coefficient and velocity defect are obtained for a rigid sphere gas and are compared with previously reported results and experimental data. In plane Poiseuille flow, the continuum limit is characterized by the Burnett distribution. Explicit results for this distribution are obtained by solving numerically the relevant integral equations for a rigid sphere gas in the context of the linearized Boltzmann equation. This distribution together with the ChapmanEnskog distribution is used to obtain asymptotic results (nearcontinuum) for mass and heat fluxes corresponding to planar thermal transpiration and mechanocaloric effects. The problem of plane Poiseuille flow of a rarefied gas is solved by the S_{rm N } method. Explicit results for the flow rates and velocity profiles for a rigid sphere intermolecular interaction are obtained, and compared with the BGK and oneterm synthetic model results. The flow rates are verified by use of variational expressions incorporating the newly developed Burnett distribution values. The rigid sphere values for the flow rates are in better agreement with the available experimental data than those based on the BGK kinetic model and the one term synthetic model. The development of the appropriate equations, the numerical work, an analysis of the results and their implications is the Ph.D. research of Keith A. Hickey.
 Publication:

Ph.D. Thesis
 Pub Date:
 1989
 Bibcode:
 1989PhDT.......109H
 Keywords:

 Physics: Fluid and Plasma