Accession Number : AD0616615

Title :   FREE-MOLECULE FLOW THROUGH AXI-SYMMETRIC TUBES,

Corporate Author : TORONTO UNIV (ONTARIO) INST FOR AEROSPACE STUDIES

Personal Author(s) : Townsend,S. J.

Report Date : MAR 1965

Pagination or Media Count : 124

Abstract : The properties of the flow field of a gas passing through an internally reflecting, axi-symmetric tube have been calculated. The major assumptions are (1) that the mean free path of molecules in the external gas is large compared with the tube dimensions, (2) that molecules incident on the internal surface undergo complete energy accommodation, (3) that there is no accumulation or ablation at the wall and (4) that the boundary distribution functions for the gases are Maxwellian. Expressions for convection of mass, axial momentum and kinetic energy through the tube are derived. Radial distributions of these flow quantities across the inlet and exit planes are treated. Integrations over the inlet and exit planes give the total quantities convected through the tube. The density and pressure fields within the tube have been derived. All the flow parameters mentioned have taken into consideration both the geometry and the temperature of the tube wall. There are no restrictions on geometry except that no portion of the wall may shield any other portion. Line of sight trajectories prevail. Temperature profiles have been imposed along the wall in the form of boundary constraints. As a specific application, the density at the center of a hemispherical reflector has been derived for arbitrary speed ratios of the flow into the hemisphere. A representative sampling of numerical results is included. Mass flow calculations are in agreement with those of other investigators. Results show that it is possible to develop a net thrust on an internal flow system under free-molecule flow conditions. (Author)

Descriptors :   (*GAS FLOW, TRANSPORT PROPERTIES), MOLECULES, MOMENTUM, ENERGY, DIFFERENTIAL GEOMETRY, BOUNDARY VALUE PROBLEMS

Distribution Statement : APPROVED FOR PUBLIC RELEASE