An application of relaxation methods to transonic nozzle flow

An application of relaxation techniques to the solution of transonic flow in a converging - diverging nozzle is presented. The assumptions of steady, isentropic flow of a perfect gas were made. Successive line relaxation, similar to that of Garabedian and Korn, was employed in a transformed computational plane. The potential function at interior points was obtained column by column through repeated application of the Thomas algorithm. Once the interior-point calculations were complete the values of the potential function on the boundaries were obtained by extrapolation using the wall-tangency and centerline-symmetry conditions where appropriate. A final solution was considered obtained when negligible changes were observed in the Mach number at all flow-field points from one iteration to the next. To determine the accuracy of the method, the flow through a hyperbolic converging - diverging nozzle was calculated and the results were compared with an existing solution obtained by a series expansion method. The calculated lines of constant Mach number were in excellent agreement with the series expansion solution. The time required for this solution was faster than time-dependent and error-minimization-type solutions by more than a factor of four even though no attempt was made to optimize the computational efficiency of the program logic.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Mechanical Engineering

Department dc:contributor.department

Mechanical Engineering

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

1974

Author dc:creator

• Walsh, Kevin Eugene

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-07282010-020109

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/43932