{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/43932"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/43932","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"An application of relaxation methods to transonic nozzle flow","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Walsh, Kevin Eugene"],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Mechanical Engineering","degree_department":"Mechanical Engineering","school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1974,"date_issued":"1974","date_published":"1974","updated_at":"2026-07-22T22:19:18Z","subjects":[],"languages":[],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-07282010-020109"],"render_values":[{"text":"etd-07282010-020109","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/43932","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.department","label":"Department","values":["Mechanical Engineering"]},{"key":"dc:creator","label":"Author","values":["Walsh, Kevin Eugene"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-03-14T21:41:22Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-03-14T21:41:22Z","2010-07-28"]},{"key":"dc:date.issued","label":"Date","values":["1974"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.dcmitype","label":"Dc Type Dcmitype","values":["Text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mechanical Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-07282010-020109"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/43932"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["An application of relaxation techniques to the solution of transonic flow in a converging - diverging nozzle is presented. 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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."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["BTD"]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["An application of relaxation methods to transonic nozzle flow"]}]}],"canonical_facts":{"dc:contributor.department":["Mechanical Engineering"],"dc:creator":["Walsh, Kevin Eugene"],"dc:date.accessioned":["2014-03-14T21:41:22Z"],"dc:date.available":["2014-03-14T21:41:22Z","2010-07-28"],"dc:date.issued":["1974"],"dc:description.abstract":["An application of relaxation techniques to the solution of transonic flow in a converging - diverging nozzle is presented. 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