{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/85951"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/85951","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Applications of Lie Groups in Turbulence Modeling","abstract":"Group analysis is applied to the general two-dimensional k-epsilon turbulence model. Symmetry algebras for the k-epsilon turbulence model have been calculated by Khor'kova. and Verbovetsky. This systematic approach is applied to the specific flow problem of turbulent submerged free plane jets. Similarity solutions obtained through Lie group analysis of the zero-equation turbulence model are equivalent to those obtained through traditional mathematical techniques. Lie groups are then applied to the k-epsilon turbulence model's PDEs for submerged free plane jets. A numerical simulation is performed on the subsequent system of ODEs obtained from this model. The results for the turbulent properties obtained from the numerical computation are in good agreement with the similarity profiles obtained from the zero-equation model. These properties include the axial and transverse velocities, stream function, vorticity and transverse eddy viscosity.","abstract_html":"Group analysis is applied to the general two-dimensional k-epsilon turbulence model. Symmetry algebras for the k-epsilon turbulence model have been calculated by Khor'kova. and Verbovetsky. This systematic approach is applied to the specific flow problem of turbulent submerged free plane jets. Similarity solutions obtained through Lie group analysis of the zero-equation turbulence model are equivalent to those obtained through traditional mathematical techniques. Lie groups are then applied to the k-epsilon turbulence model's PDEs for submerged free plane jets. A numerical simulation is performed on the subsequent system of ODEs obtained from this model. The results for the turbulent properties obtained from the numerical computation are in good agreement with the similarity profiles obtained from the zero-equation model. These properties include the axial and transverse velocities, stream function, vorticity and transverse eddy viscosity.","abstract_has_math":false,"creators":["DeMers, Louis Joseph"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Nuclear Engineering","degree_department":null,"school":null,"contributors":["Axford, Roy A."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-28T14:51:30Z","date_published":"2015-09-28T14:51:30Z","updated_at":"2026-07-22T22:26:26Z","subjects":["Applied Mechanics"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI9955605"],"render_values":[{"text":"(MiAaPQ)AAI9955605","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/85951","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Axford, Roy A."]},{"key":"dc:creator","label":"Author","values":["DeMers, Louis Joseph"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-28T14:51:30Z","10000-01-01","2000"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Nuclear Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Applied Mechanics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/85951","(MiAaPQ)AAI9955605"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Group analysis is applied to the general two-dimensional k-epsilon turbulence model. Symmetry algebras for the k-epsilon turbulence model have been calculated by Khor'kova. and Verbovetsky. This systematic approach is applied to the specific flow problem of turbulent submerged free plane jets. Similarity solutions obtained through Lie group analysis of the zero-equation turbulence model are equivalent to those obtained through traditional mathematical techniques. Lie groups are then applied to the k-epsilon turbulence model's PDEs for submerged free plane jets. A numerical simulation is performed on the subsequent system of ODEs obtained from this model. The results for the turbulent properties obtained from the numerical computation are in good agreement with the similarity profiles obtained from the zero-equation model. These properties include the axial and transverse velocities, stream function, vorticity and transverse eddy viscosity.","Made available in DSpace on 2015-09-28T14:51:30Z (GMT). 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This systematic approach is applied to the specific flow problem of turbulent submerged free plane jets. Similarity solutions obtained through Lie group analysis of the zero-equation turbulence model are equivalent to those obtained through traditional mathematical techniques. Lie groups are then applied to the k-epsilon turbulence model's PDEs for submerged free plane jets. A numerical simulation is performed on the subsequent system of ODEs obtained from this model. The results for the turbulent properties obtained from the numerical computation are in good agreement with the similarity profiles obtained from the zero-equation model. These properties include the axial and transverse velocities, stream function, vorticity and transverse eddy viscosity.","Made available in DSpace on 2015-09-28T14:51:30Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 9955605.pdf: 7048537 bytes, checksum: aa4faf92c5c11b2c576f80ff03c1a5e0 (MD5) Previous issue date: 2000","Embargo set by: Seth Robbins for item 87232 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","213 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2000."],"dc:identifier":["http://hdl.handle.net/2142/85951","(MiAaPQ)AAI9955605"],"dc:language":["eng"],"dc:subject":["Applied Mechanics"],"dc:title":["Applications of Lie Groups in Turbulence Modeling"],"dc:type":["text"],"thesis:degree_discipline":["Nuclear Engineering"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:26Z"}