{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/105690"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/105690","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"The stabilization and extinction of a microjet diffusion flame","abstract":"The steady jet diffusion micro-flame is mathematically modeled and its extinction properties and investigated in this study. The diffusion flame of interest is one that results from the reaction of a fuel present in a weak jet issuing from a nozzle into an unbounded medium containing the oxidizer. Various flame properties such as flame location, temperature and reactant leakage are investigated in the study. The analysis presented makes use of an asymptotic approximation for large activation energy chemical reactions as per the general theory of Cheatham and Matalon where the reaction is confined to a surface and the mathematical problem reduces to a free boundary problem with jump relations across the flame sheet. Constant density approximation decouples the hydrodynamic equations from the full system of governing equations. The flow field is described by an exact solution to the Navier-Stokes and continuity equations modeling an axis-symmetric jet issuing from a point source of momentum into an unbounded fluid domain, as solved for by both Landau and Squire. The flame location and associated combustion fields are first solved in the Burke-Schumann limit of complete combustion for unity Lewis number flames in jets of arbitrary strength. The solution is then attempted for the case of non-unity Lewis number Burke-Schumann flames in weak jets (micro-jets). Finally, the solution associated with non-unity Lewis number micro-flames with reactant leakage across the flame is investigated over the entire range of Damkohler numbers in order to ascertain extinction properties. Effects of varying the Lewis and Damkohler numbers on extinction and flame shape are presented.","abstract_html":"The steady jet diffusion micro-flame is mathematically modeled and its extinction properties and investigated in this study. The diffusion flame of interest is one that results from the reaction of a fuel present in a weak jet issuing from a nozzle into an unbounded medium containing the oxidizer. Various flame properties such as flame location, temperature and reactant leakage are investigated in the study. The analysis presented makes use of an asymptotic approximation for large activation energy chemical reactions as per the general theory of Cheatham and Matalon where the reaction is confined to a surface and the mathematical problem reduces to a free boundary problem with jump relations across the flame sheet. Constant density approximation decouples the hydrodynamic equations from the full system of governing equations. The flow field is described by an exact solution to the Navier-Stokes and continuity equations modeling an axis-symmetric jet issuing from a point source of momentum into an unbounded fluid domain, as solved for by both Landau and Squire. The flame location and associated combustion fields are first solved in the Burke-Schumann limit of complete combustion for unity Lewis number flames in jets of arbitrary strength. The solution is then attempted for the case of non-unity Lewis number Burke-Schumann flames in weak jets (micro-jets). Finally, the solution associated with non-unity Lewis number micro-flames with reactant leakage across the flame is investigated over the entire range of Damkohler numbers in order to ascertain extinction properties. Effects of varying the Lewis and Damkohler numbers on extinction and flame shape are presented.","abstract_has_math":false,"creators":["Krishnan, Gautham"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Mechanical Engineering","degree_department":null,"school":null,"contributors":["Matalon, Moshe"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2019,"date_issued":"2019-11-26T20:35:07Z","date_published":"2019-11-26T20:35:07Z","updated_at":"2026-07-22T22:24:44Z","subjects":["Jet diffusion micro-flames","Extinction limit","Burke-Schumann flame","Large activation-energy asymptotics"],"languages":["en"],"rights":["Copyright 2019 Gautham Krishnan"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/105690","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Matalon, Moshe"]},{"key":"dc:creator","label":"Author","values":["Krishnan, Gautham"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2019-11-26T20:35:07Z","2019-07-16","2019-08"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mechanical Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"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":["Jet diffusion micro-flames","Extinction limit","Burke-Schumann flame","Large activation-energy asymptotics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2019 Gautham Krishnan"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/105690"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["The steady jet diffusion micro-flame is mathematically modeled and its extinction properties and investigated in this study. The diffusion flame of interest is one that results from the reaction of a fuel present in a weak jet issuing from a nozzle into an unbounded medium containing the oxidizer. Various flame properties such as flame location, temperature and reactant leakage are investigated in the study. The analysis presented makes use of an asymptotic approximation for large activation energy chemical reactions as per the general theory of Cheatham and Matalon where the reaction is confined to a surface and the mathematical problem reduces to a free boundary problem with jump relations across the flame sheet. Constant density approximation decouples the hydrodynamic equations from the full system of governing equations. The flow field is described by an exact solution to the Navier-Stokes and continuity equations modeling an axis-symmetric jet issuing from a point source of momentum into an unbounded fluid domain, as solved for by both Landau and Squire. The flame location and associated combustion fields are first solved in the Burke-Schumann limit of complete combustion for unity Lewis number flames in jets of arbitrary strength. The solution is then attempted for the case of non-unity Lewis number Burke-Schumann flames in weak jets (micro-jets). Finally, the solution associated with non-unity Lewis number micro-flames with reactant leakage across the flame is investigated over the entire range of Damkohler numbers in order to ascertain extinction properties. Effects of varying the Lewis and Damkohler numbers on extinction and flame shape are presented.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2019-11-26 without embargo terms","The student, Gautham Krishnan, accepted the attached license on 2019-07-12 at 12:13.","The student, Gautham Krishnan, submitted this Thesis for approval on 2019-07-12 at 15:45.","This Thesis was approved for publication on 2019-07-16 at 17:28.","DSpace SAF Submission Ingestion Package generated from Vireo submission #14304 on 2019-11-26 at 12:53:35","Made available in DSpace on 2019-11-26T20:35:07Z (GMT). No. of bitstreams: 2 KRISHNAN-THESIS-2019.pdf: 8633833 bytes, checksum: efc0bd9a2488dc8db03f9d568d1db17c (MD5) LICENSE.txt: 4213 bytes, checksum: 521473bb2b9d46badcf4f71453d837c6 (MD5) Previous issue date: 2019-07-16"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["The stabilization and extinction of a microjet diffusion flame"]}]}],"canonical_facts":{"dc:contributor":["Matalon, Moshe"],"dc:creator":["Krishnan, Gautham"],"dc:date":["2019-11-26T20:35:07Z","2019-07-16","2019-08"],"dc:description":["The steady jet diffusion micro-flame is mathematically modeled and its extinction properties and investigated in this study. The diffusion flame of interest is one that results from the reaction of a fuel present in a weak jet issuing from a nozzle into an unbounded medium containing the oxidizer. Various flame properties such as flame location, temperature and reactant leakage are investigated in the study. The analysis presented makes use of an asymptotic approximation for large activation energy chemical reactions as per the general theory of Cheatham and Matalon where the reaction is confined to a surface and the mathematical problem reduces to a free boundary problem with jump relations across the flame sheet. Constant density approximation decouples the hydrodynamic equations from the full system of governing equations. The flow field is described by an exact solution to the Navier-Stokes and continuity equations modeling an axis-symmetric jet issuing from a point source of momentum into an unbounded fluid domain, as solved for by both Landau and Squire. The flame location and associated combustion fields are first solved in the Burke-Schumann limit of complete combustion for unity Lewis number flames in jets of arbitrary strength. The solution is then attempted for the case of non-unity Lewis number Burke-Schumann flames in weak jets (micro-jets). Finally, the solution associated with non-unity Lewis number micro-flames with reactant leakage across the flame is investigated over the entire range of Damkohler numbers in order to ascertain extinction properties. Effects of varying the Lewis and Damkohler numbers on extinction and flame shape are presented.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2019-11-26 without embargo terms","The student, Gautham Krishnan, accepted the attached license on 2019-07-12 at 12:13.","The student, Gautham Krishnan, submitted this Thesis for approval on 2019-07-12 at 15:45.","This Thesis was approved for publication on 2019-07-16 at 17:28.","DSpace SAF Submission Ingestion Package generated from Vireo submission #14304 on 2019-11-26 at 12:53:35","Made available in DSpace on 2019-11-26T20:35:07Z (GMT). No. of bitstreams: 2 KRISHNAN-THESIS-2019.pdf: 8633833 bytes, checksum: efc0bd9a2488dc8db03f9d568d1db17c (MD5) LICENSE.txt: 4213 bytes, checksum: 521473bb2b9d46badcf4f71453d837c6 (MD5) Previous issue date: 2019-07-16"],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/2142/105690"],"dc:language":["en"],"dc:rights":["Copyright 2019 Gautham Krishnan"],"dc:subject":["Jet diffusion micro-flames","Extinction limit","Burke-Schumann flame","Large activation-energy asymptotics"],"dc:title":["The stabilization and extinction of a microjet diffusion flame"],"dc:type":["text"],"thesis:degree_discipline":["Mechanical Engineering"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["M.S."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:44Z"}