{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/19407"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/19407","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"The dynamics of multi-dimensional detonation","abstract":"\"An asymptotic theory is presented for the dynamics of detonation when the radius of curvature of the detonation shock is large compared with the one-dimensional steady Chapman-Jouguet (CJ) detonation reaction-zone thickness. The analysis considers additional time-dependence in the slowly-varying reaction zone than that considered in previous works. The detonation is assumed to have a sonic point in the reaction-zone structure behind the shock, and is referred to as an eigenvalue detonation. A new iterative method is used to calculate the eigenvalue relation, which ultimately is expressed as an intrinsic partial differential equation (PDE) for the motion of the shock surface. Two cases are considered for an ideal equation of state. The first corresponds to a model of a condensed phase explosive, with modest reaction-rate sensitivity, and the intrinsic shock surface PDE is a relation between the normal detonation shock velocity $\\.D\\sb{n}$, the first normal time derivative of the normal shock velocity $D\\sb{n}$, and the shock curvature $\\kappa$. The second case corresponds to a gaseous explosive mixture, with the large reaction-rate sensitivity of Arrhenius kinetics, and the intrinsic shock surface PDE is a relation between the normal detonation shock velocity $D\\sb{n}$, its first and second normal time derivatives $\\.D\\sb{n},\\\"\"D\\sb{n}$, the shock curvature $\\kappa$, and the first normal time derivative of the curvature $\\.\\kappa$. For the second case, one obtains a one-dimensional theory of pulsation of plane CJ detonation and a theory that predicts the evolution of self-sustained cellular detonation. Versions of the theory include the limit of near-CJ detonation, and the limit in which the normal detonation velocity is significantly below its CJ value. The curvature of the detonation can also be of either sign corresponding to either diverging or converging geometry.\"","abstract_html":""An asymptotic theory is presented for the dynamics of detonation when the radius of curvature of the detonation shock is large compared with the one-dimensional steady Chapman-Jouguet (CJ) detonation reaction-zone thickness. The analysis considers additional time-dependence in the slowly-varying reaction zone than that considered in previous works. The detonation is assumed to have a sonic point in the reaction-zone structure behind the shock, and is referred to as an eigenvalue detonation. A new iterative method is used to calculate the eigenvalue relation, which ultimately is expressed as an intrinsic partial differential equation (PDE) for the motion of the shock surface. Two cases are considered for an ideal equation of state. The first corresponds to a model of a condensed phase explosive, with modest reaction-rate sensitivity, and the intrinsic shock surface PDE is a relation between the normal detonation shock velocity $\\.D\\sb{n}$, the first normal time derivative of the normal shock velocity $D\\sb{n}$, and the shock curvature $\\kappa$. The second case corresponds to a gaseous explosive mixture, with the large reaction-rate sensitivity of Arrhenius kinetics, and the intrinsic shock surface PDE is a relation between the normal detonation shock velocity $D\\sb{n}$, its first and second normal time derivatives $\\.D\\sb{n},\\""D\\sb{n}$, the shock curvature $\\kappa$, and the first normal time derivative of the curvature $\\.\\kappa$. For the second case, one obtains a one-dimensional theory of pulsation of plane CJ detonation and a theory that predicts the evolution of self-sustained cellular detonation. Versions of the theory include the limit of near-CJ detonation, and the limit in which the normal detonation velocity is significantly below its CJ value. The curvature of the detonation can also be of either sign corresponding to either diverging or converging geometry."","abstract_has_math":true,"creators":["Yao, Jin"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Theoretical and Applied Mechanics","degree_department":null,"school":null,"contributors":["Stewart, Donald S."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T12:06:34Z","date_published":"2011-05-07T12:06:34Z","updated_at":"2026-07-22T22:25:12Z","subjects":["Engineering, Aerospace","Engineering, Mechanical","Physics, Astronomy and Astrophysics"],"languages":["eng"],"rights":["Copyright 1996 Yao, Jin"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["9780591089363","AAI9702723","(UMI)AAI9702723"],"render_values":[{"text":"9780591089363","href":null,"code":true},{"text":"AAI9702723","href":null,"code":true},{"text":"(UMI)AAI9702723","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/19407","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Stewart, Donald S."]},{"key":"dc:creator","label":"Author","values":["Yao, Jin"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T12:06:34Z","10000-01-01","1996"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Theoretical and Applied Mechanics"]},{"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":["Engineering, Aerospace","Engineering, Mechanical","Physics, Astronomy and Astrophysics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 1996 Yao, Jin"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["9780591089363","AAI9702723","(UMI)AAI9702723","http://hdl.handle.net/2142/19407"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["\"An asymptotic theory is presented for the dynamics of detonation when the radius of curvature of the detonation shock is large compared with the one-dimensional steady Chapman-Jouguet (CJ) detonation reaction-zone thickness. The analysis considers additional time-dependence in the slowly-varying reaction zone than that considered in previous works. The detonation is assumed to have a sonic point in the reaction-zone structure behind the shock, and is referred to as an eigenvalue detonation. A new iterative method is used to calculate the eigenvalue relation, which ultimately is expressed as an intrinsic partial differential equation (PDE) for the motion of the shock surface. Two cases are considered for an ideal equation of state. The first corresponds to a model of a condensed phase explosive, with modest reaction-rate sensitivity, and the intrinsic shock surface PDE is a relation between the normal detonation shock velocity $\\.D\\sb{n}$, the first normal time derivative of the normal shock velocity $D\\sb{n}$, and the shock curvature $\\kappa$. The second case corresponds to a gaseous explosive mixture, with the large reaction-rate sensitivity of Arrhenius kinetics, and the intrinsic shock surface PDE is a relation between the normal detonation shock velocity $D\\sb{n}$, its first and second normal time derivatives $\\.D\\sb{n},\\\"\"D\\sb{n}$, the shock curvature $\\kappa$, and the first normal time derivative of the curvature $\\.\\kappa$. For the second case, one obtains a one-dimensional theory of pulsation of plane CJ detonation and a theory that predicts the evolution of self-sustained cellular detonation. Versions of the theory include the limit of near-CJ detonation, and the limit in which the normal detonation velocity is significantly below its CJ value. The curvature of the detonation can also be of either sign corresponding to either diverging or converging geometry.\"","The linear instability of a weakly curved, slowly varying detonation wave is also investigated under the assumption of frozen curvature. The governing equations and the boundary conditions required to formulate the instability problem are derived. The steady $D\\sb{n}-\\kappa$ relation and the quasi-steady state of the weakly curved detonation have been obtained numerically. The eigenvalues of the acoustic instability are calculated by a numerical shooting method.","Made available in DSpace on 2011-05-07T12:06:34Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9702723.pdf: 4122091 bytes, checksum: eca75879ec5574c31768b544c9bdd560 (MD5) Previous issue date: 1996","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:36:45Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:14:56-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"]},{"key":"dc:title","label":"Title","values":["The dynamics of multi-dimensional detonation"]}]}],"canonical_facts":{"dc:contributor":["Stewart, Donald S."],"dc:creator":["Yao, Jin"],"dc:date":["2011-05-07T12:06:34Z","10000-01-01","1996"],"dc:description":["\"An asymptotic theory is presented for the dynamics of detonation when the radius of curvature of the detonation shock is large compared with the one-dimensional steady Chapman-Jouguet (CJ) detonation reaction-zone thickness. The analysis considers additional time-dependence in the slowly-varying reaction zone than that considered in previous works. The detonation is assumed to have a sonic point in the reaction-zone structure behind the shock, and is referred to as an eigenvalue detonation. A new iterative method is used to calculate the eigenvalue relation, which ultimately is expressed as an intrinsic partial differential equation (PDE) for the motion of the shock surface. Two cases are considered for an ideal equation of state. The first corresponds to a model of a condensed phase explosive, with modest reaction-rate sensitivity, and the intrinsic shock surface PDE is a relation between the normal detonation shock velocity $\\.D\\sb{n}$, the first normal time derivative of the normal shock velocity $D\\sb{n}$, and the shock curvature $\\kappa$. The second case corresponds to a gaseous explosive mixture, with the large reaction-rate sensitivity of Arrhenius kinetics, and the intrinsic shock surface PDE is a relation between the normal detonation shock velocity $D\\sb{n}$, its first and second normal time derivatives $\\.D\\sb{n},\\\"\"D\\sb{n}$, the shock curvature $\\kappa$, and the first normal time derivative of the curvature $\\.\\kappa$. For the second case, one obtains a one-dimensional theory of pulsation of plane CJ detonation and a theory that predicts the evolution of self-sustained cellular detonation. Versions of the theory include the limit of near-CJ detonation, and the limit in which the normal detonation velocity is significantly below its CJ value. The curvature of the detonation can also be of either sign corresponding to either diverging or converging geometry.\"","The linear instability of a weakly curved, slowly varying detonation wave is also investigated under the assumption of frozen curvature. The governing equations and the boundary conditions required to formulate the instability problem are derived. The steady $D\\sb{n}-\\kappa$ relation and the quasi-steady state of the weakly curved detonation have been obtained numerically. The eigenvalues of the acoustic instability are calculated by a numerical shooting method.","Made available in DSpace on 2011-05-07T12:06:34Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9702723.pdf: 4122091 bytes, checksum: eca75879ec5574c31768b544c9bdd560 (MD5) Previous issue date: 1996","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:36:45Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:14:56-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"],"dc:identifier":["9780591089363","AAI9702723","(UMI)AAI9702723","http://hdl.handle.net/2142/19407"],"dc:language":["eng"],"dc:rights":["Copyright 1996 Yao, Jin"],"dc:subject":["Engineering, Aerospace","Engineering, Mechanical","Physics, Astronomy and Astrophysics"],"dc:title":["The dynamics of multi-dimensional detonation"],"dc:type":["text"],"thesis:degree_discipline":["Theoretical and Applied Mechanics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:12Z"}