{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/18646"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/18646","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Instability of steady and quasi-steady detonations","abstract":"The stability properties and dynamic behavior of steady and quasi-steady detonation theories are investigated through linear stability analysis and numerical simulation. A general, unsteady, three-dimensional formulation of the reactive Euler equations in a shock-fitted reference frame is derived. The formulation is specialized to three configurations: planar one-dimensional detonation, radially symmetric one-dimensional detonation, and two-dimensional detonation in a rectangular channel. High-order convergent numerical simulation schemes for these configurations are derived and used to study the linear and nonlinear stability of detonations. Shock-fitted numerical simulation is used to study the two-dimensional instability of steady solutions to the Zel'dovich, von Neumann, and Doring (ZND) model of detonation. It is demonstrated through several methods of analysis that the dependence of instability growth rates and oscillation frequencies on the initial disturbance wavelength, as predicted by linear stability theory, is quantitatively reproduced by shock-fitted simulations. Agreement with the theorized temporal and spatial structure of the instability is demonstrated by a functional expansion of the solution perturbations, obtained from simulation data, in terms of the linear stability eigenfunctions. Three regimes of unstable behavior - linear, weakly non-linear, and fully non-linear - are explored and characterized in terms of the power spectrum of the normal detonation velocity. Using solutions obtained from Detonation Shock Dynamics (DSD) theory, the behavior of cylindrically and spherically expanding symmetric detonations is studied by one-dimensional shock-fitted numerical simulation. We consider idealized models of gaseous and condensed phase detonation, as well as a realistic model calibrated for the high explosive PBX-9501. We study the behavior of detonations initialized with solutions of DSD as they expand radially. The various models and calibrations exhibit regimes of hydrodynamic stability, in which the detonation evolves slowly in time and agreement with DSD theory is good, and regimes of instability, which in some cases leads to failure of the detonation wave.","abstract_html":"The stability properties and dynamic behavior of steady and quasi-steady detonation theories are investigated through linear stability analysis and numerical simulation. A general, unsteady, three-dimensional formulation of the reactive Euler equations in a shock-fitted reference frame is derived. The formulation is specialized to three configurations: planar one-dimensional detonation, radially symmetric one-dimensional detonation, and two-dimensional detonation in a rectangular channel. High-order convergent numerical simulation schemes for these configurations are derived and used to study the linear and nonlinear stability of detonations. Shock-fitted numerical simulation is used to study the two-dimensional instability of steady solutions to the Zel'dovich, von Neumann, and Doring (ZND) model of detonation. It is demonstrated through several methods of analysis that the dependence of instability growth rates and oscillation frequencies on the initial disturbance wavelength, as predicted by linear stability theory, is quantitatively reproduced by shock-fitted simulations. Agreement with the theorized temporal and spatial structure of the instability is demonstrated by a functional expansion of the solution perturbations, obtained from simulation data, in terms of the linear stability eigenfunctions. Three regimes of unstable behavior - linear, weakly non-linear, and fully non-linear - are explored and characterized in terms of the power spectrum of the normal detonation velocity. Using solutions obtained from Detonation Shock Dynamics (DSD) theory, the behavior of cylindrically and spherically expanding symmetric detonations is studied by one-dimensional shock-fitted numerical simulation. We consider idealized models of gaseous and condensed phase detonation, as well as a realistic model calibrated for the high explosive PBX-9501. We study the behavior of detonations initialized with solutions of DSD as they expand radially. The various models and calibrations exhibit regimes of hydrodynamic stability, in which the detonation evolves slowly in time and agreement with DSD theory is good, and regimes of instability, which in some cases leads to failure of the detonation wave.","abstract_has_math":false,"creators":["Taylor, Brian D."],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Theoretical & Applied Mechans","degree_department":null,"school":null,"contributors":["Matalon, Moshe","Stewart, Scott","Austin, Joanna M.","Pantano-Rubino, Carlos A."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-01-21T22:53:01Z","date_published":"2011-01-21T22:53:01Z","updated_at":"2026-07-22T22:25:11Z","subjects":["Detonation","Shock-fitting","stability","numerical simulation"],"languages":["en"],"rights":["Copyright 2010 Brian Dow Taylor"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/18646","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Matalon, Moshe","Stewart, Scott","Austin, Joanna M.","Pantano-Rubino, Carlos A."]},{"key":"dc:creator","label":"Author","values":["Taylor, Brian D."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-01-21T22:53:01Z","2013-01-22T11:00:18Z","2010-12"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Theoretical & Applied Mechans"]},{"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":["Detonation","Shock-fitting","stability","numerical simulation"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2010 Brian Dow Taylor"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/18646"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["The stability properties and dynamic behavior of steady and quasi-steady detonation theories are investigated through linear stability analysis and numerical simulation. A general, unsteady, three-dimensional formulation of the reactive Euler equations in a shock-fitted reference frame is derived. The formulation is specialized to three configurations: planar one-dimensional detonation, radially symmetric one-dimensional detonation, and two-dimensional detonation in a rectangular channel. High-order convergent numerical simulation schemes for these configurations are derived and used to study the linear and nonlinear stability of detonations. Shock-fitted numerical simulation is used to study the two-dimensional instability of steady solutions to the Zel'dovich, von Neumann, and Doring (ZND) model of detonation. It is demonstrated through several methods of analysis that the dependence of instability growth rates and oscillation frequencies on the initial disturbance wavelength, as predicted by linear stability theory, is quantitatively reproduced by shock-fitted simulations. Agreement with the theorized temporal and spatial structure of the instability is demonstrated by a functional expansion of the solution perturbations, obtained from simulation data, in terms of the linear stability eigenfunctions. Three regimes of unstable behavior - linear, weakly non-linear, and fully non-linear - are explored and characterized in terms of the power spectrum of the normal detonation velocity. Using solutions obtained from Detonation Shock Dynamics (DSD) theory, the behavior of cylindrically and spherically expanding symmetric detonations is studied by one-dimensional shock-fitted numerical simulation. We consider idealized models of gaseous and condensed phase detonation, as well as a realistic model calibrated for the high explosive PBX-9501. We study the behavior of detonations initialized with solutions of DSD as they expand radially. The various models and calibrations exhibit regimes of hydrodynamic stability, in which the detonation evolves slowly in time and agreement with DSD theory is good, and regimes of instability, which in some cases leads to failure of the detonation wave.","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2010-11-17T14:17:53Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Taylor_Brian.pdf: 15782528 bytes, checksum: 938c1fe8ce9ad9d8936f372b8f04d2d6 (MD5)","Made available in DSpace on 2011-01-21T22:53:01Z (GMT). No. of bitstreams: 2 Taylor_Brian.pdf: 15782528 bytes, checksum: 938c1fe8ce9ad9d8936f372b8f04d2d6 (MD5) license.txt: 4062 bytes, checksum: c0c474b1407cd3ea0e7dbce4aff7da71 (MD5)","Item marked as restricted to the 'Administrator' Group (id=1) by William Ingram (wingram2@illinois.edu) on 2011-01-21T22:54:06Z Item is restricted until 2013-01-21T22:53:34Z","Item reinstated by Sarah Shreeves (sshreeve@illinois.edu) on 2013-01-22T11:00:18Z Item was in collections: University of Illinois Dissertations and Theses (ID: 204) Dissertations and Theses - Mechanical Science and Engineering (ID: 675) No. of bitstreams: 3 Taylor_Brian.pdf.txt: 194617 bytes, checksum: f443e0f9482f262598a72eced2a254f1 (MD5) Taylor_Brian.pdf: 15782528 bytes, checksum: 938c1fe8ce9ad9d8936f372b8f04d2d6 (MD5) license.txt: 4062 bytes, checksum: c0c474b1407cd3ea0e7dbce4aff7da71 (MD5)","Item released from any restrictions by Sarah Shreeves (sshreeve@illinois.edu) on 2013-01-22T11:00:18Z"]},{"key":"dc:title","label":"Title","values":["Instability of steady and quasi-steady detonations"]}]}],"canonical_facts":{"dc:contributor":["Matalon, Moshe","Stewart, Scott","Austin, Joanna M.","Pantano-Rubino, Carlos A."],"dc:creator":["Taylor, Brian D."],"dc:date":["2011-01-21T22:53:01Z","2013-01-22T11:00:18Z","2010-12"],"dc:description":["The stability properties and dynamic behavior of steady and quasi-steady detonation theories are investigated through linear stability analysis and numerical simulation. A general, unsteady, three-dimensional formulation of the reactive Euler equations in a shock-fitted reference frame is derived. The formulation is specialized to three configurations: planar one-dimensional detonation, radially symmetric one-dimensional detonation, and two-dimensional detonation in a rectangular channel. High-order convergent numerical simulation schemes for these configurations are derived and used to study the linear and nonlinear stability of detonations. Shock-fitted numerical simulation is used to study the two-dimensional instability of steady solutions to the Zel'dovich, von Neumann, and Doring (ZND) model of detonation. It is demonstrated through several methods of analysis that the dependence of instability growth rates and oscillation frequencies on the initial disturbance wavelength, as predicted by linear stability theory, is quantitatively reproduced by shock-fitted simulations. Agreement with the theorized temporal and spatial structure of the instability is demonstrated by a functional expansion of the solution perturbations, obtained from simulation data, in terms of the linear stability eigenfunctions. Three regimes of unstable behavior - linear, weakly non-linear, and fully non-linear - are explored and characterized in terms of the power spectrum of the normal detonation velocity. Using solutions obtained from Detonation Shock Dynamics (DSD) theory, the behavior of cylindrically and spherically expanding symmetric detonations is studied by one-dimensional shock-fitted numerical simulation. We consider idealized models of gaseous and condensed phase detonation, as well as a realistic model calibrated for the high explosive PBX-9501. We study the behavior of detonations initialized with solutions of DSD as they expand radially. The various models and calibrations exhibit regimes of hydrodynamic stability, in which the detonation evolves slowly in time and agreement with DSD theory is good, and regimes of instability, which in some cases leads to failure of the detonation wave.","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2010-11-17T14:17:53Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Taylor_Brian.pdf: 15782528 bytes, checksum: 938c1fe8ce9ad9d8936f372b8f04d2d6 (MD5)","Made available in DSpace on 2011-01-21T22:53:01Z (GMT). No. of bitstreams: 2 Taylor_Brian.pdf: 15782528 bytes, checksum: 938c1fe8ce9ad9d8936f372b8f04d2d6 (MD5) license.txt: 4062 bytes, checksum: c0c474b1407cd3ea0e7dbce4aff7da71 (MD5)","Item marked as restricted to the 'Administrator' Group (id=1) by William Ingram (wingram2@illinois.edu) on 2011-01-21T22:54:06Z Item is restricted until 2013-01-21T22:53:34Z","Item reinstated by Sarah Shreeves (sshreeve@illinois.edu) on 2013-01-22T11:00:18Z Item was in collections: University of Illinois Dissertations and Theses (ID: 204) Dissertations and Theses - Mechanical Science and Engineering (ID: 675) No. of bitstreams: 3 Taylor_Brian.pdf.txt: 194617 bytes, checksum: f443e0f9482f262598a72eced2a254f1 (MD5) Taylor_Brian.pdf: 15782528 bytes, checksum: 938c1fe8ce9ad9d8936f372b8f04d2d6 (MD5) license.txt: 4062 bytes, checksum: c0c474b1407cd3ea0e7dbce4aff7da71 (MD5)","Item released from any restrictions by Sarah Shreeves (sshreeve@illinois.edu) on 2013-01-22T11:00:18Z"],"dc:identifier":["http://hdl.handle.net/2142/18646"],"dc:language":["en"],"dc:rights":["Copyright 2010 Brian Dow Taylor"],"dc:subject":["Detonation","Shock-fitting","stability","numerical simulation"],"dc:title":["Instability of steady and quasi-steady detonations"],"thesis:degree_discipline":["Theoretical & Applied Mechans"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:11Z"}