Asymptotic analysis in the limit of large activation energy is performed to investigate the ignition of a reactive gas in the laminar boundary layer behind a propagating shock front. The study is based on a one-step, irreversible Arrhenius reaction of a premixed gas; therefore, the ignition phenomenon is thermally induced. The boundary layer consists of a thin, diffusive, reaction region at the point where the temperature is maximum and diffusive-convective non-reacting regions adjacent to the reacting region. Both adiabatic and isothermal boundary conditions are examined. For the adiabatic wall, the reaction zone is near the insulated boundary. The reaction zone is in the interior for the isothermal wall. The effects of various parameters on the non-dimensional ignition distance and the ignition point are investigated. It is found that the ignition distance decreases almost linearly with the Mach number for both the adiabatic and the isothermal wall cases. In the isothermal wall case with fixed Mach number, the non-dimensional ignition point decreases linearly with the surface temperature, and the non-dimensional ignition distance has a minimum as the surface temperature varies.
Since the kinetic energy of the supersonic flow is converted into thermal energy through viscous heating in the boundary layer, the dependence of the viscosity on temperature is of particular importance. Sutherland's temperature-viscosity law is used in this research since it is a better approximation and provides a more rapid variation of viscosity with respect to temperature than the linear temperature-viscosity law. Use of the Sutherland's temperature-viscosity law results in coupled momentum and energy equations that are analyzed accordingly. Im, Bechtold and Law (10) did not account for the effects of the shock and used the linear temperature-viscosity law resulting in uncoupled momentum and energy equations. All four cases--Sutherland's law with shock, linear law with shock, Sutherland's law without shock, and linear law without shock--are considered for comparison.
","abstract_html":"<p>Asymptotic analysis in the limit of large activation energy is performed to investigate the ignition of a reactive gas in the laminar boundary layer behind a propagating shock front. The study is based on a one-step, irreversible Arrhenius reaction of a premixed gas; therefore, the ignition phenomenon is thermally induced. The boundary layer consists of a thin, diffusive, reaction region at the point where the temperature is maximum and diffusive-convective non-reacting regions adjacent to the reacting region. Both adiabatic and isothermal boundary conditions are examined. For the adiabatic wall, the reaction zone is near the insulated boundary. The reaction zone is in the interior for the isothermal wall. The effects of various parameters on the non-dimensional ignition distance and the ignition point are investigated. It is found that the ignition distance decreases almost linearly with the Mach number for both the adiabatic and the isothermal wall cases. In the isothermal wall case with fixed Mach number, the non-dimensional ignition point decreases linearly with the surface temperature, and the non-dimensional ignition distance has a minimum as the surface temperature varies.</p> <p>Since the kinetic energy of the supersonic flow is converted into thermal energy through viscous heating in the boundary layer, the dependence of the viscosity on temperature is of particular importance. Sutherland's temperature-viscosity law is used in this research since it is a better approximation and provides a more rapid variation of viscosity with respect to temperature than the linear temperature-viscosity law. Use of the Sutherland's temperature-viscosity law results in coupled momentum and energy equations that are analyzed accordingly. Im, Bechtold and Law (10) did not account for the effects of the shock and used the linear temperature-viscosity law resulting in uncoupled momentum and energy equations. All four cases--Sutherland's law with shock, linear law with shock, Sutherland's law without shock, and linear law without shock--are considered for comparison.</p>","abstract_has_math":false,"creators":["Khan, Mushtaq Ahmed"],"institution":null,"degree_name":"Master of Science (MS)","degree_level":"Dissertation","degree_discipline":"Mathematics & Statistics","degree_department":null,"school":null,"contributors":["David Glenn Lasseigne","Fang Q. Hu","Thomas L. Jackson","Chester Grosch"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1995,"date_issued":"1995-04-01T08:00:00Z","date_published":"1995-04-01T08:00:00Z","updated_at":"2026-07-24T03:34:53Z","subjects":["Ignition","Shock flow","Mathematics"],"languages":[],"rights":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.odu.edu/mathstat_etds/26","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["David Glenn Lasseigne","Fang Q. Hu","Thomas L. Jackson","Chester Grosch"]},{"key":"dc:creator","label":"Author","values":["Khan, Mushtaq Ahmed"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2019-06-06T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics & Statistics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science (MS)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Ignition","Shock flow","Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.odu.edu/mathstat_etds/26"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Asymptotic analysis in the limit of large activation energy is performed to investigate the ignition of a reactive gas in the laminar boundary layer behind a propagating shock front. The study is based on a one-step, irreversible Arrhenius reaction of a premixed gas; therefore, the ignition phenomenon is thermally induced. The boundary layer consists of a thin, diffusive, reaction region at the point where the temperature is maximum and diffusive-convective non-reacting regions adjacent to the reacting region. Both adiabatic and isothermal boundary conditions are examined. For the adiabatic wall, the reaction zone is near the insulated boundary. The reaction zone is in the interior for the isothermal wall. The effects of various parameters on the non-dimensional ignition distance and the ignition point are investigated. It is found that the ignition distance decreases almost linearly with the Mach number for both the adiabatic and the isothermal wall cases. In the isothermal wall case with fixed Mach number, the non-dimensional ignition point decreases linearly with the surface temperature, and the non-dimensional ignition distance has a minimum as the surface temperature varies.
Since the kinetic energy of the supersonic flow is converted into thermal energy through viscous heating in the boundary layer, the dependence of the viscosity on temperature is of particular importance. Sutherland's temperature-viscosity law is used in this research since it is a better approximation and provides a more rapid variation of viscosity with respect to temperature than the linear temperature-viscosity law. Use of the Sutherland's temperature-viscosity law results in coupled momentum and energy equations that are analyzed accordingly. Im, Bechtold and Law (10) did not account for the effects of the shock and used the linear temperature-viscosity law resulting in uncoupled momentum and energy equations. All four cases--Sutherland's law with shock, linear law with shock, Sutherland's law without shock, and linear law without shock--are considered for comparison.
"]},{"key":"dc:title","label":"Title","values":["Thermal Ignition Analysis in the Laminar Boundary Layer Behind a Propagating Shock Front"]}]}],"canonical_facts":{"dc:contributor":["David Glenn Lasseigne","Fang Q. Hu","Thomas L. Jackson","Chester Grosch"],"dc:creator":["Khan, Mushtaq Ahmed"],"dc:date.available":["2019-06-06T07:00:00Z"],"dc:description.abstract":["Asymptotic analysis in the limit of large activation energy is performed to investigate the ignition of a reactive gas in the laminar boundary layer behind a propagating shock front. The study is based on a one-step, irreversible Arrhenius reaction of a premixed gas; therefore, the ignition phenomenon is thermally induced. The boundary layer consists of a thin, diffusive, reaction region at the point where the temperature is maximum and diffusive-convective non-reacting regions adjacent to the reacting region. Both adiabatic and isothermal boundary conditions are examined. For the adiabatic wall, the reaction zone is near the insulated boundary. The reaction zone is in the interior for the isothermal wall. The effects of various parameters on the non-dimensional ignition distance and the ignition point are investigated. It is found that the ignition distance decreases almost linearly with the Mach number for both the adiabatic and the isothermal wall cases. In the isothermal wall case with fixed Mach number, the non-dimensional ignition point decreases linearly with the surface temperature, and the non-dimensional ignition distance has a minimum as the surface temperature varies.
Since the kinetic energy of the supersonic flow is converted into thermal energy through viscous heating in the boundary layer, the dependence of the viscosity on temperature is of particular importance. Sutherland's temperature-viscosity law is used in this research since it is a better approximation and provides a more rapid variation of viscosity with respect to temperature than the linear temperature-viscosity law. Use of the Sutherland's temperature-viscosity law results in coupled momentum and energy equations that are analyzed accordingly. Im, Bechtold and Law (10) did not account for the effects of the shock and used the linear temperature-viscosity law resulting in uncoupled momentum and energy equations. All four cases--Sutherland's law with shock, linear law with shock, Sutherland's law without shock, and linear law without shock--are considered for comparison.
"],"dc:identifier":["https://digitalcommons.odu.edu/mathstat_etds/26"],"dc:rights":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
"],"dc:subject":["Ignition","Shock flow","Mathematics"],"dc:title":["Thermal Ignition Analysis in the Laminar Boundary Layer Behind a Propagating Shock Front"],"thesis:degree_discipline":["Mathematics & Statistics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Master of Science (MS)"]},"updated_at":"2026-07-24T03:34:53Z"}