Date of Award

Spring 1995

Document Type

Dissertation

Degree Name

Master of Science (MS)

Department

Mathematics and Statistics

Program/Concentration

Computational and Applied Mathematics

Committee Director

David Glenn Lasseigne

Committee Member

Fang Q. Hu

Committee Member

Thomas L. Jackson

Committee Member

Chester Grosch

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.

DOI

10.25777/txv1-8e24

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Mathematics Commons

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