Date of Award

Fall 2001

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematical Sciences - (Ph.D.)

Department

Mathematical Sciences

First Advisor

John Kenneth Bechtold

Second Advisor

Michael R. Booty

Third Advisor

Burt S. Tilley

Fourth Advisor

Dawn A. Lott

Fifth Advisor

Eliza Zoi-Heleni Michalopoulou

Abstract

In this dissertation, a new model of premixed flames in near-stoichiometric mixtures is derived. Unlike most previous theories, which are valid only for very lean or very rich, i.e. off-stoichiometric conditions, our model remains valid over the entire spectrum of mixture compositions, from lean to rich, including the near-stoichiometric regime. Since fuel-mixture composition is known to have a significant effect on flame behavior, such a model is expected to contribute new insights into classical problems in premixed combustion.

In the first part of this dissertation, we describe the derivation of a model for premixed flames in two-reactant mixtures in a formal asymptotic way. Using the method of matched asymptotics we are able to simplify the complicated governing equations of combustion and effectively decouple the hydrodynamic equations from those of heat and mass transport. Our model considers a two reactant mixture in which one reactant is slightly in excess and the other deficient. We show that, if the initially excess reactant is less mobile, then it doesn't diffuse as rapidly across a strained flow field and can be locally deficient, and hence consumed, at the reaction zone. This can have a significant effect on burning characteristics of the flame. There are two major differences between our model and previous models. First, we have an additional react ion-diffusion equation governing the transport of the second species. Second, the derived conditions relating the gradients across the reaction sheet are shown to take one of two different forms, depending on which of the two species is consumed in the reaction.

In the second part of the thesis, we use our model to study the behavior of planar and strained flames. For the planar flame in uniform flow, we find that many of the results of single-reactant theory apply under near-stoichiometric conditions, provided an effective Lewis number is introduced. On the other hand, for a flame in a nonuniform flow, the dynamics depend significantly on the mass diffusivities as well as mixture strength. In particular, we have analyzed the structure of flame in stagnation point flow and given a complete description of the combustion process including extinction conditions. Results are shown to compare favorably with experiments.

Included in

Mathematics Commons

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