Date of Award

Spring 2000

Document Type

Dissertation

Degree Name

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

Department

Mathematical Sciences

First Advisor

Michael R. Booty

Second Advisor

Gregory A. Kriegsmann

Third Advisor

John Kenneth Bechtold

Fourth Advisor

Jonathan H.C. Luke

Fifth Advisor

Anthony D. Rosato

Abstract

We consider a small drop of liquid fuel that burns in an oxidizing gaseous environment and translates slowly (relative to flow 'at infinity') under the action of gravity. Practical applications include the burning of liquid fuels as sprays in domestic and industrial oil-fired burners, diesel engines, and liquid-propellant rocket motors. More relevant to the simple physical set-up of the present study are wellcharacterized laboratory experiments on the burning of a single, isolated fuel drop.

The drop burns in a nearly spherical, diffusion flame, flame sheet regime. We consider a specific example, or limit, referred to as 'nearly adiabatic burning', in which the temperature of the gas mixture at the flame sheet is close to the ambient temperature at infinity. Temperature gradients everywhere outside the flame sheet are therefore small. The problem is solved by perturbation methods, primarily, with a distinguished limit between the inverse nondimensional activation energy ε and the translational Reynolds number Re. We include time dependence far from the drop as a quasisteady effect, and this influences the near field region of the drop via matching between near field and far field.

Evaluation of quantities such as the 'drag' force exerted by the fluid on the drop, the flame sheet shape, and the speed of translation necessitates numerical solution of a higher order problem in the perturbation scheme. Results predicted for the behavior of a heptane fuel drop will be presented.

Included in

Mathematics Commons

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