Structure and stability of buoyant diffusion flames

by Fleming, Graham Christopher

Abstract (Summary)
The structure and stability of the convecting fluid flow generated by a diffusion flame in gaseous reactants has been investigated. The flame extends vertically upwards from a solid horizontal boundary, and separates the fuel from the oxidizer which can be of a different density. Real fuels are modelled by choosing appropriate values for the density difference and stoichiometric ratio of the reaction. A self-similar solution for the steady flow is obtained incorporating the Howarth transformation, which allows the large density variations inherent in the combustion of gases to be accommodated. The stoichiometric ratio and fuel/oxidizer density ratio are varied to examine their effects on the structure and flow properties of the flame. An Orr-Sommerfeld equation governing the stability of buoyant flows is developed, incorporating all the variable density terms. Two different steady flows are studied, the symmetric flame (unit stoichiometry), and a flame with the stoichiometric ratio corresponding to methane burning in air. It was found that using the Boussinesq approximation which neglects density variations except for a buoyancy term is not applicable for the flame, and also introduced inaccuracy in the stability diagram for the buoyant plume. Although the flame bears a superficial similarity to the buoyant plume, the several differences cause a large difference in their stability. Empirically interpreting the stability diagrams to obtain an expected transition point gives ReT ~ 250 for the flame compared to the less stable buoyant plume with ReT ~ 140. A new unstable region consisting of waves with negative phase velocity but positive group velocity was found for both the buoyant flame and the buoyant plume. The local analysis is inappropriate for disturbances with wavelengths long compared to the flame thickness, therefore an analysis treating the flame and associated plume as negligibly thin was undertaken. This showed that the primary cause of instability was centrifugal forces generated by the momentum flux following a curved path. Reasonably good agreement was obtained with the local analysis.
Bibliographical Information:

Advisor:Toshi Kubota; Frank E. Marble

School:California Institute of Technology

School Location:USA - California

Source Type:Master's Thesis

Keywords:applied mechanics


Date of Publication:03/17/1982

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