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In this study we examine theoretically the structure of a simple one-dimensional spray diffusion flame. The analysis is carried out along two complementary routes: an asymptotic approach, that treats the limiting behaviors of fast vaporization followed by fast chemical reaction and illustrates the various physical mechanisms involved in the complex multi-phase field, and a numerical approach that validates and extends the solution to arbitrary parameter values. The results emphasize the importance of heat and mass transfer rates, the supply conditions, the droplet loading, the size distribution of the droplets in the spray and the effects of volumetric heat loss. Particular attention is given to the conditions for flame extinguishment and those effects that may promote or delay extinction.

Early treatments of flames as gasdynamic discontinuities in a fluid flow are based on several hypotheses and/or on phenomenological assumptions. The simplest and earliest of such analyses, by Landau and by Darrieus prescribed the flame speed to be constant. Thus, in their analysis they ignored the structure of the flame, i.e. the details of chemical reactions, and transport processes. Employing this model to study the stability of a plane flame, they concluded that plane flames are unconditionally unstable. Yet plane flames are observed in the laboratory. To overcome this difficulty, others have attempted to improve on this model, generally through phenomenological assumptions to replace the assumption of constant velocity. In the present work we take flame structure into account and derive an equation for the propagation of the discontinuity surface for arbitrary flame shapes in general fluid flows. The structure of the flame is considered to consist of a boundary layer in which the chemical reactions occur, located inside another boundary layer in which transport processes dominate. We employ the method of matched asymptotic expansions to obtain an equation for the evolution of the shape and location of the flame front. Matching the boundary-layer solutions to the outer gasdynamic flow, we derive the appropriate jump conditions across the front. We also derive an equation for the vorticity produced in the flame, and briefly discuss the stability of a plane flame, obtaining corrections to the formula of Landau and Darrieus.

The interaction of a premixed flame with the flow near the front stagnation point of a body has rightly received considerable attention in combustion theory. Virtually all the investigations so far have been concerned with high strain rates, when the flame lies inside the boundary layer and can be extinguished. By contrast, we consider moderate strain rates, when the flame stands clear of the boundary layer and pushes the incident flow away from the body. The object is to determine this displacement effect, which is much more pronounced than that of the boundary layer.