ASYMPTOTIC DERIVATION OF ISOLA AND S RESPONSES FOR CHAMBERED DIFFUSION FLAMES.

The asymptotic solution of the nonlinear ordinary differential equation with two-point boundary conditions which describes a steady diffusion flame in a chamber is considered. The solution is characterized by the unburnt fuel fraction R as a function of the fuel injection rate M. The shape of the corresponding response curve depends on the Damkoehler number D (representing either the constant chamber pressure or the chamber's length) for which two critical values, D//o and D//a, are uncovered. For D greater than D//a the only possibility is R identically 1 (extinguished states). When D//a less than D less than D//o, a closed curve called an isola is also a possible response, its base lying on R equals O (complete burning). As D approaches D//a the isola shrinks to a point and disappears. But when D is increased towards D//o it expands until its left side swells into the end of the strip M greater than O, O less than R less than 1. Then it breaks and joins the extinguished response (which is now limited on the left) to form an S, which is the nature of the response when D greater than D//o. The transitions between the various responses require special asymptotics which are also described herein.