AN UNEXPECTED STABILITY RESULT OF THE NEAR-EXTINCTION DIFFUSION FLAME FOR NON-UNITY LEWIS NUMBERS

Abstract

The fast-time stability of the near-ignition and near-extinction diffusion flame for unity fuel and oxidant Lewis numbers were studied respectively by Matalon and Ludford (1) and Buckmaster et al. (2). In the context of non-unity Lewis numbers, the steady-state response for chambered diffusion flames has recently been obtained (3). It is therefore natural to examine the effect of non-unity Lewis numbers on the near-ignition and near-extinction stability. In this paper we present the stability results of the diffusion flame. (A brief account of near-ignition stability results will be given in section 1.) The steady response of the near-extinction chambered diffusion flame is represented by the lower portion of the usual S-shaped curve (Fig. 1) or part of an isola. It has been proved analytically in (2) that the change-of-stability point lies exactly at the bend of the steady response curve in the unity-Lewis-numbers case. The near-extinction stability analysis of the case of the general Lewis numbers necessitates, in general, the study of the spectrum of a non-self-adjoint system of three second-order differential equations, which incurs tremendous difficulty. However, for neutral stability which is characterized by zero eigenvalues, we can construct, through a simple transformation and argument, solutions to our system of equations in terms of that obtained in (2) for the scalar equation in the unity-Lewis-number case. We find that the neutral stability point need not lie below the bend of the steady response curve (cf. Fig. 1). This important result is at variance with the common belief of the combustion community (cf. (4, p. 82)).