Nonlinear dynamic characteristics of flame stripes formed in strained diffusion flames by diffusional—thermal instability

Abstract

The nonlinear dynamics of striped diffusion flames, formed in the two-dimensional counterflow field by the diffusional-thermal instability with Lewis numbers sufficiently less than unity, is investigated numerically by examining the nonlinear two-dimensional transient flame-structure solutions bifurcating from the one-dimensional steady solution by various initial perturbations. The Lewis numbers for the fuel and oxidizer are assumed to be identical and an overall single-step Arrhenius-type chemical reaction rate is employed as the chemistry model. Attention is focused on two nonlinear phenomena, namely the development of the two-dimensional flame-stripe structure and the extension of the flammability limit beyond the static extinction condition of a one-dimensional flame. A time-dependent solution, carried out for a Damköhler number slightly above the static extinction Damköhler number, exhibited the developmental procedure of flame stripes with the most unstable wavelength from a long-wave initial perturbation with a small amplitude. In contrast to the chaotic cellular premixed-flame structures predicted from numerical integration of the Kuramoto-Sivashinsky equation, the stripe structure in diffusion flames is found to be stationary, consequently leading to the conclusion that the nonlinear term in the corresponding nonlinear bifurcation equation would be a simple cubic term. Two-dimensional flame-stripe solutions are also found to be able to survive Damköhler numbers significantly below the static extinction Damköhler number of the one-dimensional flame structure. Extension of the flammability is found to be greatest if the imposed initial perturbation possesses the wavenumber of the fastest growing mode.