Oscillatory flame edge propagation, isolated flame tubes and stability in a non-premixed counterflow

Abstract

An investigation is carried out into the ranges of Damköhler number and Lewis number, less than unity, in which different forms of combustion phenomena arise within a non-premixed counterflow; cases that are symmetrical across the counterflow are chosen for study. These link oscillatory and steady propagation of flame edges, zero propagation speeds, isolated flame tubes, quenching and marginal stability of planar diffusion flames. Over a range of Lewis numbers, the transition between steady and oscillatory propagation of a flame edge has characteristics that are consistent with a subcritical Hopf bifurcation. Isolated flame tubes are found to persist up to a Lewis number that is very close to unity.

Steady and unsteady flame propagation in a premixed counterflow

“…The movie clip, see Appendix A, shows a weakly burning flame developing into a positively propagating flame tube at δ = 20. This particular calculation does not develop into an isolated flame tube but into two flame tubes showing that, as with the results previously found for stationary flame tubes [4], not only can isolated moving flame tubes be found but also multiple moving flame tubes.…”

“…Our results show that the continuation solutions move smoothly into a regime of moving flame tubes. This is quite different from what happens at low Lewis number at the transition from flame edge to flame tube which is strongly associated with cellular instability, see for example [4], for which there is a phase of non-steady edge propagation. The speed of these moving flame tubes is also given in figure 9, on the curve between δ 1 and δ 3 .…”

“…This shows that for the weakly burning flame the maximum temperature is on the centre line and not all the fuel is consumed in the combustion process. The rate of reaction ω is defined as ω = δβ 2 F T β , see (4), and the normalized rate of reaction is given by ω/||ω|| where ||ω|| is the maximum value of ω, in figures 5 and 6 shows that the twin flames for the weakly burning flame are much closer together than for the strongly burning flame. And the size of ||ω|| shows that it is about ten times greater for the strongly burning flame.…”

“…Much of the work reported here can be viewed as an extension and consolidation of the results in the recent paper [2] for premixed combustion with heat loss. Of some relevance to this work is the cellular instability of planar flames at low Lewis numbers and the existence of flame tubes in both premixed [3] and non-premixed combustion [4,5].…”

Flame dynamics and structure within sub‐millimeter combustors

“…Stabilization of premixed flame structures with acoustic emission in tubes of about 1 mm diameter has also been investigated 19. Numerical studies have also focused on onset of oscillations, stability criteria, and oscillatory flame propagation in non‐premixed configurations 34–36…”