Triple-flame propagation against a Poiseuille flow in a channel with porous walls

Abstract

We present an essentially numerical study of triple-flame propagation in a non-strained two-dimensional mixing layer against a Poiseuille flow, within a thermo-diffusive model. The aim of the study is twofold. First, to examine the recent analytical findings derived in the asymptotic limit of infinite Zeldovich number β for flame fronts thin compared with their typical radius of curvature and to extend these to finite-values of β. Second, to gain insight into the influence of the flow on the flame in situations where the flame in not necessarily thin, as assumed analytically. The study has focused on the effect of two main non-dimensional parameters on flame propagation, namely the flow amplitude A and the flame-front thickness ε. For moderate values of A, the flow is found to have a negligible effect on the structure of the flame, while modifying its speed by an amount proportional to A, in agreement with the asymptotic findings. Two new qualitative behaviours are found however. The first is obtained for sufficiently large values of A where the flow is shown to modify the flame structure significantly for small values of ε; more precisely, the concavity of the triple-flame front is found to turn towards the unburnt gas for A larger than a critical value. This inversion of the front curvature, which cannot be captured by the infinitely-large β asymptotic study, is found to be intimately linked to the finite values of β, which are necessarily found in any realistic model or computational study. The second new behaviour, which is also obtained for small ε, is the existence of termination-points on the flame front, or flame-tips. These termination-points are shown to exist for ε ≪ 1 only if A takes on positive values of order unity or larger; in particular they are absent for thin triple-flames without the presence of a non-uniform flow field. Furthermore, several additional novel contributions are made in the present context of triple-flame interaction with a non-uniform parallel flow. These include a fairly complete description of the flame propagation regimes for a wide range of variations in A and ε. In particular, it is found that larger values of A promote combustion by increasing the ε-range of existence of ignition fronts, while a decrease in the value of A towards zero or negative values increases the ε-range of existence of extinction fronts.

Keywords:

• Triple-flames
• flame–flow interaction
• partially premixed flames
• Poiseuille flow
• porous-walls channel

Notes

¹Here we found it convenient to rescale V and A in the asymptotic formula by multiplying them by the (numerically computed) laminar flame speed of the stoichiometric planar flame. Of course, this rescaling (of the asymptotic results) is equivalent to the rescaling of the numerical results in Figure 3.

²Justification for retaining the non-uniformity term necessitates, strictly speaking, revisiting the analytical work of [15] under a different distinguished limit, such as β → ∞ with , to allow for large values of A. This will not be undertaken here.