Premixed flame quenching distance between cold walls: effects of flow and Lewis number

TL;DR

The paper addresses how the quenching distance for premixed flames in channels with cold walls depends on the Lewis number $Le$ and the flow amplitude $A$, using a combined stationary and time-dependent numerical approach in both variable-density and constant-density models. It maps steady-flame existence, symmetry, and stability across a range of $Le$, $A$, and width $\epsilon$, revealing that smaller $Le$ and aiding flow ($A<0$) reduce the quenching distance, while opposing flow ($A>0$) and larger $Le$ increase it. Importantly, symmetry-breaking can yield stable asymmetric flames that set the quenching limit at large $A$, altering the conventional symmetric-quenching picture. The results advance understanding of flame stability in confined geometries with heat losses and have implications for designing safe, efficient combustion systems under cold-wall conditions.

Abstract

This study investigates the critical conditions for flame propagation in channels with cold walls. We analyze the impact of the Lewis number and flow amplitude ($A$) on the minimum channel width required to sustain a premixed flame. Our results span a wide range of Lewis numbers, encompassing both aiding and opposing flow conditions. Results are presented for both variable and constant density models. A combined numerical approach, involving stationary and time-dependent simulations, is employed to determine quenching distances and solution stability. We find that smaller Lewis numbers and aiding flows ($A < 0$) facilitate flame propagation in narrower channels, while opposing flows ($A > 0$) tend to destabilize the flame, promoting asymmetric solutions. For sufficiently large positive values of $A$, the quenching distance is determined by asymmetric solutions, rather than the typical symmetric ones.

Figures (13)

• Figure 1: A schematic representation of a premixed flame propagating through a Poiseuille flow at (non-dimesnional) speed $U$ relative to the channel walls, which are maintained at the unburnt gas temperature.
• Figure 2: The propagation speed $U$ versus $\epsilon$ for $A=0$ and selected values of $\hbox{Le}$. Solid lines represent solutions symmetric with respect to $y=0$ and dashed lines asymmetric solutions.
• Figure 3: The propagation speed $U$ versus $\epsilon$ for $A=0$ and $\hbox{Le}=0.7$. As in the previous figure, solid lines represent solutions symmetric with respect to $y=0$ and dashed lines represent asymmetric solutions. These symmetric and asymmetric solutions are illustrated by the insets for selected values of $\epsilon$. Shown in each inset are colour-coded temperature fields as well as a single reaction rate contour ($\omega=0.1 \,\omega_{\max}$) marked by a black line to locate the reaction zone. The points marked by asterisks labelled by capital letters A to E refer to solutions which will be discussed later in section \ref{['sec:ResultsStab']} on stability.
• Figure 4: Existence domains of the steady solutions for $A=0$. Quenching distance: lower black curve. Asymmetric solutions: left of red curve. Symmetric solutions: left of black curve; these symmetric solutions are single-headed flames to the right of the blue curve and multi-headed flames to its left.
• Figure 5: The effective propagation speed $\widetilde{U}\equiv U+2A/3$ versus $\epsilon$ for selected values of $\hbox{Le}$. The top, middle and lower subfigures correspond to $A=-2$, $A=0$ and $A=2$, respectively. Solid lines represent solutions symmetric with respect to $y=0$ and dashed lines asymmetric solutions.