Stability of diffusion flames under shear flow: Taylor dispersion and the formation of flame streets

TL;DR

This paper investigates how Taylor dispersion influences the stability of diffusion flames under shear flow, explaining the formation of flame streets through a coupling of diffusive-thermal instabilities and flow-enhanced diffusion effects.

Contribution

It introduces a novel mechanism linking Taylor dispersion with flame stability, providing a theoretical explanation for flame street formation in shear flows with high Lewis number fuels.

Findings

High Lewis number fuels exhibit cellular instabilities above a critical Peclet number.

Longwave instabilities can lead to flame extinction below the critical Peclet number.

Stability diagrams identify regions of stable and unstable flame behavior in the Le-Pe plane.

Abstract

Diffusion flame streets, observed in non-premixed micro-combustion devices, align parallel to a shear flow. They are observed to occur in mixtures with high Lewis number ($Le$) fuels, provided that the flow Reynolds number, or the Peclet number $Pe$, exceeds a critical value. The underlying mechanisms behind these observations have not yet been fully understood. In the present paper, we identify the coupling between diffusive-thermal instabilities and Taylor dispersion as a mechanism which is able to explain the experimental observations above. The explanation is largely based on the fact that Taylor dispersion enhances all diffusion processes in the flow direction, leading effectively to anisotropic diffusion with an effective (flow-dependent) Lewis number in the flow direction which is proportional to $1/Le$ for $Pe\gg 1$. Validation of the identified mechanism is demonstrated within a simple model by investigating the stability of a planar diffusion flame established parallel to a plane Poiseuille flow in a narrow channel. A linear stability analysis, leading to an eigenvalue problem solved numerically, shows that cellular (or finite wavelength) instabilities emerge for high Lewis number fuels when the Peclet number exceeds a critical value. Furthermore, for Peclet numbers below this critical value, longwave instabilities with or without time oscillations are obtained. Stability regime diagrams are presented for illustrative cases in a $Le$-$Pe$ plane where various instability domains are identified. Finally, the linear analysis is supported and complemented by time dependent numerical simulations, describing the evolution of unstable diffusion flames. The simulations demonstrate the existence of stable cellular structures and show that the longwave instabilities are conducive to flame extinction.