Influence of heat loss on the stability of diffusion flames in a narrow-channel shear flow

Under shear-enhanced diffusion (Taylor dispersion), a planar diffusion flame has been found recently to undergo a new cellular instability in mixtures with Lewis number 𝐿⁢𝑒>1 under adiabatic conditions, which may explain the formation of so-called flame streets in microcombustion experiments. Since heat losses are expectedly significant in such experiments, it is important to examine how they influence this Taylor dispersion-induced cellular instability. The paper is mainly dedicated to clarifying this issue, using a linear stability analysis and time-dependent numerical simulations, based on a two-dimensional depth-averaged model accounting for heat losses and Taylor dispersion. The investigation is focused on near-extinction conditions where the planar diffusion flame is known to become unstable, that is near the two extinction points a non-adiabatic diffusion flame possesses, namely the so-called diffusive extinction point occurring at a relatively small Damköhler number and the heat-loss extinction point, occurring at a larger Damköhler number. The results confirm that the cellular instability in 𝐿⁢𝑒>1 mixtures survive in the presence of heat losses, provided the Péclet number 𝑃⁢𝑒 exceeds a critical value. Stability regime diagrams in the 𝐿⁢𝑒-𝑃⁢𝑒 plane are presented, identifying the three types of instabilities encountered, namely, the cellular instability aforementioned, an oscillatory planar instability and a non-oscillatory planar instability. The time-dependent numerical simulations demonstrate the development of the instabilities predicted by the linear stability analysis. In particular, flames undergoing the cellular instability are found to evolve ultimately into one of the three states: an extinguished state, an apparently stable steady cellular structure, and an unsteady state with complex dynamics involving triple-flame propagation, splitting and merging of cells. In general, for the cellular structures generated by the instability to be stabilized, larger values of 𝑃⁢𝑒 and 𝐿⁢𝑒 are found to be required, in order to counteract quenching by heat losses.