A three-dimensional study on premixed flame propagation in narrow channels considering hydrodynamic and thermodiffusive instabilities

In numerical studies of quasi-2D problems, such as laminar flame propagation through a slit, the quasi-2D assumption is commonly applied to simplify the problem. However, the impact of the third dimension (in the thickness between walls) can be significant due to strong curvature. The intrinsic Darrieus–Landau instability, the Saffman–Taylor instability, and the thermodiffusive instability lead to curved flame fronts in both the transverse and normal directions and radically change the global flame speed. This study investigates the interaction of these instabilities and their impact on premixed flames freely propagating in narrow channels. Two lean fuel–air mixtures are considered: one with unity Lewis number $Le=1$ and another with $Le=0.5$. A single-step Arrhenius-type reaction is used for combustion modeling. Joulin Sivashinsky’s model Joulin and Sivashinsky (1994), termed the 2D+ model, is implemented to capture the confinement effect due to walls. By comparing 3D Direct Numerical Simulations (DNS) and 2D simulations at unity $Le$, we find that the 2D+ model accurately reproduces confinement effects for channel width $h$ up to 3.6${\delta }_T$ (${\delta }_T$: thermal flame thickness), extending the validity of Darcy’s law.

However, for larger $h$, interactions between flame curvatures in two directions result in higher flame surface increment and consumption speed. Besides, for 3D cases with $Le=0.5$, positive curvature regions on the flame front primarily contribute to the global reaction due to the Lewis effect. Statistical studies on flame dynamics between walls in 3D cases are also conducted, and results show that both the flame surface increment and the Lewis effect on curvature (if $Le=0.5$) are approximately consistent. 2D simulations for the thickness between walls can predict the acceleration from flame dynamics between walls in the 3D domain for both mixtures.

Novelty and significance statement

This study is the first three-dimensional study on premixed flame freely propagating in narrow channels considering both hydrodynamic, including Darrieus–Landau (DL) and Saffman–Taylor (ST) instabilities, and thermodiffusive (TD) instabilities. It is also the first to validate the Joulin–Sivashinsky model’s ability to incorporate wall confinement effects in 2D simulations across various narrow channel widths through comparisons with 3D direct numerical simulations. This research is significant as it explores the interplay between confinement effect and DL and TD instabilities. It is also significant for its investigation on the interaction of flame curvature in both normal and transverse directions, a phenomenon previously underexplored in confined geometries, and its exploration on the essential impact of flame curvature and the Lewis effect ($Le<1$) between walls on global flame dynamics at wider channels.