Study on symmetric/asymmetric hydrogen flame shapes in the thickness of a Hele-Shaw burner

Premixed flame front shape, which drastically depends on boundary conditions, is closely related to its propagation speed. In this work, we focus on the symmetry of steady premixed hydrogen-air flames propagating in a narrow channel, like a Hele-Shaw burner. A wide range of equivalence ratios ($0.35\text{–}2.0$) and channel widths ($1.8mm\text{–}4.8mm$) are analyzed by performing detailed simulations validated by experiments.

A multiplicity of steady flame shape is found for channel widths above a certain critical value, that is related to flame cutoff wavelength. Our numerical results successfully reproduce steady flame fronts observed in experiments. Notably, transitions from symmetric to asymmetric with equivalence ratio are reproduced. Additionally, an increase in channel width reduces the region of symmetric solutions. Furthermore, The study explores the effects of the Darrieus-Landau instability and thermodiffusive effects on flame shapes, presenting a stability diagram for symmetric/asymmetric flame configurations. Throughout the study, an increase in flame area is associated with the asymmetry level of the flame front, showing a trend that first increases and then decreases with the equivalence ratio. The global consumption rate relative to laminar flame speed decreases monotonously with increasing equivalence ratio. It is determined by the flame area increment and stabilizing (destabilizing) effects on convex flame fronts at Lewis number greater (smaller) than 1. This effect is quantified and proved independent of flame symmetry and channel width. For very lean mixtures, the differential species diffusion significantly strengthens the consumption rate. A prediction model is established to determine the flame front length given a certain equivalence ratio and channel width.

Novelty and Significance Statement

This study is, to the best of our knowledge, the first attempt to recover stable premixed hydrogen-air flame shapes observed in experiments in the thickness of a Hele-Shaw burner by performing detailed simulations. The evolution of stable flame shapes has been qualitatively and quantitatively analyzed for a wide range of equivalence ratios (0.35–2.0) and channel widths ($1.8mm-4.8mm$). The impacts of hydrodynamic instability and thermodiffusive effects are investigated, and the correlation between flame shape and consumption rate is analyzed. A prediction model is established to determine the flame front length. It is significant because the prediction of flame shape and velocity is crucial to hydrogen combustion safety and enables to mimic 3D problem by 2D simulations.