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Dendritic combustion in Hele–Shaw cells is investigated qualitatively using a simplified one-dimensional thermo-diffusive model. Formulas for the velocity, size, and temperature of the flamelets are derived. The temperature and velocity of the flames increase for small radii to allow for their survival regardless of the activation energy. In addition, the results obtained with very large activation energy were compared with experimental results, finding that additional tests are required due to the strong influence of gravity on the velocity and size estimations. Conditions for the existence of this anomalous propagation are investigated, confirming analytically that it can only happen for low Lewis numbers. [ABSTRACT FROM AUTHOR]

Thermoacoustic instabilities arise for lean hydrogen-air flames propagating in narrow channels. We provide here a detailed experimental analysis of such phenomena in a semi-confined vessel, analyzing the effect of the mixture composition, geometry and gravity on the onset of acoustic-driven flame vibrations. Downward-propagating flames leaner than a critical value vibrate smoothly and transit to the secondary oscillating instability, which develops strong variations of pressure that couple with the propagation dynamics. The transition threshold changes during the propagation along very narrow channels, where heat losses are no longer negligible. The parametric region of equivalence ratio for the secondary thermoacoustic instability diminishes, showing an additional transition for very lean flames. There, the front breaks into several structures and the flame-wave feedback becomes weaker. The influence of gravity is studied by comparing upward and downward propagating flames, where the Rayleigh–Taylor instability arises for sufficiently small values of the Froude number in slow-propagating lean flames. For a constant mixture, buoyancy-driven upward-propagating flames develop less wrinkled fronts than those propagating downwards, and remain unresponsive to acoustic-front interaction. We show here a direct relation between front shape and thermoacoustics. In agreement with previous studies [1–3] , curvature and strain effects on conduction and diffusion characterize the response of the flame to pressure perturbations, with the Markstein number controlling the aforementioned transition. Nevertheless, the theoretical analyses found in the literature can only be used on nearly equidiffusional mixtures, and are not accurate enough to describe the highly diffusive fuel mixtures (i.e. lean hydrogen-air flames) considered in our experiments. [ABSTRACT FROM AUTHOR]