Darrieus–Landau instability and Markstein numbers of premixed flames in a Hele-Shaw cell

Abstract

Hydrodynamic flame instabilities are studied in a Hele-Shaw burner. By studying the development of perturbations, starting from a 2D Bunsen flame at the top of the burner, growth rates are measured for propane and methane-air mixtures, and compared to theoretical predictions. It is found that the dispersion relation in a Hele-Shaw cell has the same dependence with wavenumber σ = k − k 2 as the one predicted in tubes. Markstein numbers relative to fresh gases are obtained for propane and methane flames and compared to the literature.

Coupling of vibro-acoustic waves with premixed flame

“…When focusing on the topology of the flame interface, both parametric restabilization and parametric resonance are possible to be forced, as predicted by the Searby and Rochwerger [8] theory. It has been shown that the plate modes may be excited by the flame propagation itself and are certainly responsible for the flame speed oscillations with unexpected frequencies observed in recent experiments [18,26,27].…”

“…We analyze the downward propagation of propane-air flame with equivalence ratios in the range 0.7 to 1.5 with each plates set. This range corresponds to the range where the flame can propagate inside the Hele-Shaw cell of 5mm gap without thermal extinction due to heat loss on the walls [18]. Acoustic instability usually appears during propagation in tubes [8].…”

“…The interaction mechanism between acoustic waves and flame dynamics originally proposed by Markstein [9,10] has been analytically [11,12], numerically [13,14], and experimentally [15][16][17] studied. A main outcome is that acoustic instabilities are more likely to emerge when the Markstein number is low [8], (e.g rich propane-air flame [18]). Controlling the primary instability in tubes, by using an acoustic source (loudspeaker) or an acoustic damper (sub-millimeter aperture) at the closed end of the tube, allowed to study the Darrieus-Landau intrinsic wrinkling [19,20] in the linear [21] and non linear [22] regimes.…”

“…More recently, accurate studies of the Darrieus-Landau wrinkling have been performed in an experimental device which allows to reduce the flame dynamics to a quasi-bidimensionnal one [18,[23][24][25][26][27][28][29]. The two dimensional dynamics has been shown to be similar to that of freely propagating flames [18]. In particular, the front corrugations undergo a complex motion causing permanent fluctuations of the total flame area.…”

Experimental and numerical Lattice-Boltzmann investigation of the Darrieus–Landau instability

“…The experiments are carried out in a Hele-Shaw burner [14][15][16][17][18][19][20]. The apparatus used here is made of two borosilicate glass plates (1500 ×500 ×5mm)…”