Flame propagation in narrow channels:

What Darrieus and Landau didn't tell you

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Abstract

The flame speeds and wrinkling spectra of premixed flames propagating in quasi-2D channels (Hele-Shaw cells) were studied using CH₄ and C₃H₈ fuels with N₂ and CO₂ diluents. Upward, downward and horizontal propagation configurations were tested for varying mixture strength and thus laminar burning velocity (S_L). In this way the effects of buoyancy, thermal expansion, heat loss and Lewis number were studied.  Wrinkling and thus flame speed enhancement was observed even for downward propagating (buoyantly stable) flames have high Le (diffusive-thermally stable) due to the effects of thermal expansion (Darrieus-Landau, DL) and viscosity increase (Saffman-Taylor, ST) across the front. The quasi-steady flame speed (U_T) was always higher than (S_L), typically by a factor of 3. Values of U_T/S_L correlated well with a scaled growth rate parameter (K) based on the Joulin-Sivashinsky model of flame instabilities in narrow channels due to DL, ST and buoyancy effects.  The observed correlation was U_T/S_L = 1 + K, thus K serves a role similar to u' in turbulent combustion in the laminar flamelet regime.  Wrinkling spectra exhibited a marked change as the cell thickness decreased due to a change in the dominant instability mechanism from DL to ST. Flame wrinkling in the plane of the cell and front curvature in the transverse dimension are found to be of similar importance in affecting U_T. These results indicate that the behavior of practical flames in confined geometries such as internal combustion engines or gas turbines is quite different from that inferred from laboratory experiments conducted in open geometries such as Bunsen, counterflow or V-flames, where thermal expansion is relaxed in the transverse directions.