Axisymmetric versus non-axisymmetric flames in cylindrical tubes

The assumption of an axisymmetric flame shape is a typical compromise when the three-dimensional curved flame structure cannot be resolved because of numerical limitations. However, as demonstrated in the present paper, such an assumption is not realistic for the usual numerical configuration of a flame propagating in an "ideal" tube with no heat transfer to the walls. The stability of the axisymmetric flames (both convex and concave) is investigated with respect to non-axisymmetric perturbations. The eigenvalue stability problem is solved for different tube widths and thermal expansions of the burning matter. It is shown that the axisymmetric flames are unstable for any tube width in the case of realistically large thermal expansion. The obtained instability is stronger for concave than for convex flames. When thermal expansion is small, the axisymmetric flames are also found to be unstable for all tube radii of interest. This result agrees only in part with previous simulations of axisymmetric/nonaxisymmetric flames in cylindrical tubes within the limit of ultimately small thermal expansion. Possible reasons for the disagreement are discussed. It is also demonstrated that thermal losses to the walls modify the flame shape. The critical level of the losses is obtained at which the axisymmetric flame shape is restored. (C) 2003 Published by Elsevier Inc. on behalf of The Combustion Institute.