FLAME PROPAGATION IN VERTICAL CHANNELS: BIFURCATION TO BIMODAL CELLULAR FLAMES.

The authors derive a nonlinear evolution equation and associated boundary conditions which, under certain circumstances, describe downward adiabatic flame propagation in long, vertical channels. They analyze this problem for the case of axial symmetry and show that there exist two critical parameters, the channel radius R and a gravitational acceleration parameter G, which determine the stability and bifurcation characteristics of the flame. In particular, it is shown that there exist discrete critical points in the (G,R) plane at which either one or three solutions corresponding to bimodal cellular flames bifurcate from the basic planar solution. A nonlinear stability and bifurcation analysis in arbitrary neighborhoods of these critical points shows that either zero, one or two of the branches are stable, and the remaining branches are unstable. Thus new stable modes of cellular flame propagation are described.