TY - JOUR

T1 - FLAME PROPAGATION IN VERTICAL CHANNELS

T2 - BIFURCATION TO BIMODAL CELLULAR FLAMES.

AU - Margolis, Stephen B.

AU - Sivashinsky, Gregory I.

PY - 1984

Y1 - 1984

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0021406167&partnerID=8YFLogxK

U2 - 10.1137/0144024

DO - 10.1137/0144024

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AN - SCOPUS:0021406167

SN - 0036-1399

VL - 44

SP - 344

EP - 368

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

IS - 2

ER -