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Rotating polyhedral flames
Author(s) -
Class A. G.
Publication year - 2001
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200108115164
Subject(s) - polyhedron , computation , bifurcation , conical surface , bunsen burner , rotation (mathematics) , mechanics , combustor , geometry , nonlinear system , materials science , physics , mathematical analysis , classical mechanics , mathematics , combustion , chemistry , algorithm , organic chemistry , quantum mechanics
By systematically changing the mixture composition of a flame on a Bunsen burner the conical shape of the flame can suddenly be transform into triangular cells forming a polyhedron. Often the polyhedron rotates rapidly about its vertical axis. We present a weakly nonlinear analysis which results in a Kuramoto‐Sivashinsky equation describing cellular flames, which is coupled to a heat equation modeling the temperature of the burner rim. Numerical computations of the coupled set of equations exhibit rapidly rotating polyhedral patterns, which show the typical saw‐toothed shape of the corrugations of the flame. In contrast to earlier considerations of this problem, where the rotation is explained as a result of mode interactions, we find a primary bifurcation to a rotating state, which may explain the high speeds of revolution.