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Talk Abstract
Pattern Formation in Cellular Flames

Institute for Mathematics and Its Applications

Talk abstract:

Pattern Formation in Cellular Flames

Michael J. Gorman, University of Houston

A uniform, circular, flat flame front stabilized on a porous plug burner at low pressures can undergo bifurcations to an ordered pattern of concentric rings of brighter, hotter cells demarked by darker, cooler cusps and folds that extend away from the burner. As the control parameters of total gas flow rate and equivalence ratio are varied, bifurcations to dynamic states are observed: rotating states in which rings of cells rotate uniformly or nonuniformly; hopping states in which individual cells abruptly change their angular position; ratcheting states in which one or more rings of cells rotate (very) slowly and nonuniformly, speeding up and slowing down in a manner charatericistic to each particular state; and intermittently ordered states in which ordered patterns of concentric rings appear and disappear at irregular intervals. Each of these states raises its own significant theoretical issues, such as bifurcations with symmetry and numerical solutions of the 2-d KuramotouSivashinsky equation, and its own experimental issues, such as precise measurments of the position, size, and shape of each cell. The relevance of these experimental results to other pattern-forming systems and also to controlling instabilities in other combustion systems will be discussed.

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