Studies of Curvature Effects on Laminar Premixed Flames: Stationary Cylindrical Flames

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Abstract
A solution of the stationary cylindrical flame in both source and sink configurations is obtained analytically using simplified reaction rate and diffusion models. The solution is used to investigate the effects of curvature in the absence of stretch and identify the ranges where ducting and source/sink effects are dominant. We also investigate the concept of a minimum radius of curvature by introducing non-local effects on the flame. For both configurations a stable solution may be found for any imposed source flow rate. Ducting, a purely hydrodynamic process, is dominant at low curvature when the flame is far from the source or sink. Near a source, however, source effects become important. This occurs when the flame radius of curvature is comparable to the flame thickness. The modification of the reaction zone structure and the burning rate is not significant since the flame still completely burns the reactants. At Le ≠ 1 the reaction zone thickness is further increased for Le > 1 and further reduced for Le < 1. Non-local effects were modeled by varying the source temperature. A wide range of burning rates is obtained by increasing the initial source temperature at a fixed flame location. Sink effects result in an increase in the preheat zone thickness and a reduction in the flame temperature due to a reduction in residence time. When the flame radius of curvature is of the order of the reaction zone thickness, the propagation rate becomes dependent on curvature. At Le ≠ 1, curvature enhances non-unity Lewis number effects on the burning rate. The results show that curvature alone does not alter the flame propagation rate except near the source/sink. The sink configuration is more susceptible to these effects due to finite residence time.