The Reactive Rayleigh-Bénard Problem with Throughflow

We consider the Rayleigh--Benard problem for a combustible gaseous mixture in a two-dimensional channel formed by upper and lower horizontal plates, with periodic boundary conditions employed in the horizontal direction. Fresh unburned fluid is injected through the upper plate and burned products removed through the lower plate. The lower plate is heated to the burning temperature of the mixture so that, for appropriate injection rates, a flame forms within the channel. Using the Boussinesq model we describe the results of numerical computations to illustrate fluid-flame interactions. The model we consider is motivated by recent experiments on flames in the thin annular region between two closely spaced, finite, coaxial cylinders, formed by upper and lower horizontal plates. Here, the angular direction in the annulus corresponds to the horizontal direction in the channel. Our model results if the curvature of the cylinders is ignored, as is reasonable for relatively large cylindrical radii. Instabilities ...

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