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IMA Journal of Applied Mathematics Advance Access originally published online on October 18, 2007
IMA Journal of Applied Mathematics 2008 73(1):107-122; doi:10.1093/imamat/hxm045
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© The Author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Numerical solutions of a model for the propagation of a surface-catalysed flame in a tube

G. J. Sharpe{dagger}

School of Mechanical Engineering, University of Leeds, Leeds LS2 9JT, UK

S. A. E. G. Falle

Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK

J. Billingham

School of Mathematical Sciences, The University of Nottingham, Nottingham NG7 2RD, UK

{dagger} Email: mengis{at}leeds.ac.uk

Received on October 25, 2006; Accepted on January 26, 2007

Numerical simulations of a surface-catalysed flame in a tube are performed, corresponding to an experiment where a premixed fuel is fed into a tube whose inner surface is coated with a catalyst. In these experiments, subsequent to ignition, a reaction wave can be seen as a red-hot region which propagates back along the tube towards the inlet, and is due to low temperature combustion occurring only on the inner surface of the tube where the catalyst is present. The solutions of a mathematical model for this behaviour show that initial-value problems do indeed result in such steadily propagating waves. The numerically obtained wave speeds and steady solution are compared to a previous large Damköhler number (Da) asymptotic analysis using a simple reaction rate model, and agreement is very good even for moderately large values of Da. However, for such Damköhler numbers, the wave speeds are found to be much larger than observed experimentally. Indeed, the simulations show that O(1) values of Da are required to obtain the lower experimental wave speeds. Nevertheless, the wave speeds as a function of flow rate through the tube do not agree well with the preliminary experimental results for any choice of the parameters. A more realistic, Arrhenius reaction rate model is then considered. The Arrhenius model predicts a rapid change in temperature at the wave front, in much better agreement with the experiments than for the simpler reaction model.

Keywords: Catalytic combustion; Numerical simulation; Reactive Navier-Stokes equations; Solid Oxide Fuel Cells.


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