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An asymptotic theory for the propagation of a surface-catalysed flame in a tube

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An asymptotic theory for the propagation of a surface-catalysed flame in a tube. / Bate, Fiona; Billingham, J; King, A C; Kendall, K.

In: Journal of Fluid Mechanics, Vol. 546, 10.01.2006, p. 363-393.

Research output: Contribution to journalArticlepeer-review

Harvard

Bate, F, Billingham, J, King, AC & Kendall, K 2006, 'An asymptotic theory for the propagation of a surface-catalysed flame in a tube', Journal of Fluid Mechanics, vol. 546, pp. 363-393. https://doi.org/10.1017/S0022112005007172

APA

Bate, F., Billingham, J., King, A. C., & Kendall, K. (2006). An asymptotic theory for the propagation of a surface-catalysed flame in a tube. Journal of Fluid Mechanics, 546, 363-393. https://doi.org/10.1017/S0022112005007172

Vancouver

Bate F, Billingham J, King AC, Kendall K. An asymptotic theory for the propagation of a surface-catalysed flame in a tube. Journal of Fluid Mechanics. 2006 Jan 10;546:363-393. https://doi.org/10.1017/S0022112005007172

Author

Bate, Fiona ; Billingham, J ; King, A C ; Kendall, K. / An asymptotic theory for the propagation of a surface-catalysed flame in a tube. In: Journal of Fluid Mechanics. 2006 ; Vol. 546. pp. 363-393.

Bibtex - Download

@article{57c4f02da86641d4aa44a7c1aebc8e96,
title = "An asymptotic theory for the propagation of a surface-catalysed flame in a tube",
abstract = "Experiments have shown that when a mixture of fuel and oxygen is passed through a zirconia tube whose inner surface is coated with a catalyst, and then ignited at the end of the tube, a reaction front, or flame, propagates back along the tube towards the fuel inlet. The reaction front is visible as a red hot region moving at a speed of a few millimetres per second. In this paper we study a model of the flow, which takes into account diffusion, advection and chemical reaction at the inner surface of the tube. By assuming that the flame propagates at a constant speed without change of form, we can formulate a steady problem in a frame of reference moving with the reaction front. This is solved using the method of matched asymptotic expansions, assuming that the Reynolds and Damk{\"o}hler numbers are large. We present numerical and, where possible, analytical results, first when the change in fluid density is small (a simplistic but informative limit) and secondly in the variable-density case. The speed of the travelling wave decreases as the critical temperature of the surface reaction increases and as the mass flow rate of fuel increases. We also make a comparison between our results and some preliminary experiments.",
author = "Fiona Bate and J Billingham and King, {A C} and K Kendall",
note = "This is an author-produced version of the published paper. Uploaded in accordance with the publisher{\textquoteright}s self-archiving policy. Further copying may not be permitted; contact the publisher for details.",
year = "2006",
month = jan,
day = "10",
doi = "10.1017/S0022112005007172",
language = "English",
volume = "546",
pages = "363--393",
journal = "Journal of Fluid Mechanics",
issn = "0022-1120",
publisher = "Cambridge University Press",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - An asymptotic theory for the propagation of a surface-catalysed flame in a tube

AU - Bate, Fiona

AU - Billingham, J

AU - King, A C

AU - Kendall, K

N1 - This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details.

PY - 2006/1/10

Y1 - 2006/1/10

N2 - Experiments have shown that when a mixture of fuel and oxygen is passed through a zirconia tube whose inner surface is coated with a catalyst, and then ignited at the end of the tube, a reaction front, or flame, propagates back along the tube towards the fuel inlet. The reaction front is visible as a red hot region moving at a speed of a few millimetres per second. In this paper we study a model of the flow, which takes into account diffusion, advection and chemical reaction at the inner surface of the tube. By assuming that the flame propagates at a constant speed without change of form, we can formulate a steady problem in a frame of reference moving with the reaction front. This is solved using the method of matched asymptotic expansions, assuming that the Reynolds and Damköhler numbers are large. We present numerical and, where possible, analytical results, first when the change in fluid density is small (a simplistic but informative limit) and secondly in the variable-density case. The speed of the travelling wave decreases as the critical temperature of the surface reaction increases and as the mass flow rate of fuel increases. We also make a comparison between our results and some preliminary experiments.

AB - Experiments have shown that when a mixture of fuel and oxygen is passed through a zirconia tube whose inner surface is coated with a catalyst, and then ignited at the end of the tube, a reaction front, or flame, propagates back along the tube towards the fuel inlet. The reaction front is visible as a red hot region moving at a speed of a few millimetres per second. In this paper we study a model of the flow, which takes into account diffusion, advection and chemical reaction at the inner surface of the tube. By assuming that the flame propagates at a constant speed without change of form, we can formulate a steady problem in a frame of reference moving with the reaction front. This is solved using the method of matched asymptotic expansions, assuming that the Reynolds and Damköhler numbers are large. We present numerical and, where possible, analytical results, first when the change in fluid density is small (a simplistic but informative limit) and secondly in the variable-density case. The speed of the travelling wave decreases as the critical temperature of the surface reaction increases and as the mass flow rate of fuel increases. We also make a comparison between our results and some preliminary experiments.

U2 - 10.1017/S0022112005007172

DO - 10.1017/S0022112005007172

M3 - Article

VL - 546

SP - 363

EP - 393

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -