Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-12-04T10:14:59.320Z Has data issue: false hasContentIssue false
  • English
  • Français

Propagation of flame fronts

Published online by Cambridge University Press:  17 February 2009

N. F. Smyth
N. F. Smyth
Affiliation:
Department of Mathematics, University of Wollongong, P.O. Box 1144, Wollongong, N.S.W. 2500, Australia.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The propagation of a flame front in a combusting gas is considered in the limit in which the width of the reaction-zone is small compared with some overall flow dimension. In this approximation, the front propagates along its normals at a speed dependent on the local curvature of the front and is governed by a nonlinear equivalent of the geometric optics equations. Some exact solutions of this equation are found and a numerical scheme is developed to solve the equation for more complicated geometries.

Type
Research Article
Information
The ANZIAM Journal , Volume 31 , Issue 4 , April 1990 , pp. 385 - 396
Copyright
Copyright © Australian Mathematical Society 1990

References

[1] Bdzil, J. B., “Steady-state two-dimensional detonation”, J. Fluid Mech. 108 (1981) 195–226.Google Scholar
[2] Ben-Jacob, E., Goldenfeld, N., Langer, J. S. and Schön, G., “Boundary- layer model of pattern formation in solidification,” Phys. Rev. A 29 (1) (1984) 330–340.Google Scholar
[3] Courant, R. and Hilbert, D., Methods of Mathematical Physics, Vol. 1 (John Wiley and Sons, Inc., New York, 1953).Google Scholar
[4] Henshaw, W. D., Smyth, N. F. and Schwendeman, D. W., “Numerical shock propagation using geometrical shock dynamics,” J. Fluid Mech. 171 (1986) 519–545.Google Scholar
[5] Miles, J. W., “Diffraction of solitary waves”, Z. Agnew. Math. Phys. 28 (1977) 889–901.Google Scholar
[6] Stewart, D. S. and Bdzil, J. B., “The shock dynamics of stable multidimensional detonation”, Comb. and Flame 72 (1988) 311–323.CrossRefGoogle Scholar
[7] Whitham, G. B., “A new approach to problems of shock dynamics. Part I Two-dimensional problems”, J. Fluid Mech. 2 (1957) 145–171.CrossRefGoogle Scholar
[8] Whitham, G. B., “A new approach to problems of shock dynamics. Part II Three-dimensional problems”, J. Fluid Mech. 5 (1959) 369–386.CrossRefGoogle Scholar
[9] Whitham, G. B., Linear and Nonlinear Waves (J. Wiley and Sons Inc., New York, 1974).Google Scholar