Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-25T07:18:50.665Z Has data issue: false hasContentIssue false
  • English
  • Français

Modes of burning in filtration combustion†

Published online by Cambridge University Press:  16 July 2009

M. R. Booty  and
B. J. Matkowsky
M. R. Booty
Affiliation:
Department of Mathematics, Southern Methodist University, Dallas, Texas 75275, USA
B. J. Matkowsky
Affiliation:
Department of Engineering Science and Applied Mathematics, Northwestern University, Evanston, Illinois 60208, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

We describe and analyze a model of filtration combustion, in which a gas is forced at high pressure into a porous solid matrix so that after ignition and under favourable conditions a combustion wave can propagate through the medium. We consider the case of counter flow, where the gas is forced into the reaction zone through the unreacted part of the porous solid. Relations are derived for the steady state propagation of a planar combustion wave or front in the limit of high-activation energy, from which the propagation speed, reaction temperature, and reacted mass fraction of the solid product can be found in terms of the mass flux of the injected gas, the gas pressure and mass flux on exit from the front, and other physico-chemical parameters describing the system. Two distinct modes of combustion are discussed, corresponding to the reaction being driven to completion by exhaustion of either the gaseous or the solid component, these being referred to as the gas-deficient and solid-deficient modes of burning respectively. For both homogeneous and heterogeneous forms of the reaction rate we find that there is a critical inlet mass flux for the incoming gas below which steady state solutions no longer exist and that there are parameter values for which multiple steady states occur.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 2 , Issue 1 , March 1991 , pp. 17 - 41
Copyright
Copyright © Cambridge University Press 1991

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aldushin, A. P., Martemyanova, T. M., Merzhanov, A. G., Khaikin, B. I. & Shkadinsky, K. G. 1972 Propagation of the front of an exothermic reaction in condensed mixtures with the interaction of the components through a layer of high-melting product. Combustion, Explosion and Shock Waves 8, 159–167.Google Scholar
Aldushin, A. P., Merzhanov, A. G. & Khaikin, B. I. 1974 Conditions for the layer filtration combustion of porous metals. Dokl. Phys. Chem. 215 (3), 295–298.Google Scholar
Erdélyi, A., Magnus, W., Oberhettinger, F. & Tricomi, F. G. 1953 Higher Transcendental Functions, Vol. 1, McGraw-Hill.Google Scholar
Hardt, A. P. & Phung, P. V. 1973 Propagation of gasless reactions in solids. 1. Analytic study of exothermic intermetallic reaction rates. Combust. Flame 21, 77–97.Google Scholar
Holt, J. B. 1984 Combustion synthesis: a new area of research in materials science. Energy and Technology Review. Lawrence Livermore National Laboratory.Google Scholar
Kaper, H. G., Leaf, G. K., Margolis, S. B. & Matkowsky, B. J. 1987 On nonadiabatic condensed phase combustion. Combust. Sci. Tech. 53, 289–314.Google Scholar
Matkowsky, B. J. & Sivashinsky, G. I. 1979 An asymptotic derivation of two models in flame theory associated with the constant density approximation. SIAM J. Appl. Math. 37 (3), 686–699.Google Scholar
Matkowsky, B. J. & Sivashinsky, G. I. 1978 Propagation of a pulsating reaction front in solid fuel combustion. SIAM J. Appl. Math. 35 (3), 465–478.Google Scholar
Merzhanov, A. G. 1990 Self-propagating high temperature synthesis: twenty years of search and findings. In Holt, J. B. & Munir, Z., eds, Proc. Int. Symp. Comb. and Plasma Synth. High-Temp. Materials. Verlag Chemie. To appear.Google Scholar
Merzhanov, A. G., Borovinskaya, I. P. & Volodin, Yu E. 1972 The burning mechanism of porous metallic samples in nitrogen. Dokl. Phys. Chem. 206 (4), 833–835.Google Scholar
Norbury, J. & Stuart, A. M. 1989 A model for porous-medium combustion. Q. J. Mech. Appl. Math. 42 (1), 159–178.Google Scholar
Pityulin, A. N., Shcherbakov, V. A., Borovinskaya, I. P. & Merzhanov, A. G. 1979 Laws and mechanisms of diffusional surface burning of metals. Combustion, Explosion and Shock Waves 15, 432–437.Google Scholar