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Bifurcation phenomena for an oxidation reaction in a continuously stirred tank reactor. III The inhibiting effect of an inert species

Published online by Cambridge University Press:  17 February 2009

M. I. Nelson
M. I. Nelson
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW 2522, Australia; e-mail: nelsonm@member.ams.org.
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Abstract

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We extend an investigation into the static and dynamic multiplicity exhibited by the reaction of a fuel/air mixture in a continuously stirred tank reactor by considering the effect of adding a chemically inert species to the reaction mixture. The primary bifurcation parameter is taken to be the fuel fraction as this is the most important case from the perspective of fire-retardancy. We show how the addition of the inert species progressively changes the steady-state diagrams and flammability limits. We also briefly outline how heat-sink additives can be incorporated into our scheme.

Type
Research Article
Information
The ANZIAM Journal , Volume 46 , Issue 3 , January 2005 , pp. 399 - 416
Copyright
Copyright © Australian Mathematical Society 2005

References

[1]Atkins, P. W., Physical Chemistry, 3rd ed. (Oxford Univ. Press, Oxford, 1987).Google Scholar
[2]Babushok, V.. Noto, T., Burgess, D. R. F.. Hammins, A. and Tsang, W., “Inhibitor influence on the bistability of a CSTR”, Combustion and Flame 108 (1997) 61–70.CrossRefGoogle Scholar
[3]Brown, N. J. and Schefer, R. W., “A computational study of physical and chemical inhibition in a perfectly stirred reactor”, Fire and Materials 5 (1981) 14–23.CrossRefGoogle Scholar
[4]Doedel, E. J., Fairgrieve, T. F., Sandstede, B., Champneys, A. R., Kuznetsov, Y. A. and Wang, X., “AUTO 97: Continuation and bifurcation software for ordinary differential equations (with HormCont)”, March 1998. Available by anonymous ftp fromftp.cs.concordia.ca/pub/doedel/auto.Google Scholar
[5]Drysdale, D., An introduction to fire dynamics, 2nd ed. (John Wiley and Sons, New York, 1999).Google Scholar
[6]Ewing, C. T., Beyler, C. L. and Carthard, H. W., “Extinguishment of class B flames by thermal mechanisms: Principles underlying a comprehensive theory; prediction of flame extinguishing effectiveness”, J. Fire Protection Engng 6 (1994) 23–54.CrossRefGoogle Scholar
[7]Glassman, I., “Flammability limits”, in Combustion, 3rd ed., Chapter 4D.1, (Academic Press, New York, 1996) 162–170.Google Scholar
[8]Gray, B. F., Kalliadasis, S., Lazarovich, A., Macaskill, C., Merkin, J. H. and Scott, S. K., “The suppression of an exothermic branched-chain flame through endothermic reaction and radical scavenging”, Proc. Roy. Soc. London A 458 (2002) 2119–2138.CrossRefGoogle Scholar
[9]Griffiths, J. F. and Barnard, J. A., Flame and Combustion, 3rd ed. (Blackie Academic and Professional, London, 1995).CrossRefGoogle Scholar
[10]Mulcahy, M. F. R., Gas kinetics, Studies in Modern Chemistry (Nelson, London, 1973).Google Scholar
[11]Nelson, M. I., “Decomposition and inhibition schemes for polymeric combustion”, Ph.D. Thesis, Dept of Appl. Math. Studies, The University of Leeds (UK), 1994.Google Scholar
[12]Nelson, M. I. and Sidhu, H. S., “Bifurcation phenomena for an oxidation reaction in a continuously stirred tank reactor. I Adiabatic operation”, J. Math. Chem. 31 (2002) 155–186.CrossRefGoogle Scholar
[13]Nelson, M. I. and Sidhu, H. S., “Bifurcation phenomena for an oxidation reaction in a continuously stirred tank reactor. II Diabatic operation”, The ANZIAM J. 45 (2004) 303–326.CrossRefGoogle Scholar
[14]Sidhu, H. S., Nelson, M. I., Mercer, G. N. and Weber, R. O., “Dynamical analysis of an elementary X + Y → P reaction in a continuously stirred tank reactor”, J. Math. Chem. 28 (2000) 353–375.CrossRefGoogle Scholar
[15]Simon, P. L., Kalliadasis, S., Merkin, J. H. and Scott, S. K., “Quenching of flame propagation through endothermic reaction”, J. Math. Chem. 32 (2002) 73–98.CrossRefGoogle Scholar
[16]Wierzba, I., Bade, S. O., Shrestha, O. B. and Karim, G. A., “An approach for predicting the flammability limits of fuel/diluent mixtures in air”, J. Institute of Energy 69 (1996) 122–130.Google Scholar