Hostname: page-component-848d4c4894-x24gv Total loading time: 0 Render date: 2024-05-03T02:52:46.303Z Has data issue: false hasContentIssue false
  • English
  • Français

Nonlinear wave-kinetic interactions in irreversibly reacting media

Published online by Cambridge University Press:  20 April 2006

G. E. Abouseif  and
T. Y. Toong
G. E. Abouseif
Affiliation:
Mechanical Engineering Department, Massachusetts Institute of Technology
T. Y. Toong
Affiliation:
Mechanical Engineering Department, Massachusetts Institute of Technology
Get access Rights & Permissions [Opens in a new window]

Abstract

Nonlinear wave-kinetic interactions are analysed by examining the propagation of finite-amplitude waves in a gaseous medium undergoing non-equilibrium exothermic reaction. An exact nonlinear wave equation is developed, and the various coupling mechanisms are identified.

An approximate equation, which takes into account the chemical and transport effects, is derived for high-frequency weak nonlinear waves. The equation is numerically integrated to predict the amplification rates of weak shock pulses and changes in their wave forms under different reaction conditions.

Dramatic nonlinear amplification is predicted for mixtures of high activation energies. Furthermore, the amplification rates are enhanced with increased shock strength and pulse duration. In the latter instance, a threshold value is identified, above which wave amplification is a maximum.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 103 , February 1981 , pp. 1 - 22
Copyright
© 1981 Cambridge University Press

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

Abouseif, G. E., Toong, T. Y. & Converti, J. 1979 17th Symp. (Int.) on Combustion, p. 1341. The Combustion Institute.
Abouseif, G. E. 1979 Ph.D. thesis, Massachusetts Institute of Technology.
Blythe, P. A. 1979 17th Symp. (Int.) on Combustion, p. 909. The Combustion Institute.
Clarke, J. F. 1977 J. Fluid Mech. 81, 257.
Clarke, J. F. 1978a Acta Astronautica 5, 543.
Clarke, J. F. 1978b J. Fluid Mech. 89, 343.
Clarke, J. F. 1979 J. Fluid Mech. 94, 195.
Garris, C. A., Toong, T. Y. & Patureau, J. P. 1975 Acta Astronautica 2, 981.
Lee, J. H. et al. 1972 Comb. & Flame 18, 321.
Lighthill, M. J. 1950 Phil. Mag. 41, 1101.
Lighthill, M. J. 1956 Surveys in Mechanics (ed. G. K. Batchelor and S. H. Davies), p. 250. Cambridge University Press.
Patureau, J. P., Toong, T. Y. & Garris, C. A. 1977 16th Symp. (Int.) on Combustion, p. 929.
Prigogine, I. 1967 Introduction to Thermodynamics of Irreversible Processes. Wiley-Interscience.
Roache, P. J. 1976 Computational Fluid Mechanics. Hermosa.
Toong, T. Y. 1972 Comb. & Flame, 18, 207.
Toong, T. Y. 1974 Acta Astronautica 1, 317.
Toong, T. Y., Arbeau, P., Garris, C. A. & Patureau, J. P. 1975 15th Symp. (Int.) on Combustion, p. 87.
Wood, W. W. & Kirkwood, J. G. 1957 J. Appl. Phys. 23, 395.