Abstract
After a brief review of the literature, a simplified model for flame propagation based on high activation energy asymptotics is used to explain the effects of an incident, external soundwave on a uniformly propagating flame. It is shown, that due to the interaction with the chemical reaction kinetics at the flamefront, the incident wave is partially reflected. A system of equations for the transmission coefficient, T, the reflection coefficient, R, and the induced oscillation amplitude of the flame, F, is derived and its solution as a function of the frequency ω is graphically analyzed. It appears, that both acoustic attenuation and acoustic amplification are possible. Especially, if the Lewis number is close to the critical value, where the uniformly propagating flame loses its stability to a pulsating flame, ànd, if the frequency is close to the corresponding frequency of self-oscillation of the flame, resonance leads to strong acoustic amplifications.
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References
Rayleigh, J.W.S., 1896 Theory of sound, Macmillan, London.
Patureau, J.P., Toong, T.Y., Garris, C.A., 1977 Experimental investigation of acoustic-kinetic interactions in non-equilibrium H2-Cl2 reactions, 16th Symp. (Int.) on Combustion, Combustion Inst., Pittsburgh.
Abouseif, G.E., Toong, T.Y., Converti, J., 1979 Acoustic and shock kinetic interactions in non-equilibrium H2-Cl2 reactions, 17th Symp. (Int.) on Combustion, Combustion Inst., Pittsburgh.
Jones, H., 1977 The mechanics of vibrating flames in tubes, Proc. R. Soc., A 353, London.
Jones, H., 1979 The generation of sound by flames, Proc. R. Soc., A 367, London.
Buckmaster, J.D., Ludford, G.S.S., 1982 Theory of laminar flames, Cambridge Un. Press, London.
Matkowsky, B.J., Sivashinsky, G.I., 1979 An asymptotic derivation of two models in flame theory associated with the constant density approximation, SIAM J. on Appl. Math., vol. 37.
Matkowsky, B.J., Olagunju, D.O., 1980 Propagation of a pulsating flamefront in a gaseous combustible mixture, SIAM J. on Appl. Math., vol. 39.
van Harten, A., Matkowsky, B.J., 1981 Coupling between fluid dynamics and transport processes in a simplified model of flames, report 222, Math. Inst., Un. of Utrecht, to appear in SIAM J. on Appl. Math.
van Harten, A., 1981 Applications of singular perturbation techniques to combustion theory, in: Theory and Applications of Singular Perturbations, Proceedings Oberwolfach, Springer Lecture Notes, 942.
Clarke, J.F., Mc. Chesney, M., 1964 The dynamics of real gases, Butterworths, 1964.
Toong, T.Y., Arbeau, P., Garris, C.A., Patureau, J.P., 1975 Acoustic-kinetic interactions in an irreversibly reacting medium, 15th Symp. (Int.) on Combustion, Combustion Inst., Pittsburgh.
Garris, C.A., Toong, T.Y., Patureau, J.P., 1975 Chemi-acoustic instability structure in irreversibly reacting systems, Acta Astronautica, vol. 2.
Clarke, J.F., 1977 Chemical amplification at the wave head of a finite amplitude gasdynamic disturbance, J. Fluid Mechanics, vol. 81.
Clarke, J.F., 1978, Acta Astronautica, vol. 5. Acta Astronautica, vol. 5
Clarke, J.F., 1978 Small amplitude gasdynamic disturbances in an exploding atmosphere, J. Fluid Mechanics, vol. 89.
Abouseif, G.E., Toong, T.Y., 1981 Non-linear wave-kinetic interactions in irreversibly reacting media, J. Fluid Mech., vol. 103.
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© 1983 Springer-Verlag
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van Harten, A. (1983). On the interaction of flames and sound. In: Verhulst, F. (eds) Asymptotic Analysis II —. Lecture Notes in Mathematics, vol 985. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062374
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DOI: https://doi.org/10.1007/BFb0062374
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