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One-dimensional model for the Rijke tube

Published online by Cambridge University Press:  26 April 2006

C. Nicoli  and
P. Pelcé
C. Nicoli
Affiliation:
Laboratoire de Recherche en Combustion, Université de Provence, Centre de St Jerôme, U.A 1117, Bôite 252, 13397 Marseille, Cedex 13, France
P. Pelcé
Affiliation:
Laboratoire de Recherche en Combustion, Université de Provence, Centre de St Jerôme, U.A 1117, Bôite 252, 13397 Marseille, Cedex 13, France
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Abstract

We develop a simple model in which longitudinal, compressible, unsteady heat transfer between heater and gas is computed in the small-Mach-number limit. This calculation is used to determine the transfer function of the heater, which plays an important role in the stability limits of the thermoacoustic instability of the Rijke tube. The transfer function is determined analytically in the limit of small expansion parameter γ, and numerically for γ of order unity. In the case ρμ/cp = constant, an analytical solution can be found.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 202 , May 1989 , pp. 83 - 96
Copyright
© 1989 Cambridge University Press

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