Hostname: page-component-7dd5485656-tbj44 Total loading time: 0 Render date: 2025-10-31T05:58:38.558Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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.

Information

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

Article purchase

Temporarily unavailable

References

Bayly, B. J.: 1985 Phys. Fluids 28, 3451.
Carrier, G. F.: 1955 Q. Appl. Maths 12, 383.
Cole, J. & Roshko, A., 1956–57 Appl. Sci. Res. A A6, 317.
Lighthill, M. J.: 1954 Proc. R. Soc. Lond. A A224, 1.
Merk, H. J.: 1956–57 Appl. Sci. Res. A A6, 317.
Press, W. H., Flannery, B. P., Teukolsky, S. A. & Vetterling, W. T., 1986 Numerical Recipes. The Art of Scientific Computing. Cambridge University Press.
Putman, A. A.: 1964 General considerations of autonomous combustion oscillations. In Non-Steady Flame Propagation (ed. G. H. Markstein). Pergamon.
Rayleigh, Lord: 1945 The Theory of Sound, vol. 2, Dover.
Strehlow, R. A.: 1979 Fundamentals of Combustion. McGraw Hill.