Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-06T02:30:51.770Z Has data issue: false hasContentIssue false
  • English
  • Français

The analysis of nonlinear density-wave oscillations in boiling channels

Published online by Cambridge University Press:  20 April 2006

Jean-Luc Achard ,
Donald A. Drew  and
Richard T. Lahey
Jean-Luc Achard
Affiliation:
Institute de Mécanique de Grenoble, B.P. 53 X, 38041 Grenoble Cedex
Donald A. Drew
Affiliation:
Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, New York 12181
Richard T. Lahey
Affiliation:
Department of Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, New York 12181
Get access Rights & Permissions [Opens in a new window]

Abstract

Thermally induced flow instabilities in uniformly heated boiling channels have been studied analytically. The classical homogeneous equilibrium model was used. This distributed model was transformed into an integrodifferential equation for inlet velocity. A linear analysis showed interesting features (i.e. islands of instability) of the marginal stability boundary which appear when the effects of gravity and friction were systematically considered. A quasilinear Hopf-bifurcation analysis, valid near the marginal-stability boundaries, gives the amplitude and frequency of limit-cycle oscillations that can appear on the unstable side of the boundary. The analysis also shows cases where a finite-amplitude perturbation can cause a divergent instability on the stable side of the linear-stability boundary.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 155 , June 1985 , pp. 213 - 232
Copyright
© 1985 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

Achard, J. L. & Lespinard, G. M. 1981 Structure of the transient wall-friction law in onedimensional models of laminar pipe flows. J. Fluid Mech. 113, 183–298.Google Scholar
Achard, J. L., Drew, D. A. & Lahey, R. T. 1980 The analysis of linear and nonlinear instability phenomena in heated channels. NUREG/CR-1718.
Achard, J. L., Drew, D. A. & Lahey, R. T. 1981 The effect of gravity and friction on the stability of boiling flow in a channel. Chem. Engng Commun. 11, 59–79.Google Scholar
Akinjiola, O. & Friedly, J. C. 1982 Experimental study of thermal hydraulic instabilities in a cryogenic evaporator. In Proc. AIChE Annual Meeting.
Atkinson, M. J. & Friedly, J. C. 1983 Limitations of simple models in describing two-phase flow oscillations. In Heat Exchangers for Two-Phase Applications (ed. J. B. Kitto & J. M. Robinson). ASME.
Bouré J. 1965 Contribution a l'étude théorique des oscillations dans les canaux chauffants à ébullition. Thése de Docteur-Ingénieur, Faculté des Sciences de l'Université de Grenoble.
Hopf, E. 1942 Abzweigung einer periodischen Lösung von einer stationären Lösung eines Differential-Systems. Ber. Math. Phys. Kl. Sächs Acad. Wiss. Leipzig 94, 1–22; Ber. Verh. Sächs. Acad. Wiss. Leipzig Math.-Nat. Kl. 95 (1), 3–22. Translated by L. Howard and N. Koeppel in The Hopf Bifurcation and its Applications (ed. J. E. Marsden & M. McCracken), Dover, 1976.Google Scholar
Howard, L. & Koeppel, N. 1976 Editorial comments. In The Hopf Bifurcation and its Applications (ed. J. E. Marsden & M. McCracken). Dover.
Ishii, M. 1971 Thermally induced flow instabilties in two-phase mixtures in thermal equilibrium. Ph.D. Thesis, Georgia Institute of Technology, Atlanta.
Kazarinoff, N. D., Wan, Y. H. & Van Der Dreische, P. 1978 Hopf bifurcation and stability of periodic solutions of differential-difference and integro-differential equations. J. Inst. Maths Applics, 21, 461–477.Google Scholar
Krishnan, V. S., Atkinson, M. J. & Friedly, J. C. 1980 Nonlinear flow oscillations in boiling channels. AIChE Symp. Ser. 76.Google Scholar
Lahey, R. T. & Moody, F. 1977 The Thermal-Hydraulics of a Boiling Water Nuclear Reactor. ANS Monograph.
Serov, E. P. 1953 The operation of once-through boilers in variable regimes. Trudy, Moscow Energ. Inst. 11.Google Scholar
Yadigaroglu, G. & Bergles, A. E. 1972 Fundamental and higher-mode density wave oscillations in two-phase flow. Trans. ASME C: J. Heat Transfer 94, 189–195.Google Scholar
Yadigaroglu, G. 1978 Two-phase flow instabilities and propagation phenomena: Two-phase flows in nuclear reactors. Von Kármán Inst. for Fluid Dyn., Lecture Series, 1978–5.