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On the stability and flow reversal of an asymmetrically heated open convection loop

Published online by Cambridge University Press:  20 April 2006

Haim H. Bau  and
K. E. Torrance
Haim H. Bau
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York 14853 Present address: Department of Mechanical Engineering and Applied Mechanics, 111 Towne Building D3, University of Pennsylvania, Philadelphia, Pennsylvania, 19104.
K. E. Torrance
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York 14853
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Abstract

Experimental results are reported for a U-shaped, free convection loop. The top of the loop is open to an isothermal reservoir. The horizontal leg and one vertical leg are heated at rates Q1 and Q2, respectively. The loop is filled either with water or a water-saturated porous medium. Symmetric heating and asymmetric heating favouring the ascending leg of the loop both yield stable flows. Asymmetric heating favouring the descending leg leads to stable flows when the ratio Q1/Q2 is above a critical value. Below this critical value, the flow is observed to oscillate with increasing amplitude until the direction of flow in the loop undergoes a reversal. A steady flow follows the reversal. Analytical results include a stability analysis and time-dependent, one-dimensional numerical calculations, both of which compare favourably with experiment.

The disturbance amplification mechanism is explained in terms of thermal anomalies which move through the loop with the material motion of the fluid. Since the heating and buoyancy generation processes are in phase in the heated, descending leg, a thermal anomaly can amplify as it flows through that leg. As the anomaly moves through the ascending leg, it initiates a subsequent anomaly of opposite sign in the descending leg. The result is an oscillating flow which, under appropriate conditions, can amplify.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 109 , August 1981 , pp. 417 - 433
Copyright
© 1981 Cambridge University Press

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References

Bau, H. & Tokrance, K. E. 1981 Transient and steady behavior of an open, symmetrically-heated, free convection loop. Int. J. Heat Mass Transfer 24, 597.Google Scholar
Bear, J. 1972 Dynamics of Fluids in Porous Media. Elsevier.
Carrier, G. F., Krook, M. & Pearson, C. E. 1966 Functions of a Complex Variable — Theory and Techniques. McGraw-Hill.
Creveling, H. F., De Paz, J. F., Baladi, J. Y. & Schoenhals, R. J. 1975 Stability characteristics of a single-phase free convection loop. J. Fluid Mech. 67, 65.Google Scholar
Damerell, P. S. & Schoenhals, R. J. 1979 Flow in a toroidal thermosyphon with angular displacement of heated and cooled sections. J. Heat Transfer 101, 672.Google Scholar
Eckert, E. R. G. & Drake, R. M. 1972 Analysis of Heat and Mass Transfer. McGraw-Hill.
Keller, J. B. 1966 Periodic oscillations in a model of thermal convection. J. Fluid Mech. 26, 599.Google Scholar
Martin, S. 1970 A hydrodynamic curiosity: the salt oscillator. Geophys. Fluid Dynamics 1, 143.Google Scholar
Scheele, G. F. & Hanratty, T. J. 1962 Effects of natural convection on stability of flow in a vertical pipe. J. Fluid Mech. 14, 244.Google Scholar
Welander, P. 1957 Note on the self-sustained oscillations of a simple thermal system. Tellus 9, 419.Google Scholar
Welander, P. 1967 On the oscillatory instability of a differentially heated fluid loop. J. Fluid Mech. 29, 17.Google Scholar