TECHNICAL PAPERS: Natural and Mixed Convection

Spatial and Temporal Stabilities of Flow in a Natural Circulation Loop: Influences of Thermal Boundary Condition

[+] Author and Article Information
Y. Y. Jiang, M. Shoji

Department of Mechanical Engineering, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan

J. Heat Transfer 125(4), 612-623 (Jul 17, 2003) (12 pages) doi:10.1115/1.1571846 History: Received April 29, 2002; Revised March 05, 2003; Online July 17, 2003
Copyright © 2003 by ASME
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Greif,  R., 1988, “Natural Circulation Loops,” ASME J. Heat Transfer, 110, pp. 1243–1258.
Zvirin,  Y., 1981, “A Review of Natural Circulation Loops in Pressurized Water Reactors and Other Systems,” Nucl. Eng. Des., 67, pp. 203–225.
Lorenz,  E. N., 1963, “Deterministic Nonperiodic Flow,” J. Atmos. Sci., 20, pp. 130–141.
Keller,  J. B., 1966, “Periodic Oscillations in a Model of Thermal Convection,” J. Fluid Mech., 26, pp. 599–606.
Welander,  P., 1967, “On the Oscillatory Instability of a Differentially Heated Fluid Loop,” J. Fluid Mech., 29, pp. 17–30.
Malkus, W. R. V., 1972, “Non-Periodic Convection at High and Low Prandtl Number,” mem. Soc. R. Sci. Liege., 4kk, pp. 125–128.
Creveling,  H. F., Depaz,  J. F., Baladi,  J. Y., and Schoenhals,  R. J., 1975, “Stability Characteristics of a Single-Phase Convection Loop,” J. Fluid Mech., 67, pp. 65–84.
Gorman,  M., Widmann,  P. J., and Robbins,  K. A., 1986, “Nonlinear Dynamics of Convection Loop: A Quantitative Comparison of Experiment With Theory,” Physica D, 19D, pp. 255–267.
Ehrhard,  P., and Muller,  U., 1990, “Dynamical Behavior of Natural Convection in a Single-Phase Loop,” J. Fluid Mech., 217, pp. 487–518.
Yorke,  J. A., Yorke,  E. D., and Mallet-Paret,  J., 1987, “Lorenz-Like Chaos in a Partial Differential Equation for a Heated Fluid Loop,” Physica D, 24D, pp. 279–292.
Jiang,  Y. Y., Shoji,  M., and Naruse,  M., 2002, “Boundary Condition Effects on Flow Stability in a Toroidal Thermosyphon,” Int. J. Heat Fluid Flow, 23(1), pp. 81–91.
Wang,  Y., Singer,  J., and Bau,  H. H., 1992, “Controlling Chaos in a Thermal Convection Loop,” J. Fluid Mech., 237, pp. 479–498.
Yuen,  P. K., and Bau,  H. H., 1996, “Rendering a Subcritical Hopf Bifurcation Supercritical,” J. Fluid Mech., 317, pp. 91–109.
Yuen,  P. K., and Bau,  H. H., 1999, “Optimal and Adaptive Control of Chaotic Convection-Theory and Experiments,” Phys. Fluids, 11(6), pp. 1435–1448.
Sano,  O., 1991, “Cellular Structure in a Natural Convection Loop and Its Chaotic Behavior, I. Experiment,” Fluid Dyn. Res., 8, pp. 189–204.
Sano,  O., 1991, “Cellular Structure in a Natural Convection Loop and Its Chaotic Behavior, II. Theory,” Fluid Dyn. Res., 8, pp. 205–220.
Damerell,  P. S., and Schoenhals,  R. J., 1979, “Flow in a Toroidal Thermosyphon With Angular Displancement of Heated and Cooled Sections,” ASME J. Heat Transfer, 101, pp. 672–676.
Lavine,  A. S., Grief,  R., and Humphrey,  J. A. C., 1986, “Three-Dimensional Analysis of Natural Convection in a Toroidal Loop: Effect of Tilt Angle,” ASME J. Heat Transfer, 108, pp. 796–805.
Stern,  C. H., Greif,  R., and Humphrey,  J., 1988, “An Experimental-Study of Natural-Convection in a Toroidal Loop,” ASME J. Heat Transfer, 107, pp. 877–884.
Cross,  M. C., and Hohenberg,  P. C., 1993, “Pattern Formation out of Equilibrium,” Rev. Mod. Phys., 65(3), pp. 851–1112.
Haken, H., 1983, Synergetics, An Introduction. Nonequilibrium Phase Transitions and Self-Organization in Physics, Chemistry and Biology, Springer-Verlag, Berlin, Chap. 5.
Landau, L. D., and Lifshitz, E. M., 1958, Statistical Physics, Addison Wesley, Reading, MA, Chap. XIV.
Newell,  A. L., Passot,  T., and Lega,  J., 1993, “Order Parameter Equations for Patterns,” Annu. Rev. Fluid Mech., 25, pp. 399–453.
Nicolis, G., and Prigogine, I., 1977, Self-Organization in Nonequilibrium Systems: from Dissipative Structures to Order through Fluctuations, Wiley, New York.
Newell,  A. L., and Whitehead,  J. A., 1969, “Finite Bandwidth, Finite Amplitude Convection,” J. Fluid Mech., 38, pp. 279–303.
Segel,  L. A., 1969, “Distant Side-Walls Cause Slow Amplitude Modulation of Cellular Convection,” J. Fluid Mech., 38, pp. 203–224.
Pomeau,  Y., and Manneville,  P., 1979, “Stability and Fluctuations of a Spatially Periodic Convective Flow,” J. Phys. Lett.,40, pp. 609–612.
Newell,  A. L., Passot,  T., and Souli,  M., 1990, “The Phase Diffusion and Mean Drift Equations for Convection at Finite Rayleigh Numbers in Large Containers,” J. Fluid Mech., 220, pp. 187–252.
Cross,  M. C., 1980, “Derivation of the Amplitude Equation at the Rayleigh-Benard Instability,” Phys. Fluids, 23(9), pp. 1727–1731.
Swift,  J., and Hohenberg,  P. C., 1977, “Hydrodynamic Fluctuations at the Convective Instability,” Phys. Rev. A, 15(1), pp. 319–328.
Thompson, J. M. T., and Stewart, H. B., 1993, Nonlinear Dynamics and Chaos, John Wiley and Sons Ltd., New York, pp. 212–227.


Grahic Jump Location
Schematic configuration of a natural circulation loop and its coordinate system (r,φ,θ)
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Velocity and temperature fields of the basic flow; In each graph the right half shows streamlines ψ, and velocity components (u,w), while the left one shows isotherms (solid and broken lines correspond to positive and negative values, respectively)
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Transitions of flow behavior as functions of δ and Ra. The curves are fitted by numerical data; each designates a margin of its two neighboring domains.
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Typical decaying processes of perturbation about the steady flow (a) toward a node (b) toward a focus
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Two typical bifurcation routes predicted the model
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Trajectories of the flow at different Rayleigh number for δ=0.5
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Typical return maps of z in flows for δ=0.5: (a) Lorenz chaos, (b) periodic flow
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Trajectories of the flow at different Rayleigh number for δ=1
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Transition from Lorenz chaos to periodic cellular flow (Ra=1630, δ=0.86)




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