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An experimental study of oscillatory convection in liquid gallium

Published online by Cambridge University Press:  26 April 2006

Manfred G. Braunsfurth  and
T. Mullin
Manfred G. Braunsfurth
Affiliation:
Department of Atmospheric Oceanic and Planetary Physics, Oxford University, Parks Road, Oxford, OX1 3PU, UK
T. Mullin
Affiliation:
Department of Atmospheric Oceanic and Planetary Physics, Oxford University, Parks Road, Oxford, OX1 3PU, UK
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Abstract

Results are presented of an experimental study of the onset of time-dependent flows in a sample of liquid gallium subjected to a horizontal temperature gradient. The primary control parameter is the Grashof number which is set by the temperature difference. However, we have also taken the novel approach of varying the Prandtl number in a systematic way using the applied mean temperature. This has uncovered some surprising new dynamical states. Furthermore, the interaction between competing oscillatory flows has produced interesting dynamical behaviour including secondary Hopf bifurcations where both the frequency and amplitude grow from zero as the critical point is passed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 327 , 25 November 1996 , pp. 199 - 219
Copyright
© 1996 Cambridge University Press

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References

ASM International, 1990 Metals Handbook, 10th edn., vol. 2. ASM.
Afrid, M. & Zebib, A. 1990 Oscillatory three-dimensional convection in rectangular cavities and enclosures. Phys. Fluids A 2, 1318–1327.Google Scholar
Behnia, M. & Davies, G. de vahl 1990 Finite mesh solutions using stream function—vorticity formulation. In Numerical Simulation of Oscillatory Convection in Low-Pr Fluids (ed. B. Roux). Notes on Numerical Fluid Mechanics, vol. 27, pp. 11–18. Vieweg.
Behnia, M., Davies, G. de vahl, Stella, F. & Guj, G. 1990 A comparison of velocity-vorticity and stream function-vorticity formulations for Pr=0. In Numerical Simulation of Oscillatory Convection in Low-Pr Fluids (ed. B. Roux). Notes on Numerical Fluid Mechanics, vol. 27, pp. 19–24. Vieweg.
Ben Hadid, H. & Roux, B. 1990 Buoyancy-driven oscillatory flows in shallow cavities filled with low-Prandtl number fluids. In Numerical Simulation of Oscillatory Convection in Low-Pr Fluids (ed. B. Roux). Notes on Numerical Fluid Mechanics, vol. 27, pp. 25–34. Vieweg.
Bergé, P., Pomeau, Y. & Vidal, C. 1984 Order within Chaos. John Wiley & Sons / Hermann.
Brandes, E. A. & Brook, G. B. (eds.) 1992 Smithells Metals Reference Book, 7th edn. Butterworth/Heinemann.
Braunsfurth, M. G., Skeldon, A. C., Juel, A., Mullin, T. & Riley, D. S. 1995 Free convection in liquid gallium. J. Fluid Mech. (submitted).Google Scholar
Broomhead, D. S. & Jones, R. 1989 Time series analysis. Proc. R. Soc. Lond. A 423, 103–121.Google Scholar
Broomhead, D. S. & King, G. P. 1986 Extracting qualitative dynamics from experimental data. Physica D 6, 217–236.Google Scholar
Brown, R. A. 1989 Theory of transport processes in semiconductor crystal growth. Adv. Chem. Series 221, 35–103.Google Scholar
Chabbard, J. B. & Lalanne, P. 1990 Application of the N3S Finite Element Code to simulation of oscillatory convection in low Prandtl fluids. In Numerical Simulation of Oscillatory Convection in Low-Pr Fluids (ed. B. Roux). Notes on Numerical Fluid Mechanics, vol. 27, pp. 163–170. Vieweg.
Crespo del Arco, E., Pulicani, P.-P. & Randriamampianina, A. 1989 Complex solutions and hysteresis cycles near the onset of oscillatory convection in a Pr=0 liquid submitted to a horizontal temperature gradient. C. R. Acad. Sci. Paris 309, Série II, 1869–1876.Google Scholar
Crochet, M. J., Geyling, F. T. & Schaftingen, J. J. van 1983 Numerical simulation of the horizontal Bridgeman growth of a Gallium Arsenide crystal. J. Cryst. Growth 65, 166–172.Google Scholar
Crochet, M. J., Geyling, F. T. & Schaftingen, J. J. van 1987 Numerical simulation of the horizontal Bridgeman growth. Part I: Two-dimensional flow. Intl J. Numer. Meth. Fluids 7, 29–48.Google Scholar
Davis, S. H. & Rosenblat, S. 1977 On bifurcating solutions at low frequency. Stud. Appl. Maths 57, 59–76.Google Scholar
Extremet, G. P., Fontaine, J.-P., Chaouche, A. & Sani, R. L. 1990 Two- and three-dimensional finite element simulations of buoyancy-driven convection in a confined Pr=0.015 liquid. In Numerical Simulation of Oscillatory Convection in Low-Pr Fluids (ed. B. Roux). Notes on Numerical Fluid Mechanics, vol. 27, pp. 171–181. Vieweg.
Filyand, M. A. & Semenova, E. I. 1968 Handbook of the Rare Elements, Vol. 1: Trace Elements and Light Elements. MacDonald Technical and Scientific.
Garrec, S. le & Magnaud, J. P. 1990 Numerical simulation of oscillatory convection in low Prandtl fluids. In Numerical Simulation of Oscillatory Convection in Low-Pr Fluids (ed. B. Roux). Notes on Numerical Fluid Mechanics, vol. 27, pp. 189–198. Vieweg.
Gervasio, C., Bottaro, A., Afrid, M. & Zebib, A. 1990 Oscillatory natural convection in a long horizontal cavity. In Numerical Simulation of Oscillatory Convection in Low-Pr Fluids (ed. B. Roux). Notes on Numerical Fluid Mechanics, vol. 27, pp. 136–143. Vieweg.
Gils, S. A. van, Krupa, M. & Langford, W. F. 1990 Hopf bifurcation with non-semisimple 1:1 resonance. Nonlinearity 3, 825–850.Google Scholar
Golubitsky, M. & Langford, W. F. 1981 Classification and unfoldings of degenerate Hopf bifuractions. J. Diffl Equat. 41, 375–415.Google Scholar
Guckenheimer, J. & Holmes, P. 1983 Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer.
Hampel, C. A. 1954 Rare Metals Handbook. Reinhold.
Hart, J. E. & Pratte, J. M. 1990 A laboratory study of oscillations in differentially heated layers of Mercury. In Numerical Simulation of Oscillatory Convection in Low-Pr Fluids (ed. B. Roux). Notes on Numerical Fluid Mechanics, vol. 27, pp. 329–337. Vieweg.
Henry, D. & Buffat, M. 1990 Two and three-dimensional numerical simulations of the transition to oscillatory convection in low-Prandtl number fluids. Prepublication.
Hultgren, R. et al. 1973 Selected Values of the Thermodynamic Properties of the Elements. ASM.
Hurle, D. T. J. 1966 Temperature oscillations in molten metals and their relationship to growth striae in melt-grown crystals. Phil. Mag. (8) 13, 305–310.Google Scholar
Hurle, D. T. J., Jakeman, E. & Johnson, C. P. 1974 Convective temperature oscillations in molten Gallium. J. Fluid Mech. 64, 565–576.Google Scholar
Iida, T. & Guthrie, R. I. L. 1993 The Physical Properties of Liquid Metals. Clarendon.
Kaye, G. W. C. & Laby, T. H. 1982 Tables of Physical and Chemical Constants, 14th edn. Longman.
Kobine, J. J., Mullin, T. & Price, T. J. 1995 The dynamics of driven rotating flow in a stadium-shaped domains. J. Fluid Mech. 294, 47–69.Google Scholar
Lange, N. A. 1967 Handbook of Chemistry, revised 10th edn. McGraw-Hill.
Langlois, W. E. 1985 Buoyancy-driven flows in crystal-growth melts. Ann. Rev. Fluid Mech. 17, 191–215.Google Scholar
McKell, K. E., Broomhead, D. S., Jones, R. & Hurle, D. T. J. 1990 Torus doubling in convecting molten Gallium. Europhys. Lett. 12, 513–518.Google Scholar
Müller, A. & Wiehelm, M. 1964 Periodische Temperaturschwankungen in flüssigem InSb als Ursache schichtweisen Einbaus von Te in Kristallisierendes InSb. Z. Naturf. A 19, 254–263.Google Scholar
Mullin, T. (ed.) 1993 The Nature of Chaos. Clarendon.
Okada, K. & Ozoe, H. 1993 The effect of aspect ratio on the critical Grashof number for oscillatory natural convection of zero Prandtl number fluid; numerical approach. J. Cryst. Growth 126, 330–334.Google Scholar
Pimputkar, M. & Ostrach, S. 1981 Convective effects in crystals grown from melts. J. Cryst. Growth 55, 614–646.Google Scholar
Pratte, J. M. & Hart, J. E. 1990 Endwall driven, low Prandtl number convection in a shallow rectangular cavity. J. Cryst. Growth 102, 54–68.Google Scholar
Pulicani, J. P., Del Arco, E. C., Randriamampianina, A., Bontoux, P. & Peyret, R. 1990 Spectral simulations of oscillatory convection at low Prandtl number. Intl J. Numer. Meth. Fluids 10, 481–517.Google Scholar
Le Quéré, P. 1990 Contribution to the GAMM Workshop with a pseudo-spectral Chebyshev algorithm on a staggered grid. In Numerical Simulation of Oscillatory Convection in Low-Pr Fluids (ed. B. Roux). Notes on Numerical Fluid Mechanics, vol. 27, pp. 227–236. Vieweg.
Roux, B. (ed.) 1990 Numerical Simulation of Oscillatory Convection in Low-Pr Fluids. Notes on Numerical Fluid Mechanics, vol. 27. Vieweg.
Roux, B., Ben Hadid, H. & Laure, P. 1989 Hydrodynamical regimes in metallic melts subject to a horizontal temperature gradient. Eur. J. Mech. B 8, 375–396.Google Scholar
Thevenard, D., Rouzaud, A., Comera, J. & Favier, J. J. 1991 Influence of convective thermal oscillations on a solidification interface in Bridgeman growth. J. Cryst. Growth 108, 572–582.Google Scholar
Touloukian, Y. S. et al. (eds.) 1979 Thermophysical Properties of Matter, Vol.1: Thermal Conductivity: Metallic Elements and Alloys. The TPRC Data Series. IFI/Plenum.
Weast, R. C. (ed.) 1983 CRC Handbook of Chemistry and Physics, 64th edn. CRC.
Weast, R. C. (ed.) 1993 CRC Handbook of Chemistry and Physics, 74th edn. CRC.
Wiggins, S. 1990 Introduction to Applied Nonlinear Dynamical Systems and Chaos. Springer.
Winters, K. H. 1988 Oscillatory convection in liquid metals in a horizontal temperature gradient. Intl J. Numer. Meth. Engng NSI, pp. 401–414.Google Scholar
Winters, K. H. 1990 A bifurcation analysis of oscillatory convection in liquid metals. In Numerical Simulation of Oscillatory Convection in Low-Pr Fluids (ed. B. Roux). Notes on Numerical Fluid Mechanics, vol. 27, pp. 319–326. Vieweg.
Winters, K. H. & Jack, R. O. 1989 Anomalous convection at low Prandtl number. Commun. Appl. Numer. Meth. 5, 401–404.Google Scholar