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Liquid Metal Magneto-Hydraulics Flows in Ducts and Cavities

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Magnetohydrodynamics

Part of the book series: International Centre for Mechanical Sciences ((CISM,volume 418))

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Abstract

This contribution gives an overview on liquid metal flow in engineering applications such as duct flows in various geometries and buoyant flows in cavities. Early results, some of them may be termed classical, are presented as well as results obtained in recent years. It is not the aim to give a complete overview but to introduce the reader to fascinating subject of liquid metal magnetohydrodynamics.

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References

  • Albousiére, T., Garandet, J., and Moreau, R. (1993). Buoyancy-driven convection with a uniform magnetic field. part 1. asymptotic analysis. Journal of Fluid Mechanics 253: 545–563.

    Article  Google Scholar 

  • Alboussiére, T., Neubrand, A. C., Garandet, J. P., and Moreau, R. (1995). Magnetic field and segregation duringBridgeman growth. Magnetohydrodynamics 31: 228–235.

    Google Scholar 

  • Alboussière, T., Garandet, J. P., and Moreau, R. (1996). Asymptotic analysis and symmetry in MHD convection. Physics of Fluids 8 (8): 2215–2226.

    Article  MathSciNet  MATH  Google Scholar 

  • Alboussière, T., Neubrand, A. C., Garandet, J. P., and Moreau, R. (1997). Segregation during horizontal Bridgeman growth under an axial magnetic field. Journal of Crystal Growth 181: 133–144.

    Article  Google Scholar 

  • Alty, C. J. N. (1971). Magnetohydrodynamic duct flow in a uniform transverse magnetic field of arbitrary orientation. Journal of Fluid Mechanics 48: 429–461.

    Article  Google Scholar 

  • Barleon, L., Lenhart, L., Mack, H. J., Sterl, A., and Thomauske, K. (1989). Investigations on liquid metal MHD in straight ducts at high Hartmann numbers and interaction parameters. In Müller, U., Rehme, K., and Rust, K., eds., Proceedings of the 4th International Topical Meeting on Nuclear Reactor Thermal-Hydraulics, Karlsruhe, October 10–13. G. Braun, Karlsruhe. 857–862.

    Google Scholar 

  • Barleon, L., Mack, K. J., Kirchner, R., Frank, M., and Stieglitz, R. (1995). MHD heat transfer and pressure drop in electrically insulated channels at fusion relevant parameters. In Herschbach, K., Maurer, W., and Vetter, J. E., eds., Fusion Technology 1994. Elsevier. 1201–1204.

    Google Scholar 

  • Ben Hadid, H., and Henri, D. (1997). Numerical study of convection in a horizontal Bridgeman configuration under the action of a constant magnetic field. Part 2. three-dimensional flow. Journal of Fluid Mechanics 333: 57–83.

    Article  MATH  Google Scholar 

  • Blúms, E., Mikhailov, Y., and Ozols, R. (1987). Heat and mass transfer in MHD flows. World Scientific Publishing Co. Pte. Ltd.

    Google Scholar 

  • Branover, H., Vasil’ev, H., and Gelfgat, Y. (1967). Hydraulic resistance of MHD pipes. Magnitnaya Gidrodynamica 4 (3): 1.

    Google Scholar 

  • Branover, H. (1978). Magnetohydrodynamic flow in ducts. John Wiley & Sons, New York, Toronto.

    Google Scholar 

  • Bühler, L. (1994). Magnetohydrodynamic flows in arbitrary geometries in strong, nonuniform magnetic fields.-a numerical code for the design of fusion reactor blankets. Fusion Technology 27: 3–24.

    Google Scholar 

  • Bühler, L. (1996). Instabilities in quasi-two-dimensional magnetohydrodynamic flows. Journal of Fluid Mechanics 326: 125–150.

    Article  MATH  Google Scholar 

  • Bühler, L. (1998). Laminar buoyant magnetohydrodynamic flow in vertical rectangular ducts. Physics of Fluids 10 (1): 223–236.

    Article  Google Scholar 

  • Burr, U., Barleon, L., Mack, K.-J., and Müller, U. (1999a). The effect of a horizontal magnetic field on liquid metal rayleigh-bénard convection. Technical Report FZKA 6277, Forschungszentrum Karlsruhe.

    Google Scholar 

  • Burr, U., Barleon, L., Mack, K.-J., and Müller, U. (1999b). The effect of a vertical magnetic field on liquid metal rayleigh-bénard convection. Technical Report FZKA 6267, Forschungszentrum Karlsruhe.

    Google Scholar 

  • Chandrasekhar, S. (1961). Hydrodynamic and hydromagnetic stability. New York: Dover Publications, Inc.

    Google Scholar 

  • Chang, C., and Lundgren, S. (1961). Duct flow in magnetohydrodynamics. Zeitschrift für angewandte Mathematik und Physik XII: 100–114.

    Article  MathSciNet  Google Scholar 

  • Debray, F. (1997). Measurement of the onset of MHD-turbulence caused by a step in the electrical conductivity in the channel walls of GALINKA Il and comparison with theoretical models. Technical Report FZKA 5972, Forschungszentrum Karlsruhe.

    Google Scholar 

  • Frank, M., Barleon, L., and Müller, U. (1997). Experimentelle Untersuchung zweidimensionaler MHD-Turbulenz. Technical Report FZKA 6021, Forschungszentrum Karlsruhe. Diplomarbeit.

    Google Scholar 

  • Garandet, J., Albousière, T., and Moreau, R. (1992). Buoyancy driven convection in a rectangular enclosure with a transverse magnetic field. Int. J. Heat Mass Transfer 35 (4): 741–748.

    Article  MATH  Google Scholar 

  • Gold, R. R. (1962). Magnetohydrodynamic pipe flow. Part 1. Journal of Fluid Mechanics 13: 505–512.

    Article  MathSciNet  MATH  Google Scholar 

  • Hartmann, J. (1937). Hg-Dynamics I Theory of the laminar flow of an electrically conductive liquid in a homogeneous magnetic field. Det Kgl. Danske Videnskabernes Selskab. Mathematisk-fysiske Meddelelser XV (6): 1–27.

    Google Scholar 

  • Huges, W. F., and Young, F. J. (1966). The electromagnetics. John Wiley & Sons Inc.

    Google Scholar 

  • Hunt, J. C. R., and Leibovich, S. (1967). Magnetohydrodynamic flow in channels of variable cross-section with strong transverse magnetic fields. Journal of Fluid Mechanics 28 (Part 2): 241–260.

    Article  MATH  Google Scholar 

  • Hunt, J. C. R., and Stewartson, K. (1965). Magnetohydrodynamic flow in rectangular ducts. Journal of Fluid Mechanics 23: 563–581.

    Article  MathSciNet  Google Scholar 

  • Hunt, J. C. R., and Williams, W. E. (1968). Some electically driven flows in magnetohydrodynamics. Part 1. Theory. Journal of Fluid Mechanics 31 (4): 705–722.

    Article  MATH  Google Scholar 

  • Hunt, J. C. R. (1965). Magnetohydrodynamic flow in rectangular ducts. Journal of Fluid Mechanics 21: 577–590.

    Article  MathSciNet  MATH  Google Scholar 

  • Khine, Y., and Walker, J. (1998). Thermoelectric magnetohydrodynamic effects during bridgman semicon- ductor crystal growth with a uniform axial magnetic field. Journal of Crystal Growth 183: 159–158.

    Article  Google Scholar 

  • Lenhart, L., and McCarthy, K. (1991). Comparison of the core flow solution and the full solution for MHD flow. In Proceedings of the Sixth Beer-Sheva International Seminar on MHD Flows and Turbulence, Jerusalem, 1990. American Institute of Aeronautics and Astronautics, Inc. 482–499. Beer-Sheva.

    Google Scholar 

  • Ludford, G. S. S. (1960). The effect of a very strong magnetic cross-field on steady motion through a slightly conducting fluid. Journal of Fluid Mechanics 10: 141–155.

    Article  MathSciNet  Google Scholar 

  • Lykoudis, P. S. (1996). Natural convection in a cubic enclosure in the presence of a horizontal magnetic field. Journal of Heat Transfer 118: 215–218.

    Article  Google Scholar 

  • Ma, N., and Walker, J. S. (1995). Liquid-metal buoyant convection in a vertical cylinder with a strong vertical magnetic field and with nonaxisymmetric temperature. Physics of Fluids 7 (8): 2061–2071.

    Article  MATH  Google Scholar 

  • Ma, N., and Walker, J. S. (1996). Buoyant convection during the growth of compound semiconductors by the liquid-encapsulated Czochralski process with an axial magnetic field and with non-axisymmetric temperature. Journal of Fluids Engineering 118 (8): 155–159.

    Article  Google Scholar 

  • Molokov, S., and Bühler, L. (1994). Liquid metal flow in a U-bend in a strong uniform magnetic field. Journal of Fluid Mechanics 267: 325–352.

    Article  MATH  Google Scholar 

  • Molokov, S. (1993). Fully developed liquid-metal flow in multiple rectangular ducts in a strong uniform magnetic field. European Journal of Mechanics, B/Fluids 12 (6): 769–787.

    MATH  Google Scholar 

  • Molokov, S. (1994). Liquid metal flows in manifolds and expansions of insulating rectangular ducts in the plane perpendicular to a strong magnetic field. Technical Report KfK 5272, Kernforschungszentrum Karlsruhe.

    Google Scholar 

  • Moon, T. J., Hua, T. Q., and Walker, J. S. (1991). Liquid-metal flow in a backward elbow in the plane of a strong magnetic field. Journal of Fluid Mechanics 227: 273–292.

    Article  MATH  Google Scholar 

  • Moreau, R. (1990). Magnetohydrodynamics. Kluwer Academic Publisher.

    Google Scholar 

  • Mößner, R. (1996). Dreidimensionale numerische Simulation von Naturkonvektionsströmungen unter dem Einfluß von Magnetfeldern. Technical Report FZKA 5748, Forschungszentrum Karlsruhe.

    Google Scholar 

  • Murgatroyd, W. (1953). Experiments on magneto-hydrodynamic channel flow. Phil. Mag. 44: 1348–1354.

    Google Scholar 

  • Okada, K., and Ozoe, H. (1992). Experimental heat transfer rates of natural convcection of molten gallium suppressed under an external magnetic field in either the x, y, or z direction. Journal of Heat Transfer 114: 107–114.

    Article  Google Scholar 

  • Reed, C. B., Picologlou, B. E, Hua, T. Q., and Walker, J. S. (1987). Alex results–A comparison of measurements from a round and a rectangular duct with 3-D code predictions. In IEEE 12th Symposium on Fusion Engineering, Monterey, California, October 13–16. 1267–1270.

    Google Scholar 

  • Roberts, P. H. (1967). Singularities of Hartmann layers. Proceedings of the Royal Society of London 300 (A): 94–107.

    Article  MATH  Google Scholar 

  • Rosant, M. (1976). Ecoulements hydromagnétiques turbulents en conduites rectangulaires. Ph.D. Dissertation, Grenoble. see Moreau (1990), p149.

    Google Scholar 

  • Series, R. W., and Hurle, D. T. J. (1991). The use of magnetic fields in semiconductor crystal growth. Journal of Crystal Growth 113: 305–321.

    Article  Google Scholar 

  • Shercliff, J. A. (1953). Proc.Camb.Phil.Soc. 49: 136.

    Article  MathSciNet  MATH  Google Scholar 

  • Shercliff, J. A. (1962). Magnetohydrodynamic pipe flow Part 2. High Hartmann number. Journal of Fluid Mechanics 13: 513–518.

    Article  MathSciNet  MATH  Google Scholar 

  • Sterl, A. (1990). Numerical simulation of liquid-metal MHD flows in rectangular ducts. Journal of Fluid Mechanics 216: 161–191.

    Article  MATH  Google Scholar 

  • Stieglitz, R., and Molokov, S. (1997). Experimental study of magnetohydrodynamic flows in electrically coupled bends. Journal of Fluid Mechanics 343: 1–28.

    Article  Google Scholar 

  • Stieglitz, R., Barleon, L., Bühler, L., and Molokov, S. (1996). Magnetohydrodynamic flow through a right-angle bend in a strong magnetic field. Journal of Fluid Mechanics 326: 91–123.

    Article  MATH  Google Scholar 

  • Tabeling, P. (1982). Magnetohydrodynamic flows in rectilinear ducts of rectangular cross-section: the question of the corners. Journal de Mécanique Théoretique et Appliquée 1 (1): 25–38.

    MathSciNet  MATH  Google Scholar 

  • Temperley, D. J., and Todd, L. (1971). The effect of wall conductivity in magnetohydrodynamic duct flow at high Hartmann number. Proc. Camb. Phil. Soc. 69: 337–351.

    Article  MATH  Google Scholar 

  • Ufland, Y. S. (1961). Hartman problem for a circular tube. Soviet Physics Technical Physics 5: 1194–1196.

    Google Scholar 

  • Walker, J. S. (1981). Magnetohydrodynamic flows in rectangular ducts with thin conducting walls. Journal de Mécanique 20 (1): 79–112.

    MATH  Google Scholar 

  • Walker, J. (1998). Bridgman crystal growth with a strong, low-frequency, rotating magnetic field. Journal of Crystal Growth 192: 318–327.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Forschungszentrum Karlsruhe, Germany

    U. Müller & L. Bühler

Authors
  1. U. Müller
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  2. L. Bühler
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Editor information

Editors and Affiliations

  1. University of Cambridge, UK

    Peter A. Davidson

  2. University of Ilmenau, Germany

    Andre Thess

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© 2002 Springer-Verlag Wien

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Müller, U., Bühler, L. (2002). Liquid Metal Magneto-Hydraulics Flows in Ducts and Cavities. In: Davidson, P.A., Thess, A. (eds) Magnetohydrodynamics. International Centre for Mechanical Sciences, vol 418. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2546-5_1

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  • DOI: https://doi.org/10.1007/978-3-7091-2546-5_1

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-83686-6

  • Online ISBN: 978-3-7091-2546-5

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