Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-19T03:47:05.707Z Has data issue: false hasContentIssue false

Liquid-metal magnetohydrodynamics with strong magnetic fields: a report on Euromech 70

Published online by Cambridge University Press:  11 April 2006

J. C. R. Hunt
Affiliation:
Department of Applied Mathematics and Theoretical Physics and Department of Engineering, Cambridge University
R. Moreau
Affiliation:
Institut de Mécanique, Université de Grenoble

Abstract

This paper is a summary of the first Euromech Colloquium to be held on Magnetohydrodynamics (MHD). It was organized in conjunction with the Centre National de la Recherche Scientifique and held at Grenoble from 16–19 March 1976 with 60 participants from 10 countries present. Papers were presented on laminar and turbulent MHD duct flows; heat transfer and two-phase flows in MHD; the effects of magnetic fields on instabilities and turbulence; the motion of and forces on solid objects in MHD flows; flow-measurement methods, and applications of MHD in the metallurgical industries, in sodium technology and in liquid-metal power generation. Our main conclusion is that there are many industrial applications of the existing body of research findings in MHD, but that quite new research problems have arisen as a result of the new applications, and that these need investigation. MHD lives!

Type
Research Article
Copyright
© 1976 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

Alberny, R., Badker, L., Birat, J-P, Gosselin, P. & Wanin, M. 1974 Quality improvement of strand-cast billets through electromagnetic stirring Electric Furnace Proc., Cincinnati Metall. Soc. A.I.M.E. 31, 237.Google Scholar
Alemany, A. [dagger] Experimental study of homogeneous turbulence in MHD.
Alemany, A. & Moreau, R. [dagger] Flow of an electrically conducting liquid in the presence of a rotating multipolar magnetic field.
Alemany, A. & Rosant, J. M. [dagger] Observations on the use of hot-film anemometers in mercury.
Allibert, C. & Driole, J. [dagger] Some metallurgical examples of the action of a magnetic field on the separation of metallic phases.
Baker, R. C. 1970 Linearity of motion induced magnetic field flowmeter. Proc. I.E.E. 117, (3), 629.Google Scholar
Baylis, J. A. 1971 Experiments on laminar flow in curved channels of square section J. Fluid Mech. 48, 417.Google Scholar
Baylis, J. A. & Hunt, J. C. R. 1971 MHD flow in an annular channel; theory and experiment J. Fluid Mech. 48, 423.Google Scholar
Berger, E. [dagger] The influence of the magnetic pressure on Pitot-tube readings in liquidmetal MHD flow.
Bevir, M. K. [dagger] Ideal induced field flow meters.
Bevir, M. K. 1970 The theory of induced voltage electromagnetic flowmeters J. Fluid Mech. 43, 577.Google Scholar
Block, F. R. [dagger] Measuring the velocity of electrically conducting solids and liquids.
Branover, G. G., Gel'fygat, Yu. M., Kit, L. G. & Platnieks, I. A. 1970 Effect of a transverse magnetic field on the intensity profiles of turbulent velocity fluctuations in a channel of rectangular cross section. Magn. Gidro. 6, 336 (MDH 6 (3), 41).Google Scholar
Branover, G. G., Gel'fgat, Yu. M., Tsinober, A. B., Schtern, A. B. & Shcherbinin, E. V. 1966 The application of Pitot and Prandtl tubes in MHD experiments. Magn. Gidro. 2, 1, 98 (MHD 2, 55).Google Scholar
Branover, G. G. & Gershon, P. [dagger] Experimental verification of the hypothesis of two-dimensional turbulence in MHD flows.
Branover, G. G. & Tsinober, A. 1970 Magnetohydrodynamics of Incompressible Media. Moscow: Nauka.
Brouillette, E. C. & Lykoudis, P. S. 1967 Magneto-fluid-mechanic channel flow. I. Experiment. Phys. Fluids, 10, 955. II. Theory. Phys. Fluids, 10, 1002.Google Scholar
Buckmaster, J. 1969 Separation and magnetohydrodynamics J. Fluid Mech. 38, 481.Google Scholar
Cercignani, C. [dagger] On the dynamics of a liquid layer subjected to magnetic forces.
Chabrerie, J-P., Fournet, G. & Maillefert, A. 1976 Studies of plane parallel turbulent flows with moving walls Rev. Phys. Appl. 11, 353.Google Scholar
Chabrerie, J-P. & Tabeling, P. [dagger] Study of laminar to turbulent transition in an MHD annular flow.
Chabrerie, J-P., & Tabeling, P. [dagger] Rectilinear MHD flow in rectangular cross-sections with sliding walls.
Chambarel, A., Ricou, R. & Vives, Ch. [dagger] Electrical method for determining values of local electromagnetic parameters and the velocity in an MHD flow.
Chambarel, A. & Vivès, Ch. [dagger] Pressure distributions on cylindrical obstacles with various electrical and magnetic properties in the presence of a magnetic field.
Cheng, K. C. & Akiyama, M. 1970 Laminar force convection heat transfer in curved rectangular channels Int. J. Heat Mass Transfer, 13, 471.Google Scholar
Cook, L. P., Ludford, G. S. S. & Walker, J. S. 1972 Corner regions in the asymptotic solution of ε Δ2u = ∝u/∝y with reference to MHD duct flow. Proc. Camb. Phil. Soc. 72, 117.Google Scholar
Dahlberg, E. 1971 On the action of a rotating magnetic field on a conducting liquid. Atomic Energi, Sweden, Rep. AE 447.Google Scholar
Davidson, D. F. & Thatcher, G. [dagger] Sodium electrotechnology at UKAEA Reactor group.
Driole, J., Allibert, C., Bonnier, E. & Wicker, A. 1969 Procédé de séparation d'un corps en phase solide hors d'une matrice en phase liquide. French Patent, no. 69.164.23.Google Scholar
Driole, J., Allibert, C., Bonnier, E. & Wicker, A. 1975 2nd Suppl. Cert. to patent request, no. 69.164.23.
Energy Research and Development Administration 1975 Magnetohydrodynamic Power Generation and Theory — a Bibliography. Available from Nat. Tech. Information Service. TID-33–56.
Fraim, F. W. & Heiser, W. H. 1968 The effect of a strong longitudinal magnetic field on the flow of mercury in a circular tube J. Fluid Mech. 33, 397.Google Scholar
Gammerman, M. Ya. & Mezhburd, V. I. 1971 Weight functions for electromagnetic flow meters in the 3-dimensional approximation. Magn. Gidro. 7 (3), 130 (MHD 7, 406).Google Scholar
Gardner, R. & Lykoudis, P. 1971 Magneto-fluid-mechanic pipe flow in a transverse magnetic field. Part 1. Isothermal flow J. Fluid Mech. 47, 737.Google Scholar
Garnier, M. [dagger] Kelvin—Helmholtz and Rayleigh—Taylor instabilities in the presence of alternating magnetic fields.
Garnier, M. [dagger] Duct flows in the presence of a travelling magnetic field.
Garnier, M. [dagger] Electromagnetic confinement of liquid metals.
Getselev, Z. N. 1971 Knibyskevski Metull. Zarod Inreni V.I. Lenina. French Patent, no. 71, 41163.Google Scholar
Givry, J. P. 1967 Computer calculation of magnetic effects in the batch of aluminium cells Trans. Met. Soc. A.I.M.E. 239, 1161.Google Scholar
Gnatyuk, V. V. & Paramonova, T. P. 1969 Calibration of Pitot tubes in a transverse magnetic field. Magn. Gidro. 5 (4), 143 (MHD 5, 96).Google Scholar
Gnatyuk, V. V. & Paramonova, T. A. 1971 Effect of wall conductance on the velocity profile in a pipe. Magn. Gidro. 7 (1), 145 (MHD 7, 126).Google Scholar
Hervé, R. & Poirier, J. [dagger] Study of rectilinear fluid flow in a rectangular duct one of whose walls is highly conducting, the others being non-conducting.
Holroyd, R. J. 1976 Magnetohydrodynamic duct flows in non-uniform magnetic fields. Ph.D. dissertation, University of Cambridge.
Holroyd, R. J. & Hunt, J. C. R. [dagger] A review of MHD flows in ducts with changing cross-sectional areas and non-uniform magnetic fields.
Hühns, T. & Djamali-Schami, D. [dagger] Comparison of three types of free-jet MHD induction generators; three-dimensional field distributions and performance.
Hunt, J. C. R. 1965 Magnetohydrodynamic flow in a rectangular duct J. Fluid Mech. 21, 577.Google Scholar
Hunt, J. C. R. 1966 On the stability of parallel flows with parallel magnetic fields. Proc. Roy. Soc. A 293, 342.Google Scholar
Hunt, J. C. R. 1970 Bluff body drag in strong transverse magnetic field. Magn. Gidro. 6 (1), 35 (MHD 6, 30).Google Scholar
Hunt, J. C. R. & Hancox, R. 1971 The use of liquid lithium as a coolant in a toroidal fusion reactor. Part 1. Calculation of pumping power. U.K. Atom. En. Auth. Rep. CLM-R115.Google Scholar
Hunt, J. C. R. & Ludford, G. S. S. 1968 Three-dimensional MHD duct flows with strong transverse magnetic fields. Part 1. Obstacles in constant area channel J. Fluid Mech. 33, 693.Google Scholar
Hunt, J. C. R. & Malcolm, D. G. 1968 Some electrically driven flows in MHD. Part 2. Theory and experiment J. Fluid Mech. 33, 775.Google Scholar
Hunt, J. C. R. & Shercliff, J. A. 1971 Magnetohydrodynamics at high Hartmann number Ann. Rev. Fluid Mech. 3, 37.Google Scholar
Hunt, J. C. R. & Stewartson, K. 1965 Magnetohydrodynamic flow in rectangular ducts. II J. Fluid Mech. 23, 563.Google Scholar
Hunt, J. C. R. & Stewartson, K. 1969 Some electrically driven flows in MHD. Part 3. The asymptotic theory for flow between circular electrodes J. Fluid Mech. 35, 225.Google Scholar
Jameson, A. 1964 Magnetohydrodynamic waves. Ph.D. dissertation, University of Cambridge.
Kant, M. [dagger] Contribution to the study of the electrical continuity of two-phase flows under the action of a magnetic field.
Kapusta, A. B. 1968 Motion of a conducting fluid under the action of a rotating magnetic field. Magn. Gidro. 4, 71 (MHD 4, 71).Google Scholar
Khaletzky, D. [dagger] Numerical study of the motions in an induction furnace used for separating impurities.
Khalis, K. E., Slyusarev, N. M., Tsinober, A. B. & Schtern, A. G. 1966 Resistance of bluff bodies at high Stewart numbers. Magn. Gidro. 2, 152 (MHD 2, 93).Google Scholar
Kisis, A. Ya. 1968 Electromagnetic measurement of the parameters of MHD processes. Latvian Acad. Sci.Google Scholar
Kit, L. G. 1970 Turbulent velocity fluctuation measurements using a conduction anemometer with a three electrode probe. Magn. Gidro. 6, 41 (MHD 6, 480).Google Scholar
Kochetkova, G. Ya., Stolov, M. Ya., Tit, L. L. & Chaikin, P. M. 1966 The circulation of metal in an induction furnace. Magn. Gidro. 2 (2), 139 (MHD 2, 85).Google Scholar
Kolmogorov, A. N. 1941 The local structure of turbulence in an incompressible viscous fluid for very large Reynolds numbers Dokl. Akad. Nauk USSR, 30, 301.Google Scholar
Kovner, D. S. & Krasil'nikov, E. In. 1965 An experimental investigation of turbulent flow of electroconductive liquid in a pipe in a parallel magnetic field Dokl. Akad. Nauk USSR, 163, 1096.Google Scholar
Kulikovskii, A. G. 1968 Slow steady flows of a conducting liquid at large Hartmann numbers. Izv. Akad. Nauk USSR, Mekh. Zhid. i Gaza, 3 (2), 3 (Fluid Dynamics, 3, 1).Google Scholar
Kulikovskii, A. G. 1973 Flows of a conducting incompressible liquid in an arbitrary region with a strong magnetic field. Mekh. Zhid. i Gaza, 8 (3), 144 (Fluid Dynamics, 8, 462).Google Scholar
Leith, C. E. 1971 Atmospheric predictability and two-dimensional turbulence J. Atmos. Sci. 28, 145.Google Scholar
Leith, C. E. & Kraichnan, 1972 Predictability of turbulent flows J. Atmos. Sci. 29, 1041.Google Scholar
Lielausis, O. A. 1975 Liquid metal magnetohydrodynamics Atomic Energy Review, 13, 527.Google Scholar
Lorenz, E. N. 1969 The predictability of a flow which possesses many scales of motion Tellus, 21, 289.Google Scholar
Ludwieg, 1951 Die ausgebildete Kanalströmung in einem rotierenden System Ing. Arch. 19, 563.Google Scholar
Lykoudis, P. [dagger] Magneto-fluid-mechanics liquid-metal turbulent shear flows.
Lykoudis, P. [dagger] Some elementary magneto-fluid-mechanic problems for two-phase fluids.
Lykoudis, P. 1962 Natural convection of an electrically conducting fluid in the presence of a magnetic field Int. J. Heat Mass Transfer, 5, 23.Google Scholar
Lykoudis, P. & Andelman, M. 1976 Liquid-metal heat transfer in pipes with aligned magnetic fields. Trans. Am. Nuc. Soc. Ann. Meeting. 21, 36, June 1975.Google Scholar
Lykoudis, P. & Brouillette, E. C. 1967 Magneto-fluid-mechanic channel flow. II. Theory Phys. Fluids, 10, 1002.Google Scholar
Malcolm, D. G. 1969 Some aspects of turbulence measurement in liquid mercury using cylindrical quartz insulated hot film sensors J. Fluid Mech. 37, 701.Google Scholar
Mead, J. J. & Ray, R. Y. 1969 Electromagnetic problems in aluminium reduction cells, TMS-AIME Annual Meeting, Washington D.C.Google Scholar
Moffatt, H. K. 1964 Electrically driven steady flows in MHD. Proc. 11th Int. Cong. Appl. Mech. p. 946. Munich.
Moffatt, H. K. 1965 On fluid flow induced by a rotating magnetic field J. Fluid Mech. 22, 521.Google Scholar
Moffatt, H. K. 1967 On the suppression of turbulence by a uniform magnetic field J. Fluid Mech. 28, 571.Google Scholar
Moffatt, H. K. 1973 MHD phenomena in rotating fluids. Report of the NATO advanced study institute J. Fluid Mech. 57, 625.Google Scholar
Moreau, R. [dagger] Reflections on the possibilities of electromagnetic separation.
Moreau, R. [dagger] Some general ideas on homogeneous turbulence in the presence of a uniform magnetic field.
Moreau, R. 1964 The effect of a transverse magnetic field on separation C. R. Acad. Sci. 258, 1732.Google Scholar
Moreau, R. 1968 On magnetohydrodynamic turbulence. Proc. of Symp. on Turbulence of Fluids and Plasmas. Polytech. Inst. of Brooklyn, p. 359.
Moreau, R. 1974 Procédé electromagnetique de controle du digazage des métaux liquides par jet sous vide. French Patent, no. 74, 21569.Google Scholar
Moreau, R. & Alemany, A. 1976 Aspects spécifiques de la turbulence homogène MHD aux faibles nombres de Reynolds magnetiques. J. Physique. Suppl. 1, 37, pp. C1101.Google Scholar
Moreau, R. & Garnier, M. 1975 Dispositifs électromagnetique de confinement des métaux liquides. French Patent, no. 75, 21075.Google Scholar
Oboukhov, A. M. 1941 On the energy distribution in the spectrum of a turbulent flow Dokl. Akad. Nauk USSR, 32, 19.Google Scholar
Orszag, S. A. & Patterson, G. S. 1971 Numerical Simulation of Turbulence. Statistical Models and Turbulence. Springer.
Otte, F. [dagger] Numerical solution of a two-dimensional liquid-metal MHD duct flow for finite magnetic Reynolds numbers in the presence of a strong transverse magnetic field varying in the flow direction.
Owen, R. G., Hunt, J. C. R. & Collier, J. G. [dagger] MHD pressure drop in ducted two-phase flows. (To appear in J. Multiphase Flow 1976.)Google Scholar
Plaschko, P. [dagger] The influence of continuously varying velocity profiles on the instability of spatially growing disturbances in a liquid metal MHD jet in the presence of a strong longitudinal magnetic field.
Radebold, R. D. [dagger] Preliminary experimental results from the MHD staustrahlrohr (convertor).
Reed, C. 1976 Ph.D. dissertation, Purdue University.
Robinson, T. [dagger] Experiments on flow measurement in a mercury loop.
Robinson, T. 1973 An experimental investigation of a magnetically driven rotating liquid-metal flow J. Fluid Mech. 60, 641.Google Scholar
Rosant, J. M. [dagger] Turbulent flows in rectangular ducts at large Hartmann numbers.
Rosant, J. M. [dagger] Comparison of different methods of local velocity measurement.
Sabjen, M. 1965 Hot wire anemometers in liquid mercury Rev. Sci. Instr. 36, 945.Google Scholar
Schumann, U. [dagger] Numerical study of nonlinear effects in homogeneous MHD turbulence.
Schumann, U. 1976 Numerical simulation of the transition from three- to two-dimensional turbulence under a uniform magnetic field J. Fluid Mech. 74, 31.Google Scholar
Shercliff, J. A. [dagger] Alfvén wave power devices.
Shercliff, J. A. 1962 Theory of Electromagnetic Flow Measurement. Cambridge University Press.
Shercliff, J. A. 1965 A Text Book of Magnetohydrodynamics. Pergamon.
Shercliff, J. A. 1975 Some duct flow problems at high Hartmann number Z. angew. Math. Phys. 26, 537.Google Scholar
Shercliff, J. A. 1976 Technological Alfvén waves. Proc. Int. Elect. Engrs, vol. 123, p. 1035.Google Scholar
Sneyd, A. 1971 Generation of fluid motion in a circular cylinder by an unsteady applied magnetic field J. Fluid Mech. 49, 817.Google Scholar
Squire, H. B. 1933 On the stability of three-dimensional disturbances of viscous fluid flow between parallel walls. Proc. Roy. Soc. A 142, 641.Google Scholar
Sulem, P. L. & Frisch, U. [dagger] Does MHD turbulence at low magnetic Reynolds number become two-dimensional in the presence of a strong external magnetic field?
Tananaev, A. B. [dagger] MHD laminar and turbulent flows in rough ducts.
Tananaev, A. B. 1975 MHD flow in rough tubes Magn. Gidro. 11, 29.Google Scholar
Temperley, D. J. [dagger] MHD flow in a rectangular duct under a uniform transverse magnetic field at high Hartmann number.
Temperley, D. J. & Todd, L. 1971 The effects of wall conductivity in MHD duct flows at high Hartmann number Proc. Camb. Phil. Soc. 69, 337.Google Scholar
Thatcher, G. 1971 Electromagnetic flowmeters for liquid metals. In Proc. Int. Conf. on Modern Developments in Flow Measurement, Harwell, Sept. 1971 (ed. Clayton).
Tir, L. L. 1965 Modelling the motion of molten metal in an induction furnace. Magn. Gidro. 1 (4), 120 (MHD 1, 76).Google Scholar
Tsinober, A. B. 1970 MHD Flow around Bodies. Riga: Zinante.
Vivès, Ch. 1974a On the coefficient of pressure drag of a cylindrical obstacle in a liquid MHD flow. C. R. Acad. Sci. B 278, 501.Google Scholar
Vivès, Ch. 1974b On the coefficient of pressure drag of a non-conducting sphere in a liquid MHD flow. C. R. Acad. Sci. B 279, 203.Google Scholar
Vivès, Ch. 1975 Study of the flow around non-conducting and conducting cylindrical obstacles in the presence of a transverse magnetic field. C. R. Acad. Sci. B 280, 677.Google Scholar
Walker, J. S. [dagger] Solitary compression waves in liquid-metal MHD duct flows.
Walker, J. S. & Ludford, G. S. S. 1974a MHD flow in conducting circular expansions with strong transverse magnetic fields. Int. J. Engng Sci. 12, 193.Google Scholar
Walker, J. S. & Ludford, G. S. S. 1974b MHD flow in insulated circular expansions with strong transverse magnetic fields. Int. J. Engng Sci. 12, 1045.Google Scholar
Walker, J. S., Ludford, G. S. S. & Hunt, J. C. R. 1972 Three-dimensional MHD duct flows with strong transverse magnetic fields. Part 3. Variable-area rectangular ducts with insulating walls J. Fluid Mech. 56, 121.Google Scholar
Wenger, N. C. 1970 A variational principle for MHD channel flow J. Fluid Mech. 43, 211.Google Scholar
Wilks, G. [dagger] Magnetohydrodynamic free convection about a semi-infinite vertical plate in a strong cross field.