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Topological analysis of separation phenomena in liquid metal flow in sudden expansions. Part 2. Magnetohydrodynamic flow

Published online by Cambridge University Press:  23 March 2011

C. MISTRANGELO
C. MISTRANGELO*
Affiliation:
Karlsruhe Institute of Technology (KIT), IKET, Herrmann-von-Helmholtz-Platz 1, Eggenstein-Leopoldshafen 76344, Germany
*
†Present address: KIT, Campus North, Postfach 3640, 76021 Karlsruhe, Germany. Email address for correspondence: chiara.mistrangelo@kit.edu
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Abstract

A numerical study has been carried out to analyse liquid metal flows in a sudden expansion of electrically conducting rectangular ducts under the influence of an imposed uniform magnetic field. Separation phenomena are investigated by selecting a reference Reynolds number and by increasing progressively the applied magnetic field. The magnetic effects leading to the reduction of the size of separation zones that form behind the cross-section enlargement are studied by considering modifications of flow topology, streamline patterns and electric current density distribution. In the range of parameters investigated, the magnetohydrodynamic flow undergoes substantial transitions from a hydrodynamic-like flow to one dominated by electromagnetic forces, where the influence of inertia and viscous forces is confined to thin internal layers aligned with the magnetic field and to boundary layers that form along the walls. Scaling laws describing the reattachment length and the pressure drop in the sudden expansion are derived for intense magnetic fields.

JFM classification

MHD and Electrohydrodynamics: High-Hartmann-number flows Mathematical Foundations: Topological fluid dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 674 , 10 May 2011 , pp. 132 - 162
Copyright
Copyright © Cambridge University Press 2011

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References

REFERENCES

Aitov, T. N., Kalyutik, A. I. & Tananaev, A. V. 1983 Numerical analysis of three-dimensional MHD flow in channel with abrupt change of cross-section. Magnetohydrodynamics 19 (2), 223–229.Google Scholar
Bühler, L. 1995 Magnetohydrodynamic flows in arbitrary geometries in strong, nonuniform magnetic fields. Fusion Technol. 27, 3–24.CrossRefGoogle Scholar
Bühler, L. 2007 a A parametric study of 3D MHD flows in expansions of rectangular ducts. Fusion Sci. Technol. 52 (3), 595–602.CrossRefGoogle Scholar
Bühler, L. 2007 b Liquid metal magnetohydrodynamics for fusion blankets. In Magnetohydrodynamics Historical Evolution and Trends (ed. Molokov, S., Moreau, R. & Moffatt, H. K.), Fluid Mechanics and Its Applications, vol. 80, pp. 171–194. Springer.CrossRefGoogle Scholar
Bühler, L. 2008 Three-dimensional liquid metal flows in strong magnetic fields. Tech. Rep. FZKA 7412. Forschungszentrum Karlsruhe, habilitationsschrift Universität Karlsruhe.Google Scholar
Bühler, L. & Horanyi, S. 2006 Experimental investigations of MHD flows in a sudden expansion. Tech. Rep. FZKA 7245. Forschungszentrum Karlsruhe.Google Scholar
Bühler, L., Horanyi, S. & Arbogast, E. 2007 Experimental investigation of liquid-metal flows through a sudden expansion at fusion-relevant Hartmann numbers. Fusion Engng Des. 82, 2239–2245.CrossRefGoogle Scholar
Davidson, P. A. 1999 Magnetohydrodynamics in materials processing. Annu. Rev. Fluid Mech. 31, 273–300.CrossRefGoogle Scholar
Davidson, P. A. 2001 An Introduction to Magnetohydrodynamics. Cambridge University Press.CrossRefGoogle 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. 15 (6), 1–27.Google Scholar
Hunt, J. C. R. 1965 Magnetohydrodynamic flow in rectangular ducts. J. Fluid Mech. 21, 577–590.CrossRefGoogle Scholar
Hunt, J. C. R. & Leibovich, S. 1967 Magnetohydrodynamic flow in channels of variable cross-section with strong transverse magnetic fields. J. Fluid Mech. 28 (2), 241–260.CrossRefGoogle Scholar
Jiang, M., Machiraju, R. & Thompson, D. S. 2005 Detection and Visualization of Vortices, chap. 14, pp. 295–309. Elsevier.Google Scholar
Kulikovskii, A. G. 1968 Slow steady flows of a conducting fluid at large Hartmann numbers. Fluid Dyn. 3 (1), 1–5.CrossRefGoogle Scholar
Ludford, G. S. S. 1960 The effect of a very strong magnetic cross-field on steady motion through a slightly conducting fluid. J. Fluid Mech. 10, 141–155.CrossRefGoogle Scholar
Mistrangelo, C. 2005 Three-dimensional MHD flow in sudden expansions. Tech. Rep. FZKA 7201. Forschungszentrum Karlsruhe, PhD thesis, University of Karlsruhe.Google Scholar
Mistrangelo, C. 2011 Topological analysis of separation phenomena in liquid metal flow in sudden expansions. Part 1. Hydrodynamic flow. J. Fluid Mech. doi:10.1017/S0022112010006439.CrossRefGoogle Scholar
Molokov, S. 2000 Two-dimensional parallel layers at high Ha, Re and N. In Proc. of Fourth Intl PAMIR Conf. on Magnetohydrodynamic at Dawn of Third Millennium, vol. 1, pp. 573–578. Giens, France, PAMIR.Google Scholar
Morley, N. B., Malang, S. & Kirillov, I. 2005 Thermofluid magnetohydrodynamic issues for liquid breeders. Fusion Sci. Technol. 47 (3), 488–501.CrossRefGoogle Scholar
Müller, U. & Bühler, L. 2001 Magnetofluiddynamics in Channels and Containers. Springer.CrossRefGoogle Scholar
Ni, M.-J., Munipalli, R., Huang, P., Morley, N. B. & Abdou, M. A. 2007 a A current density conservative scheme for incompressible MHD flows at a low magnetic Reynolds number. Part II: On an arbitrary collocated mesh. J. Comput. Phys. 227 (1), 205–228.CrossRefGoogle Scholar
Ni, M.-J., Munipalli, R., Morley, N. B., Huang, P. & Abdou, M. A. 2007 b Validation case results for 2D and 3D MHD simulations. Fusion Sci. Technol. 52 (3), 587–594.CrossRefGoogle Scholar
Patankar, S. V. 1980 Numerical Heat Transfer and Fluid Flow. Hemisphere.Google Scholar
Perry, A. E. & Chong, M. S. 1987 A description of eddying motions and flow patterns using critical-point concepts. Annu. Rev. Fluid Mech. 19, 125–155.CrossRefGoogle Scholar
Perry, E. & Hornung, H. 1984 Some aspects of three-dimensional separation. Part I: Streamsurface bifurcations. Z. Flugwiss. Weltraumforsch. 8 (2), 77–87.Google Scholar
Salavy, J.-F., Aiello, G., David, O., Gabriel, F., Giancarli, L., Girard, C., Jonqueres, N., Laffont, G., Madeleine, S., Poitevin, Y., Rampal, G., Ricapito, I. & Splichal, K. 2008 The HCLL test blanket module system: Present reference design, system integration in ITER and R&D needs. Fusion Engng Des. 83, 1157–1162.CrossRefGoogle Scholar
Shercliff, J. A. 1953 Steady motion of conducting fluids in pipes under transverse magnetic fields. Proc. Camb. Phil. Soc. 49, 136–144.CrossRefGoogle Scholar
Shercliff, J. A. 1965 A Textbook of Magnetohydrodynamics. Pergamon.Google Scholar
Sterl, A. 1990 Numerical simulation of liquid–metal MHD flows in rectangular ducts. J. Fluid Mech. 216, 161–191.CrossRefGoogle Scholar
Walker, J. S. 1981 Magnetohydrodynamic flows in rectangular ducts with thin conducting walls. J. Mécanique 20 (1), 79–112.Google Scholar
Walker, J. S. 1986 Laminar duct flows in strong magnetic fields. In Liquid–Metal Flows and Magnetohydrodynamics (ed. Branover, H., Lycoudis, P. S. & Mond, M.). AIAA.Google Scholar
Wesson, J. 1987 Tokamaks. Oxford University Press.Google Scholar
Yates, L. A. & Chapman, G. T. 1991 Streamlines, vorticity lines, and vortices. In Proc. of 29th Aerospace Sciences Meeting, 6–10 January, Reno, Nevada. AIAA 91-0731.Google Scholar
Yates, L. A. & Chapman, G. T. 1992 Streamlines, vorticity lines, and vortices around three-dimensional bodies. AIAA J. 30 (7), 1819–1826.CrossRefGoogle Scholar