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The effect of a transverse magnetic field on shear turbulence

Published online by Cambridge University Press:  19 April 2006

Claude B. Reed  and
Paul S. Lykoudis
Claude B. Reed
Affiliation:
School of Nuclear Engineering, Purdue University, West Lafayette, Indiana 47907
Paul S. Lykoudis
Affiliation:
School of Nuclear Engineering, Purdue University, West Lafayette, Indiana 47907
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Abstract

Turbulence measurements under the influence of a transverse magnetic field have been made at Purdue University's Magneto-Fluid-Mechanic Laboratory in a high aspect ratio channel. The Reynolds number range covered was 25000 ≤ Re 282000; the geometry and experimental conditions were such that the experiment approximated turbulent Hartmann flow. The aspect ratio of the channel was 5·8:1, its walls were electrically insulated and the working fluid was mercury. Measurements in the presence of a magnetic field were made of the skin friction coefficient, the mean velocity profiles, the turbulence intensity profiles (both u’ and v’) and the Reynolds stress profiles.

A sudden change in the damping of the Reynolds stresses was manifested by a ‘hump’ in the curves of Cf versus M/Re taken with the Reynolds number held constant. This ‘hump’ occurs as a gentle rise and sudden drop to the Hartmann laminar line of the Cf data. Close examination of the $\overline{u^{\prime}v^{\prime}}$ data near the wall confirms this behaviour, indicating that the turbulent contribution to the shear stress is the controlling factor in this behaviour of Cf. The Reynolds stresses were completely suppressed to zero at high values of the magnetic field, though the turbulence intensities of u’ and v’ were not. The Reynolds stress data are fundamental in revealing the mechanisms which are at work during the suppression of turbulence by a magnetic field.

It was also found that at high magnetic fields, when most of the turbulence was damped, the skin friction coefficient fell below the values predicted by Hartmann's (1937) laminar solution for high values of M/Re. This result was linked to the presence of ‘M-shaped’ velocity profiles in the direction perpendicular to both the magnetic field and the mean velocity vector. The presence of ‘M-shaped’ profiles has not previously been linked to a reduction in Cf.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 89 , Issue 1 , 14 November 1978 , pp. 147 - 171
Copyright
© 1978 Cambridge University Press

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References

Bocheninski, B. E., Branover, H. H., Tanayev, A. B. & Chereyev, YU. E. 1971 Experimental investigation of the resistance to flow of an electrically conducting fluid in plane insulated channels in a transverse magnetic field considering end effects and rough walls. Izv. AN S.S.S.R. Mekh. Zh. i Gaza 4, 10–21.Google Scholar
Branover, H. H. 1974 On some effects in laboratory MHD flows in rectangular ducts in transverse magnetic fields. 14th Symp. Engineering Aspects of Magnetohydrodynamics, pp. 3.1–3.4.
Branover, H. H. & Gel'Fgat, YU. M.1968 Stabilization of plane-parallel flow in a transverse magnetic field. Magnitnaya Gidrodynamika 4 (3), 9.Google Scholar
Branover, H. H., Gel'Fgat, YU. M., Kit, L. G. & Platnicks, E. A.1970 The effect of a transverse magnetic field on the turbulence intensity profiles in a rectangular channel. Magnitnaya Gidrodynamika 6 (3), 41.Google Scholar
Branover, H. H., Gel'Fgat, YU. M., Kit, L. G. & Tsinober, A. B.1970 Study of MHD turbulence in tubes using conduction anemometers. Izv. AN S.S.S.R. Mekh. Zh. i Gaza 5 (2), 35.Google Scholar
Branover, H. H., Gel'Fgat, YU. M., Peterson, D. A. & Tsinober, A. B.1969 Turbulent Hartmann flow. Magnitnaya Gidrodynamika 5 (1), 61.Google Scholar
Branover, H. H., Gel'Fgat, YU. M. & Tsinober, A. B.1966 Turbulent magnetohydrodynamic flows in prismatic and cylindrical ducts. Magnitnaya Gidrodynamika 2 (3), 3.Google Scholar
Branover, H. H., Gel'Fgat, YU. M., Tsinober, A. B., SHTERN, & SHERBININ, E. V. 1966 The application of Pitot and Prandtl tubes in magnetohydrodynamics experiments. Magnitnaya Gidrodynamika 2 (1), 98.Google Scholar
Branover, H. H. & Gershon, P. 1975 An experimental MHD facility for the investigation of some important features of turbulence suppression. MHD Flows and Turbulence (ed. H. Branover). Wiley and Israel University Press, Jerusalem.
Brouillette, E. C. 1966 Experimental and theoretical analysis of magneto-fluid-mechanic channel flow. Ph.D. thesis, Purdue University.
Brouillette, E. C. & Lykoudis, P. S. 1963 Measurements of skin friction for turbulent magneto-fluid-mechanic channel flow. Purdue Univ. Rep. A & ES 62–10, August 1962. See also Proc. 4th Symp. Engineering Aspects of MHD (I.E.E.E.), p. 45.
Brouillette, E. C. & Lykoudis, P. S. 1967 Magneto-fluid-mechanic channel flow I. Experiment. Phys. Fluids 10, 995.Google Scholar
Comte-Bellot, G. 1965 Turbulent flow between two parallel planes. Publ. Sci. Tech. Min. Air, no. 419.Google Scholar
Gardner, R. A. 1969 Magneto-fluid-mechanic pipe flow in a transverse magnetic field with and without heat transfer. Ph.D. thesis, Purdue University.
Gardner, R. A. & Lykoudis, P. S. 1971 Magneto-fluid-mechanic pipe flow in a transverse magnetic field. Part 1. Isothermal flow. J. Fluid Mech. 47, 737.Google Scholar
Hartmann, J. 1937 Hg Dynamics-I. Kgl. Danske Videnskab Selskab Mat.-Fys. Medd. 15, no. 6.Google Scholar
Hua, H. M. 1968 Heat transfer from a constant temperature circular cylinder in cross-flow and turbulence measurements in an MFM channel. Ph.D. thesis, Purdue University.
Hunt, J. C. R. 1965 Magnetohydrodynamic flow in rectangular ducts. J. Fluid Mech. 21, 577.Google Scholar
Hunt, J. C. R. & Moreau, R. 1976 Liquid-metal magnetohydrodynamics with strong magnetic fields: a report on Euromech 70. J. Fluid Mech. 78, 261.Google Scholar
Laufer, J. 1950 Investigation of turbulent flow in a two-dimensional channel. N.A.C.A.Tech. Note no. 2123.Google Scholar
Lecocq, P. 1964 A contribution to the study of the loss of flow and the velocity profiles for turbulent magnetohydrodynamic flow. Bulletin du Centre de Recherches et d'Essais de Chatou, suppl. 8.Google Scholar
Lykoudis, P. S. 1960 Transition from laminar to turbulent flow in magneto-fluid-mechanic channels. Rev. Mod. Phys. 32, 796.Google Scholar
Maciulaitis, A. & Loeffler, L. A. 1964 A theoretical investigation of MHD channel entrance flow. A.I.A.A. J. 2, 2100.Google Scholar
Malcolm, D. G. 1975 Hot film anemometry in liquid-metal MHD. In MHD Flows and Turbulence, Proc. Bat-Sheva Inter. Seminar, Beersheva, p. 119.
Malcolm, D. G. & Verma, V. 1973 Dynamic response of forced convective heat transfer from cylinders to low Prandlt number fluids. Proc. 3rd Symp. Turbulence in Liquids, Univ. Missouri-Rolla, p. 15.
Murgatroyd, W. 1953 Experiments on magneto-hydrodynamic channel flow. Phil. Mag. 44, 1348.Google Scholar
Nickuradse, J. 1929 Forsch.-Arb. Geb. Ing.-Wes. 289.
Papailiou, D. D. & Lykoudis, P. S. 1974 Magneto-fluid-mechanics free convection turbulent flow. Int. J. Heat Mass Transfer 17, 1181.Google Scholar
Patrick, R. P. 1976 MFM turbulence suppression. Ph.D. thesis, Purdue University.
Reed, C. B. 1976 An investigation of shear turbulence in the presence of magnetic fields. Ph.D. thesis, Purdue University.
Reed, C. B. & Lykoudis, P. S. 1977 Turbulence measurements in mercury under the influence of a magnetic field. Proc. 5th Biennial Symp. Turbulence, Univ. Missouri-Rolla, session V, p.1.
Schlichting, H. 1960 Boundary Layer Theory. 4th edn. p. 515. Pergamon.
Shercliff, J. A. 1953 Steady motion of conducting fluids in pipes under transverse magnetic fields, Proc. Camb. Phil. Soc. 49, 136.Google Scholar
Shercliff, J. A. 1956 Edge effects in electromagnetic flowmeters. J. Nuclear Energy I 3, 305.Google Scholar
Sleicher, C. A. & Lim, G. B. 1973 Measurement of unsteady flows in mercury with hot-film anemometers. Proc. 3rd Symp. Turbulence in Liquids, Univ. Missouri-Rolla, p. 1.
Slyusarev, N. M. 1971 Effect of a transverse magnetic field on turbulent channel flows. Magnitnaya Gidrodynamica 7 (1), 18.Google Scholar