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Turbulent duct flows in a liquid metal magnetohydrodynamic power generator

Published online by Cambridge University Press:  17 October 2012

Hiromichi Kobayashi ,
Hiroki Shionoya  and
Yoshihiro Okuno
Hiromichi Kobayashi*
Affiliation:
Department of Physics & Research and Education Center for Natural Sciences, Keio University, Yokohama, 223-8521, Japan
Hiroki Shionoya
Affiliation:
Department of Energy Sciences, Tokyo Institute of Technology, Yokohama, 226-8503, Japan
Yoshihiro Okuno
Affiliation:
Department of Energy Sciences, Tokyo Institute of Technology, Yokohama, 226-8503, Japan
*
†Email address for correspondence: [email protected]
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Abstract

We numerically assess the influence of non-uniform magnetic flux density and connected load resistance on turbulent duct flows in a liquid metal magnetohydrodynamic (MHD) electrical power generator. When increasing the magnetic flux density (or Hartmann number), an M-shaped velocity profile develops in the plane perpendicular to the magnetic field; the maximum velocity in the sidewall layer of the M-shaped profile increases to maintain the flow rate. Under the conditions of a relaminarized flow, the turbulence structures align along the magnetic field and flow repeatedly like a von Kármán vortex sheet. At higher Hartmann numbers, the wall-shear stress in the sidewall layer increases and the sidewall jets transit to turbulence. The sidewall jets in the MHD turbulent duct flows have profiles similar to the non-MHD wall jets, i.e. a mean velocity profile with outer scaling, Reynolds shear stress with the opposite sign in a sidewall jet, and two maxima for the turbulent intensities in a sidewall jet. The Lorentz force suppresses the vortices of the secondary mean flow near the Hartmann layer for low Hartmann numbers, whereas the secondary vortices remain near the Hartmann layer for high Hartmann numbers. An optimal load resistance (or load factor) to obtain a maximum electrical efficiency exists, because the strong Lorentz force for a low load factor and unextracted eddy currents for a high load factor reduce efficiency. When the value of the load factor is changed, the profiles of mean velocity and r.m.s. for the optimal load factor produce almost the same profiles as the high load factor near the open-circuit condition.

JFM classification

MHD and Electrohydrodynamics: MHD turbulence Turbulent Flows: Turbulent transition
Type
Papers
Information
Journal of Fluid Mechanics , Volume 713 , 25 December 2012 , pp. 243 - 270
Copyright
©2012 Cambridge University Press

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References

Abrahamsson, H., Johansson, B. & Löfdahl, L. 1994 A turbulent plane two-dimensional wall-jet in a quiescent surrounding. Eur. J. Mech. B 13, 553–411.Google Scholar
Andreev, O., Kolesnikov, Y. & Thess, A. 2007 Experimental study of liquid metal channel flow under the influence of a non-uniform magnetic field. Phys. Fluids 19, 039902.Google Scholar
Branover, H. & Gershon, P. 1979 Experimental investigation of the origin of residual disturbances in turbulent MHD flows after laminarization. J. Fluid Mech. 94, 629–647.Google Scholar
Burr, U., Barleon, L., Müller, A. & Tsinober, 2000 Turbulent transport of momentum and heat in magnetohydrodynamic rectangular duct flow with strong sidewall jets. J. Fluid Mech. 406, 247–279.CrossRefGoogle Scholar
Chaudhary, R., Vanka, S. P. & Thomas, B. G. 2010 Direct numerical simulations of magnetic field effects on turbulent flow in a square duct. Phys. Fluids 22, 075102.CrossRefGoogle Scholar
Davidson, P. A. 2001 An Introduction to Magnetohydrodynamics. Cambridge University Press.Google Scholar
Demuren, A. O. & Rodi, W. 1984 Calculation of turbulence-driven secondary motion in non-circular ducts. J. Fluid Mech. 140, 189–222.Google Scholar
Elliott, D. G. 1966 Direct current liquid-metal magnetohydrodynamic power generator. AIAA J. 4, 627–634.Google Scholar
Fujimura, K. 1989 Stability of MHD flow through a square duct. UCLA Technical Report, UCLA-FNT-023.Google Scholar
George, W. K., Abrahamsson, H., Eriksson, J., Karlsson, R. I., Löfdahl, L. & Wosnik, M. 2000 A similarity theory for the turbulent plane wall jet without external stream. J. Fluid Mech. 425, 367–411.Google Scholar
Inagaki, M., Kondoh, T. & Nagano, Y. 2005 A mixed-time scale SGS model with fixed model-parameters for practical LES. Trans. ASME: J. Fluids Engng 127, 1–13.Google Scholar
Kakizaki, K., Maeda, T., Shimizu, K. & Ishikawa, M. 2003 MHD simulation of liquid metal MHD power generator: effect of magnetic field distribution on the generator performance. In Papers of Technical Meeting on Frontier Technology and Engineering, vol. FTE-03, pp. 65–70. IEE Japan.Google Scholar
Kinet, M., Knaepen, B. & Molokov, S. 2009 Instabilities and transition in magnetohydrodynamic flows in ducts with electrically conducting walls. Phys. Rev. Lett. 103, 154501.CrossRefGoogle ScholarPubMed
Kitoh, O. 1991 Experimental study of turbulent swirling flow in a straight pipe. J. Fluid Mech. 225, 445–479.CrossRefGoogle Scholar
Kobayashi, H. 2005 The subgrid-scale models based on coherent structures for rotating homogeneous turbulence and turbulent channel flow. Phys. Fluids 17, 045104.CrossRefGoogle Scholar
Kobayashi, H. 2008 Large eddy simulation of magnetohydrodynamic turbulent duct flows. Phys. Fluids 20, 015102.CrossRefGoogle Scholar
Kobayashi, H., Ham, F. & Wu, X. 2008 Application of a local SGS model based on coherent structures to complex geometries. Intl J. Heat Fluid Flow 29, 640–653.Google Scholar
Krasnov, D., Zikanov, O., Rossi, M. & Boeck, T. 2010 Optimal linear growth in magnetohydrodynamic duct flow. J. Fluid Mech. 653, 273–299.Google Scholar
Launder, B. E. 1969 The Prandtl–Kolmogorov model of turbulence with the inclusion of second-order terms. Trans. ASME: J. Basic Engng 91, 855–856.Google Scholar
Launder, B. E. & Rodi, W. 1983 The turbulent wall jet measurements and modelling. Annu. Rev. Fluid Mech. 15, 429–459.CrossRefGoogle Scholar
Li, J., Peng, Y., Liu, B., Sha, C., Zhao, L., Xu, Y., Li, R. & Li, X. 2010 Preliminary experimental study on LMMHD wave energy conversion system. In Proceedings of Twentieth (2010) International Offshore and Polar Engineering Conference, pp. 907–910. ISOPE.Google Scholar
Maeda, T., Shimizu, K., Hasegawa, Y., Kakizaki, K., Ishikawa, M., Yamasaki, H. & Okuno, Y. 2003 The fundamental characteristics of liquid metal MHD engine generator. J. Jpn. Soc. Appl. Electromagn. Mech. 11, 249–255.Google Scholar
Moreau, R. 1991 Magnetohydrodynamics. Springer.Google Scholar
Priede, J., Aleksandrova, S. & Molokov, S. 2010 Linear stability of Hunt’s flow. J. Fluid Mech. 649, 115–134.Google Scholar
Reed, C. B. & Lykoudis, P. S. 1978 The effect of a transverse magnetic field on shear turbulence. J. Fluid Mech. 89, 147–171.Google Scholar
Rosa, R. J. 1968 Magnetohydrodynamic Energy Conversion. McGraw-Hill.Google Scholar
Satake, S., Fujino, T., Ishikawa, M. & Maeda, T. 2008 Experimental study of proof-of-principle of liquid metal MHD generation. In Proceedings of New Energy Technology Symposium, B-1-4.Google Scholar
Shatrov, V. & Gerbeth, G. 2010 Marginal turbulent magnetohydrodynamic flow in a square duct. Phys. Fluids 22, 084101.Google Scholar
Smagorinsky, J. 1963 General circulation experiments with the primitive equations. Part 1. The basic experiment. Mon. Weath. Rev. 91, 99–164.Google Scholar
Smolentsev, S., Vetcha, N. & Moreau, R. 2012 Study of instabilities and transitions for a family of quasi-two-dimensional magnetohydrodynamic flows based on a parametrical model. Phys. Fluids 24, 024101.Google Scholar
Sommeria, J. & Moreau, R. 1982 Why, how and when MHD turbulence becomes two-dimensional. J. Fluid Mech. 118, 507–518.Google Scholar
Sutton, G. W. & Carlson, A. W. 1961 End effects in inviscid flow in a magnetohydrodynamic channel. J. Fluid Mech. 11, 121–132.Google Scholar
Sutton, G. W., Hurwitz, H. Jr & Poritsky, H. 1962 Electrical and pressure losses in magnetohydrodynamic channel due to end current loops. Trans. AIEE 80, 687–695.Google Scholar
Sutton, G. W. & Sherman, A. 2006 Engineering Magnetohydrodynamics. Dover.Google Scholar
Uhlmann, M., Pinell, A., Kawahara, G. & Sekimoto, A. 2007 Marginally turbulent flow in a square duct. J. Fluid Mech. 588, 153–162.CrossRefGoogle Scholar
Votyakov, E. V., Kolesnikov, Y., Andreev, O., Zienicke, E. & Thess, A. 2007 Structure of the wake of a magnetic obstacle. Phys. Rev. Lett. 98, 144504.Google Scholar
Votyakov, E. V., Zienicke, E. & Kolesnikov, Y. 2008 Constrained flow around a magnetic obstacle. J. Fluid Mech. 610, 131–156.Google Scholar
Yamada, K., Maeda, T., Hasegawa, Y. & Okuno, Y. 2004 Two-dimensional numerical simulation on performance of liquid metal MHD generator. T. IEE Japan B 124, 971–976.Google Scholar
Yamada, K., Maeda, T., Hasegawa, Y. & Okuno, Y. 2006 Three-dimensional numerical simulation on performance of liquid metal MHD generator. T. IEE Japan B 125, 141–146.Google Scholar