Abstract
In the current study, investigated are steady-state, three-dimensional liquid metal (LM) magnetohydrodynamic (MHD) flows in a conduit system including three sub-channels with co-current flows under a uniform magnetic field. Though there have been numerous analytic, experimental and numerical studies on MHD duct flow, detailed flow characteristics of a LMMHD flow in a conduit system with multiple channels have not been reported much. The current study predicts detailed behaviors of the flow velocity, pressure, current and electric potential of LMMHD flows in multiple channels in the plane perpendicular to the magnetic field. Here, the characteristics of the MHD flow in a conduit system with multiple channels are elucidated. The mass flow rate in each of outer channel turns out to be higher than that in the central channel. The mechanism governing the imbalance of mass flow rate in the sub-channels is discussed in detail based on the interdependency of flow variables in LMMHD flow.
Similar content being viewed by others
References
L. Barleon, V. Casal and L. Lenhart, MHD flow in liquidmetal-cooled blankets, Fusion Engineering and Design, 14 (1991) 401–412.
I. R. Kirillov, C. B. Reed, L. N. Barleon and K. Miyazaki, Present understanding of MHD and heat transfer phenomena for liquid metal blankets, Fusion Engineering Design, 27 (1995) 553–569.
N. B. Morley, S. Smolentsev, L. Barleon, I. R. Kirillov and M. Takahashi, Liquid magnetohydrodynamics — recent progress and future directions for fusion, Fusion Engineering and Design, 51–52 (2000) 701–713.
L. Buhler, S. Horanyi and E. Arbogast, Experimental investigation of liquid -metal flows through a sudden expansion at fusion -relevant Hartmann numbers, Fusion Engineering and Design, 82 (2007) 2239–2245.
C. Mistrangelo and L. Buhler, Magnetohydrodynamic pressure drops in geometric elements forming a HCLL blanket mock-up, Fusion Engineering and Design, 86 (2011) 2304–2307.
J. C. R. Hunt, Magnetohydrodynamic flow in rectangular ducts, Journal of Fluid Mech., 21 (4) (1965) 577–590.
S. Molokov, Liquid metal flows in manifolds and expansions of insulating rectangular ducts in the plane perpendicular to a strong magnetic field, Forschungszentrum Karlsruhe (1994).
S. Cuevas, B. F. Picologlou, J. S. Walker and G. Talmage, Liquid-metal MHD flow in rectangular ducts with thin conducting or insulating walls: laminar and turbulent solutions, International Journal of Engineering Science, 35 (5) (1997) 485–503.
L. Buhler, Laminar buoyant magnetohydrodynamic flow in vertical rectangular ducts, Physics of Fluids, 10 (1) (1998) 223–236.
M. H. Lin and C. T. Chen, Effect of magnetic field on thermal instability in mixed convection flow over a rotating cylinder, Heat and Mass Transfer, 471 (2011) 1581–1589.
C. N. Kim, A. H. Hadid and M. A. Abdou, Development of a computational method for the full solution of MHD flow in fusion blankets, Fusion Engineering and Design, 8 (1989) 256–270.
C. N. Kim and M. A. Abdou, Numerical method for fluid and heat transfer in magneto-hydrodynamic flow, Fusion Technology, 15 (2) (1989) 1163–1168.
M. N. Ni, R. Munipalli, N. Morley, P. Huang and M. Abdou, Validation case results for 2D and 3D MHD simulations, Fusion Science and Technology, 52 (2007) 587–594.
M. N. Ni, R. Munipalli, N. B. Morley, P. Huang and M. A. Abdou, A current density conservation scheme for incompressible MHD lows at a low magnetic Reynolds number Part I: On a rectangular collocated mesh, Journal of Computational Physics, 227 (2007) 174–204.
M. N. Ni, R. Munipalli, P. Huang, N. Morley and M. Abdou, A current density conservation scheme for incompressible MHD lows at a low magnetic Reynolds number Part II: On an arbitrary collocated mesh, Journal of Computational Physics, 227 (2007) 205–228.
T. Zhou, Z. Yang, M. Ni and H. Chen, Code development and validation for analyzing liquid metal MHD flow in rectangular ducts, Fusion Engineering and Design, 85 (2010) 1736–1741.
T. Zhou, H. Chen and Z. Yang, Effect of fringing magnetic field on magnetohydrodynamic flow in rectangular duct, Fusion Engineering and Design, 86 (2011) 2352–2357.
S. J. Xu and M. J. Ni, Direct simulation of MHD flows in dual-coolant liquid metal fusion blanket using a consistent and conservative scheme, Theoretical and Applied Mechanics Letters, 1 (2011) 012006.
I. D. Piazza and L. Buhler, Numerical simulations of buoyant magnetohydrodynamic flows using the CFX code, Forschungszentrum Karlsruhe GmbH, Karlsruhe (1999).
J. Reimann, L. Buhler, C. Mistrangelo and S. Molokov, Magneto-hydrodynamic issues of the HCLL blanket, Fusion Engineering and Design, 81 (2006) 625–629.
C. Mistrangelo and L. Buhler, Numerical investigation of liquid metal flows in rectangular sudden expansions, Fusion Engineering and Design, 82 (2007) 2176–2182.
C. Mistrangelo and L. Buhler, Electric flow coupling in the HCLL blanket concept, Fusion Engineering and Design, 83, (2008) 1232–1237.
S. H. Kim, M. H. Kim, D. W. Lee and C. Choi, Code validation and development for MHD analysis of liquid metal flow in Korean TBM, Fusion Engineering and Design, 87 (2012) 951–955.
N. B. Morley et al., MHD simulations of liquid metal flow through a toroidally oriented manifold, Fusion Engineering and Design, 83 (2008) 1335.
C. Mistrangelo, Three-dimensional MHD flow in sudden expansions, Forschungszentrum Karlsruhe, FZKA 7201.
B. R. Hutchinson and G. D. Raithby, A multi-grid method based on the additive correction strategy, Numerical Heat Transfer, 9 (1986) 511–537.
M. Raw, Robustness of coupled algebraic multi-grid for the Navier-Stokes equations, AIAA Meeting Papers on Disc, A9618260, AIAA Paper 96-0297 (1996).
W. Z. Shen, J. A Michelsen and J. N. Sorensen, Improved Rhie-Chow interpolation for unsteady flow computations, AIAA Journal, 39 (12) (2001) 2406–2409.
J. S. Walker, Magnetohydrodynamic flows in rectangular ducts with thin conducting wall, J. de Mecanique, 20 (1) (1981) 79–112.
Author information
Authors and Affiliations
Corresponding author
Additional information
Recommended by Associate Editor Donghyun You
Chang Nyung Kim is a professor in Department of Mechanical Engineering, College of Engineering, Kyung Hee University, Korea. His research interests include numerical analysis of magnetohydrodynamics and thermoelectricity.
Rights and permissions
About this article
Cite this article
Kim, C.N. Numerical examination of liquid metal magnetohydrodynamic flow in multiple channels in the plane perpendicular to the magnetic field. J Mech Sci Technol 28, 4959–4968 (2014). https://doi.org/10.1007/s12206-014-1117-z
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12206-014-1117-z