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Combining an obstacle and electrically driven vortices to enhance heat transfer in a quasi-two-dimensional MHD duct flow

Published online by Cambridge University Press:  03 March 2016

Ahmad H. A. Hamid
The Sheard Lab, Department of Mechanical and Aerospace Engineering, Monash University, Victoria 3800, Australia Faculty of Mechanical Engineering, Universiti Teknologi MARA, 40450 Selangor, Malaysia
Wisam K. Hussam
The Sheard Lab, Department of Mechanical and Aerospace Engineering, Monash University, Victoria 3800, Australia
Gregory J. Sheard*
The Sheard Lab, Department of Mechanical and Aerospace Engineering, Monash University, Victoria 3800, Australia
Email address for correspondence:


The design of vortex promoters in a heated-wall duct is often limited by the considerations of practicality, especially in complex systems such as fusion blankets. The present study investigates the use of current injection to invoke a street of vortices in quasi-two-dimensional high transverse magnetic field magnetohydrodynamic duct flows to enhance instability behind a cylinder. The intent is to generate intensive flow vorticity parallel to a magnetic field downstream of a field-aligned cylinder. Electric current enters the flow through an electrode embedded in one of the Hartmann walls, radiates outward, imparting a rotational forcing around the electrode due to the Lorentz force. The quasi-two-dimensional nature of these flows then promotes a vortical rotation across the interior of the duct with axis aligned to the magnetic field. The hot and cold walls are parallel to the magnetic field. Electric current amplitude and pulse width, excitation frequency and electrode position are systematically varied to explore their influences on the convective heat transport phenomenon. This investigation builds on a recommendation from previous work of Bühler (J. Fluid Mech., vol. 326, 1996, pp. 125–150) dedicated to understanding of the flow stability in a similar configuration. This study provides supportive evidence for the use of current injection as an alternative to the conventional mechanically actuated turbuliser, with heat transfer almost doubled for negligible additional pumping power requirements.

© 2016 Cambridge University Press 

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Alboussière, T., Uspenski, V. & Moreau, R. 1999 Quasi-2D MHD turbulent shear layers. Exp. Therm. Fluid Sci. 20 (1), 1924.Google Scholar
Ali, M. S. M., Doolan, C. J. & Wheatley, V. 2009 Grid convergence study for a two-dimensional simulation of flow around a square cylinder at a low Reynolds number. In Seventh International Conference on CFD in The Minerals and Process Industries (ed. Witt, P. J. & Schwarz, M. P.), pp. 16. CSIRO.Google Scholar
Baker, N. T., Pothérat, A. & Davoust, L. 2015 Dimensionality, secondary flows and helicity in low- $Rm$ MHD vortices. J. Fluid Mech. 779, 325350.Google Scholar
Barleon, L., Mack, K.-J. & Stieglitz, R.1996 The MEKKA-facility a flexible tool to investigate MHD-flow phenomena. Tech. Rep. ZKA 5821. Institute of Applied Thermo- and Fluid Dynamics, Research Centre Karlsruhe.Google Scholar
Beskok, A., Raisee, M., Celik, B., Yagiz, B. & Cheraghi, M. 2012 Heat transfer enhancement in a straight channel via a rotationally oscillating adiabatic cylinder. Intl J. Therm. Sci. 58, 6169.Google Scholar
Branover, H., Eidelman, A. & Nagorny, M. 1995 Use of turbulence modification for heat transfer enhancement in liquid metal blankets. Fusion Engng Des. 27, 719724.Google Scholar
Brouillette, E. C. & Lykoudis, P. S. 1967 Magneto-fluid-mechanic channel flow. I. Experiment. Phys. Fluids 10 (5), 9951001.Google Scholar
Bühler, L. 1996 Instabilities in quasi-two-dimensional magnetohydrodynamic flows. J. Fluid Mech. 326, 125150.Google Scholar
Burr, U., Barleon, L., Müller, U. & Tsinober, A. 2000 Turbulent transport of momentum and heat in magnetohydrodynamic rectangular duct flow with strong sidewall jets. J. Fluid Mech. 406, 247279.Google Scholar
Cassells, O. G. W., Hussam, W. K. & Sheard, G. J. 2016 Heat transfer enhancement using rectangular vortex promoters in confined quasi-two-dimensional magnetohydrodynamic flows. Intl J. Heat Mass Transfer 93, 186199.Google Scholar
Celik, B., Akdag, U., Gunes, S. & Beskok, A. 2008 Flow past an oscillating circular cylinder in a channel with an upstream splitter plate. Phys. Fluids 20, 103603.Google Scholar
Celik, B., Raisee, M. & Beskok, A. 2010 Heat transfer enhancement in a slot channel via a transversely oscillating adiabatic circular cylinder. Intl J. Heat Mass Transfer 53, 626634.Google Scholar
Cuevas, S., Picologlou, B. F., Walker, J. S., Talmage, G. & Hua, T. Q. 1997 Heat transfer in laminar and turbulent liquid-metal MHD flows in square ducts with thin conducting or insulating walls. Intl J. Engng Sci. 35 (5), 505514.Google Scholar
Davidson, P. A. 2001 An Introduction to Magnetohydrodynamics, vol. 25. Cambridge University Press.Google Scholar
Frank, M., Barleon, L. & Müller, U. 2001 Visual analysis of two-dimensional magnetohydrodynamics. Phys. Fluids 13, 22872295.Google Scholar
Fu, Wu-Shung & Tong, Bao-Hong 2004 Numerical investigation of heat transfer characteristics of the heated blocks in the channel with a transversely oscillating cylinder. Intl J. Heat Mass Transfer 47, 341351.Google Scholar
Gardner, R. A. & Lykoudis, P. S. 1971 Magneto-fluid-mechanic pipe flow in a transverse magnetic field Part 2. Heat transfer. J. Fluid Mech. 48 (1), 129141.Google Scholar
Griffin, O. M. & Ramberg, S. E. 1976 Vortex shedding from a cylinder vibrating in line with an incident uniform flow. J. Fluid Mech. 75 (2), 257271.Google Scholar
Hamid, A. H. A., Hussam, W. K., Pothérat, A. & Sheard, G. J. 2015 Spatial evolution of a quasi-two-dimensional Kármán vortex street subjected to a strong uniform magnetic field. Phys. Fluids 27, 053602.Google Scholar
Hartmann, J. & Lazarus, F. 1937 Hg-dynamics II: experimental investigations on the flow of mercury in a homogeneous magnetic field. Math.-fys. Med. 15 (7), 145.Google Scholar
Hunt, J. C. R. 1965 Magnetohydrodynamic flow in rectangular ducts. J. Fluid Mech. 21 (4), 577590.Google Scholar
Hunt, J. C. R. & Malcolm, D. G. 1968 Some electrically driven flows in magnetohydrodynamics Part 2. Theory and experiment. J. Fluid Mech. 33 (04), 775801.Google Scholar
Hussam, W. K. & Sheard, G. J. 2013 Heat transfer in a high Hartmann number MHD duct flow with a circular cylinder placed near the heated side-wall. Intl J. Heat Mass Transfer 67, 944954.Google Scholar
Hussam, W. K., Thompson, M. C. & Sheard, G. J. 2011 Dynamics and heat transfer in a quasi-two-dimensional MHD flow past a circular cylinder in a duct at high Hartmann number. Intl J. Heat Mass Transfer 54, 10911100.Google Scholar
Hussam, W. K., Thompson, M. C. & Sheard, G. J. 2012a Enhancing heat transfer in a high Hartmann number magnetohydrodynamic channel flow via torsional oscillation of a cylindrical obstacle. Phys. Fluids 24, 113601.Google Scholar
Hussam, W. K., Thompson, M. C. & Sheard, G. J. 2012b Optimal transient disturbances behind a circular cylinder in a quasi-two-dimensional magnetohydrodynamic duct flow. Phys. Fluids 24, 024105.Google Scholar
Kanaris, N., Albets, X., Grigoriadis, D. & Kassinos, S. 2013 Three-dimensional numerical simulations of magnetohydrodynamic flow around a confined circular cylinder under low, moderate, and strong magnetic fields. Phys. Fluids 25, 074102.Google Scholar
Karniadakis, G. E. & Triantafyllou, G. S. 1989 Frequency selection and asymptotic states in laminar wakes. J. Fluid Mech. 199, 441469.Google Scholar
Kieft, R. N., Rindt, C. C. M., Van Steenhoven, A. A. & Van Heijst, G. J. F. 2003 On the wake structure behind a heated horizontal cylinder in cross-flow. J. Fluid Mech. 486, 189211.Google Scholar
Klein, R., Pothérat, A. & Alferenok, A. 2009 Experiment on a confined electrically driven vortex pair. Phys. Rev. E 79, 016304.Google Scholar
Kolesnikov, Y. B. & Andreev, O. V. 1997 Heat-transfer intensification promoted by vortical structures in closed channel under magnetic field. Exp. Therm. Fluid Sci. 15, 8290.Google Scholar
Koopmann, G. H. 1967 The vortex wakes of vibrating cylinders at low Reynolds numbers. J. Fluid Mech. 28 (3), 501512.Google Scholar
Krasnov, D., Zikanov, O. & Boeck, T. 2012 Numerical study of magnetohydrodynamic duct flow at high Reynolds and Hartmann numbers. J. Fluid Mech. 704, 421446.Google Scholar
Lahjomri, J., Capéran, Ph. & Alemany, A. 1993 The cylinder wake in a magnetic field aligned with the velocity. J. Fluid Mech. 253, 421448.Google Scholar
Lam, K. M. 2009 Vortex shedding flow behind a slowly rotating circular cylinder. J. Fluids Struct. 25, 245262.Google Scholar
Lundquist, S. 1949 Experimental investigations of magneto-hydrodynamic waves. Phys. Rev. 76 (12), 18051809.Google Scholar
Lyon, R. N. 1952 Liquid-Metals Handbook, 2nd edn. Navexos P-733.Google Scholar
Mahfouz, F. M. & Badr, H. M. 2000 Forced convection from a rotationally oscillating cylinder placed in a uniform stream. Intl J. Heat Mass Transfer 43, 30933104.Google Scholar
Malang, S. & Tillack, M. S.1995 Development of self-cooled liquid metal breeder blankets. Tech. Rep. FZKA 5581. Forschungszentrum Karlsruhe GmbH Karlsruhe.Google Scholar
Miyazaki, K., Inoue, H., Kimoto, T., Yamashita, S., Inoue, S. & Yamaoka, N. 1986 Heat transfer and temperature fluctuation of lithium flowing under transverse magnetic field. J. Nucl. Sci. Technol. 23 (7), 582593.Google Scholar
Molokov, S.1994 Liquid metal flows in manifolds and expansions of insulating rectangular ducts in the plane perpendicular to a strong magnetic field. Tech. Rep. KfK 5272. Kernforschungszentrum Karlsruhe GmbH Karlsruhe.Google Scholar
Morley, N. B., Burris, J., Cadwallader, L. C. & Nornberg, M. D. 2008 GaInSn usage in the research laboratory. Rev. Sci. Instrum. 79, 056107.Google Scholar
Mück, B., Günther, C., Müller, U. & Bühler, L. 2000 Three-dimensional MHD flows in rectangular ducts with internal obstacles. J. Fluid Mech. 418 (1), 265295.Google Scholar
Müller, U. & Bühler, L. 2001 Magnetofluiddynamics in Channels and Containers. Springer.Google Scholar
Neild, A., Ng, T. W., Sheard, G. J., Powers, M. & Oberti, S. 2010 Swirl mixing at microfluidic junctions due to low frequency side channel fluidic perturbations. Sensors Actuators 150, 811818.Google Scholar
Polyanin, A. D. 2001 Handbook of Linear Partial Differential Equations for Engineers and Scientists. Chapman & Hall/CRC.Google Scholar
Pothérat, A. 2007 Quasi-two-dimensional perturbations in duct flows under transverse magnetic field. Phys. Fluids 19, 074104.Google Scholar
Pothérat, A. & Klein, R. 2014 Why, how and when MHD turbulence at low $Rm$ becomes three-dimensional. J. Fluid Mech. 761, 168205.Google Scholar
Pothérat, A. & Kornet, K. 2015 The decay of wall-bounded MHD turbulence at low. J. Fluid Mech. 783, 605636.Google Scholar
Pothérat, A. & Schweitzer, J.-P. 2011 A shallow water model for magnetohydrodynamic flows with turbulent Hartmann layers. Phys. Fluids 23 (5), 055108.Google Scholar
Pothérat, A., Sommeria, J. & Moreau, R. 2000 An effective two-dimensional model for MHD flows with transverse magnetic field. J. Fluid Mech. 424, 75100.Google Scholar
Pothérat, A., Sommeria, J. & Moreau, R. 2002 Effective boundary conditions for magnetohydrodynamic flows with thin Hartmann layers. Phys. Fluids 14, 403410.Google Scholar
Pothérat, A., Sommeria, J. & Moreau, R. 2005 Numerical simulations of an effective two-dimensional model for flows with a transverse magnetic field. J. Fluid Mech. 534, 115143.Google Scholar
Rhoads, J. R., Edlund, E. M. & Ji, H. 2014 Effects of magnetic field on the turbulent wake of a cylinder in free-surface magnetohydrodynamic channel flow. J. Fluid Mech. 742, 446465.Google Scholar
Roberts, P. H. 1967 An Introduction to Magnetohydrodynamics. Longmans.Google Scholar
Shatrov, V. & Gerbeth, G. 2010 Marginal turbulent magnetohydrodynamic flow in a square duct. Phys. Fluids 22 (8), 084101.Google Scholar
Sheard, G. J. 2011 Wake stability features behind a square cylinder: focus on small incidence angles. J. Fluids Struct. 27, 734742.Google Scholar
Shercliff, J. A. 1953 Steady motion of conducting fluids in pipes under transverse magnetic fields. Math. Proc. Cambridge 49, 136144.Google Scholar
Smolentsev, S & Moreau, R 2007 One-equation model for quasi-two-dimensional turbulent magnetohydrodynamic flows. Phys. Fluids 19, 078101.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
Smolentsev, S., Wong, C., Malang, S., Dagher, M. & Abdou, M. 2010 MHD considerations for the DCLL inboard blanket and access ducts. Fusion Engng Des. 85 (7), 10071011.Google Scholar
Sommeria, J. 1986 Experimental study of the two-dimensional inverse energy cascade in a square box. J. Fluid Mech. 170, 139168.Google Scholar
Sommeria, J. 1988 Electrically driven vortices in a strong magnetic field. J. Fluid Mech. 189, 553569.Google Scholar
Sommeria, J. & Moreau, R. 1982 Why, how, and when, MHD turbulence becomes two-dimensional. J. Fluid Mech. 118, 507518.Google Scholar
Sukoriansky, S., Klaiman, D., Branover, H. & Greenspan, E. 1989 MHD enhancement of heat transfer and its relevance to fusion reactor blanket design. Fusion Engng Des. 8, 277282.Google Scholar
Takahashi, M., Aritomi, M., Inoue, A. & Matsuzaki, M. 1998 MHD pressure drop and heat transfer of lithium single-phase flow in a rectangular channel under transverse magnetic field. Fusion Engng Des. 42, 365372.Google Scholar
Walsh, M. J. & Weinstein, L. M. 1979 Drag and heat-transfer characteristics of small longitudinally ribbed surfaces. AIAA J. 17 (7), 770771.Google Scholar
Yang, S.-J. 2003 Numerical study of heat transfer enhancement in a channel flow using an oscillating vortex generator. Heat Mass Transfer 39, 257265.Google Scholar