Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-19T16:44:41.306Z Has data issue: false hasContentIssue false
  • English
  • Français

Decay of turbulence in a liquid metal duct flow with transverse magnetic field

Published online by Cambridge University Press:  26 March 2019

Oleg Zikanov Open the ORCID record for Oleg Zikanov [Opens in a new window] ,
Dmitry Krasnov ,
Thomas Boeck  and
Semion Sukoriansky
Oleg Zikanov*
Affiliation:
Department of Mechanical Engineering, University of Michigan, Dearborn, MI 48128-1491, USA
Dmitry Krasnov
Affiliation:
Institute for Thermodynamics and Fluid Mechanics, Technische Universität Ilmenau, PO Box 100565, D-98684 Ilmenau, Germany
Thomas Boeck
Affiliation:
Institute for Thermodynamics and Fluid Mechanics, Technische Universität Ilmenau, PO Box 100565, D-98684 Ilmenau, Germany
Semion Sukoriansky
Affiliation:
Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beer-Sheva, 84105, Israel
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Decay of honeycomb-generated turbulence in a duct with a static transverse magnetic field is studied via direct numerical simulations. The simulations follow the revealing experimental study of Sukoriansky et al. (Exp. Fluids, vol. 4 (1), 1986, pp. 11–16), in particular the paradoxical observation of high-amplitude velocity fluctuations, which exist in the downstream portion of the flow when the strong transverse magnetic field is imposed in the entire duct including the honeycomb exit, but not in other configurations. It is shown that the fluctuations are caused by the large-scale quasi-two-dimensional structures forming in the flow at the initial stages of the decay and surviving the magnetic suppression. Statistical turbulence properties, such as the energy decay curves, two-point correlations and typical length scales are computed. The study demonstrates that turbulence decay in the presence of a magnetic field is a complex phenomenon critically depending on the state of the flow at the moment the field is introduced.

JFM classification

MHD and Electrohydrodynamics: High-Hartmann-number flows MHD and Electrohydrodynamics: MHD turbulence Turbulent Flows: Turbulence simulation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 867 , 25 May 2019 , pp. 661 - 690
Copyright
© 2019 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adams, J. C., Swarztrauber, P. & Sweet, R. 1999 Efficient fortran subprograms for the solution of separable elliptic partial differential equations. In Elliptic Problem Solvers, pp. 187–190. Academic. http://www.cisl.ucar.edu/css/software/fishpack/.Google Scholar
Alemany, A., Moreau, R., Sulem, P. L. & Frisch, U. 1979 Influence of an external magnetic field on homogeneous MHD turbulence. J. Méc. 18, 277–313.Google Scholar
Andreev, O., Kolesnikov, Y. & Thess, A. 2006 Experimental study of liquid metal channel flow under the influence of a nonuniform magnetic field. Phys. Fluids 18 (6), 65108.Google Scholar
Boeck, T., Krasnov, D., Thess, A. & Zikanov, O. 2008 Large-scale intermittency of liquid-metal channel flow in a magnetic field. Phys. Rev. Lett. 101, 244501.Google Scholar
Braiden, L., Krasnov, D., Molokov, S., Boeck, T. & Bühler, L. 2016 Transition to turbulence in Hunt’s flow in a moderate magnetic field. Europhys. Lett. 115 (4), 084501.Google Scholar
Branover, H. 1978 Magnetohydrodynamic Flow in Ducts. Wiley.Google Scholar
Branover, H. H., Gelfgat, Y. M., Kit, L. G. & Platnieks, I. A. 1970 Effect of a transverse magnetic field on the intensity profiles of turbulent velocity fluctuations in a channel of rectangular cross section. Magnetohydrodynamics 6, 336–342.Google Scholar
Brethouwer, G., Duguet, Y. & Schlatter, P. 2012 Turbulent-laminar coexistence in wall flows with Coriolis, buoyancy or Lorentz forces. J. Fluid Mech. 704, 137–172.Google Scholar
Burattini, P., Zikanov, O. & Knaepen, B. 2010 Decay of magnetohydrodynamic turbulence at low magnetic Reynolds number. J. Fluid Mech. 657, 502–538.Google Scholar
Davidson, P. 1997 The role of angular momentum in the magnetic damping of turbulence. J. Fluid Mech. 336, 123–150.Google Scholar
Davidson, P. A. 2016 Introduction to Magnetohydrodynamics. Cambridge University Press.Google Scholar
Favier, B., Godeferd, F. S., Cambon, C. & Delache, A. 2010 On the two-dimensionalization of quasistatic magnetohydrodynamic turbulence. Phys. Fluids 22 (7), 75104.Google Scholar
Favier, B., Godeferd, F. S., Cambon, C., Delache, A. & Bos, W. J. T. 2011 Quasi-static magnetohydrodynamic turbulence at high Reynolds number. J. Fluid Mech. 681, 434–461.Google Scholar
Kim, J. & Choi, H. 2009 Large eddy simulation of a circular jet: effect of inflow conditions on the near field. J. Fluid Mech. 620, 383–411.Google Scholar
Kljukin, A. A. & Kolesnikov, J. B. 1989 MHD turbulence decay behind spatial grids. In Liquid Metal Magnetohydrodynamics, pp. 153–159. Springer.Google Scholar
Knaepen, B., Kassinos, S. & Carati, D. 2004 Magnetohydrodynamic turbulence at moderate magnetic Reynolds number. J. Fluid Mech. 513, 199–220.Google Scholar
Knaepen, B. & Moin, P. 2004 Large-eddy simulation of conductive flows at low magnetic Reynolds number. Phys. Fluids 16 (5), 1255.Google Scholar
Kobayashi, H., Shionoya, H. & Okuno, Y. 2012 Turbulent duct flows in a liquid metal magnetohydrodynamic power generator. J. Fluid Mech. 713, 243–270.Google Scholar
Kolesnikov, Y. B. & Tsinober, A. B. 1974 Experimental investigation of two-dimensional turbulence behind a grid. Fluid Dyn. 9 (4), 621–624.Google Scholar
Krasnov, D., Thess, A., Boeck, T., Zhao, Y. & Zikanov, O. 2013 Patterned turbulence in liquid metal flow: computational reconstruction of the Hartmann experiment. Phys. Rev. Lett. 110, 084501.Google Scholar
Krasnov, D., Zikanov, O. & Boeck, T. 2011 Comparative study of finite difference approaches to simulation of magnetohydrodynamic turbulence at low magnetic Reynolds number. Comput. Fluids 50, 46–59.Google Scholar
Krasnov, D., Zikanov, O., Schumacher, J. & Boeck, T. 2008 Magnetohydrodynamic turbulence in a channel with spanwise magnetic field. Phys. Fluids 20 (9), 095105.Google Scholar
Krasnov, D. S., Zikanov, O. & Boeck, T. 2012 Numerical study of magnetohydrodynamic duct flow at high Reynolds and Hartmann numbers. J. Fluid Mech. 704, 421–446.Google Scholar
Li, Y. & Zikanov, O. 2013 Laminar pipe flow at the entrance into transverse magnetic field. Fusion Engng Des. 88 (4), 195–201.Google Scholar
Moffatt, K. 1967 On the suppression of turbulence by a uniform magnetic field. J. Fluid Mech. 23, 571–592.Google Scholar
Müller, U. & Bühler, L. 2001 Magnetohydrodynamics in Channels and Containers. Springer.Google Scholar
Pothérat, A. & Klein, R. 2014 Why, how and when MHD turbulence at low Rm becomes three-dimensional. J. Fluid Mech. 761, 168–205.Google Scholar
Pothérat, A. & Klein, R. 2017 Do magnetic fields enhance turbulence at low magnetic Reynolds number? Phys. Rev. Fluids 2 (6), 063702.Google Scholar
Reddy, K. S. & Verma, M. K. 2014 Strong anisotropy in quasi-static magnetohydrodynamic turbulence for high interaction parameters. Phys. Fluids 26 (2), 025109.Google Scholar
Schumann, U. 1976 Numerical simulation of the transition from three- to two-dimensional turbulence under a uniform magnetic field. J. Fluid Mech. 74, 31–58.Google Scholar
Sommeria, J. & Moreau, R. 1982 Why, how and when MHD-turbulence becomes two-dimensional. J. Fluid Mech. 118, 507–518.Google Scholar
Sukoriansky, S., Zilberman, I. & Branover, H. 1986 Experimental studies of turbulence in mercury flows with transverse magnetic fields. Exp. Fluids 4 (1), 11–16.Google Scholar
Thess, A. & Zikanov, O. 2007 Transition from two-dimensional to three-dimensional magnetohydrodynamic turbulence. J. Fluid Mech. 579, 383–412.Google Scholar
Verma, M. K. 2017 Anisotropy in quasi-static magnetohydrodynamic turbulence. Rep. Prog. Phys. 80 (8), 087001.Google Scholar
Verma, M. K. & Reddy, K. S. 2015 Modeling quasi-static magnetohydrodynamic turbulence with variable energy flux. Phys. Fluids 27 (2), 025114.Google Scholar
Vorobev, A. & Zikanov, O. 2007 Smagorinsky constant in LES modeling of anisotropic MHD turbulence. Theor. Comput. Fluid Dyn. 22 (3–4), 317–325.Google Scholar
Vorobev, A., Zikanov, O., Davidson, P. A. & Knaepen, B. 2005 Anisotropy of magnetohydrodynamic turbulence at low magnetic Reynolds number. Phys. Fluids 17 (12), 125105.Google Scholar
Voronchikhin, V. A., Genin, L. G., Levin, V. B. & Sviridov, V. G. 1985 Experimental investigation of grid turbulence decay in a uniform magnetic field. Magnetohydrodynamics 21, 131–134.Google Scholar
Votsish, A. D. & Kolesnikov, Y. B. 1976a Spatial correlation and vorticity in two-dimensional homogeneous turbulence. Magnetohydrodynamics 12, 271–274.Google Scholar
Votsish, A. D. & Kolesnikov, Y. B. 1976b Study of transition from three-dimensional to two-dimensional turbulence in a magnetic field. Magnetohydrodynamics 12, 378–379.Google Scholar
Votyakov, E. V., Kassinos, S. C. & Albets-Chico, X. 2009 Analytic models of heterogenous magnetic fields for liquid metal flow simulations. Theor. Comput. Fluid Dyn. 23, 571–578.Google Scholar
Zikanov, O., Krasnov, D., Boeck, T., Thess, A. & Rossi, M. 2014a Laminar-turbulent transition in magnetohydrodynamic duct, pipe, and channel flows. Appl. Mech. Rev. 66 (3), 030802.Google Scholar
Zikanov, O., Krasnov, D., Li, Y., Boeck, T. & Thess, A. 2014b Patterned turbulence in spatially evolving magnetohydrodynamic tube flows. Theor. Comput. Fluid Dyn. 28 (3), 319–334.Google Scholar
Zikanov, O., Listratov, Y. & Sviridov, V. G. 2013 Natural convection in horizontal pipe flow with strong transverse magnetic field. J. Fluid Mech. 720, 486–516.Google Scholar
Zikanov, O. & Thess, A. 1998 Direct numerical simulation of forced MHD turbulence at low magnetic Reynolds number. J. Fluid Mech. 358, 299–333.Google Scholar