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Numerical simulations of magnetohydrodynamic flows driven by a moving permanent magnet
Phys. Rev. Fluids 1, 043601 – Published 1 August, 2016
DOI: https://doi.org/10.1103/PhysRevFluids.1.043601
Abstract
We present results from numerical reconstructions of magnetic obstacle experiments performed in liquid metal flows. The experimental setup consists of an open rectangular container filled with a thin layer of liquid metal (GaInSn). A permanent magnet is installed on a rail beneath the container and is moved with a constant velocity , which in turn induces a flow inside the liquid metal due to Lorentz forces. The setup allows experiments in a parameter range that is accessible by direct numerical simulations (DNS). We present results from realizations with four different parameter sets, covering flows with stable stationary vortex structures in the reference system of the moving magnet as well as time-dependent flow regimes. Although the liquid metal layer is very thin, the flow shows a highly three-dimensional character in the near and in the far wake of the magnetic obstacle. We conclude that the streamline visualization in the experiment (using gas bubbles at the surface of the liquid metal layer) is insufficient to picture the flow structure occurring in the liquid metal. To underpin our conclusions, we introduce a modified numerical model which aims to mimic the movement of these gas bubbles. Although this model is a strong simplification of the highly complicated behavior of bubbles at a fluid-fluid interface, it captures the main effects and provides a good reproduction of the experimental results. Furthermore, transient effects are investigated when the flow is initiated, i.e., when the magnet approaches the container and crosses its front wall. We conclude that the process of vortex formation is accompanied by a decrease of the streamwise component of the Lorentz force compared to the time when the fluid is still quiescent. This decrease occurs only for flows with stable vortex structures, which might be of interest for practical applications like Lorentz force velocimetry. The Lorentz forces obtained from our DNS are in good agreement with the values measured in experiment.
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References (23)
- P. A. Davidson, An Introduction to Magnetohydrodynamics (Cambridge University Press, Cambridge, U.K., 2001).
- J. A. Shercliff, A Textbook of Magnetohydrodynamics (Pergamon Press, Oxford, U.K., 1965).
- P. H. Roberts, An Introduction to Magnetohydrodynamics (Longman, London, U.K., 1967).
- A. Thess, E. V. Votyakov, and Yu. Kolesnikov, Lorentz Force Velocimetry, Phys. Rev. Lett. 96, 164501 (2006).
- A. Thess, E. Votyakov, B. Knaepen, and O. Zikanov, Theory of the Lorentz force flowmeter, New J. Phys. 9, 299 (2007).
- E. V. Votyakov, E. Zienicke, and Y. B. Kolesnikov, Constrained flow around a magnetic obstacle, J. Fluid Mech. 610, 131 (2008).
- E. V. Votyakov, Yu. Kolesnikov, O. Andreev, E. Zienicke, and A. Thess, Structure of the Wake of a Magnetic Obstacle, Phys. Rev. Lett. 98, 144504 (2007).
- S. Cuevas, S. Smolentsev, and M. A. Abdou, On the flow past a magnetic obstacle, J. Fluid Mech. 553, 227 (2006).
- S. Kenjereš, Energy spectra and turbulence generation in the wake of magnetic obstacles, Phys. Fluids 24, 115111 (2012).
- S. Tympel, T. Boeck, and J. Schumacher, Laminar and transitional liquid metal duct flow near a magnetic point dipole, J. Fluid Mech. 735, 553 (2013).
- E. V. Votyakov and S. C. Kassinos, On the analogy between streamlined magnetic and solid obstacles, Phys. Fluids 21, 097102 (2009).
- A. Beltrán, E. Ramos, S. Cuevas, and M. Brøns, Bifurcation analysis in a vortex flow generated by an oscillatory magnetic obstacle, Phys. Rev. E 81, 036309 (2010).
- F. Samsami, Y. Kolesnikov, and A. Thess, Vortex dynamics in the wake of a magnetic obstacle, J. Visualization 17, 245 (2014).
- Y. Kolesnikov and A. Thess, Experimental investigation of liquid metal flow across a nonhomogeneous magnetic field, in 6th International Conference on Electromagnetic Processing of Materials, 19–23 October 2009, Dresden, Germany, edited by G. Gerbeth and Y. Fautrelle (2009).
- D. Krasnov, O. Zikanov, and T. Boeck, Comparative study of finite difference approaches in simulation of magnetohydrodynamic turbulence at low magnetic Reynolds number, Comput. Fluids 50, 46 (2011).
- E. P. Furlani, Permanent Magnet and Electromechanical Devices: Materials, Analysis, and Applications (Academic Press, London, U.K., 2001).
- Y. Morinishi, T. S. Lund, O. V. Vasilyev, and P. Moin, Fully conservative higher order finite difference schemes for incompressible flow, J. Comput. Phys. 143, 90 (1998).
- O. Zikanov, D. Krasnov, Y. Li, T. Boeck, and A. Thess, Patterned turbulence in spatially evolving magnetohydrodynamic duct and pipe flows, Theor. Comput. Fluid Dyn. 28, 319 (2013).
- J. C. Adams, P. Swarztrauber, and R. Sweet, Efficient fortran subprograms for the solution of separable elliptic partial differential equations, https://www2.cisl.ucar.edu/resources/legacy/fishpack/ (1999).
- J. C. Adams, Mudpack: Multigrid software for elliptic partial differential equations, https://www2.cisl.ucar.edu/resources/legacy/mudpack/ (1999).
- J. Jeong and F. Hussain, On the identification of a vortex, J. Fluid Mech. 285, 69 (1995).
- E. Nishikata, T. Ishii, and T. Ohta, Viscosities of aqueous hydrochloric acid solutions, and densities and viscosities of aqueous hydroiodic acid solutions, J. Chem. Eng. Data 26, 254 (1981).
- G. Alcalá and S. Cuevas, Surface waves generated on electrolytes by a traveling electromagnetic force, in Experimental and Computational Fluid Mechanics (Springer, Berlin, Germany, 2014), p. 369.