Study on a falling metal drop in a perpendicular magnetic field
Keywords:Navier-Stokes equations, particle image velocimetry
A theoretical and experimental study of a falling metal drop which interacts with a perpendicular non-localized magnetic field is addressed. As the metal drops traverses the magnetic field, it suffers a braking due to induced electromagnetic effects. An analytical solution for the velocity of the falling drop is obtained thought a balance of forces which affect its motion. A numerical solution from the incompressible Navier-Stokes equations for two phase flows is also obtained. A numerical model for the solution of the incompresible Navier-Stokes for two-phase flows is also implemented. This model is based in the fron-tracking/finite volume method. The simulation allows observe a more detailed dynamics such as the deformation of the drop. Both the theoretical and numerical results validate the experimental data obtained through the Particle Image Velocimetry.
P. A. Davidson, Introduction to Magnetohydrodynamics, (Cambridge University Press 2017).
L. Bühler, C. Mistrangelo and H. J. Brinkmann ¨ Experimental investigation of liquid metal MHD flow entering a flow channel insert. Fusion Engineering and Design, 154 (2020) 111484, https://doi.org/10.1016/j.fusengdes.2020.111484
Z. H. Wang and T. Y. Lei, Liquid metal MHD effect and heat transfer research in a rectangular duct with micro-channels under a magnetic field. International Journal of Thermal Sciences, 155 (2020) 106411, https://doi.org/10.1016/j.ijthermalsci.2020.106411
. L. Bühler, J.Brinkmann and C. Koehly, Experimental study of liquid metal magnetohydrodynamic flows near gaps between flow channel inserts. Fusion Engineering and Design, 146 (2019) 1399, https://doi.org/10.1016/j.fusengdes.2018.11.034
Y. Mori, K. Hijikata, and I. Kuriyama, Experimental Study of Bubble Motion in Mercury With and Without a Magnetic Field. Journal of Heat Transfer, 99 (1977) 404, https://doi.org/10.1115/1.3450710
T. Tagawa, Numerical simulation of two-phase flows in the presence of a magnetic field. Mathematics and Computers in Simulation, 72 (2006) 212, https://doi.org/10.1016/j.matcom.2006.05.040
J. Zhang, and M. J. Ni, Direct simulation of single bubble motion under vertical magnetic field: Paths and wakes. Physics of
Fluids, 26 (2014) 102102, https://doi.org/10.1063/1.4896775
P. Nikos, B. Lefteris, and G. Rui, Deflection of a liquid metal jet/drop in a tokamak environment, Fusion Engineering and Design, 89 (2014) 2930, https://doi.org/10.1016/j.fusengdes.2014.09.004.
T. Wanga, T. Kwokb, C. Zhoua and S. Vaderc, In-situ droplet inspection and closed-loop control system using machine learning for liquid metal jet printing. Journal of Manufacturing Systems, 47 (2018) 83, https://doi.org/10.1016/j.jmsy.2018.04.003.
D. Ehrenreich et al., Nightside condensation of iron in an ultrahotgiant exoplanet. Nature, 580 (2020) 597, https://doi.org/10.1038/s41586-020-2107-1
J. Walker and W.M. Wells, Drag force on a conductive spherical drop in a nonuniform magnetic field.ORNL/TM-6976 (Sept. 1979).
T. Tagawa, Numerical Simulation of a Falling Droplet of Liquid Metal into a Liquid Layer in the Presence of a Uniform Vertical
Magnetic Field. ISIJ International, 45 (2005) 954, https://doi.org/10.2355/isijinternational.45.954
S. Wu, J. Zhang and M.J. Ni, Numerical study of a single droplet falling through a nonuniform horizontal magnetic field with a constant gradient. Int. J. Multiph. Flow, 110 (2019) 18, https://doi.org/10.1016/j.ijmultiphaseflow.2018.08.006
B. Gol, M.E. Kurdzinski, F.J. Tovar-Lopez, P. Petersen, A. Mitchell and K. Khoshmanesh Hydrodynamic directional control of liquid metal droplets within a microfluidic flow focusing system. Appl. Phys. Lett, 108 (2016) 164101, https://doi.org/10.1063/1.4947272
W. Thielicke and E.-J. Stamhuis, PIVlab - Time-Resolved Digital Particle Image Velocimetry Tool for MATLAB, Version 1.41. (2014), http://dx.doi.org/10.6084/m9.figshare.1092508
A. Figueroa, F. Demiaux, S. Cuevas and E. Ramos, Electrically driven vortices in a weak dipolar magnetic field in a shallow electrolytic layer. J. Fluid Mech. 641 (2009) 245, https://doi.org/10.1017/S0022112009991868
G. Tryggvason, R. Scardovelli, S. Zaleski, Direct numerical simulations of gas-liquid multiphase flows, Cambridge Press, 1st edn., 2011.
S. Piedra, E. Ramos and J.-R. Herrera, Dynamics of twodimensional bubbles. Phys. Rev. E., 91 (2015) 063013, https://doi.org/10.1103/PhysRevE.91.063013
Moreau R. (1990) Magnetohydrodynamics, Kluwer.
S. A. Morsi and A. J. Alexander, An investigation of particle trajectories in two-phase flow systems. J. Fluid Mech., 55 (1971) 193, https://doi.org/10.1017/S0022112072001806
How to Cite
Copyright (c) 2022 Fernando Garzón, Guillermo Ramirez, Saúl Piedra, Aldo Figueroa
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Authors retain copyright and grant the Revista Mexicana de Física right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.