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Instability and transition of a vertical ascension or fall of a free sphere affected by a vertical magnetic field

Published online by Cambridge University Press:  16 November 2018

Jun-Hua Pan ,
Nian-Mei Zhang  and
Ming-Jiu Ni Open the ORCID record for Ming-Jiu Ni [Opens in a new window]
Jun-Hua Pan
Affiliation:
School of Engineering Science, University of Chinese Academy of Sciences, Beijing 101408, China
Nian-Mei Zhang
Affiliation:
School of Engineering Science, University of Chinese Academy of Sciences, Beijing 101408, China
Ming-Jiu Ni*
Affiliation:
School of Engineering Science, University of Chinese Academy of Sciences, Beijing 101408, China
*
†Email address for correspondence: mjni@ucas.ac.cn
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Abstract

When the Galileo number is below the first bifurcation, the instability and transition of a vertical ascension or the fall of a free sphere affected by a vertical magnetic field are investigated numerically. A compact model is used to explain that the magnetic field can destabilize the fluid–solid system. When the interaction parameter exceeds a critical value, the sphere trajectory is transitioned from a steady vertical trajectory to a steady oblique one. Furthermore, the trajectory will remain vertical at a sufficiently large magnetic field because of a double effect of the magnetic field on the fluid–solid system. Under the influence of an external vertical magnetic field, four wake patterns at the rear of the sphere are found and the physical behaviour of the free sphere is independent of the density ratio. The wake or trajectory of the free sphere is only determined by the Galileo number $G$ and the interaction parameter $N$. A close relationship between the streamwise vorticity and the sphere motion is found. An interesting ‘agglomeration phenomenon’ is also found, which shows that the vertical velocities are agglomerated into a point for a certain magnetic field regardless of the Galileo number and satisfy a scaling law $V_{z}\sim N^{-1/4}$, when $N>1$. The principal results of the present work are summarized in a map of regimes in the $\{G,N\}$ plane.

JFM classification

Materials Processing Flows: Materials Processing Flows Multiphase and Particle-laden Flows: Multiphase and Particle-laden Flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 859 , 25 January 2019 , pp. 33 - 48
Copyright
© 2018 Cambridge University Press 

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