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Wake structure of laminar flow past a sphere under the influence of a transverse magnetic field

Published online by Cambridge University Press:  20 June 2019

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, PR China
Nian-Mei Zhang
Affiliation:
School of Engineering Science, University of Chinese Academy of Sciences, Beijing 101408, PR China
Ming-Jiu Ni*
Affiliation:
School of Engineering Science, University of Chinese Academy of Sciences, Beijing 101408, PR China
*
†Email address for correspondence: mjni@ucas.ac.cn
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Abstract

The wake structure of an incompressible, conducting, viscous fluid past an electrically insulating sphere affected by a transverse magnetic field is investigated numerically over flow regimes including steady and unsteady laminar flows at Reynolds numbers up to 300. For a steady axisymmetric flow affected by a transverse magnetic field, the wake structure is deemed to be a double plane symmetric state. For a periodic flow, unsteady vortex shedding is first suppressed and transitions to a steady plane symmetric state and then to a double plane symmetric pattern. Wake structures in the range $210<Re\leqslant 300$ without a magnetic field have a symmetry plane. An angle $\unicode[STIX]{x1D703}$ exists between the orientation of this symmetry plane and the imposed transverse magnetic field. For a given transverse magnetic field, the final wake structure is found to be independent of the initial flow configuration with a different angle $\unicode[STIX]{x1D703}$. However, the orientation of the symmetry plane tends to be perpendicular to the magnetic field, which implies that the transverse magnetic field can control the orientation of the wake structure of a free-moving sphere and change the direction of its horizontal motion by a field–wake–trajectory control mechanism. An interesting ‘reversion phenomenon’ is found, where the wake structure of the sphere at a higher Reynolds number and a certain magnetic interaction parameter ($N$) corresponds to a lower Reynolds number with a lower $N$ value. Furthermore, the drag coefficient is proportional to $N^{2/3}$ for weak magnetic fields or to $N^{1/2}$ for strong magnetic fields, where the threshold value between these two regimes is approximately $N=4$.

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 873 , 25 August 2019 , pp. 151 - 173
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Copyright
© 2019 Cambridge University Press 

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