ALBERT

Description: 〈div data-abstract-type="normal"〉〈p〉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 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190619122052543-0765:S0022112019004233:S0022112019004233_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 without a magnetic field have a symmetry plane. An angle 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190619122052543-0765:S0022112019004233:S0022112019004233_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 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 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190619122052543-0765:S0022112019004233:S0022112019004233_inline3.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. 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 (〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190619122052543-0765:S0022112019004233:S0022112019004233_inline4.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉) corresponds to a lower Reynolds number with a lower 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190619122052543-0765:S0022112019004233:S0022112019004233_inline5.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 value. Furthermore, the drag coefficient is proportional to 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190619122052543-0765:S0022112019004233:S0022112019004233_inline6.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 for weak magnetic fields or to 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190619122052543-0765:S0022112019004233:S0022112019004233_inline7.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 for strong magnetic fields, where the threshold value between these two regimes is approximately 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190619122052543-0765:S0022112019004233:S0022112019004233_inline8.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉.〈/p〉〈/div〉