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Electromagnetic and hydrodynamic transient coupling

Linards Goldsteins, CEA

In this model transient electromagnetics and hydrodynamics are coupled
in a so-called strong MHD coupling in a 2D axisymmetric geometry, with
k-epsilon RANS turbulence equations for the fluid flow.

This model focuses on the strong coupling process involved and no
specific checking regarding solver or mesh convergence analysis has been
performed here. Moreover, there is no special treatment of the Hartmann
boundary layer (interaction between the fluid boundary layer and the
transverse magnetic field). Default wall functions available with
k-epsilon model have been used, together with a continuity in the
magnetic vector potential Aphi at the wall. Aphi is in this model not
modified by the turbulent boundary layer.
To be successful, one should take into account that good initial
conditions for the fluid flow must be provided to the time-dependent
solver. This process makes use of 5 stationary steps.
It is possible to use fewer stationary steps, however it may cause more
convergence errors (Tfails and NLfails) or even not converge at all.

Also, one should adjust the time-dependent solver by segregating the
magnetic vector potential Aphi in a separated segregated step. Sometimes
it might be useful also to exclude algebraic degrees of freedom from the
evauation of error in the time-dependent algorithm. This is done in the
advanced options of the solver.

One should note that the conductivity of mercury if significantly
increased in order to better illustrate the physical phenomena that
appears at this moderate magnetic Reynolds number. Highly conducting
flow "takes" magnetic field in the direction of the flow and therefore
it is not symetric as it would be in case of zero velocity (magnetic
Reynods number 0). The full time-dependent solution reveals the
behaviour in time of this kind of strong coupling, which is not
frequently described in the literature.

Many thanks to Eric Favre, from COMSOL France, for his technical support
associated with this case.

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