The velocity profile of laminar MHD flows in circular conducting pipes

We present numerical simulations without modeling of an incompressible, laminar, unidirectional circular pipe flow of an electrically conducting fluid under the influence of a uniform transverse magnetic field. Our computations are performed using a finite-volume code that uses a charge-conserving formulation [called current-conservative formulation in references (Ni et al J Comput Phys 221(1):174-204, 2007, Ni et al J Comput Phys 227(1):205-228, 2007)]. Using high resolution unstructured meshes, we consider Hartmann numbers up to 3000 and various values of the wall conductance ratio c. In the limit $${c{\ll}{\rm Ha}^{-1}}$$ (insulating wall), our results are in excellent agreement with the so-called asymptotic solution (Shercliff J Fluid Mech 1:644-666, 1956). For higher values of the wall conductance ratio, a discrepancy with the asymptotic solution is observed and we exhibit regions of velocity overspeed in the Roberts layers. We characterise these overspeed regions as a function of the wall conductance ratio and the Hartmann number; a set of scaling laws is derived that is coherent with existing asymptotic analysis. © 2009 Springer-Verlag.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Turbulent effects of liquid metal flow under strong fringing magnetic fields

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Numerical simulation of a liquid-metal flow in a poorly conducting pipe subjected to a strong fringing magnetic field

Using high resolution numerical simulations, we study the flow of a liquid metal in a pipe subjected to an intense decreasing magnetic field (fringing magnetic field). The chosen flow parameters are such that our study is directly relevant for the design of fusion breeder blankets. Our objectives are to provide a detailed description of the numerical method and of the results for benchmarking purposes but also to assess the efficiency of the so-called "core flow approximation" that models liquid-metal flows under the influence of intense magnetic fields. Our results are in excellent agreement with available experimental measurements. As far as the pressure drop is concerned, they also match perfectly the predictions of the core flow approximation. On the other hand, the velocity profiles obtained in our numerical simulations show a significant departure from this approximation beyond the inflection point of the magnetic field's profile. By plotting the momentum budget of the MHD equations, we provide evidence that this discrepancy can be attributed to the role of inertia that is neglected in the core flow approximation. We also consider a case with vanishing outlet magnetic field and we briefly illustrate the transition to turbulence arising in the outlet region of the pipe. © 2011 American Institute of Physics.SCOPUS: ar.jinfo:eu-repo/semantics/publishe