The velocity profile of laminar MHD flows in circular conducting pipes

Original Article

DOI: 10.1007/s00162-009-0163-0

Cite this article as:
Vantieghem, S., Albets-Chico, X. & Knaepen, B. Theor. Comput. Fluid Dyn. (2009) 23: 525. doi:10.1007/s00162-009-0163-0

Abstract

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.

Keywords

MHDNumericsCircular pipeWall conductivity

PACS

47.65.-d47.11.Fg

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Physique statistique et des plasmas (PSP), Faculté des SciencesUniversité Libre de Bruxelles (ULB)BrusselsBelgium