The velocity profile of laminar MHD flows in circular conducting pipes

S. Vantieghem, X. Albets-Chico, B. Knaepen

Research output: Contribution to journalArticle

23 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)525-533
Number of pages9
JournalTheoretical and Computational Fluid Dynamics
Volume23
Issue number6
DOIs
Publication statusPublished - Nov 2009
Externally publishedYes

Keywords

  • Circular pipe
  • MHD
  • Numerics
  • Wall conductivity

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Fluid Flow and Transfer Processes
  • Engineering(all)
  • Computational Mechanics

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