# The velocity profile of laminar MHD flows in circular conducting pipes

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

Research output: Contribution to journalArticlepeer-review

24 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 language English 525-533 9 Theoretical and Computational Fluid Dynamics 23 6 https://doi.org/10.1007/s00162-009-0163-0 Published - Nov 2009 Yes

## Keywords

• Circular pipe
• MHD
• Numerics
• Wall conductivity

## ASJC Scopus subject areas

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