Magneto-Fluid-Mechanic Channel Flow. II. Theory

Abstract

A semi-empirical theoretical analysis is presented describing the fully established turbulent channel flow of an electrically conducting fluid in the presence of a transverse and uniform magnetic field. The channel is assumed to be electrically insulated and of such geometry that two-dimensional flow prevails. The magnetic Reynolds number is assumed to be small so that the distortion of the externally imposed magnetic field is negligible. The paper establishes that a straightforward generalization of Prandtl's mixing length concept providing for the damping of the turbulent fluctuation is sufficient in predicting skin friction coefficients and velocity profiles over the whole range of Reynolds and Hartmann numbers for which experimental data are available.

Transport and deposition of neutral particles in magnetohydrodynamic turbulent channel flows at low magnetic Reynolds numbers

“…For the case of the wall-normal magnetic field, this is due to the small value of the Stuart number studied. Qualitatively similar results have been found both experimentally and numerically (Lykoudis and Brouillette, 1968;Sarris et al, 2007;Krasnov et al, 2008).…”

“…A significant advance in the existing knowledge of MHD flows has been achieved by experiments (Lykoudis and Brouillette, 1968;Moresco and Alboussière, 2004) and by direct numerical simulations (DNS) in homogeneous turbulence (Zikanov and Thess, 1998;Kassinos et al, 2006Kassinos et al, , 2007, in turbulent channel (Lee and Choi, 2001;Boeck et al, 2007;Shatrov and Gerbeth, 2007;Krasnov et al, 2008) or pipe flows (Satake et al, 2002), and in natural convection in cylindrical cavities (Kakarantzas et al, 2009;Sarris et al, 2010) at low magnetic Reynolds numbers. A summary of related studies is provided by Knaepen and Moreau (2008).…”

A direct-numerical-simulation-based second-moment closure for turbulent magnetohydrodynamic flows

“…Among the first attempts to model magnetohydrodynamic ͑MHD͒ wall-bounded turbulent flows was reported by Lykoudis and Brouillette 1 where the mixing-length model was modified in order to introduce additional damping of turbulence due to the magnetic field. In more recent studies, the two-equations k -and the second-moment closures have been used as standard framework for modeling of additional electromagnetic effects on turbulence.…”

A new forward-backward sweeping parabolized Navier-Stokes algorithm with application to magnetohydrodynamic flows

“…This modification for MHD flows is due to Lykoudis [33], and only the expression for turbulent viscosity in the inner layer is changed.…”

“…Upstream elliptic effects can be accounted for by using multiple streamwise sweeps with either the IPNS, TIPNS, or FBIPNS algorithms. Turbulence has been included by modifying the BaldwinLomax turbulence model [32] to account for MHD effects using the approach of Lykoudis [33].…”