For turbulent channel flows with a uniform magnetic field perpendicular to insulated walls, the performance of the coherent structure Smagorinsky model (CSM) is investigated in comparison to the Smagorinsky model (SM) and the dynamic Smagorinsky model (DSM). The Lorentz force acts against a streamwise flow. The effect of the Hartmann flattening leads to an increase in the wall shear stress, so that the skin friction coefficient increases. In contrast, the turbulence suppression by the magnetic field results in a decrease of the Reynolds shear stress near the wall, so that the skin friction coefficient decreases. As the magnetic field increases, a turbulent magnetohydrodynamic (MHD) flow transits to a laminar MHD flow at a critical Hartmann number. The CSM predicts a higher transition Hartmann number than the DSM and SM, because the model parameter of the CSM is locally determined based on coherent structures and the fluctuations are reflected in the shear stress. On the other hand, the model parameter of the DSM is averaged in the homogeneous directions, so that the shear stress is somewhat underestimated for the subcritical Hartmann number. The SM with a model constant and a wall damping function of the Van Driest type reproduces the laminar MHD flow at the lowest transition Hartmann number, because the model parameter (which does not change in the magnetic field) provides significant energy dissipation. Moreover, the CSM and DSM can reproduce properly the laminar MHD flow at high Hartmann number, because the model parameters of the CSM and DSM are drastically damped near the wall and the Reynolds shear stresses are suppressed to zero. The skin friction coefficients predicted by the CSM and DSM agree with the "two-dimensional" laminar solution, whereas the SM gives higher values than the laminar solution. The coherent structures become large and align themselves along the magnetic field in the transition to the laminar MHD flow.
ASJC Scopus subject areas