The subgrid-scale ͑SGS͒ models based on the coherent structure in grid-scale flow fields are proposed and are applied to ͑non-͒rotating homogeneous turbulences and turbulent channel flows. The eddy viscosity is modeled by a coherent structure function ͑CSF͒ with a fixed model-parameter. The CSF is defined as the second invariant normalized by the magnitude of a velocity gradient tensor and plays a role of wall damping. The probability density function of the CSF is non-Gaussian showing an intermittency effect. The model parameter is locally determined, and it is always positive and has a small variance. These models satisfy a correct asymptotic behavior to a wall for incompressible flows. It is shown that the SGS models with an energy-decay suppression function which indicates also a pseudo-backscatter are consistent with the asymptotic material frame indifference in a rotating frame. Since the CSF characterizing turbulent flows has relation to the SGS energy dissipation, the present SGS models are applicable not only to ͑non-͒rotating homogeneous and shear turbulences but also to laminar flows. The proposed models have almost the same performance as the dynamic Smagorinsky model for ͑non-͒rotating homogeneous turbulences and turbulent channel flows, but these models do not need to average or clip the model parameter, use an explicit wall-damping function, or change the fixed-parameter, so that they are suitable for engineering applications of large-eddy simulation.
For turbulent channel flows with a uniform magnetic field perpendicular to insulated walls, the performance of the coherent structure Smagorinsky model ͑CSM͒ is investigated in comparison to the Smagorinsky model ͑SM͒ and the dynamic Smagorinsky model ͑DSM͒. 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 ͑MHD͒ 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 field͒ 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.
Turbulent duct flows in a uniform magnetic field are examined at low magnetic Reynolds number. Large-eddy simulation is conducted to reveal a sidewall effect on the skin friction. The duct has a square cross section and entirely insulated walls. The duct flow has two kinds of boundary layers: Hartmann layer and sidewall layer. The Hartmann layer is located on the wall perpendicular to the magnetic field, while the sidewall layer exists on the wall parallel to the magnetic field. As the magnetic field increases in the range of turbulent flows, the Hartmann layer becomes thin because of the "Hartmann flattening"-a flattening effect of the flow by the Lorentz force. The sidewall layer, however, becomes thick because of the turbulence suppression until the laminarization takes place. When the Reynolds number, Re, based on the hydraulic diameter, molecular viscosity, and bulk velocity is 5 300, the Hartmann and sidewall layers are laminarized at the same Hartmann number that is proportional to the magnetic field. When the Hartmann layer is laminarized at Re = 29 000, the sidewall layer remains turbulence. This is due to a sidewall effect and is the condition that a local maximum takes place in the skin friction profile. When the sidewall layer is laminarized, the flow totally becomes laminar and the skin friction becomes minimum.
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