Large-eddy simulations of the turbulent Hartmann flow close to the transitional regime

Abstract

A series of large-eddy simulations (LES) of turbulent and transitional channel flows of a conductive fluid under the effect of a uniform magnetic field applied in the wall-normal direction, usually referred to as Hartmann flows, are performed using the dynamic Smagorinsky model. The flow is characterized by the hydrodynamic Reynolds number Re and the Hartmann number Ha that is related to the strength of the external magnetic field. Previous measurements and works on stability analysis have shown that a critical modified Reynolds number, based on the Hartmann layer thickness R=Re∕Ha, exists at approximately R=380. Here, the LES are used to investigate the laminarization of flow when decreasing R. Also, similarities of the turbulent flows are explored for different values of Re and Ha but the same values of R or of the interaction parameter N=Ha2∕Re. The LES confirm that R is the relevant parameter that describes the transition and a critical Reynolds number for relaminarization is observed at R≈500. However, for turbulent flows at moderate values of the Ha and Re as considered in this study, the similarity with respect to N appears to be better than for R, especially for the first order statistics. Finally, the importance of the dynamic Smagorinsky model as the Hartmann number increases is discussed.