Large-Eddy Simulations of a Turbulent Magnetohydrodynamic Channel Flow

摘要

We consider the channel flow of an electrically conducting fluid subjected to a magnetic field. In this framework, numerical predictions are particularly appealing because liquid metals are difficult to study experimentally. In many industrial processes, the magnetic Reynolds number is low. Hence, the applied magnetic field is not perturbed by the flow (quasi-static approximation) and provides an additional force term in the equations of motion. Moreover, the Lorentz force acting on the flow has globally dissipative and anisotropic effects [1, 2]. In the case of low-intensity wall-normal magnetic fields, the turbulent fluctuations tend to be suppressed at the center of the channel (flattening effect) and confined in the near-wall region, where thin layers of high shear (the Hartmann layers) appear [3]. Direct Numerical Simulations (DNS) of magnetohydrodynamic (MHD) flows require accurate numerical discretizations and are thus limited to moderate Reynolds number flows and simple geometries. In Large-Eddy Simulations (LES), the dynamics of the unresolved scales is taken into account through a subgrid-scale model. The applicability of hydrodynamic models to MHD homogeneous turbulence has been proven successful [4]. Our aim is to evaluate the performances of under-resolved DNS of a MHD channel flow (with and without subgrid model). Finite volume (FV) and spectral (PS) results are compared in terms of first and second order statistics. A particular attention is also given to the contribution of the model to the kinetic energy budget.