Magnetohydrodynamic flow in a right-angle bend in a strong magnetic field

Abstract

The magnetohydrodynamic (MHD) flow through sharp 90° bends of rectangular cross-section, in which the flow turns from a direction almost perpendicular to the magnetic field to a direction almost aligned with the magnetic field, is investigated experimentally for high values of the Hartmann number M and of the interaction parameter N. The bend flow is characterized by strong three-dimensional effects causing a large pressure drop and large deformations in the velocity profile. Since such bends are basic elements of fusion reactors, the scaling laws of magnetohydrodynamic bends flows with the main flow parameters such as M and N as well as the sensitivity to small magnetic field inclinations are of major importance. The obtained experimental results are compared to those of an asymptotic theory.In the case where one branch of the bend is perfectly aligned with the magnetic field good agreement between the results obtained by the asymptotic model and by the experiments was found at high M ≈ 8 × 10 and N ≈ 105 for pressure as well as for electric potentials on the duct surface. At lower values of N a significant influence of inertia has been detected. The pressure drop due to inertial effects was found to scale with N−1/3. The same – 1/3-power dependency on N has been found in the vicinity of the bend for the electric potentials at walls aligned with the magnetic field. At walls with a significant normal component of the field an influence neither of the Hartmann number nor of the interaction parameter has been found. This suggests that the inertial part of the pressure drop arises from inertial side layers, whereas the core flow remains inertialess and inviscid. A variation of the Hartmann number is of negligible influence compared to inertia effects with respect to pressure drop and surface potential distribution. The viscous part of the pressure drop scales with M−½.Changes of the magnetic field orientation with respect to the bend lead in general to different flow patterns in the duct, because the electric current paths are changed. The inertia–electromagnetic interaction determines the magnitude of the inertial part of the pressure drop, which scales with N−1/3 for any magnetic field orientation. The dependence of the pressure drop on M remains proportional to M−½. With increasing M and N the measured data tend to those predicted by the asymptotic model. Local measurements within the liquid metal exhibit discrepancies with the model predictions for which no adequate explanation has been found. But they show that below a critical interaction parameter flow regions exist in which the flow is time dependent. These regions are highly localized, whereas the flow in the rest of the bend remains steady.