Asymptotic structure of magnetohydrodynamic flows in bends

S. Molokov - L. Buhler - R. Stieglitz

Association KfK-EURATOM, Forschungszentrum Karlsruhe GmbH, Institut fur Angewandte Thermo- und Fluid-dynamik, Postfach 3640, D-76021 Karlsruhe, Germany

Abstract
Magnetohydrodynamic flows in bends are considered with reference to toroidal concepts of self-cooled liquid-metal blankets. The ducts composing the bends are electrically conducting and have rectangular cross sections. The applied magnetic field is aligned with the toroidal duct and perpendicular to the radial ducts. For N >> Ha^3/2, where Ha is the Hartmann number and N is the interaction parameter, the magnetohydrodynamic equations can be reduced to a system of partial differential equations governing wall electric potentials and the core pressure (the so-called Core Flow Model, CFM). The system is then solved numerically. The results of the numerical solution of this system show that flows in bends are very sensitive to variation of certain parameters, such as the wall conductance ratio and the aspect ratio of the toroidal duct cross section. Depending on these parameters the flow exhibits a variety of qualitatively different flow patterns. In particular, structures of helical and vortex types are obtained. There is a high-velocity jet at the plasma-facing first wall and a mixing of fluid in the toroidal duct. For N << Ha^3/2 a flow model other than CFM is to be used to describe the flow more adequately. In this model the core is inviscid and inertialess, while the effects of viscosity and inertia affecting the pressure drop are confined to thin boundary and internal layers. The layers which are formed at the walls parallel to the magnetic field often referred to as the side layers) and internal layers are more sensitive to inertia effects than the core, since they may carry volume flux by high-velocity jets. Such a flow pattern has found support in old and especially in recent experiments on bend flows. There is a belief that [he model, in which the concept of the inertial side layer plays a key role, allows one to predict the pressure drop in three-dimensional MHD flows for relatively low values of N (~ 100-1000).