Analysis of liquid metal MHD flow in multiple adjacent ducts using an iterative method to solve the core flow equations

AbstractA computationally fast and efficient method for analyzing MHD flow at high Hartmann number and interaction parameter is presented and used to analyze a multiple duct geometry. This type of geometry is of practical interest in fusion applications. Because the Hartmann number and interaction parameter are generally large in fusion applications, the inertial and viscous terms in the Navier-Stokes equation can often be neglected in the core flow region, making this equation linear. In addition, because the magnetic fields in a fusion reactor vary slowly and the magnetic Reynolds number is small, the induced magnetic field can be neglected. The resulting equations representing core flow have certain characteristics which make it possible to reduce them to two dimensional without losing the three dimensional characteristics.The method which has been developed is an “iterative” method. A velocity profile is assumed, then Ohm's law and the current conservation equation are combined and used to solve for the potential distribution in a plane in the fluid, and in a surface in the duct wall. The potential variation along magnetic field lines is checked, and if necessary, the velocities are adjusted. This procedure is repeated until the potentials along field lines vary to within a specified error.The analysis of the multiple duct geometry shows the importance of global effects. The results of two basic cases are presented. In the first, the average velocity in each duct is the same, but the wall conductance ratios of the walls perpendicular to the magnetic field vary from duct to duct. The total pressure drop in the electrically connected ducts was greater than or equal to the total pressure drop in the same ducts electrically isolated. In addition, the velocity profile in the ducts can be significantly affected by the presence of neighboring ducts. In the second case, the wall conductance ratios are the same for each duct, but the average velocity varies from duct to duct. The overall pressure drop is the same as if the ducts were electrically isolated, but the velocity profile and side layer flow rate can be very different from the electrically isolated case.