The Stability of Flow Between Concentric Cylindrical Surfaces with a Circular Magnetic Field

摘要

The mathematical formulation of the stability problem leads to a number of special cases, depending upon whether the walls of the containing cylinders are conductors or non-conductors relative to the fluid; and for the Taylor problem depending upon whether the cylinders are rotating in the same or opposite directions. The known results are briefly summarized for the purpose of clarity and completeness. Also, new re sults for the Dean problem with conducting walls and with non-conducting walls are given. The computations indicate that the eigenvalve problem can be solved satisfactorily by using the Galerkin method with simple sets of polynomials for the expansion functions. All of the previous theoretical investigations, as well as the present one, are limited to the small-gap case, where it is assumed that the gap between the cylinders is small compared to the mean radius. Engineering wise, such stability problems or similar ones may occur in liquid metal bearings for machines which are physically within closed loops using liquid-metal process fluids. Because of the low viscosity and high speed often associated with such machines, Taylor numbers are high. Since liquid metals are good conductors, magnetohydrodynamic effects could be significant. (Author)