Published online by Cambridge University Press: 26 April 2006
This paper treats a liquid-metal flow through a sharp elbow connecting two constant-area, rectangular ducts with thin metal walls. There is a uniform, strong magnetic field in the plane of the centrelines of the ducts. An analytical solution with a series of eigenfunctions is possible for two sectors of the geometry, while a finite-difference relaxation solution is used for the third sector. The analytical and numerical solutions are coupled at the common boundaries by a combination of a Galerkin minimization of a residual and of integrals of the basic conservation laws over cells adjacent to each boundary. Results are presented for the three-dimensional pressure, electric potential function and fluid velocity. The pressure drop due to the three-dimensional effects near the elbow is also presented. The eigenfunction series represents a quite general solution for any three-dimensional flow in a rectangular duct with a skewed magnetic field.
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