Wetting Layer and Void Fraction Nonunif ormity in a Liquid-Metal MHD Generator

Abstract

THE question of the effect of a liquid layer on the walls of an MHD channel in the case of uniform void fraction distribution in the flow core was first considered several years ago. * More recently an analytic solution for high Hartmann numbers was obtained,2 which led to the conclusion that this layer does not have a significant effect on the efficiency of large generators. This paper postulates an analytic model which makes it possible to estimate the effect of a void fraction nonuniformity, in the presence of the wetting layer on the walls, on the generator performance. Contents Statement of the Problem The flow of a conducting fluid in the channel of an MHD generator with nonconducting walls z= ±a and conducting walls y= ±d/2 is considered. It is assumed that d>a and the channel length L>a. The fluid is taken to be a homogeneous liquid-gas mixture. The assumption of * 'homogeneity makes it possible to treat the mixture as a single-phase fluid, the properties of which are a function of void fraction a. It is also assumed that a. can vary in the magnetic field direction and a (z) is a known function. Let us introduce the nondimensional quantities (designated by an asterisk) using the following expressions V=VQU* (1)