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Some Fluid Dynamic Effects in Large-Scale MHD Generators

Abstract

At the present time we are unable to carry out a complete analysis of the fluid dynamics and electrodynamics of an MHD generator. However, various aspects of the behaviour of an MHD generator may be examined by the use of simplified models, for example: (1) one-dimensional gas dynamics (Louis et al. 1964); (2) the current distribution can be found if the velocity is assumed constant across the duct (Witalis, 1965); (3) the skin friction and heat transfer to the walls can be calculated by boundary layer analysis if the flow is assumed to be laminar (Kerrebrock, 1961), and (4) a complete description of the velocity and current distribution across the duct can be given if the flow is assumed to be uniform, laminar, incompressible and not varying in the flow direction (Hunt and Stewartson, 1965). Taken together, these and other models will enable us to describe most of the effects in an MHD generator. In this paper another simplification is considered in which the electromagnetic forces are assumed to be much larger than the inertial forces. The ratio of these two forces is measured by the parameter, S = aB{sup 2}{sub 0}d/pU, where o is the conductivity, B{sub 0} the  More>>
Authors:
Hunt, J. C.R. [1] 
  1. University of Warwick, Coventry (United Kingdom)
Publication Date:
Oct 15, 1966
Product Type:
Conference
Report Number:
IAEA-SM-74/13
Resource Relation:
Conference: Symposium on Magnetohydrodynamic Electrical Power Generation, Salzburg (Austria), 4-8 Jul 1966; Other Information: 9 refs.; Related Information: In: Electricity from MHD. Vol. I. Proceedings of a Symposium on Magnetohydrodynamic Electrical Power Generation| 728 p.
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; APPROXIMATIONS; BOUNDARY LAYERS; ELECTRODYNAMICS; FLUID MECHANICS; FRICTION; HALL EFFECT; HEAT TRANSFER; MAGNETIC FIELDS; MAGNETIC REYNOLDS NUMBER; MHD GENERATORS; ONE-DIMENSIONAL CALCULATIONS; PRESSURE GRADIENTS
OSTI ID:
22113813
Research Organizations:
International Atomic Energy Agency, Vienna (Austria); European Nuclear Energy Agency of the OECD, Issy-les-Moulineaux (France)
Country of Origin:
IAEA
Language:
English
Other Identifying Numbers:
Other: ISSN 0074-1884; TRN: XA13M1699070795
Submitting Site:
INIS
Size:
page(s) 295-304
Announcement Date:
Jul 20, 2013

Citation Formats

Hunt, J. C.R. Some Fluid Dynamic Effects in Large-Scale MHD Generators. IAEA: N. p., 1966. Web.
Hunt, J. C.R. Some Fluid Dynamic Effects in Large-Scale MHD Generators. IAEA.
Hunt, J. C.R. 1966. "Some Fluid Dynamic Effects in Large-Scale MHD Generators." IAEA.
@misc{etde_22113813,
title = {Some Fluid Dynamic Effects in Large-Scale MHD Generators}
author = {Hunt, J. C.R.}
abstractNote = {At the present time we are unable to carry out a complete analysis of the fluid dynamics and electrodynamics of an MHD generator. However, various aspects of the behaviour of an MHD generator may be examined by the use of simplified models, for example: (1) one-dimensional gas dynamics (Louis et al. 1964); (2) the current distribution can be found if the velocity is assumed constant across the duct (Witalis, 1965); (3) the skin friction and heat transfer to the walls can be calculated by boundary layer analysis if the flow is assumed to be laminar (Kerrebrock, 1961), and (4) a complete description of the velocity and current distribution across the duct can be given if the flow is assumed to be uniform, laminar, incompressible and not varying in the flow direction (Hunt and Stewartson, 1965). Taken together, these and other models will enable us to describe most of the effects in an MHD generator. In this paper another simplification is considered in which the electromagnetic forces are assumed to be much larger than the inertial forces. The ratio of these two forces is measured by the parameter, S = aB{sup 2}{sub 0}d/pU, where o is the conductivity, B{sub 0} the magnetic field, d the width of the duct, p the density and U the mean velocity. Thus S >> 1. We also assume that the magnetic Reynolds number is very much less than one. In the largest experimental generators now being built S {approx} 2 . Thus, though the results of this model are not immediately applicable, they should indicate the effects of increasing the magnetic field strength and the size of MHD generators. When S >> 1, one can can consider the duct to be divided into 2 regions: (1) a core region where electromagnetic forces are balanced by the pressure gradient and where inertial as well as viscous forces are negligible, and (2) boundary layers on the walls where again inertial forces are negligible but where the viscous, electromagnetic and pressure forces are of the same order. We show how it is then possible to calculate the core flow in diverging ducts and in ducts with non-uniform magnetic fields, with the Hall effect and compressibility included, and obtain approximate answers for these otherwise very difficult problems. We also demonstrate the simplifications in the analysis of the boundary layers which result from this approximation. (author)}
place = {IAEA}
year = {1966}
month = {Oct}
}