Fluid flow phenomena in a single phase coreless induction furnace
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I.
INTRODUCTION
THE action
of a time-varying electromagnetic field inside a crucible is summarized in terms of thermal effect (melting, followed by holding at the liquid state) and in terms of hydrodynamic phenomena (motion of the bath). The Lorentz forces may be resolved into a potential part, balanced by a pressure gradient which results in the deformation of the free surface and a rotational part due only to the end effects, particularly curvature of the magnetic field lines, which is responsible for the electromagnetic stirring. A number of theoretical papers point out that, inside a crucible of average radius R, containing a molten metal of electrical conductivity o- and kinematic viscosity u and subjected to an electromagnetic field of angular velocity w, the fluid flow depends on: (1) the geometry of the crucible and its location with respect to the inductor coils as well as its filling factor. Also, it would be appropriate to add a parameter taking into account the wall roughness, although this does not seem to have been introduced yet; (2) a shielding parameter, Ro, = /zwo-R'-, connected with the penetration of the electromagnetic field (skin effect): (3) the Reynolds numbers, Re = UoR/u, where U0 is a velocity defined either from the magnetic energy per umt mass, Bo/txO (Bo being a value of the magnetic field at the wall, which gives U0 : Bo/Itxp) ~"-) or by the average velocity of the liquid stream flowing along the wall. Inside industrial scale furnaces, the Reynolds numbers are high (Re > 10-s);hence the turbulence plays a prominent role. Its influence has been taken into account by Evans and Tarapore ~e and by Szekely and Chang 34._s who" used either the K-W or the K-e turbulence models. A less costly analysis involving estimation of order of magnitude of velocities and shear stress has been developed by Hunt and Maxey 6 and Moore and Hunt. 7 The influence of the free surface shape and of the geometry of the inductor has been examined by Barbier et al. ~Finally, EI-Kaddah and Szekely9 have recently used a technique employing the concept of mutual inductances.
Ch. VIVES, Professor, and R RICOU, Maitre-A~atstant. are ~lth Umverslt6 d'Avlgnon, 33. rue Pasteur. 84000 Avignon, France Manuscript submitted Septembe~ 10, 1984 METALLURGICAL TRANSACTIONS B
Velocity measurements are difficult at high temperatures. Consequently. most of the experiments have been performed at room temperature upon laboratory models, often in smooth cylindrical vessels containing mercury. The measurement techniques have varied: measurements of surface velocity by visualization,12 measurements of pressure upon a small disk) measurements of the drag force on a perforated tantalium spherical shell.: Because of simplifying assumptions used in the theoretical studies, and because the details of the experimental devices often do not correspond exactly to those of the actual furnaces, the results which reveal the existence of two main cells of recirculating flow have mostly a qualitative value. As a first step, our aim has been to ca
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