Fluid velocities in induction melting furnaces: Part II. large scale measurements and predictions
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IN
an e a r l i e r paper1 a mathematical m o d e l for melt flow in a coreless induction furnace was formulated and tested against surface velocity measurements on a m e r c u r y pool placed within a coil connected to a 30 kW 3 kHz induction furnace power supply. The mass of the pool ranged up t o 275 kg and various coil and pool geometries were tried. The agreement between the experimental measurements and theoretical predictions was good, considering that no curve fitting by manipulation of adjustable parameters was involved. The present paper reports on the measurement of melt velocities in a 12 ton Ajax-Magnathermic furnace and compares these measurements with velocities calculated u s i n g the mathematical model. In addition, calculations were made of the effect of various changes in design and operating parameters (coil geometry, current, phasing and frequency) for a l a r g e induction melting furnace. THEORY The theory of s t i r r i n g in induction furnaces was developed at length in Part I and will not be repeated h e r e . For convenience, however, the vorticity equation appearing in Part I
-~
0z ~
r
/j
o-r[_ is reproduced h e r e . The effective viscosity, /Ze, is the sum of a laminar and turbulent component. The latter is a function of position within the melt and must be obtained by a simultaneous solution of two additional partial differential equations. This is the 'two equation model' for turbulence developed by Spalding and coworkers. 2'3 This model contains four parameters, C1, C2, Cs and C D which were assigned values by Spalding on the b a s i s of experiments on the spreading of a turbulent jet. The f i r s t term on the left of Eq. [1] corresponds t o the convective transport of momentum, the second and third to diffusive (viscous) momentum ERACH D. TARAPORE and JAMES W. EVANS are Graduate Student and Associate Professor of Metallurgy, respectively, Department of Materials Science and Mineral Engineering, University of California, Berkeley, CA94720. JOHN LANGFELDT, formerly with Airco Vacuum Metals is now self-employed. Manuscript submitted September 21, 1976. METALLURGICAL
TRANSACTIONS B
transport, while the fourth term a r i s e s from the e l e c tromagnetic stirring forces within the m e l t .
EXPERIMENTAL
PROCEDURE AND RESULTS
Measurement of surface velocities was c a r r i e d out on a twelve ton, 540 kW, 60 Hz, single phase A j a x Magnathermic furnace. The crucible had an inside diameter of 1.22 m. The melt height during the measurements was 1.42 m. The coil consisted of twenty four turns grouped in four sections and was 1.33 m high with an inside diameter of 1.52 m. The bottom of the coil and the bottom of the melt were at the same height. This furnace was used in the manufacture of " E b r i t e " stainless s t e e l by AIRCO Vacuum Metals, Berkeley, California and measurements were made during actual production runs. The molten m e t a l contained s m a l l amounts of slag and the visual appearance of the surface was of a red hot pool a c r o s s which brighter s p o
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