Flow fields in electromagnetic stirring of rectangular strands with linear inductors: Part II. computation of flow field
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I.
INTRODUCTION
IN continuous casting of steel electromagnetic stirring is used for improving the solidification structure of the strand. The optimum stirring conditions are usually explored by trial and error. Consequently, it may be helpful to provide fundamentals for the various physical and metallurgical phenomena occurring during stirring. In Part I of this paper Ill a theoretical model has been developed for the computation of flow velocities in rectangular strands stirred by linear inductors. It was tested experimentally using mercury as liquid metal. The agreement between theory and experiments was found to be satisfactory. It was concluded, therefore, that the model is sufficiently reliable to predict flow velocities in steel strands. In this part of the paper the flow fields have been computed for numerous situations of practical interest.
II. LONGITUDINAL STIRRING OF BLOOMS AND BILLETS IN CONTINUOUS CASTING The flow pattern and the size of the velocity in longitudinal stirring (in or against casting direction) of blooms and billets is influenced by a large number of parameters, viz., geometrical dimensions: length and width of the stirrer, thickness of the solid skin and of the liquid core of the strand, length of sump; electrical quantities: pole pitch, current, voltage, frequency, number of phases; and material properties: electrical conductivity, viscosity, density. More quantities have to be added if another medium (e.g., a copper plate) is located between stirrer and strand. From Part I
of the paper it may already be clear that this large number of parameters can be decreased. It was demonstrated rll that the stirring force of the inductor is completely described, using the theory for an infinitely extended stirrer and a semi-infinite steel medium, by the 2f~ existing at the surface of the strand, given by crtoBo/(2h), and the quantity Rey, which depends on h, o-, and to according to Eq. [23] of Part I of the paper. (The symbols are explained at the end of the paper.) The number of the remaining parameters, particularly of the geometrical ones, is still so large that it is impossible to present flow patterns for each combination. However, also the variation of single parameters which is carried out in the following, might give useful indications how the stirring process can be optimized.
A. Optimization of Penetration Depth In longitudinal stirring of billets and blooms (Figure 1) the reverse flow takes place at the side opposite to the inductor. This flow is directed against the electromagnetic force. Hence, the force distribution in the liquid core must be so that at the inductor side the force should be high to give stirring action, but at the other side it must be small enough so that the reverse flow is not impeded. (If the force density were constant across the core there would be no stirring at all.) Hence, it is desired to find the force distribution giving an optimum profile of stirring velocity. The force density decreases exponentially with distance y from the surface of the strand a
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