The computation of the velocity fields in mechanically agitated melts for turbulent and non-newtonian regimes
- PDF / 676,995 Bytes
- 8 Pages / 603.28 x 783.28 pts Page_size
- 20 Downloads / 190 Views
I.
INTRODUCTION
THE main
purpose of the work described in this paper is to examine whether melt-solid slurries may be adequately agitated using a mechanical stirrer. Problems of this type are of considerable practical importance, both in the preparation of dispersion-strengthened composite materials and rheocasting, m In a previous article, the authors examined the related problem, that is, the flow behavior of melt-solid slurries, upon agitation by electromagnetic forces c2J and have shown that it would be difficult to provide good stirring in such systems by conventional induction coil designs. The general problem of stirring in metallurgical systems has received a great deal of attention in recent years, in connection with steelmaking, ladle metallurgy, and the induction stirring of the melt regions in continuous casting. Indeed, good models are available for representing the majority of these systems, t3-6J Mechanical stirring is not usually employed in metallurgical practice because of the considerable practical difficulties encountered in maintaining a mechanical stirrer in the hostile environments posed by the hightemperature melts. Notable exceptions are the secondary treatments of lead and aluminum. Up to the present time, little fundamental work has been done on the behavior of mechanically stirred systems within a metallurgical context. In contrast, mechanical stirring is very commonly employed in chemical engineering practice, and a great deal of literature concerned with the theory and practice of agitated systems exists. Much of the previous work in this field has been empirical, with prime emphasis on defining the optimal stirring arrangements and relating the power input to the mixing behavior of these systems. [7-111 More recently, very useful work has been done by chemical engineers in relating fluid flow fundamentals to mixing and also on the use of computational fluid mechanics in describing these systems. Some examples of such recent work have been reviewed by Placet et a l . [12] and Middleton et al. t131 It has to be stressed, however,
that most of this work has been concerned with the behavior of Newtonian fluids in a turbulent regime and nonNewtonian fluids with dilute suspensions. The study of fluid-solid slurries represents a relatively unexplored field, even within the chemical engineering context. In the following, we shall present a mathematical formulation describing the velocity fields in a mechanically agitated melt held in a cylindrical container. Computed results will then be shown for two sets of conditions: (1) turbulent behavior of a Newtonian fluid, in order to validate the model, by a comparison with measurements reported in the literature, and (2) non-Newtonian, power-law behavior, to represent melt-solid slurries that are of primary practical interest in this study. II.
FORMULATION
Let us consider a cylindrical vessel of diameter d and of height H, which is being agitated by a mechanical stirrer, such as sketched in Figure 1. The system is axisymmetric, and the free s
Data Loading...
