On the flow criteria for suspending solid particles in inductively stirred melts: Part I. newtonian behavior
- PDF / 469,982 Bytes
- 6 Pages / 603.28 x 783.28 pts Page_size
- 10 Downloads / 276 Views
I.
INTRODUCTION
THE suspension of buoyant or heavier particles in an agitated melt is a generic problem in materials processing. In steelmaking, melts are gently agitated in order to promote the flotation of lighter, nonmetallic inclusion particles, the Stokesian rising velocity of which could be too small to effect their removal over realistic time periods. In contrast, in the preparation of dis~rsion-hardened composite materials, agitation has to be supplied in order to keep buoyant or heavier particles in suspension. The broad generic question that one seeks to answer here is: What is the role of fluid flow and turbulence in affecting the flotation or sedimentation of the solid particles for a given particle size and particle/fluid density ratio? While a great deal of work has been done on the behavior of solid particles and droplets in moving fluids, II-71 and particular attention has been paid to the coalescence of liquid droplets in a turbulent fluid flow field, [4-91 this particular problem, and the case when the fluid motion is due to externally imposed electromagnetic forces, has yet to be considered. In the following we shall present a mathematical formulation and computed results describing the flotation and sedimentation of solid particles in electromagnetically driven, recirculating melts, with special attention being paid to the role of turbulence in affecting particle behavior.
We shall now consider the behavior of solid particles suspended in this turbulent fluid flow field, with particular reference to their sedimentation or flotation. In essence, two forces will be acting on the particle: one due to gravity, and the other the drag force exerted by the fluid. This drag force will itself have two components, associated with the steady and the fluctuating velocity components. The mathematical statement of the problem will involve the following steps: (1) The electromagnetic force field has to be calculated; (2) The turbulent Navier-Stokes equations must be solved; (3) The resultant velocity fields have to be decomposed into the time-smoothed and the fluctuating components. (4) The particle trajectory must be calculated by summing the effect of gravity and the two drag-force components. In this process, steps (1) and (2) are essentially routine, representing recently established procedures, while the calculation of particle trajectories using the decomposition of turbulent velocity fields is based on earlier works such as that by Boysan and Johansen fSl who used this method to calculate gas bubble behavior in melts in the absence of induction stirring. The mathematical statement of the problem is readily formulated, as follows: V 9U = 0
[1]
(equation of continuity) II.
FORMULATION
Let us consider a metallic melt held in a cylindrical container, which is being made to interact with a coil carrying an alternating current. Passage of the current through the coil will induce a current in the melt. Interaction of the induced current with the magnetic field produced by the coil will give rise to an e
Data Loading...
