An asymptotic model of the mold region in a continuous steel caster
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1.
INTRODUCTION
THE process of continuous steel casting consists of many complex stages.V] The process is shown in Figure 1. In general, a continuous casting machine consists of steel initially solidifying in a water-cooled copper mold. Steel begins to solidify inward, forming a solid shell enclosing a molten core. For a sufficiently thick shell, the steel strand can be continuously pulled from the mold. The mold oscillates in the vertical direction as the steel strand is continuously withdrawn at the casting speed, V~. Liquid steel is delivered to the mold from the tundish through a nozzle submerged into the molten steel pool. A crystalline mold flux is placed above the liquid steel pool in the mold and consequently melts from its contact with the liquid steel. This creates portions of liquid and solid mold flux above the liquid steel in the mold. The oscillation of the mold creates a pumping action which allows the liquid mold flux to travel downward in-between the solid steel and mold watlYl The process requires sufficient lubrication at the mold so that the shell does not stick to the mold and tear. If it does tear, the shell may be too thin when it exits the mold. The hydrostatic pressure of the molten core will then cause the shell to burst, referred to as breakout, allowing liquid steel to spill out onto the caster. One means of achieving lubrication is through the mold flux. in addition to lubrication, the mold flux provides (a) protection of the metal against oxidation, (b) thermal insulation of the steel meniscus, (c) absorption of inclusions (inhomogeneous particles) rising to the surface of the liquid steel, and (d) uniform heat transfer between the steel and mold. t3-6] The liquid mold flux traveling down between the mold and steel eventually begins to cool. One of the concerns about the mold flux is that its viscosity is very temperature dependent. If the temperature of the liquid mold flux drops below a critical crystallization value, T> b. The form of Eq. [79] is seen in work done by Brimacombe tg~ and Savage and Pritchard.t~91 Examining the prediction for heat flux using Eqs. [34], [57], and [65], we see that the heat flux from the mold surface is proportional to b2, where
I)2 = r(l" + f(x))-' ~- r(j-' - j - 2 f ( x ) ) = rj-~ -
- (d, + d,&) h) + c
[72]
4=(.
1 D
D ) km -
.3--
l
z+D+~
(1--7-
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