New Insight into Combined Model and Revised Model for RTD Curves in a Multi-strand Tundish
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tremendous studies indicate that the water modeling is one of the effective methods to investigate the flow characteristics of molten steel in the tundish.[1,2] Generally, the tracer (e.g., NaCl solution or KCl solution) is injected into the incoming water stream in the ladle shroud, and its concentration at the tundish exit is monitored continuously on a personal computer via a digital card. The plot of the tracer concentration at the exit against the time is called the residence time distribution (RTD) curve. Certainly, with the
HONG LEI, Professor, is with the Key Laboratory of Electromagnetic Processing of Materials, Ministry of Education, Northeastern University, Shenyang, 110004 Liaoning, China. Contact e-mail: [email protected] Manuscript submitted March 25, 2013. Article published online September 2, 2015. 2408—VOLUME 46B, DECEMBER 2015
development of computing technology, the RTD curve can also be obtained with the help of some commercial software such as COMSOL, FLUENT, and CFX. In the past 30 years, many models were proposed to analyze the RTD curve in the tundish, but there are some problems in practice. For example, there are two popular models: the combined model (or mixed model) and the revised model (or Sahai’s model). The combined model, which originates from the chemical reaction engineering, can successfully investigate the flow characteristics in the reactor with one inlet and one exit; so it is adequate for the single-strand tundish because the single-strand tundish is a simply metallurgical reactor with one inlet and one exit. And the revised model was proposed in order to calculate the dead volume fraction precisely. But a negative dead volume fraction sometimes appeared when both of them were used to analyze the RTD curve at the outer exit in the multi-strand tundish.[3] Fortunately, the above problem can be successfully solved by the existing theory. Thus, this paper investigates the differences and relations between the combined model and the revised model on the basis of the physical concept and the mathematical formulas and provides a new insight into the existing analysis models for the RTD curve. Furthermore, the conception of the visual single-strand tundish (or the whole multistrand tundish) is introduced to estimate the flow characteristics in the multi-strand tundish, and the difference among the mean residence times at different exits is chosen to describe the difference of the flow characteristics at different exits in the multi-strand tundish. The theoretical residence time s is the time measure to describe the fluid flow from the ladle to the mold. s¼
V ; nq
½1
where V is the volume of the fluid in the tundish and q is the volume flow rate at one of the n-strand tundish exits. If the fluid flow in the tundish may be characterized by a combination of the plug flow and the well-mixed flow, there are two kinds of flow modes: plug flow before well-mixed flow and plug flow after well-mixed flow,[4] as shown in Figure 1. However, both flow modes give the same RTD curve under the condition of a pulse
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