Similarity Criteria for the Study of Removal of Spherical Non-metallic Inclusions in Physical Models of Continuous Casti
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NOWADAYS, there is a high demand for clean steels,[1] steel grades that require a very stringent control of impurities responsible for defects in the final product. An important kind of impurity is non-metallic inclusions. These inclusions are particles (solid) or droplets (liquid) that contaminate liquid steel. Non-metallic inclusions may present different shapes, such as spherical, polyhedral, plate-like and cluster. It is noteworthy that certain inclusions are beneficial for some steel grades. Physical models of continuous casting tundishes are widely employed to study fluid flow and to optimize their capabilities of flotation of non-metallic inclusions. Physical models are also used to validate mathematical models developed for the same purposes.[2–5]
BERNARDO MARTINS BRAGA and ROBERTO PARREIRAS TAVARES are with the Department of Metallurgical and Materials Engineering, Engineering School, Federal University of Minas Gerais, Ave. Presidente Antoˆnio Carlos, No. 6627, Belo Horizonte, Minas Gerais 31270-901, Brazil. Contact e-mail: [email protected] Manuscript submitted March 1, 2018.
METALLURGICAL AND MATERIALS TRANSACTIONS B
A physical model of an industrial tundish (prototype) is a replica of the equipment that operates using an alternative working fluid—usually water. It is often built in reduced scale due to costs, space restrictions, and convenience reasons. Non-metallic inclusions are simulated using particles less dense than the working fluid. The particles can be injected through a pulse or continuously depending on the method used to determine the efficiency of inclusion flotation: sieves,[6–11] ESZ (Electric Sensing Zone) probe[12–14] or laser system based on the principle of the photoelectric barrier.[15] The design and operation conditions of a physical model, the size and material of particles, and their injection load should be adequately set so that the results of the physical model represent the behavior of the industrial tundish. This is accomplished by the utilization of suitable similarity criteria. Steelmaking literature has covered this issue in many publications.[7,10,15–19] However, the analyses of inclusion dynamics are usually short and perfunctory. Consequently, some implicit hypotheses adopted during dimensional analysis are not made clear and there is a risk of researchers occasionally getting unreliable results when these assumptions are not fulfilled.
In particular, the diameter of the simulating particles is usually defined in the literature as follows: It is assumed that the relative velocity between any non-metallic inclusion and liquid steel is constant everywhere in the tundish. Most of the authors calculate this relative velocity using the Stokes’ law while Thomas[17] considers a more general case in which it depends on the particle Reynolds number. An analogous assumption is adopted for the relative velocity between the simulating particles and the working fluid of the physical model. Then, a criterion for kinematic similarity is used to relate the relative velocities ca
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