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Applied Mathematical Modelling of Continuous Casting Processes: A Review

Division of Processes, Department of Materials Science and Engineering, Brinellvägen 23, KTH Royal Institute of Technology, 100 44 Stockholm, Sweden
Current address: Department of Applied Mathematics and Statistics, Institute of Mathematical and Computer Sciences, University of São Paulo at São Carlos, P.O. Box 668, São Carlos 13560-970, São Paulo, Brazil.
Metals 2018, 8(11), 928; https://doi.org/10.3390/met8110928
Received: 21 October 2018 / Revised: 31 October 2018 / Accepted: 2 November 2018 / Published: 9 November 2018
(This article belongs to the Special Issue Continuous Casting)
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Abstract

With readily available and ever-increasing computational resources, the modelling of continuous casting processes—mainly for steel, but also for copper and aluminium alloys—has predominantly focused on large-scale numerical simulation. Whilst there is certainly a need for this type of modelling, this paper highlights an alternative approach more grounded in applied mathematics, which lies between overly simplified analytical models and multi-dimensional simulations. In this approach, the governing equations are nondimensionalized and systematically simplified to obtain a formulation which is numerically much cheaper to compute, yet does not sacrifice any of the physics that was present in the original problem; in addition, the results should agree also quantitatively with those of the original model. This approach is well-suited to the modelling of continuous casting processes, which often involve the interaction of complex multiphysics. Recent examples involving mould taper, oscillation-mark formation, solidification shrinkage-induced macrosegregation and electromagnetic stirring are considered, as are the possibilities for the modelling of exudation, columnar-to-equiaxed transition, V-segregation, centreline porosity and mechanical soft reduction. View Full-Text
Keywords: asymptotic analysis; numerical simulation; continuous casting asymptotic analysis; numerical simulation; continuous casting
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Vynnycky, M. Applied Mathematical Modelling of Continuous Casting Processes: A Review. Metals 2018, 8, 928.

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