Over the past twenty years there has been a major expansion of mathematical modelling effort directed to the continuous casting of steel. The modeling activities may be divided into three groups:
Liquid metal transfer from ladle to tundish to mould,
Mould heat transfer, shell formation, fluid flow, and
Strand cooling, solidification and thermomechanical behaviour.
The modeling of process metallurgical phenomena in continuous casting,
has been reviewed in various publications. Among them are from Brimacombe and Cramb [1],
J. Herbertson and P. Austin [247], and the ASM publication [246] edited by L. Kalsson,
which covere a very wide spectrum of activity, from simple 1-D heat conduction models to complex 3-D fluid dynamics, heat transfer, solidification, and stress models.
This mini-series makes some references to the essential points of those
publication.
Though
some process models for metallurgical phenomena are applied on-line for process control
(such as dynamic secondary cooling control), typically mathematical models are developed as off-line tools to improve process understanding. Nevertheless, the benefits of
modeling ultimately need to be measured in terms of increased yields, productivity and availability, cost reductions, and new or improved product quality capabilities of an operating (or pilot) plant. This is only achieved when the knowledge and process insights gained from
modeling are implemented as revised standard operating practices or changes in equipment design features.
The primary success factors for model implementation is illustrated in the Table 1.
Table I 'Key Success Factors' for the implementation of mathematical models
[247].
A. Plan for Implementation from the Onset
Structure the modelling exercise to ensure inputs and outputs are pertinent to the problem and based on measurable process parameters
Set the scope for modelling from customer's needs and overall objectives
Establish the degrees of freedom to change operating
practices or designs
B. Select Appropriate Model Framework
Concentrate on the significant process mechanisms
Keep the model simple if possible; fitness for purpose
C. Check Numerical Integrity
Run checks on model formulation; coding, equations
Tune the model to plant data; process parameters and boundary conditions
Relate results to product evaluation
Comparisons between measurements and predictions
F. Quantify the Uncertainties
Test the consequences of making simplifications; numerics; mesh size; 1 D, 2D, 3D; steady state vs transient
Estimate the implications of inadequate knowledge; incomplete plant data; poorly understood physical mechanisms; unknown material properties
Conduct sensitivity analyses
Run model at the upper and lower limit of uncertainties
G. Present Results to Assist Decislonmaking
Analysis of results should support the recommendations
Relate caster performance functions to changeable parameters [designs, operating practices]
Conduct parametric studies based on experimental design principles and changeable parameters
Show trends and opportunities
Present results in a customer/user-friendly format
References
[1] J.K. Brimacombe and A.W.Cramb: Steelmaking, casting and modelling.
Proc. 10th PTD Conf., ISS, Toronto, April 1992
[246] ASM: Modeling in Welding, Hot Deformation and Casting. 1997. ISBN
0-87170-616-4. Ed. By L. Kalsson.
[247] J. Herbertson and P. Austin: The Application of Mathematical Models for
Optimisation of Continuous Casting. Modeling of Casting, Welding and Advanced Solidification Processes - VI. Proceedings. TMS 1993. ISBN 0-87339-209-4.
