| Process optimization determines process parameters that maximize or minimize (optimize) some aspect of a process (the objective), while ensuring that the process operates within established limits. In this work, mathematical models that simulate heat flow and solidification in a continuously cast steel strand are coupled with mathematical optimization techniques to predict optimal process parameters for several aspects of the continuous casting process. Two dimensional slice type models are used to represent the three dimensional steady state temperature profile in the continuous cast strand. The heat transfer equations are solved numerically and provide information on the caster state, which is then used to optimize continuous casting operations. Alternating Direction Implicit finite difference methods (ADI), along with the Kirchhoff transformation and time step iterations, are used for computational efficiency. Optimization problems in continuous casting are formulated as constrained, nonlinear programming problems are solved using Successive Quadratic Programming (SQP). Problems solved include determination of operating parameters that result in maximum and minimum casting rates and maximum slab enthalpy at the cutoff station for billets and slabs. All optima are determined such that a set of process constraints is satisfied. The constraints represent quality and process feasibility by imposing limits on strand shell thickness, metallurgical length, maximum heating and cooling rate and reheating of the strand surface. In some cases, non-obvious operating strategies are found. For example, maximum strand enthalpy in slabs occurs at a casting rate which is less than the maximum possible casting rate. The determination of optimal process parameters, especially in situations where the parameters are non-obvious, is important for the casting of quality products and will become more so as advanced casting processes (horizontal and strip casting) become more prevalent. |
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