Optimization and continuous casting: Part II. Application to industrial casters
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I.
INTRODUCTION
O P E R A T I N G practices for industrial casters are normally developed with the aid of heat flow and solidification models. Trial and error execution of these models provides the thermal history of the cast strand under varying process variables to define a set that provides quality castings. Rules of thumb and/or thermal stress models provide some of the quality criteria. In this article, an alternate, versatile, and more efficient approach is presented for determining feasible and optimum operating variables for the process. This approach combines the modeling work as well the optimization formalism and problem formulation discussed in two previous articles tl'21 and applies these concepts to several operating continuous casting process scenarios (Table I). Statements of the various cases are described in the subsequent sections, as well as results and analysis of the solutions to the optimization model. Details about the simulation of the heat flow models, as well as theoretical considerations of the optimization method, can be found in our previous articles, t~,21 All of these models accurately simulate two existing, operating industrial continuous casters. All of the parameters relating to the model were supplied by industry, while the optimization formulations and the results were verified on the basis of operating experience of the billet and slab casters. In applying the optimization formalism, a variety of casting operating cases and casting geometries is considered in this work. The first group of cases concerns a billet caster used to cast a plain carbon steel. In terms of optimization variables, these are the smallest problems solved in this B. LALLY, Research Associate, Department of Metallurgical Engineering and Materials Science, and L.T. BIEGLER, Professor, Department of Chemical Engineering, are with Carnegie Mellon University, Pittsburgh, PA 15213. H. HENEIN, formerly with the Department of Metallurgical Engineering and Materials Science, Carnegie Mellon University, is Professor with the Department of Mining, Metallurgical and Petroleum Engineering, University of Alberta, Edmonton, AB T6G 2G6, Canada. Manuscript submitted February 22, 1989. METALLURGICALTRANSACTIONS B
work (there are only four spray cooling zones). Three types of optimization objectives (maximum casting rate, minimum casting rate, and maximum enthalpy at the cutoff station) are solved for this casting system. The solution of these objectives demonstrates the feasibility of the optimization concept when applied to continuous casting systems and the magnitude of the performance improvements that may be possible in caster operation. The second group of cases consists of the same three classes of optimization problems but applied to a slab caster used to make stainless steel. Here, the number of optimization variables, as well as the size of the cast section, has been increased. The effect of casting speed on mold heat flux is also explored. The constraint function values have been changed to reflect the differen
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