Optimal cooling strategies in continuous casting of steel with variable casting speed

In the soft-reduction zone of a continuous casting machine, the strand thickness is reduced slightly by compression to minimize center segregation which would decrease the steel quality. In order to successfully apply this technology, one has to ensure that final solidification takes place within the soft-reduction zone. This can be done by controlling solidification with cooling water sprayed onto the outside of the strand in the secondary cooling region. If the casting speed varies, results for the inverse problem of determining an appropriate cooling strategy for a stationary model from the literature do not apply. We model the problem with variable casting speed and develop an algorithm for solving the inverse problem numerically: the problem of computing an appropriate cooling strategy is reformulated as a finite-dimensional nonlinear optimization problem with bounds on the variables which is solved with a Quasi-Newton method. The use of adjoint problems makes it possible to compute the gradient of the objective functional fast and accurately. We demonstrate the efficiency of our method, on some numerical examples with data from steel industry