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Kinetics of casting solidification : an inverse approach

Majchrzak E., Mochnacki B., Suchy J. S.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2007

Vol. 6, nr 1

169-178

In the paper the example of inverse problems application in the thermal theory of foundry processes is discussed. The solidification of typical binary alloys is considered, at the same time the macro model basing on the substitute thermal capacity is taken into account (fixed domain approach). The information necessary in order to determine the kinetics of casting solidification results from the knowledge of cooling (heating) curves at the selected set of points from casting and/or mould sub-domains. The identified value corresponds to the volumetric latent heat of alloy and, as will be shown, the knowledge of this parameter allows to determine the course of solidification, in particular the changes of temporary values of volumetric solid state fraction at the points selected from casting domain. The inverse problem considered is solved using the gradient method. On the stage of numerical simulation the FDM algorithm is used. In the final part of paper the example of computations is shown.