BULLETIN of the

POLISH ACADEMY of SCIENCES

TECHNICAL SCIENCES

BULLETIN of the POLISH ACADEMY of SCIENCES: TECHNICAL SCIENCES
Volume 55, Issue 1, March 2007

Analysis of Dynamic Systems and Mechanical Engineering

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pp 107 - 113

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Identification of macro and micro parameters in solidification model

B. MOCHNACKI and E. MAJCHRZAK
In the paper the thermal processes proceeding in the solidifying metal are analyzed. The basic energy equation determining the course of solidification contains the component (source function) controlling the phase change. This component is proportional to the solidification rate fS/t (fS [0, 1], is a temporary and local volumetric fraction of solid state). The value of fS can be found, among others, on the basic of laws determining the nucleation and nuclei growth. This approach leads to the so called micro/macro models (the second generation models). The capacity of internal heat source appearing in the equation concerning the macro scale (solidification and cooling of domain considered) results from the phenomena proceeding in the micro scale (nuclei growth). The function fS can be defined as a product of nuclei density N and single grain volume V (a linear model of crystallization) and this approach is applied in the paper presented. The problem discussed consists in the simultaneous identification of two parameters determining a course of solidification. In particular it is assumed that nuclei density N (micro scale) and volumetric specific heat of metal (macro scale) are unknown. Formulated in this way inverse problem is solved using the least squares criterion and gradient methods. The additional information which allows to identify the unknown parameters results from knowledge of cooling curves at the selected set of points from solidifying metal domain. On the stage of numerical realization the boundary element method is used. In the final part of the paper the examples of computations are presented.
Key words: 

micro/macro model of solidification, inverse problems, boundary element method, numerical modelling


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