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Application of Thiessen polygons in control volume model of solidification

Mochnacki B., Ciesielski M.

Journal of Achievements in Materials and Manufacturing Engineering

2007

Vol. 23, nr 2

75-78

Purpose: In the paper the possibilities of Thiessen polygons (THP) application in numerical modelling of solidification process are presented. The control volumes of THP shapes (2D task is considered) are very convenient both for the construction of effective and exact control volume method algorithm and allow in simple way to approximate the real shape of domain considered. Additionally the positions of CV central points can be selected in a optional way. Design/methodology/approach: The control volume method algorithm bases of the energy balances for successive CV. They are constructed under the assumption that the boundary-initial problem considered is non-linear and the evolution of latent heat is taken into account using the one domain approach (the substitute thermal capacity of material is introduced). Findings: The method here presented allows to determine the transient temperature field in a non-homogeneous system casting-mould and to observe the course of casting solidification. The local cooling (heating) curves can be found at the optional set of points from the casting-mould system. The heat transfer model can be additionally supplemented by the model concerning the macrosegregation process. Practical implications: The control volume method in a version presented in this paper can be an effective numerical tool both on the stage of foundry technologies design and also in the case of existing technologies analysis. Originality/value: The coupling of the concept of Thiessen polygons application for 2D domain dicretization with the control volume method approach seems to be the original achievement of the authors of this paper.

Komputerowa generacja struktury pierwotnej odlewu

Ciesielski M., Mochnacki B.

Archiwum Odlewnictwa

2002

R. 2, nr 4

99--104

W pracy przedstawiono sposób generowania siatki objętości kontrolnych wykorzystywanych do modelowania procesu krzepnięcia w skali mikro/makro z wykorzystaniem teorii Johnsona-Mehla-Avrami-Kołmogorowa (zadanie 2D). Objętości kontrolne tworzone są w postaci wieloboków Thiessena, co pozwala na etapie obliczeń numerycznych w prosty sposób wykorzystać metodę bilansów elementarnych. Rozkład węzłów (środków ziaren) w rozpatrywanym podobszarze jest losowy z narzuconymi z góry pewnymi warunkami ich rozmieszczenia. W końcowej części pracy pokazano przykłady wygenerowanych siatek.

The method of the mesh generation which can be used for numerical modelling of the solidification in micro/macro scale (2D task) on the basis of Johnson-Mehl-Avrami-Kolmogorov theory is presented. The control volumes correspond to the Thiessen polygons, it allows on the stage of numerical modelling to apply, in the simple way, the control volume method. The distribution of the control volumes central points (the centers of grains) is random one, but the certain limitations and postulates can be taken into account. In the final part of the paper the examples of the structures obtained are shown.