Application of Thiessen polygons in control volume model of solidification

• Autorzy: Mochnacki B. , Ciesielski M.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

numerical techniques; control volume method; Thiessen polygons

PL

techniki numeryczne; metoda bilansów elementarnych; MBE; wielobok Thiessena

• Wydawca: International OCSCO World Press
• Czasopismo: Journal of Achievements in Materials and Manufacturing Engineering
• Rocznik: 2007
• Tom: Vol. 23, nr 2
• Strony: 75--78
• Opis fizyczny: Bibliogr. 14 poz., rys.

Twórcy

autor

Mochnacki B.

autor

Ciesielski M.

• Częstochowa University of Technology, ul. Dąbrowskiego 73, 42-200 Częstochowa, Poland,

Bibliografia

• [1] B. Mochnacki, E. Majchrzak, R. Szopa, J.S. Suchy, Inverse problems in the thermal theory of foundry processes, Scientific Research of the Institute of Mathematics and Computer Science 1/5 (2006) 154-170.
• [2] B. Mochnacki, J.S. Suchy, Numerical methods in computations of foundry processes, PFTA, Cracow, 1995.
• [3] J. Orkisz, Finite difference method, in: M. Kleiber (eds), Computer methods in solid mechanics, PWN, Warsaw, 1995 (in Polish).
• [4] M. Janik, H. Dyja, Modelling of three dimensional temperature field inside the mould during continuous casting of steel, Journal of Materials Processing Technology 157-158 (2004) 177-182.
• [5] S. Sulaiman, A.M.S. Hamouda, Modelling and experimental investigation of solidification process in sand casting, Journal of Materials Processing Technology 155-156 (2004) 1723-1726.
• [6] B. Mochnacki, J.S. Suchy, Simplified models of macrosegregation, Journal of Theoretical and Applied Mechanics 44/2 (2006) 367-381.
• [7] E. Majchrzak, J. Mendakiewicz, A. Piasecka-Belkhayat, Algorithm of mould thermal parameters identification in the system casting -mould - environment, Journal of Materials Processing Technology 162-163 (2005) 1544-1549.
• [8] M. Janik, H. Dyja, S. Berski, G. Banaszek, Two-dimensional thermomechanical analysis of continuous casting process, Journal of Materials Processing Technology 153-154 (2004) 578-582.
• [9] E. Majchrzak, M. Jasiński, G. Kaluza, Application of shape sensitivity analysis in numerical modelling of solidification process, Proceeding of the 46th International Scientific Conference on "Foundry - Solidification and Crystallisation of Metals", Wisla, 2005, 93-96.
• [10] E. Majchrzak, B. Mochnacki, Identification of thermal properties of the system casting - mould, Materials Science Forum 539-543 (2007) 2491-2496.
• [11] Z. Ignaszak, P. Popielarski, Identification of basic substitute thermophysical coefficients of mould sand, Archives of Foundary 22 (2006) 224-231 (in Polish).
• [12] R. Szopa, J. Siedlecki, Modelling of solidification using the control volume method, Solidification of Metals and Alloys 2, 44 (2000) 349-354.
• [13] J. Orkisz, Finite difference method, in: M. Kleiber (ed), Computational Methods in Solid Mechanics, PWN, Warsaw, 1995 (in Polish).
• [14] M. Ciesielski, B. Mochnacki, J.S. Suchy, Numerical model of axially-symmetrical casting solidification, Archives of Foundry 14/4 (2004) 110-119.