Simplified models of macrosegregation

• Autorzy: Mochnacki B. , Suchy J. S.

Warianty tytułu

PL

Uproszczone modele makrosegregacji

• Języki publikacji: EN

Abstrakty

EN

The macrosegregation process takes place during typical solidification of alloys. Fractions of alloy components in a liquid and solid sub-domains are time-dependent and determined by the course of border lines on the equilibrium diagram. From the mathematical point of view, the process is described by a system of partial differential equations (diffusion equations) and boundary-initial conditions. The process is coupled with the solidification one. In this paper, simplified models of macrosegregation are discussed. The volumetric solidification and the 'sharp' solid-liquid interface are considered. Examples of computations are also shown. It seems that for practical applications, the methods proposed are sufficiently exact. Additionally, they are very simple for numerical realization.

PL

W pracy przedstawiono opis matematyczny procesu segregacji składników stopowych w objętości krzepnącego odlewu. Wskazano na trudności związane z rozwiązaniem odpowiedniego problemu brzegowo-początkowego, a w dalszej części artykułu przedstawiono propozycje rozwiązań przybliżonych. Rozpatrywano zarówno problem krzepnięcia objętościowego, jak i klasyczne zadanie Stefana. Rozważania teoretyczne zilustrowano przykładami obliczeń numerycznych.

Słowa kluczowe

EN

macrosegregation; solidification; numerical simulation

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2006
• Tom: Vol. 44 nr 2
• Strony: 367--379
• Opis fizyczny: Bibliogr. 14 poz., rys.

Twórcy

autor

Mochnacki B.

autor

Suchy J. S.

• Institute of Mathematics and Computer Science, Technical University of Częstochowa,

Bibliografia

• 1. Crank J., 1984, Free and Moving Boundary Problems, Clarendon Press, Oxford
• 2. Fraś E., 1992, Crystallization of Metals and Alloys, PWN, Warsaw
• 3. Majchrzak E., Mochnacki B., Suchy J.S., 1998, Numerical model of macrosegregation proceeding during directional crystallization process, Journal of Materials Processing Technology78, 122-127
• 4. Majchrzak E., Szopa R., 1998, Simulation of heat and mass transfer in domain of solidifying binary alloy, Archives of Metallurgy, 43, 4, 341-351
• 5. Mochnacki B., Ciesielski M., 2002, Micro/macro model of solidification using the control volume method, Archives of Foundry, 2, 4, 99-104
• 6. Mochnacki B., Lara S., Pawlak E., 2004, Analysis of segregation process using the broke line model for an infinite cylinder, Scientific Research of the Institute of Mathematics and Computer Science, 1, 3, Czestochowa, 153-160
• 7. Mochnacki B., Lara S., Pawlak E., 2005, Multiscale model of segregation process, Journal of Materials Processing Technology, 162, 163, 766-769
• 8. Mochnacki B., Majchrzak E., 1995, Application of the BEM in thermal theory of foundry, Engineering Analysis with Boundary Elements, 16, 99-121
• 9. Mochnacki B., Majchrzak E., Suchy J.S., 1999, Boundary element model of coupled heat and mass transfer in solidifying casting, International Journal of Cast Metals Research, 12, 4, 227-232
• 10. Mochnacki B., Suchy J.S., 1995, Numerical Methods in Computations of Foundry Processes, PFTA, Cracow
• 11. Mochnacki B., Suchy J.S., 1997, Numerical modelling of casting solidification: the concept of problem linearization, ASF Transactions, 96, 11, 203-209
• 12. Mochnacki B., Suchy J.S., Prażmowski M., 2003, Analysis of segregation process using the broken line model. Numerical realization, Archives of Foundry, 3, 10, 235-240
• 13. Suchy J.S., 1983, Segregation of Alloy Components During the Directional Solidification, Silesian Technical University Publishers, Mechanics, Gliwice
• 14. Suchy J.S., Mochnacki B., 2003, Analysis of segregation process using the broken line model, Archives of Foundry, 3, 10, 229-234