ARTIFICIAL BEE COLONY ALGORITHM IN THE SOLUTION OF SELECTED INVERSE PROBLEM OF THE BINARY ALLOY SOLIDIFICATION

Abstract

The paper presents a procedure for reconstructing, on the basis of known measurements of temperature, the heat transfer coefficient and the distribution of temperature in given region of solidifying binary alloy in the casting mould. Solution of the considered inverse problem is found by applying the finite element method for solving the corresponding direct problem and the Artificial Bee Colony algorithm for minimizing the functional representing the error of approximate solution.

Dates

  • Submission Date2014-07-15
  • Revision Date2014-11-28
  • Acceptance Date2014-11-28
  • Online Date2014-12-14

DOI Reference

10.2298/TSCI140715136H

References

  1. Okamoto, K., Li, B.Q., A regularization method for the inverse design of solidification processes with natural convection, Int. J. Heat Mass Transfer, 50 (2007), pp. 4409-4423
  2. Szeliga, D., Gawęda, J., Pietrzyk, M., Parameters identification of material models based on the inverse analysis, Int. J. Appl. Math. Comput. Sci., 14 (2004), pp. 549-556
  3. Hristov, J., An inverse Stefan problem relevant to boilover: heat balance integral solutions and analysis, Therm. Sci., 11 (2007), pp. 141-160
  4. Beck, J.V., Blackwell, B., St.Clair, C.R., Inverse Heat Conduction: Ill Posed Problems, Wiley Intersc., New York, USA, 1985
  5. Beck, J.V., Blackwell, B., Inverse Problems. In: Handbook of Numerical Heat Transfer, Wiley Intersc., New York, USA, 1988
  6. Mochnacki, B., Suchy, J.S., Numerical Methods in Computations of Foundry Processes, PFTA, Cracow, Poland, 1995
  7. Majchrzak, E., Mochnacki, B., Application of the BEM in the thermal theory of foundry, Eng. Anal. Bound. Elem., 16 (1995), pp. 99-121
  8. Mochnacki, B., Numerical modeling of solidification process, in: Computational Simulations and Applications, (Ed. J. Zhu), InTech, Rijeka, 2011, pp. 513-542
  9. Santos, C.A., Quaresma, J.M.V., Garcia, A., Determination of transient interfacial heat transfer coefficients in chill mold castings, J. Alloys and Compounds, 319 (2001), pp. 174-186
  10. Meyer, G.H., A numerical method for the solidification of a binary alloy, Int. J. Heat Mass Transfer, 24 (1981), pp. 778-781
  11. Mochnacki, B., Suchy, J.S., Prazmowski, M., Modelling of segregation in the process of Al-Si alloy solidification, Soldification of Metals and Alloys, 2 (2000), 44, pp. 229-234
  12. Samanta, D., Zabaras, N., Control of macrosegregation during the solidification of alloys using magnetic fields, Int. J. Heat Mass Transfer, 49 (2006), pp. 4850-4866
  13. Yang, G.Z., Zabaras, N., The adjoint method for an inverse design problem in the directional solidification of binary alloys, J. Comput. Phys., 140 (1998), pp. 432-452
  14. Słota, D., Reconstruction of the boundary condition in the problem of the binary alloy solidification, Arch. Metall. Mater., 56 (2011), pp. 279-285
  15. Hetmaniok, E., Słota, D., Numerical procedure of solving some inverse problem in solidification of the binary alloy, Comput. Assisted Meth. Eng. Sci., 19 (2012), pp. 393-402
  16. Hetmaniok, E., Słota, D., Experimental verification of the procedure of reconstructing the boundary condition in the problem of binary alloy solidification, Steel Res. Int., special edition Metal Forming (2012), pp. 1043-1046
  17. Mochnacki, B., Suchy, J.S., Simplified models of macrosegregation, J. Theor. Appl. Mech., 44 (2006), pp. 367-379
  18. Mochnacki, B., Majchrzak, E., Szopa, R., Simulation of heat and mass transfer in domain of casting made from binary alloy, Arch. Foundry Eng., 8 (2008), 4, pp. 121-126
  19. Karaboga, D., An idea based on honey bee swarm for numerical optimization, Technical report, Computer Engineering Department, Engineering Faculty, Erciyes University, Turkey, 2005
  20. Karaboga, D., Basturk, B., On the performance of artificial bee colony (ABC) algorithm, Appl. Soft Computing, 8 (2007), pp. 687-697
  21. Karaboga, D., Akay, B., A comparative study of artificial bee colony algorithm, Appl. Math. Comput., 214 (2009), pp. 108-132
  22. Szargut, J., Mochnacki, B., Difference mathematical model of ingot solidification, Arch. Hutn., 16 (1971), 3, pp. 269-289
  23. Hetmaniok, E., Słota, D., Zielonka, A., Solution of the inverse heat conduction problem by using the ABC algorithm, Lect. Notes Comput. Sc., 6086 (2010), pp. 659-668
  24. Hetmaniok, E., Słota, D., Zielonka, A., Wituła, R., Comparison of ABC and ACO algorithms applied for solving the inverse heat conduction problem, Lect. Notes Comput. Sc., 7269 (2012), pp. 249-257
  25. Kasprzak, M., Sokolowski, J., Kierkus, W., Kasprzak, W., Method and apparatus for Universal Metallurgical Simulation and Analysis, US Patent No. US 7,354,491 B2, 2008
  26. Ohura, K., Makinouchi, A., Teodosiu C., Nagai Y., and Nagse J., Warpage simulation and the experimental verification of an L-plate sand mold casting by using the thermoelastoplastic FEM code, AIP Conference Proceedings 1252, 523 (2010); doi: 10.1063/1.3457597
  27. Susac, F., Ohura, K., Banu, M., Naidim, O., Experimental study of the heat transfer and air gap evolution during casting of an AC4CH aluminum alloy, RIKEN International Symposium, Japan, 2008, pp. 49-52