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Sensitivity Analysis of Micro Models for Solidification of Pure Metals

  • B. MochnackiEmail author
  • R. Szopa
Chapter
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 49)

Abstract

Theoretical aspects and examples of the application of sensitivity analysis in the thermal theory of foundry processes are presented. In particular, the so-called second generation models of solidification (micro models) are considered. The sensitivity information can be applied for different purposes, among which it is possible to use the results obtained for a given set of input data to obtain the solution for different input data. The sensitivity coefficients are also necessary for the numerical solution of inverse problems using gradient methods. The application examples concern the sensitivity of the temperature field of a casting-mould system with respect to perturbations of parameters appearing in the micro/macro model of solidification. Numerical computations are performed using the finite difference method.

Keywords

Sensitivity Function Sensitivity Model Micro Model Solidification Point Growth Coefficient 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

The work was done as a part of Project 2012/05/B/ST8/01477.

References

  1. 1.
    Stefanescu D.M.: Critical review of the second generation of solidification models for casting. In: Pivonka, T.S., Voller, V., Katgerman, L. (eds.) Modeling of Casting, Welding and Advanced Solidification Processes VI. The Minerals, Metals & Material s Society, pp. 3–20 (1993)Google Scholar
  2. 2.
    Rubinstein, L.I.: The Stefan problem, Translations of Mathematical Monographs 27. American Mathematical Society, Providence, R.I. (1971)Google Scholar
  3. 3.
    Mochnacki, B., Suchy, J.S.: Numerical Methods in Computations of Foundry Processes. PFTA, Cracow (1995)Google Scholar
  4. 4.
    Majchrzak, E., Mochnacki, B., Suchy, J.S.: Identification of substitute thermal capacity of solidifying alloy. J. Theor. Appl. Mech. 46(2), 257–268 (2008)Google Scholar
  5. 5.
    Mochnacki, B.: Numerical modeling of solidification process (Chapter 24). In: Zhu, J. (ed.) Computational Simulations and Applications, pp. 513–542. INTECH (2011)Google Scholar
  6. 6.
    Fraś, E., Kapturkiewicz, W., Lopez, H.F.: Macro and micro modelling of the solidification kinetics of casting. AFS Trans. 92–48, 583–591 (1993)Google Scholar
  7. 7.
    Majchrzak, E., Piasecka, A.: Numerical micro/macro model of solidification process. J. Mater. Process. Technol. 64, 267–276 (1997)CrossRefGoogle Scholar
  8. 8.
    Mochnacki, B., Szopa, R.: Model of pure metal solidification using the power-type function. J. Achiev. Mater. Manuf. Eng. 22, 65–71 (2007)Google Scholar
  9. 9.
    Mochnacki, B., Szopa, R.: Application of sensitivity analysis in numerical simulation of solidification process. In: Szajnar, J. (ed.) Progress of Foundry Theory and Practice, pp. 271–286. Polish Ac. of Sciences, Foundry Commission (2009)Google Scholar
  10. 10.
    Cattaneo, C.: A form of heat conduction equation which eliminates the paradox of instantaneous propagation. Comput. Rend. 247, 431–433 (1958)MathSciNetGoogle Scholar
  11. 11.
    Chen, J.K., Beraun, J.E.: Numerical study of ultrashort laser pulse interactions with metal films. Numer. Heat Transf. Part A 40, 1–20 (2001)Google Scholar
  12. 12.
    Mochnacki, B., Majchrzak, E.: Modelling of microscale heat transfer in cylindrical domains. Comput. Methods Mater. Sci. 11(2), 337–342 (2011)Google Scholar
  13. 13.
    Majchrzak, E.: Parabolic and hyperbolic two-temperature models. Comparison of numerical solutions. Mater. Sci. Forum 706–709, 1454–1459 (2012)CrossRefGoogle Scholar
  14. 14.
    Chen, J.K., Tzou, D.Y., Beraun, J.E.: A semiclassical two-temperature model for ultrafast laser heating. Int. J. Heat Mass Transf. 49, 307–316 (2006)CrossRefzbMATHGoogle Scholar
  15. 15.
    Kleiber, M.: Parameter sensitivity in nonlinear mechanics. Wiley, Chichester, England (1997)Google Scholar
  16. 16.
    Dems, K.: Sensitivity analysis in thermal problems, 1: variation of material parameters within fixed domain. J. Therm. Stresses 9, 303–324 (1996)CrossRefGoogle Scholar
  17. 17.
    Mochnacki, B., Majchrzak, E.: Identification of macro and micro parameters in solidification model. Bull. Polish Acad. Sci. Tech. Sci. 55(1), 107–113 (2007)zbMATHGoogle Scholar
  18. 18.
    Szopa, R.: Sensitivity Analysis and Inverse Problems in the Thermal Theory of Foundry Processes. Czestochowa University of Technology, Czestochowa (2006)Google Scholar
  19. 19.
    Majchrzak, E., Suchy, J.S., Szopa, R.: Linear model of crystallization. Identification of nuclei density, Giessereiforschung. Int. Foundry Res. 2, 29–32 (2006)Google Scholar
  20. 20.
    Kapturkiewicz, W.: Modeling of Cast Iron Solidification. AKAPIT, Cracow (2003)Google Scholar
  21. 21.
    Szopa, R.: Modelling of solidification using the combined variant of the BEM, Metallurgy. Publication of the Silesian University of Technology, Gliwice (1999)Google Scholar
  22. 22.
    Mochnacki, B., Szopa, R.: Generalized micro/macro model of crystallization and its numerical realization. Int. J. Multiscale Comput. Eng. 8(3), 259–266 (2010)CrossRefGoogle Scholar
  23. 23.
    Fraś, E.: Crystallization of Metals and Alloys. PWN, Warsaw (1992)Google Scholar
  24. 24.
    Majchrzak, E., Mochnacki, B.: Sensitivity analysis of transient temperature field in microdomains with respect to the dual lag phase model parameters. Int. J. Multiscale Comput. Eng. 12(1), 65–77 (2014)CrossRefGoogle Scholar
  25. 25.
    Majchrzak, E., Mendakiewicz, J.: Sensitivity analysis as a tool of optimal sensors location for solidification parameters estimation. Mater. Sci. Forum 638–642, 2640–2645 (2010)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Higher School of Labour Safety ManagementKatowicePoland
  2. 2.Czestochowa University of TechnologyCzęstochowaPoland

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