Solution of the Pure Metals Solidification Problem by Involving the Material Shrinkage and the Air-Gap Between Material and Mold

• Autorzy: Matlak J. , Słota D.
• Języki publikacji: EN

Abstrakty

EN

In this paper we describe an algorithm for solving the pure metals solidification problem by involving the metal shrinkage and air-gap between material and mold. In this algorithm we use the finite element method supplemented by the procedures allowing to define the position of the moving interface and the change of the material size associated with the shrinkage. We present also an example illustrating the precision of presented method.

Słowa kluczowe

EN

solidification process; air-gap; Stefan problem; metal shrinkage

PL

proces krzepnięcia; szczelina powietrzna; problem Stefana; skurcz stopu

• Wydawca: Komisja Odlewnictwa Polskiej Akademii Nauk Oddział w Katowicach
• Czasopismo: Archives of Foundry Engineering
• Rocznik: 2015
• Tom: Vol. 15, iss. 3 spec.
• Strony: 47--52
• Opis fizyczny: Bibliogr. 37 poz., tab., wykr.

Twórcy

autor

Matlak J.

• Institute of Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland

autor

Słota D.

• Institute of Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland

Bibliografia

• [1] Gupta, S.C. (2003). The Classical Stefan Problem. Basic Concepts, Modelling and Analysis. Amsterdam. Elsevier.
• [2] Mochnacki, B. Suchy, J.S. (1995). Numerical Methods in Computations of Foundry Processes. Cracov. PFTA.
• [3] Özişik, M.N. (1993). Heat Conduction. New York. Wiley & Sons.
• [4] Voller, V. & Falcini, F. (2013). Two exact solutions of a Stefan problem with varying diffusivity. Int. J. Heat Mass Transfer. 58. 80-85.
• [5] Zhou, Y. Wang, Y. & Bu, W. (2014). Exact solution for a Stefan problem with latent heat a power function of position. Int. J. Heat Mass Transfer 69. 451-454.
• [6] Onyejekwe, O. & Onyejekwe, O. (2011). Numerical solutions of the one-phase classical Stefan problem using an enthalpy green element formulation. Adv. Eng. Soft. 42, 743-749.
• [7] Yoon, Y. (2011). Explicit and implicit extended MLS difference methods for Stefan problems. Procedia Eng. 14, 2751-2755.
• [8] Jana S., Ray, S. & Durst, F. (2007). A numerical method to compute solidification and melting processes. Appl. Math. Modelling 31, 93-119.
• [9] Kim, S. (2014). Two simple numerical methods for the free boundary in one-phase Stefan problem. J. Appl. Math. 2014. article ID 764532, 10 pages.
• [10] Qu, L.-H. Ling, F. & Xing, L. (2013). Numerical study of one-dimensional Stefan problem with periodic boundary conditions, Thermal Science 17, 1453-1458.
• [11] Hetmaniok, E. & Pleszczyński, M. (2011). Analytical method of determining the freezing front location. Zeszyty Naukowe Politechniki Śląskiej, Matematyka Stosowana 1, 121-136.
• [12] Hetmaniok, E. & Pleszczyński, M. (2012). Application of the analytic-numerical method in solving the problem with moving boundary. Zeszyty Naukowe Politechniki Śląskiej, Matematyka Stosowana 2, 57-74.
• [13] Grzymkowski, R., Hetmaniok, E. & Pleszczyński, M. (2011). Analytic-numerical method of determining the freezing front location. Arch. Foundry Eng. 11, 75-80.
• [14] Grzymkowski, R., Hetmaniok, E. & Pleszczyński, M. (2013). Problem of the moving boundary in continuous casting solved by the analytic-numerical method, Arch. Foundry Eng. 13, 33-38.
• [15] Grzymkowski, R., Hetmaniok, E., Pleszczyński, M. & Słota, D. (2013). A certain analytical method used for solving the Stefan problem, Thermal Science 17, 635-642.
• [16] Mitchell, S.L. & Myers, T.G. (2010). Application of standard and refined heat balance integral methods to one-dimensional Stefan problems, SIAM Rev. 52, 57-86.
• [17] Myers, T. & Mitchell, S. (2011). Application of the combined integral method to Stefan problems, Appl. Math. Modelling 35, 4281-4294.
• [18] Layeni, O. & Johnson, J. (2012). Hybrids of the heat balance integral method, Appl. Math. Comput. 218, 7431-7444.
• [19] Hristov, J. (2009). The heat-balance integral method by a parabolic profile with unspecified exponent: analysis and benchmark exercises, Thermal Science 13, 27-48.
• [20] Szopa, R. & Siedlecki, J. (2010). Application of standard and refined heat balance integral methods to one-dimensional Stefan problems, SIAM Rev. 52, 394-354.
• [21] Mochnacki, B. & Ciesielski, M. (2002). Micro/macro model of solidification using the control volume method, Arch. Foundry 2 (4), 161-166.
• [22] Suchy, J.S. & Mochnacki, B. (2003). Analysis of segregation process using the broken line model. Theoretical base, Arch. Foundry 3 (10), 229-234.
• [23] Ciesielski, M., Mochnacki, B. & Suchy, J.S. (2004). Numerical model of axiallysymmetrical casting solidification. Part I, Arch. Foundry 4 (14), 110-113.
• [24] Majchrzak, E. & Mendakiewicz, J. (2007). Gradient method of cast iron latent heat identification, Arch. Foundry Eng. 7 (4), 121-126.
• [25] Majchrzak, E., Mochnacki, B. & Kałuża, G. (2007). Shape sensitivity analysis in numerical modelling of solidification, Arch. Foundry Eng. 7 (4), 115-120.
• [26] Mochnacki, B., Majchrzak E. & Szopa, R. (2008). Simulation of heat and mass transfer in domain of casting made from binary alloy, Arch. Foundry Eng. 8 (4), 121-126.
• [27] Piasecka-Belkhayat, A. (2008). Numerical modelling of solidification process using interval boundary element method, Arch. Foundry Eng. 8 (4), 171-176.
• [28] Brociek, R., Hetmaniok, E., Matlak, J. & Słota, D. (2014). Solving of the two-dimensional unsteady heat transfer problem by using the homotopy analysis method, Zeszyty Naukowe Politechniki Śląskiej, Matematyka Stosowana 4, 89-102.
• [29] Hetmaniok, E., Pleszczyński, M., Słota, D. & Zielonka, A. (2014). Usage of the homotopy analysis method for determining the temperature in the castingmould system, Hutnik 81 (1), 50-54.
• [30] Hetmaniok, E., Słota, D. & Zielonka, A. (2014). Solution of the inverse continuous casting problem with application of the invasive weed optimization algorithm, Computer Methods in Materials Science 14, 114-122.
• [31] Hetmaniok, E., Słota, D.& Zielonka, A. (2014). Experimental verification of selected artificial intelligence algorithms used for solving the inverse Stefan problem, Numer. Heat Transfer B 66, 343-359.
• [32] Hetmaniok, E., Słota, D. & Zielonka, A. (2015) Using the swarm intelligence algorithms in solution of the two-dimensional inverse Stefan problem, Comput. Math. Appl. 69, 347-361.
• [33] Purlis, E. & Salvadori, V. (2010). A moving boundary problem in a food material undergoing volume change - simulation of bread baking. Food Research International 43, 949-958.
• [34] Natale, M., Marcusa, E. & Tarzia, D. (2010) Explicit solutions for one-dimensional two-phase free boundary problems with either shrinkage or expansion, Nonlinear Anal.: Real World Appl. 11, 1946-1952.
• [35] Yang, Z., Sen, M. & Paolucci, S. (2003). Solidification of a finite slab with convective cooling and shrinkage, Appl. Math. Modelling 27, 733-762.
• [36] Matlak J. & Słota D., (accepted) Solution of the Stefan Problem by Involving the Material Shrinkage, Czasopismo Techniczne.
• [37] Grzymkowski, R. Kapusta, A. Nowak, I. Słota, D. (2009). Numerical Methods. The Initial-Boundary Value Problems. Gliwice. WPKJS (in Polish).