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Modelling Methodologies for Convection-Diffusion Phase-Change Problems

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Book cover Phase Change with Convection: Modelling and Validation

Part of the book series: International Centre for Mechanical Sciences ((CISM,volume 449))

Abstract

In recent years numerical simulation of phase-change problems have attracted much interest due to their significance for several technological process. Melting and solidification are typical examples of phase change met in the metallurgical industries or crystal growth technology. These processes involve complex phenomena of mass and heat transfer that determines the quality of the solid phase.

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References

  • Abbaschian, R., de Groh III, H.C, Leonardi, E., de Vahl Davis, G., Coriell, S., and Cambon, G., 2001. ‘Final report for the shuttle flight experiment on USMP-4: In Situ Monitoring of Crystal Growth Using MEPHISTO’, NASA Technical Publication, NASA/TP-2001–210825.

    Google Scholar 

  • Banaszek, J., Rebow, M. and Kowalewski, T. A. (1998). Fixed grid finite element analysis of solidification, In de Vahl Davis, G. and Leonardi, E., eds., Advances in computational heat transfer CHT-97, 471–478, Cesme, Belgell House.

    Google Scholar 

  • Bennon, W. D. and Incropera, F. P. (1987). A continuum model for momentum, heat and species transport in binary solid-liquid phase change systems I, Model formulation, Int. J. of Heat and Mass Transfer 30, 2161–2170.

    Article  MATH  Google Scholar 

  • Bennon, W. D. and Incropera, F. P. (1988). Numerical analysis of binary solid-liquid phase change using a continuum model. Num. Heat Transfer 13, 207–216.

    Google Scholar 

  • Bertrand, O., Binet, B., Combeau, H., Coutier, S., Dellanoy, Y., Gobin, D. Lacroix, M., Lequere, P., Medale, M., Mencinger, J., Sadat, H. and Veira, G. (1999). Melting driven by natural convection. A comparison exercise: first results, Int. J. Thermal Sci. 38, 5–26.

    Article  Google Scholar 

  • Brent, A. D., Voller, V. R. and Reid, K. J. (1988). Enthalpy-porosity technique for modelling convection-diffusion phase-change: application to the melting of a pure metal, Num. Heat Transfer 13, 297–318.

    Google Scholar 

  • Buell, C. and Shuck, F., 1970. Diffusion in the liquid Bi-Sn system, Metallurgical Transactions, 1, 1875–1880.

    Article  Google Scholar 

  • Caginalp, G. and Socolovski, E. A., (1991). J. Comput. Phys., 95, 85.

    Article  MathSciNet  MATH  Google Scholar 

  • Caginalp, G., (1989). Phys. Rev. A. 39, 11, 5887.

    Article  MathSciNet  MATH  Google Scholar 

  • Caginalp, G. and Chen X. (1992). On the evolution of Phase Boundaries, Spring Verlag New York.

    Google Scholar 

  • Chen, P.Y.P., Timchenko, V., Leonardi, E., de Vahl Davis, G. and de Groh III, H.C., 1998. A numerical study of directional solidification and melting in microgravity, HTD-Vol. 361–3/PID-Vol. 3. Proc. Of ASME Heat Transfer Divn., HTD-Vol.361–3/PID-Vol.3, Proc. of the ASME Heat Transfer Division–Volume 3, R.A. Nelson Jr., L.W. Swanson, M.V.A. Bianchi, C. Camci (eds), ASME, New York, 75–83.

    Google Scholar 

  • CFX-4.2:Solver, 1997. Harwell Laboratory, Didcot, Oxfordshire OX11 ORA, U.K.

    Google Scholar 

  • Crank, J. (1984). Free and moving boundary problems. Oxford Science Publications.

    Google Scholar 

  • Dantzig, J. (1989). Modelling liquid-solid phase change with melt convection, Int. J. Num. Meth. In Eng. 28, 1769–1785.

    Google Scholar 

  • Fabbri, M. and Voller, V. R. (1997). The phase-field method in the sharp interface limit: a comparison between model potential. J. Comp. Physics 130, 256–265.

    Article  MATH  Google Scholar 

  • Gau, C. Viskanta, R. (1986), Melting and solidification of a pure metal on a vertical wall, Transaction of the ASME 108, 174–181.

    Article  Google Scholar 

  • Garling, D. K. (1980). Finite element analysis of convective heat transfer problems with change of phase, Computer Meth. Fluids, 257–284.

    Google Scholar 

  • Giangi, M., Stella, F. and Kowalewski, T. A. (1999). Phase change with free convection: fixed grid simulation, Comp. Visual. Sci. 2, 123–130.

    Article  MATH  Google Scholar 

  • Giangi, M., Stella, F. (1999). Analysis of natural convection during solidification of a pure metal, Int. J. Comp. Fluid Dynamics, 11, 341–349.

    Article  MATH  Google Scholar 

  • Giangi, M., Stella, F., Leonardi E. and de Vahl Davis G. (2002). A numerical study of solidification in the presence of a free surface under microgravity condition, Num. Heat Transfer: Part. A, 41, 579–595.

    Article  Google Scholar 

  • Golub G. and Van Loan C. (1990). Matrix computations, Johns Hopkins University Press, Baltimore, MD.

    Google Scholar 

  • Guj, G. and Stella, F. (1988). Numerical Solution of High-Re Recirculating Flows in Vorticity-Velocity Form, Int. J. Num. Meth. in Fluids, 8, 405–416.

    Google Scholar 

  • Hirsch C. (1983). Numerical computation of internal and external flows, Spring Verlag New-York, 1, Fondamental of numerical discretization.

    Google Scholar 

  • Kobayashi R. (1993), Physica D., 63, 410.

    Article  MATH  Google Scholar 

  • Kobayashi, R. (1994), Exp. Math. 3, 59.

    Article  MATH  Google Scholar 

  • Kowalewski, T. A. and Rebow, M. (1998). An experimental benchmark for freezing water in the cubic cavity, In de Vahl Davis, G. and Leonardi, E., eds., Advances in Computational Heat Transfer CHT-97, 149–156, Cesme, Belgell House.

    Google Scholar 

  • Laouadi, A., Lacroix, M. and Galanis, N., 1998. A numerical method for the treatment of discontinuous thermal conductivity in phase change problems, International Journal of Numerical Methods for Heat and Fluid Flow, 8, 265–287.

    Article  MATH  Google Scholar 

  • Lee, Y. and Korpela S.A. (1983). Multicellular natural convection in a vertical slot, J Fluid Mech., 126, 91–121.

    Article  MATH  Google Scholar 

  • Morgan, K. (1981). A numerical analysis of freezing and melting with convection, Comp. Meth. Applied in Eng. 28, 275–284.

    Article  Google Scholar 

  • Niwa, K., Shimoji, M., Kado, S., Watanabe, Y. and Yokokawa, T., 1957. Studies of diffusion in molten metals, AIME Tran., 209, 96–101.

    Google Scholar 

  • Ralston A. and Rabinowitz P. (1978). A first course in numerical analysis, McGraw-Hill International Editions, Singapore.

    MATH  Google Scholar 

  • Raw, W.Y. and Lee, S.L., 1991. Application of weighting function scheme on convection-conduction phase-change problems, Int. Heat and Mass Transfer, 34, 1503–1513.

    Article  Google Scholar 

  • Rouzaud A., Favier J.J. and Thevenard D., 1988. A space instrument for fundamental materials science problems: the MEPHISTO program, Adv. Space Res., Vol. 8, No. 12, 49–59.

    Article  Google Scholar 

  • Richtmyer, R. D. and Morton, K. W. (1967). Difference methods for initial value problems. Interscience, New York.

    MATH  Google Scholar 

  • Saad Y. and Schultz M.H. (1986). Gmres: A generalized minimum residual algorithm for solving non-symmetric linear systems, SIAM J. Sci. Stat. Comput., 7, 856–869.

    Article  MathSciNet  MATH  Google Scholar 

  • Scheudergger, A. E. (1963). The physics of flow trough porous media, Oxford University Press, London.

    Google Scholar 

  • Shyy W., Udaykumar H.S., Madhukar M.Rao, Smith R.W. (1996). Computational fluid dynamics with moving boundaries, Taylor & Francis, London.

    Google Scholar 

  • Slattery, J. C. (1978) Momentum Energy and Mass Transfer in Continua, Krieger, New York.

    Google Scholar 

  • Smith, V.G., Tiller, W.A. and Rutter, J.W., 1955. A mathematical analysis of solute redistribution during solidification. Canadian J. of Physics, 33, 723–743.

    Article  Google Scholar 

  • Sonneveld P. (1989). CGS, A fast lanczos type type solver for nonsymmetric linear systems, SIAM. Sci. Stat. Comput., 10, 36–52.

    Article  MathSciNet  MATH  Google Scholar 

  • Stella, F. and Giangi, M. (2000). Melting of a Pure Metal on a Vertical Wall: Numerical Simulation, Numerical Heat Transfer: Part. A, 38, 2, 193–208.

    Article  Google Scholar 

  • Stella F. and Bucchignani E. (1996). True transient vorticity-velocity method using preconditioned BiCGSTAB, Numerical Heat Transfer: Part. B, 30, 315–339.

    Article  Google Scholar 

  • Tacke, K., Discretization of the explicit enthalpy method for planar phase change, 1985. Int. J. Num. Methods in Eng., 21, 543–554.

    Article  MATH  Google Scholar 

  • Timchenko, V., Chen, P.Y.P., de Vahl Davis, G. and Leonardi, E., 1998. Directional Solidification in Microgravity, Heat Transfer 98, J.S. Lee (ed.), Taylor & Francis, 241–246.

    Google Scholar 

  • Timchenko, V., Chen, P.Y.P., de Vahl Davis, G., Leonardi, E and Abbaschian, R., 2000. A computational study of transient plane front solidification of alloys in a Bridgman apparatus under microgravity conditions, Int. J. Heat and Mass Transfer, 43, 963–980.

    Article  MATH  Google Scholar 

  • Timchenko, V., Chen, P.Y.P., de Vahl Davis, G., Leonardi, E and Abbaschian, R., 2001. A numerical study of the MEPHISTO experiment, CHT’01 Advances in Computational Heat Transfer II, G. de Vahl Davis and E. Leonardi (eds), Begell House Inc., New York, 1089–1096.

    Google Scholar 

  • Unverdi, S. O. and Tryggvason, G. (1992). A front-tracking method for viscous incompressible, multi-fluid flows. J. Comp. Physics 100, 25–37.

    Article  MATH  Google Scholar 

  • Van De Worst H. (1992). A fast and smoothly converging variant of Bi-Cgstab for the solution of non-symmetric linear sistems, SIAM J. Sci. Stat. Comput., 132, 631–644.

    Google Scholar 

  • Viswanath, R. and Jaluria, Y. (1993). A comparison of different solution methodologies for melting and solidification problems in enclosures, Num. Heat Transfer, Part B, 24, 77–105.

    Google Scholar 

  • Voller, V. R., Cross, M. and Markatos, N. C. (1987). An enthalpy method for convection-diffusion phase change. Mt. J. Num. Meth. Eng. 24, 271–284.

    Article  MATH  Google Scholar 

  • Voller, V. R., Swaminathan C.R. (1993). Treatment of discontinuous thermal conductivity in control volume solutions of phase change problems. Numerical Heat Transfer, Part B, 24, 161–180.

    Google Scholar 

  • Voller, V.R., Fabbri, M. (1995). Numerical solution of plane-front solidification with kinetic undercooling, Numerical Heat Transfer, Part B, 32, 467–486.

    Google Scholar 

  • Voller, V.R., Brent, A.D. and Prakash, C., 1989. The modelling of heat, mass and solute transport in solidification systems. Int. J. Heat Mass Transfer, 32, 1719–1731.

    Article  Google Scholar 

  • Wang S.L. et al. (1993), Physica D. 69, 189.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Meccanica e Aeronautica, Università degli studi di Roma “La Sapienza”, Via Eudossiana 18, 00184, Rome, Italy

    F. Stella & M. Giangi

Authors
  1. F. Stella
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  2. M. Giangi
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Editors and Affiliations

  1. Academy of Sciences Warsaw, Poland

    Tomasz A. Kowalewski

  2. Campus Universitaire Orsay, France

    Dominique Gobin

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Stella, F., Giangi, M. (2004). Modelling Methodologies for Convection-Diffusion Phase-Change Problems. In: Kowalewski, T.A., Gobin, D. (eds) Phase Change with Convection: Modelling and Validation. International Centre for Mechanical Sciences, vol 449. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2764-3_5

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  • DOI: https://doi.org/10.1007/978-3-7091-2764-3_5

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-20891-5

  • Online ISBN: 978-3-7091-2764-3

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