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An Optimum Enthalpy Approach for Melting and Solidification with Volume Change

Author

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  • Moritz Faden

    (Chair of Thermodynamics and Transport Processes (LTTT), Centre of Energy Technology (ZET), University of Bayreuth, Universitätsstraße 30, 95440 Bayreuth, Germany)

  • Andreas König-Haagen

    (Chair of Thermodynamics and Transport Processes (LTTT), Centre of Energy Technology (ZET), University of Bayreuth, Universitätsstraße 30, 95440 Bayreuth, Germany)

  • Dieter Brüggemann

    (Chair of Thermodynamics and Transport Processes (LTTT), Centre of Energy Technology (ZET), University of Bayreuth, Universitätsstraße 30, 95440 Bayreuth, Germany)

Abstract

Classical numerical methods for solving solid–liquid phase change assume a constant density upon melting or solidification and are not efficient when applied to phase change with volume expansion or shrinkage. However, solid–liquid phase change is accompanied by a volume change and an appropriate numerical method must take this into account. Therefore, an efficient algorithm for solid–liquid phase change with a density change is presented. Its performance for a one-dimensional solidification problem and for the quasi two-dimensional melting of octadecane in a cubic cavity was tested. The new algorithm requires less than 1/9 of the iterations compared to the source based method in one dimension and less than 1/7 in two dimensions. Moreover, the new method is validated against PIV measurements from the literature. A conjugate heat transfer simulation, which includes parts of the experimental setup, shows that parasitic heat fluxes can significantly alter the shape of the phase front near the bottom wall.

Suggested Citation

  • Moritz Faden & Andreas König-Haagen & Dieter Brüggemann, 2019. "An Optimum Enthalpy Approach for Melting and Solidification with Volume Change," Energies, MDPI, vol. 12(5), pages 1-21, March.
    • Handle: RePEc:gam:jeners:v:12:y:2019:i:5:p:868-:d:211210
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    References listed on IDEAS

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    1. Sebastian Kuboth & Andreas König-Haagen & Dieter Brüggemann, 2017. "Numerical Analysis of Shell-and-Tube Type Latent Thermal Energy Storage Performance with Different Arrangements of Circular Fins," Energies, MDPI, vol. 10(3), pages 1-14, February.
    2. Vélez, C. & Khayet, M. & Ortiz de Zárate, J.M., 2015. "Temperature-dependent thermal properties of solid/liquid phase change even-numbered n-alkanes: n-Hexadecane, n-octadecane and n-eicosane," Applied Energy, Elsevier, vol. 143(C), pages 383-394.
    3. Zhang, P. & Ma, Z.W. & Wang, R.Z., 2010. "An overview of phase change material slurries: MPCS and CHS," Renewable and Sustainable Energy Reviews, Elsevier, vol. 14(2), pages 598-614, February.
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    Cited by:

    1. Xu, Minghan & Akhtar, Saad & Zueter, Ahmad F. & Alzoubi, Mahmoud A. & Sushama, Laxmi & Sasmito, Agus P., 2021. "Asymptotic analysis of a two-phase Stefan problem in annulus: Application to outward solidification in phase change materials," Applied Mathematics and Computation, Elsevier, vol. 408(C).
    2. Andreas König-Haagen & Erwin Franquet & Moritz Faden & Dieter Brüggemann, 2021. "A Study on the Numerical Performances of Diffuse Interface Methods for Simulation of Melting and Their Practical Consequences," Energies, MDPI, vol. 14(2), pages 1-16, January.
    3. Akhtar, Saad & Xu, Minghan & Mohit, Mohammaderfan & Sasmito, Agus P., 2023. "A comprehensive review of modeling water solidification for droplet freezing applications," Renewable and Sustainable Energy Reviews, Elsevier, vol. 188(C).

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