Sensitivity of Numerical Predictions to the Permeability Coefficient in Simulations of Melting and Solidification Using the Enthalpy-Porosity Method

Amin Ebrahimi, Chris R. Kleijn and Ian M. Richardson
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Amin Ebrahimi: Department of Materials Science and Engineering, Delft University of Technology, Mekelweg 2, 2628 CD Delft, The Netherlands
Chris R. Kleijn: Department of Chemical Engineering, Delft University of Technology, van der Maasweg 9, 2629 HZ Delft, The Netherlands
Ian M. Richardson: Department of Materials Science and Engineering, Delft University of Technology, Mekelweg 2, 2628 CD Delft, The Netherlands

Energies, 2019, vol. 12, issue 22, 1-18

Abstract: The high degree of uncertainty and conflicting literature data on the value of the permeability coefficient (also known as the mushy zone constant), which aims to dampen fluid velocities in the mushy zone and suppress them in solid regions, is a critical drawback when using the fixed-grid enthalpy-porosity technique for modelling non-isothermal phase-change processes. In the present study, the sensitivity of numerical predictions to the value of this coefficient was scrutinised. Using finite-volume based numerical simulations of isothermal and non-isothermal melting and solidification problems, the causes of increased sensitivity were identified. It was found that depending on the mushy-zone thickness and the velocity field, the solid–liquid interface morphology and the rate of phase-change are sensitive to the permeability coefficient. It is demonstrated that numerical predictions of an isothermal phase-change problem are independent of the permeability coefficient for sufficiently fine meshes. It is also shown that sensitivity to the choice of permeability coefficient can be assessed by means of an appropriately defined Péclet number.

Keywords: melting; solidification; mushy zone; permeability coefficient; enthalpy-porosity method (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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