Exploring mushy zone constant in enthalpy-porosity methodology for accurate modeling convection-diffusion solid-liquid phase change of calcium chloride hexahydrate

• Published in: International communications in heat and mass transfer Vol. 152; p. 107294
• Main Authors: Ye, Wei-Biao, Arıcı, Müslüm
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01-03-2024
• Subjects: CaCl2·6H2O melting; Dimensionless analysis; Driving temperature difference; Enthalpy-porosity technique; Mushy zone constant; Novel correlation; Enthalpy-porosity technique; Novel correlation; Driving temperature difference; CaCl2·6H2O melting; Mushy zone constant; Dimensionless analysis
• ISSN: 0735-1933; 1879-0178
• DOI: 10.1016/j.icheatmasstransfer.2024.107294

Mushy zone constant (Am) is a crucial parameter in the momentum source term of enthalpy-porosity technique for modeling convection-diffusion solid-liquid phase change. Literature survey on the computations of Am found that the oriented customizable approaches have not revealed it in detail. Although the literature conducted an attempt on Am relationship by investigating the unconstrained melting of Calcium Chloride Hexahydrate (CaCl2·6H2O), they failed to directly establish the correlation between Am and ΔT; where ΔT is the driving temperature difference, which denotes an excess temperature of the hot wall above melting point of the CaCl2·6H2O. In view of the shortcoming in the literature, the relationship between Am and ΔT is here explored by the dimensionless analysis of the CaCl2·6H2O melting. The analysis finds a perfect correlation of dimensionless mushy zone constant (A) in terms of Grashof number (Gr) and Stefan number (Ste), i.e., A=Gr0.639Ste−2.947. Hence, a quick calculating method concerning Am values is established successfully. Then, the numerical verifications and validations for Am values implemented in enthalpy-porosity model are carefully taken into account. In addition, the theoretical reasonability is confirmed for the extrapolated Am values, and two interesting solid shapes of “Cap” and “Umbrella” are presented. Considering all of the applicable conditions herein, a generalized expression for melting fraction vs. dimensionless time is finally proposed.
•Rebuild relationship between mushy zone constant and driving temperature difference.•Verify simulation validation of mushy zone constant vs. driving temperature difference.•Extrapolate correlation of mushy zone constant and confirm its feasibility theoretically.