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

Abstract

Mushy zone constant ( A m ) 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 A m found that the oriented customizable approaches have not revealed it in detail. Although the literature conducted an attempt on A m relationship by investigating the unconstrained melting of Calcium Chloride Hexahydrate (CaCl 2 ·6H 2 O), they failed to directly establish the correlation between A m and Δ T ; where Δ T is the driving temperature difference, which denotes an excess temperature of the hot wall above melting point of the CaCl 2 ·6H 2 O. In view of the shortcoming in the literature, the relationship between A m and Δ T is here explored by the dimensionless analysis of the CaCl 2 ·6H 2 O 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 = G r 0.639 St e − 2.947 . Hence, a quick calculating method concerning A m values is established successfully. Then, the numerical verifications and validations for A m values implemented in enthalpy-porosity model are carefully taken into account. In addition, the theoretical reasonability is confirmed for the extrapolated A m 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.

Topics & Concepts