ABSTRACT
The present work deals with the numerical simulation of contact melting using a cell-splitting enthalpy method, which is an improvement over the conventional enthalpy-porosity method. It is demonstrated that such a method is far superior to the enthalpy-porosity method which not only is unable to capture the interface precisely but is also unable to capture the melt rates, unless the coefficients are back-fitted with the experimental data. In contact melting, the contact layer is thin and hence to resolve the flow, fine grids have to be used. A novel integral model is proposed where a single control volume is used in the contact layer. A parametric study is performed for contact melting in a square geometry and a correlation is evolved for the melt rates. The shapes of the solid during contact and noncontact melting are discussed and the physical mechanisms that decide the evolution are articulated.
Nomenclature
Ar | = | Archimedes number |
CP | = | specific heat (J/kg K) |
FBody | = | body force on the solid (N) |
FSurface | = | surface force on the solid (N) |
f | = | liquid fraction |
g | = | acceleration due to gravity (m/s2) |
= | unit vector along the acceleration due to gravity vector | |
h | = | enthalpy (J/kg) |
k | = | thermal conductivity (W/m K) |
L | = | characteristic length (m) |
= | unit normal | |
P | = | pressure (N/m2) |
Pr | = | Prandtl number |
Ra | = | Rayleigh number |
St | = | Stefan number |
T | = | temperature (K) |
TM | = | melting temperature (K) |
t | = | time (s) |
u,v | = | velocity components (m/s) |
V | = | volume (m3) |
V | = | velocity vector (m/s) |
x,y | = | coordinate directions (m) |
α | = | thermal diffusivity (m2/s) |
β | = | thermal expansion coefficient (1/K) |
γ | = | diffusion coefficient of a generic transport variable |
δ | = | thickness of the contact layer (m) |
ΔHM | = | latent heat of melting (J/kg) |
θ | = | nondimensional temperature |
μ | = | dynamic viscosity (N s/m2) |
ν | = | kinematic viscosity (m2/s) |
ρ | = | density (kg/m3) |
τ | = | nondimensional time |
ϕ | = | generic transport variable |
Subscripts | = | |
g | = | grid |
I | = | solid–liquid interface |
L | = | liquid |
M | = | evaluated at melting temperature |
S | = | solid |
W | = | wall |
Superscript | = | |
* | = | nondimensional variables |
Nomenclature
Ar | = | Archimedes number |
CP | = | specific heat (J/kg K) |
FBody | = | body force on the solid (N) |
FSurface | = | surface force on the solid (N) |
f | = | liquid fraction |
g | = | acceleration due to gravity (m/s2) |
= | unit vector along the acceleration due to gravity vector | |
h | = | enthalpy (J/kg) |
k | = | thermal conductivity (W/m K) |
L | = | characteristic length (m) |
= | unit normal | |
P | = | pressure (N/m2) |
Pr | = | Prandtl number |
Ra | = | Rayleigh number |
St | = | Stefan number |
T | = | temperature (K) |
TM | = | melting temperature (K) |
t | = | time (s) |
u,v | = | velocity components (m/s) |
V | = | volume (m3) |
V | = | velocity vector (m/s) |
x,y | = | coordinate directions (m) |
α | = | thermal diffusivity (m2/s) |
β | = | thermal expansion coefficient (1/K) |
γ | = | diffusion coefficient of a generic transport variable |
δ | = | thickness of the contact layer (m) |
ΔHM | = | latent heat of melting (J/kg) |
θ | = | nondimensional temperature |
μ | = | dynamic viscosity (N s/m2) |
ν | = | kinematic viscosity (m2/s) |
ρ | = | density (kg/m3) |
τ | = | nondimensional time |
ϕ | = | generic transport variable |
Subscripts | = | |
g | = | grid |
I | = | solid–liquid interface |
L | = | liquid |
M | = | evaluated at melting temperature |
S | = | solid |
W | = | wall |
Superscript | = | |
* | = | nondimensional variables |