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ABSTRACT
A Cartesian grid solver is developed that is capable of simulating the convection-dominated melting processes in a latent-heat thermal storage device (TSD). The Navier-Stokes equations are solved using a dynamically refined mesh. The phase boundary is tracked using the enthalpy method. Conjugate heat transfer is calculated with a strongly coupled implicit scheme. The approach does not require the creation of a geometry-specific grid, and so allows for efficient prototyping of different complex geometric designs. Systematic benchmarking of the results against other numerical approaches is conducted, followed by tests of two basic prototypes for the design of a TSD.
Nomenclature
| A | = | Fliqud nondimensional multiplier |
| Cp | = | heat capacity |
| Fliquid | = | liquid fraction of cell |
| g | = | gravitational force |
| Gr | = | Grashof number |
| k | = | thermal conductivity |
| L | = | length |
| Pr | = | Prandtl number |
| St | = | Stefan number |
| t | = | time |
| T | = | temperature |
| Tmelt | = | melting temperature |
| u | = | dimensional velocity in x direction |
| U | = | dimensionless velocity in x direction |
| v | = | dimensional velocity in y direction |
| V | = | dimensionless velocity in y direction |
| x | = | dimensional coordinate |
| X | = | dimensionless coordinate |
| y | = | dimensionless coordinate |
| y | = | dimensional coordinate |
| α | = | thermal diffusivity |
| β | = | coefficient of expansion |
| ΔT | = | change in temperature |
| ε | = | half of phase-change temperature range |
| θ | = | dimensionless temperature |
| ν | = | kinematic viscosity |
| τ | = | dimensionless time |
| Subscripts | = | |
| ghost | = | condition at a ghost point |
| hot | = | condition at a heated wall |
| init | = | condition at time = 0 |
| interface | = | condition at interface between b/t fin and PCM |
| mtr1 | = | material 1 |
| mtr2 | = | material 2 |
| o | = | characteristic condition |
Nomenclature
| A | = | Fliqud nondimensional multiplier |
| Cp | = | heat capacity |
| Fliquid | = | liquid fraction of cell |
| g | = | gravitational force |
| Gr | = | Grashof number |
| k | = | thermal conductivity |
| L | = | length |
| Pr | = | Prandtl number |
| St | = | Stefan number |
| t | = | time |
| T | = | temperature |
| Tmelt | = | melting temperature |
| u | = | dimensional velocity in x direction |
| U | = | dimensionless velocity in x direction |
| v | = | dimensional velocity in y direction |
| V | = | dimensionless velocity in y direction |
| x | = | dimensional coordinate |
| X | = | dimensionless coordinate |
| y | = | dimensionless coordinate |
| y | = | dimensional coordinate |
| α | = | thermal diffusivity |
| β | = | coefficient of expansion |
| ΔT | = | change in temperature |
| ε | = | half of phase-change temperature range |
| θ | = | dimensionless temperature |
| ν | = | kinematic viscosity |
| τ | = | dimensionless time |
| Subscripts | = | |
| ghost | = | condition at a ghost point |
| hot | = | condition at a heated wall |
| init | = | condition at time = 0 |
| interface | = | condition at interface between b/t fin and PCM |
| mtr1 | = | material 1 |
| mtr2 | = | material 2 |
| o | = | characteristic condition |