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ABSTRACT
In this study, the liquid–vapor mixture model was used for a numerical study of natural convective flow in a cryogenic tank with a capacity of 4.9 m3 under various conditions of heat flux and filling level to understand the early stages of convective flow phenomena and the consequent thermal stratification of cryogenic liquid. Two cryogens—liquefied natural gas (LNG) and liquefied nitrogen (LN2)—were compared to observe their effects. LN2 exhibited faster vaporization owing to its lower heat of vaporization. It was observed that higher heat flux and lower filling level led to faster vaporization and relatively vigorous heat transfer, showing early thermal stratification.
Nomenclature
| CP | = | specific heat at constant pressure [J/kg·K] |
| D | = | diameter of the tank [m] |
| g | = | gravitational acceleration [m/s2] |
| h | = | enthalpy [KJ/kg] |
| k | = | thermal conductivity [W/m·K] |
| keff | = | effective thermal conductivity [W/m·K] |
| = | mass change by the liquid phase | |
| n | = | normal direction |
| N | = | total number of calculation for the mesh independent study |
| Nu | = | Nusselt number |
| P | = | pressure [Pa] |
| Pr | = | Prandtl number |
| q | = | heat flux [W/m2] |
| r | = | radius [m] |
| Ra | = | Rayleigh number |
| Si | = | source term for the i-th (x, y, or z) momentum conservation equation |
| t | = | time [s] |
| T | = | temperature |
| v | = | velocity [m/s] |
| X | = | calculated value for the mesh independent study |
| Greek symbols | = | |
| α | = | volume fraction |
| β | = | coefficient of thermal expansion [K−1] |
| γ | = | time relaxation coefficient [1/s] |
| ε | = | difference between the calculated values using different grid and time-step sizes |
| μ | = | dynamic viscosity [Pa·s] |
| ρ | = | density [kg/m3] |
| Ψ | = | stream function |
| Subscripts | = | |
| a, b, c, n | = | phase |
| dr | = | drift |
| l | = | liquid |
| L | = | characteristic length [m] |
| m | = | mixture |
| r | = | radial |
| sat | = | saturation |
| vap | = | vapor |
| w | = | wall |
| z | = | axial |
| coarse, n | = | tested in total number of calculation with a coarse grid mesh |
| finer, n | = | tested in total number of calculation with a finer grid mesh |
Nomenclature
| CP | = | specific heat at constant pressure [J/kg·K] |
| D | = | diameter of the tank [m] |
| g | = | gravitational acceleration [m/s2] |
| h | = | enthalpy [KJ/kg] |
| k | = | thermal conductivity [W/m·K] |
| keff | = | effective thermal conductivity [W/m·K] |
| = | mass change by the liquid phase | |
| n | = | normal direction |
| N | = | total number of calculation for the mesh independent study |
| Nu | = | Nusselt number |
| P | = | pressure [Pa] |
| Pr | = | Prandtl number |
| q | = | heat flux [W/m2] |
| r | = | radius [m] |
| Ra | = | Rayleigh number |
| Si | = | source term for the i-th (x, y, or z) momentum conservation equation |
| t | = | time [s] |
| T | = | temperature |
| v | = | velocity [m/s] |
| X | = | calculated value for the mesh independent study |
| Greek symbols | = | |
| α | = | volume fraction |
| β | = | coefficient of thermal expansion [K−1] |
| γ | = | time relaxation coefficient [1/s] |
| ε | = | difference between the calculated values using different grid and time-step sizes |
| μ | = | dynamic viscosity [Pa·s] |
| ρ | = | density [kg/m3] |
| Ψ | = | stream function |
| Subscripts | = | |
| a, b, c, n | = | phase |
| dr | = | drift |
| l | = | liquid |
| L | = | characteristic length [m] |
| m | = | mixture |
| r | = | radial |
| sat | = | saturation |
| vap | = | vapor |
| w | = | wall |
| z | = | axial |
| coarse, n | = | tested in total number of calculation with a coarse grid mesh |
| finer, n | = | tested in total number of calculation with a finer grid mesh |
Acknowledgments
This work was supported in part by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) and the Ministry of Trade, Industry & Energy (MOTIE) of the Republic of Korea (No. 20143030040840), and in part by the Technology Advancement Research Program funded by the Ministry of Land, Infrastructure and Transport of Korean Government (16CTAPC086565-03).
