https://orcid.org/0000-0003-2776-5188
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ABSTRACT
Thermo-hydraulic behavior of a Phase Change Material (PCM) plays a crucial role in deciding the performance of Latent Heat Storage (LHS) devices. Discharge or Solidification is the prime portion that determines the performance of the LHS device. This work numerically models solidification in a vertical tube-in-tube LHS device. The phase change is accounted for using the fixed grid enthalpy porosity method. An independent numerical model built is validated with the experimental model. Dimensionless parameters, namely Rayleigh Number, Stefan number, Reynolds Number, and L/D ratio, vary in the range of 9.19x105 to 39.45x105, 0.2 to 0.5, 600 to 3000, and 1 to 15, respectively. Among all parameters, the Stefan Number has the greatest impact on the solid fraction and solidification time. For estimating the Solidification Time and Solid Fraction, correlations are proposed.
Nomenclature
| Dimensionless parameters | = | |
| Fo | = | Fourier Number |
| L/D | = | Length to Diameter ratio of Shell |
| Ra | = | Rayleigh Number |
| Re | = | Reynolds Number |
| St | = | Stefan Number |
| St* | = | Modified Stefan Number |
| MF | = | Melt Fraction |
| SF | = | Solid Fraction |
| Properties of PCM and HTF | = | |
| Cp | = | Specific Heat at constant pressure, J/kg.K |
| Do tube | = | Outer diameter of inner Tube, m |
| Dshell | = | Diameter of Shell, m |
| g | = | Acceleration due to gravity, m/s2 |
| h | = | Senible enthalpy, J/kg |
| k | = | Thermal Conductivity, W/m.K |
| L | = | Latent Heat, J/kg |
| p | = | Pressure, Pa |
| Ro tube | = | Outer radius of inner Tube, m |
| Rshell | = | Radius of Shell, m |
| t | = | Time, s |
| Tini | = | Initial Temperature of PCM |
| Tinlet | = | Inlet temperature of HTF |
| Tm | = | Melting Temperature of PCM |
| Abbreviations | = | |
| PCF | = | Phase Change Fraction |
| PCT | = | Phase Change Time |
| PCM | = | Phase Change Material |
| HTF | = | Heat Transfer Fluid |
| Greek alphabets | = | |
| α | = | Thermal Diffusivity, m2/s (ρ.Cp/k) |
| β | = | Thermal Expansion Coefficient, K-1 |
| Δh | = | Latent enthalpy, J/kg |
| ν | = | Kinematic viscosity, m2/s |
| ρ | = | Density, kg/m3 |
| µ | = | Dynamic viscosity, Pa.s |
| Coordinates in Polar System | = | |
| r | = | Radial Dimension |
| θ | = | Angular Dimension |
| z | = | Axial Dimension |
| Velocities | = | |
| u | = | velocity in r-dimension |
| v | = | velocity in z-dimension |
| Subscripts | = | |
| s | = | solid |
| l | = | liquid |
| m | = | melting |
| cm | = | complete melting |
| cs | = | complete solidification |
| ini | = | initial |
Acknowledgement
The corresponding author would like to give special thanks to VNRVJIET for the cooperation during the process of completing this work.
Disclosure statement
No potential conflict of interest was reported by the authors.