An improved equivalent heat capacity method to simulate and optimize latent thermal energy storage units

The numerical simulation of phase-change heat transfer using the traditional equivalent heat capacity method often faces challenges in stability and accurately predicting solid-liquid interface evolution. To address this issue, a novel modified equivalent heat capacity model based on the Dirac function was proposed. The heat capacity of PCM is accurately described using the properties of the Dirac function, resulting in a continuous and smooth curve. This ensures a smooth transition of heat capacity between single-phase and two-phase states, enhancing the stability and precision of numerical simulations of phase-change heat transfer. Furthermore, a new approach for quantifying the temperature range of phase transitions was proposed. By using the first derivative of the heat flux with respect to temperature, as obtained through differential scanning calorimetry (DSC), the start and end points of the phase transition can be precisely identified, thus avoiding potential human influence in conventional methods. Using this method, when the threshold value is 0.0794, the Dirac delta-based equivalent heat capacity curve of paraffin R58 exhibits a high correlation with the experimental data, with the maximum error reduced to only 4.19%. At this time, the phase transition temperature range of 47.36 degrees C to 67.38 degrees C was determined. Then, a finite element numerical model for phase change heat transfer was established and compared with experimental or numerical simulation results from other researchers. The results show that the Dirac delta-based equivalent heat capacity significantly improves the numerical model's accuracy, accurately predicts changes in the solid-liquid interface, and captures details of temperature fluctuations caused by natural convection. Finally, the established numerical model was used to optimize the topology of the fin structure within the double-tube latent heat storage unit, resulting in the design of an efficient Y-shaped fin structure. Compared with traditional straight fins, the Y-shaped fins optimized the heat transfer path, enhanced natural convection, and achieved a more uniform temperature field during phase change, reducing melting time by 27.3%. This provides a new design solution for enhancing the performance of phase change heat storage units.