Numerical and three-factor design investigation for melting process of phase-change spherical capsules in a solar thermal energy storage system

The application of spherical phase-change capsules in solar thermal energy storage systems (STESS) can enhance the sustainability and stability of energy output in solar energy utilization, making it a recent research hotspot. Nonetheless, the influence of neglecting three-dimensional effects through structural simplification on the phase-change process and the criteria for selecting the mushy zone constant in numerical studies are still not well-defined. In this context, a detailed analysis is conducted to investigate the variations in liquid fraction, temperature, flow field, and the time required for complete PCM melting caused by the structural simplification method. Subsequently, a three-factor design analysis is performed on parameters including spherical radius (R), mushy zone constant (A_mush) and phase-change temperature range (ΔT) with the aim of establishing a rational basis for selecting the mushy zone constant. Results show that the simplification of the 3D spherical encapsulation structure into a two-dimensional (2D) circular encapsulation structure introduces notable discrepancies in the PCM melting process. In contrast to the 2D circular encapsulation structure, the 3D spherical encapsulation structure demonstrates a reduction in the time required for complete PCM melting by 23 % to 36 %. The influence of simplifying the 3D spherical encapsulation structure into a 2D axisymmetric encapsulation configuration on the numerical simulation of the PCM melting process becomes more pronounced with the increase of R. For the 3D spherical encapsulation structure, the hierarchy of significance regarding the factors influencing the PCM melting process manifests in the sequence: R, A_mush, (R × A_mush), and ΔT. Furthermore, the formulated correlation based on the aforementioned four factors enables precise prediction of the time required for complete PCM melting within the 3D spherical encapsulation structure and offers a foundation for selecting the appropriate A_mush value in numerical simulation. The present work contributes novel insights into the accuracy and rationality of numerical simulations for phase-change processes in the STESS.