Constrained melting of spherically encapsulated phase-change materials with natural convection: regime transition and predictive correlations

Accurately predicting the melting of encapsulated phase-change materials (PCMs) is essential for optimising thermal energy storage (TES) systems, especially when natural convection dominates at high-Rayleigh-number conditions. This study conducts a pore-scale study on the constrained melting of spherical PCM capsules, using a multiple-relaxation-time lattice Boltzmann method for the thermal flow, combined with an immersed boundary method for the solid–liquid interface. A novel ray-based phase identification scheme is introduced to resolve concave phase boundaries under strong convection, thereby improving the model accuracy in high-Rayleigh-number simulations. The model is validated against analytical, numerical and experimental benchmarks, showing superior capability and accuracy. For constrained PCM melting, the melting behaviour is reproduced, and effects of boundary temperature ( $T_b$ ), initial subcooling ( $\Delta T_s$ ) and capsule size ( $l_z$ ) are examined with a fixed Prandtl number ( $\textit{Pr}=59.76$ ). Higher $T_b$ accelerates melting, whereas $\Delta T_s$ has only minor effects. Reducing $l_z$ shortens the melting time due to the smaller PCM volume, but increases the dimensionless melting time by suppressing natural convection and shifting the melting process from convection- to conduction-dominated regimes. Accordingly, a critical capsule size $l_{z,c}$ is identified, below which conduction governs the melting process. A unified Rayleigh number of $Ra_c\approx 1.9\times 10^4$ is obtained for all $l_{z,c}$ under varying $T_b$ , serving as a universal threshold between the two melting regimes. For predicting liquid fraction evolutions in both conduction- and convection-dominated regimes, two empirical correlations are proposed via dimensional analysis. These findings advance the understanding of constrained PCM melting and support TES system optimisation across diverse operating conditions.