Structural optimization of multi-tube latent thermal energy storage heat exchangers based on particle swarm algorithm

Latent thermal energy storage (LTES) systems employing phase change materials (PCMs) have attracted considerable attention due to their high energy storage density and near-isothermal phase transition characteristics. However, the low thermal conductivity of PCMs constrains heat transfer rates and prolongs charging/discharging times. Although multi-tube heat exchanger configurations can enhance thermal performance, the quantitative relationship between inner-tube structural parameters and melting behavior remains inadequately understood, and a systematic optimization framework for tube layout is lacking. This study aims to explore the intricate relationships between inner tube spatial distribution and thermal charging characteristics of multi-tube LTES heat exchangers. Initially, a two-dimensional enthalpy-porosity model is established, and the transient temperature evolution and liquid fraction during thermal charging process are analyzed for configurations with three, four, and five inner tubes respectively through computational fluid dynamics (CFD). To quantify the influence of spatial tube distribution on the performance of thermal charging process, evaluation metrics including Nusselt number, temperature standard deviation, and temperature growth rate are employed, and a novel Layout Optimization Coefficient (LOC) that is a purely geometric index is introduced. Subsequently, a structural optimization methodology based on Particle Swarm Optimization (PSO) algorithmic framework is proposed to discover the optimal inner tube layout that minimizes complete melting time. The results reveal that under identical total heat transfer area, the five-tube configuration reduces the complete melting time by 42.51% relative to the three-tube reference, representing the gain attributable to increased tube count. LOC exhibits an inverse relationship with the complete melting time with higher LOC values indicating superior thermal performance. The PSO three-tube configuration achieves an 87.19% reduction in complete melting time compared with the three-tube reference and a 79.92% reduction in complete melting time relative to the five-tube configuration, representing that the predominant performance enhancement originates from strategic spatial rearrangement of inner tube rather than from tube count augmentation. The optimized structure exhibits more uniform melting and enhanced convective mixing throughout the PCM domain. This investigation not only clarifies the underlying relationship between structural parameters and thermal performance in multi-tube LTES heat exchangers but also provides an effective optimization paradigm, thereby offering both theoretical and practical guidance for enhancing the thermal performance in thermal energy storage systems.