Junlin Cheng

Latent heat thermal energy storage (LHTES) is promising for solar energy utilization and waste heat recovery due to its high energy storage density and minimal temperature fluctuation. However, the low thermal conductivity of phase change materials (PCMs) severely limits charging/discharging rates. This study proposes a novel vertical shell-and-tube thermal storage structure that integrates axial cascading with a trapezoidal gradient tank. CuO nanoparticles are added to form a nano-enhanced phase change material (NePCM) to synergistically improve the thermal storage rate and temperature uniformity. The radial cascading, axial cascading, and trapezoidal layouts are systematically compared. It is found that the axial cascading and trapezoidal designs shorten the complete melting time by 28.98% and 29.22%, respectively, whereas the radial cascading exhibits poor performance due to the large interlayer thermal resistance. Building on this, with the cascading length ratios H₁ and H₂ and the radius gradient ratio R₁ as variables, an orthogonal design (L₈₁(9³)) is adopted to construct a numerical simulation scheme. Range analysis shows that the influence ranking is R₁ > H₁ > H₂. To reduce computational cost, a back propagation (BP) neural network surrogate model optimized by the crested porcupine optimizer (CPO) is developed. The maximum prediction errors on the test set are 2.41% for the thermal storage rate and 2.61% for the temperature non-uniformity index, with coefficients of determination of 0.998 and 0.969, respectively. Combined with non-dominated sorting genetic algorithm-II (NSGA-II) multi-objective optimization, Pareto optimal solutions are obtained, and the optimal parameter combination is H₁ = 1.7, H₂ = 1.7, and R₁ = 1.3. Numerical verification shows that, compared with the conventional tank, the average thermal storage rate increases by 38.81% and the temperature distribution non-uniformity index decreases by 29.02%, with prediction errors within 3%. The cascading-gradient fusion strategy and machine learning-assisted optimization method provide a theoretical basis and an efficient pathway for designing high-performance LHTES systems.