Adjoint-Based Compactness and Topology Optimization for Latent Heat Thermal Energy Storage Modules

Abstract

In this study, an integrated topology optimization (TO) framework for the design of phase-change material (PCM) based latent-heat thermal energy storage (LHTES) systems is pre-sented. The framework simultaneously optimizes both the geometric compactness of the enclosure and the spatial distribution of high-conductivity material (HCM) within the PCM region. This dual optimization is achieved by coupling two complementary parameteri-zation techniques. First, a density-based material interpolation approach is used, where a continuous design variable field, denoted as γ, governs the local distribution between HCM and PCM. Second, a space-mapping transformation employing two scaling factors, (Sx, Sy), dynamically modifies the global dimensions of the enclosure during optimization to achieve compactness. A time-dependent conduction-based melting model is developed to capture transient heat transfer and phase-change behavior within the enclosure. The proposed framework is validated through a series of two-dimensional numerical studies that explore the effects of different boundary temperatures, heat fluxes, and discharge durations. Results demonstrate that the integrated TO approach can substantially reduce the enclosure volume while maintaining the desired thermal performance. Specifically, compared to conventional parallel-fin designs, the optimized layouts achieved up to a 30% reduction in volume and a 40% decrease in temperature rise at the heat source. By combining material and geometric design within a single optimization loop, this work establishes a unified and computationally efficient method for developing compact and thermally efficient LHTES configurations. The proposed approach provides new insights for designing advanced thermal energy storage systems where space, weight, and efficiency are critical considerations.