Multi-scale concurrent material and structure design of a metal matrix for heat transfer enhancement in phase change materials

Designing thermal energy storage units with high energy and power density is a key objective for accommodating more renewable generation. The low thermal conductivity of phase change materials (PCMs) demands for finely tailored metal matrixes or foams to increase the amount of energy that can be stored/retrieved in a given amount of time. Previous design studies have explored a limited design space and never analyzed nor optimized the micro-structural topology of the matrix. This paper proposes for the first time a multi-scale design optimization of the PCM-metal composite and the metal matrix layout. The material constitutive law of the heat transfer structure at the macro-scale is governed by the layout of a representative volume element at the micro-scale, where a universal material layout is considered. The phase change problem is solved through a fixed-grid finite element method based on the enthalpy-porosity model, which accounts for natural convection in the liquid at the macro-scale. Topology optimization at both scales is formulated according to a density based approach. The optimization results indicate that: (i) the topology of the micro structure strongly influences the device performance and the macro structure layout; (ii) the multi-scale design approach yields remarkable improvements compared to a standard mono-scale approach; (iii) the optimized micro-structural layout is slightly sensitive to changes in the operating conditions.