The applicability of volume-averaging method to simulate melting in a multi-scaled periodic structure

The additively manufactured multi-scaled periodic structure is considered as a thermal enhancer to accelerate melting rate of a PCM in a storage tank. Simulating this multi-phase problem can be carried out through different techniques each of which offering a unique interplay between accuracy and computational time. Full transient 3D simulations are offered as the most accurate and computationally involved benchmark case. In parallel, porous media models of the periodic structure is offered to save the computational time albeit at the expense of accuracy. Two cases of local thermal equilibrium (LTE) and local thermal non-equilibrium (LTNE) are investigated over a range of porosity for different solid matrix materials being copper, aluminium, nickel and stainless steel. To enable the use of LTE, a theoretical model for the effective thermal conductivity is developed and validated against detailed 3D results. The LTNE model, on the other hand, has to rely on an interfacial heat transfer coefficient which is developed in this study to minimize the error between simplified porous media models and the benchmark case. The LTNE model demonstrated excellent accuracy for higher thermal conductivity ratio and/or lower porosity, on the contrary, the LTE model for lower thermal conductivity ratio (stainless-steel cases) outperforms the LTNE model.