A monolithic model of solid-liquid phase change problem

In latent heat storage, certain non phase change materials (non-PCMs) with high thermal conductivity are incorporated into the phase change materials (PCMs) with the aim of enhancing the efficiency of heat/cold storage. We term this type of non-PCMs as 'enhancer', which includes materials like graphite and copper foam, usually with a complex skeleton structure (He et al., 2023 [1]; Yang et al., 2018 [2]).In this article, we propose a phase field model to describe the solidification and melting phenomena of PCMs with enhancer from a microscopic point of view. Our model is governed by the energy equation coupled with the Allen-Cahn equation. A penalty technique is applied in the Allen-Cahn equation to describe the complex structure of the non-PCMs. We use the concept of thermal resistance to define the boundary condition on the contact interface of two materials to ensure the temperature jump. Thanks to the hybrid dual formulation, the temperature can be solved as a monolithic function while satisfying the temperature jump on the material interface. In temporal discretization, a numerical scheme is developed to decouple the phase field from the temperature. In the spatial discretization, the hybrid finite element method, the Raviart-Thomas (RT0) and P0 elements are used to solve the temperature, to satisfy the temperature jump on the interface. Simulations are performed using the open source finite element software FreeFem++. To improve computational efficiency, under the framework of FreeFem++, the mesh refinement is conducted by the Mmg module, and the parallelization is performed by the domain decomposition library ffddm. 2D and 3D simulations are carried out for both melting and solidification processes of a fossil -based organic PCM, CRODATHERM60 in the graphite skeleton on different porous structures to validate our model.