An implicit algorithm for melting and settling of phase change material inside macrocapsules

A new, implicit algorithm for melting and settling of macro-encapsulated phase change material (PCM) is presented. The fixed grid mathematical model is based on the enthalpy-porosity technique and the volume of fluid (VOF) method. An immersed boundary method is applied to calculate the solid settling velocity, which is then prescribed by an extended Darcy term. As a test case, unfixed melting in a quasi two-dimensional cubic capsule is chosen. The newly introduced implicit algorithm is compared to an existing explicit algorithm and it is shown that the implicit calculation greatly improves the stability of the model. Moreover, the numerical model is validated against experiments performed within this work, whereby for the first time the settling velocity of the solid PCM is measured directly. Good agreement is found between simulation and experiment. The abilities of the new algorithm are demonstrated by multiple calculations with varying wall temperatures. Thereby, it is found that the solid settling velocity is at a quasi steady state only for a certain time. This time span reduces for higher wall temperatures.