An enthalpy formulation for thermocline with encapsulated PCM thermal storage and benchmark solution using the method of characteristics

An enthalpy-based model of thermocline operation applicable to both single phase and encapsulated phase change filler materials was developed. Numerical simulation of the model was created using MATLAB. The method of characteristics was applied in space and time, mapping fluid temperature and filler enthalpy to a numerical grid, and in the case of a melting filler, allowed accurate tracking of PCM filler phase state interfaces to fractional positions of the grid. Careful consideration of various possible heat transfer conditions along with placement of PCM filler phase state interfaces in the numerical grid allowed for great versatility and accuracy in model application. Input of fluid and filler properties, tank size, time of operation, and initial and boundary conditions to the program returned a full representation to any desired amount of charge/discharge processes or cycles. The paper covers mathematical formulation, certain intricacies of numerical implementation, model verification, and the beginnings of application to prove proper operation and generality.