Freezing and Melting With Multiple Phase Fronts Along the Outside of a Tube

This paper addresses the modeling and analysis of thermal storage systems involving phase change with multiple phase fronts. The problem involves a fluid flowing inside a long tube surrounded by a phase-change material (PCM). The fluid temperature at the tube inlet cycles above and below the freezing temperature of the PCM, causing alternating liquid and solid layers to form and propagate from the tube outside surface. The objective of this paper is to predict the dynamic performance, temperature distribution, and phase front distribution along the tube. The problem is modeled as axisymmetric and two dimensional. Axial conduction is neglected and the problem is discretized into axial segments. Each of these axial sections is modeled as a transient, one-dimensional problem involving phase change with the possibility of multiple phase boundaries. The boundary element method (BEM) is used to obtain the transient solution in each axial section. Each axial segment communicates with downstream segments through the fluid flowing inside the tube. In order to ensure numerically stable results, a fully implicit discretization is used in both the axial and time variables. Results are presented for the time and axial evolution of the phase fronts and temperatures in response to a fluid inlet temperature that periodically alternates between values above and below the freezing temperature. This BEM is tested against the thermal network method (TNM) and the negligible sensible heat approximation (NSH) by comparing the outlet temperature and the latent state of charge. Results are found to be consistent and accurate.