Experimental and Numerical Analysis of a PCM-Supported ...

properties that are associated with a single phase, such as the solid phase
temperature, while the volume averaged properties are associated with the spatial
average values of fluid motion, such as the superficial fluid velocity. It is extremely
important to distinguish and make use of both types of averaging concepts in the
model equations.
Because of the fact that PCM candidates usually exhibit low thermal conductivities
and are available commercially encapsulated in relatively large containers, adopting
the assumption of local thermal equilibrium can limit the validity and generality of the
mathematical model. In addition, due to the complexity of coupled heat and mass
transfer phenomena in the evaporator and condenser as described in figure (4.2), it
is not a simple task to assess the validity of this assumption, since the temperature
of the solid phase at the interface with the gas phase could be different from its
temperature at the interface with the liquid phase.
Moreover, assuming the lumped capacitance is valid during the phase change
process, the solid temperature inside the PCM beads varies between the liquid
temperature, the gas temperature, and the melting temperature. Hence existence of
deformable moving interface with its motion being not easily predicted and significant
discontinuities of properties at the interface cause a complicated coupling between
the field equations of each phase, which suggests that the use of a non-local thermal
equilibrium assumption is a possible solution to the problem. Therefore, the nonlocal
thermal equilibrium assumption or the two-energy equation models will be
adopted for the present study.
In this study, a mathematical model and numerical procedures shall be proposed to
determine the macroscopic transport and time history of the crucial field variables
such as the temperature, evaporation and condensation rates, pressure, and
velocities of the working fluids. These procedures will be developed first for the
single phase flow problem (i.e. the external thermal buffer) and then will be extended
to the multi-phase flow in the evaporator and condenser. Upon extending the
mathematical model to the case of dual phase change regenerators, a macroscopic
balance analysis for the whole plant with peripheries will be developed to couple the
three heat exchangers with the solar collector field to conduct numerical experiments
for a wide range of operation conditions and design features.
4.2.1 Model assumptions
Detailed pore scale modeling of momentum, heat, and mass transfer for the complex
flow in porous media would be difficult and especially the process dynamics would
be impracticable [12]. In all the physical systems under consideration, the phase
change heat transfer takes place on the length scale of the encapsulated PCM
spheres. In the evaporator and condenser, evaporation and condensation of water
vapor at different interfaces with gas and solid phases occur simultaneously with the
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