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

solid-liquid phase change inside the PCM beads. However, the objective is to model
the bulk heat and mass transfer in these systems with no interest in tracking the
moving boundaries. Such microscopic details are neither easy to be captured nor
needed, instead, the macroscopic aspects of the flow are much more interesting as
an engineering problem. Therefore, dealing with such a multi-scale problem, a
fundamental question arises as how to bridge the computational scale and reduce
the problem to a simple form of solution. In order to establish a simplified
mathematical treatment, the underlying assumptions will be given in the subsequent
points and discussions.
The column wall is assumed to be perfectly insulated (adiabatic)
Thermal conductivity of PCM in the transverse direction is assumed to be infinite,
i.e. one layer of PCM is assumed to have the same temperature over the cross
section area of the tank. The thermal resistance of the spherical plastic shells
was neglected, since they are very thin and have a thermal conductivity close to
that of the PCM candidate. The heat flow inside the PCM beads is dominated by
conduction, and the convection heat transfer induced by internal recirculation
during the melting process was neglected.
The spherical PCM capsules behave as a continuous medium (i.e. continuous
solid model approach) with effective thermophysical properties, so that the liquid
film and the gas mixture could keep continuous and uniform flows.
The radial temperatures of liquid and gas phases are uniform (i.e. the transverse
temperature gradients within each phase are neglected) and the velocity profiles
are assumed to be fully developed and uniform at the entry point where heat and
mass transfer start.
Furthermore the wall effects on porosity, which may be present due to large
packing-to-column diameter ratio and results in greater porosity near the wall
than the central region of the column, are neglected for simplicity.
The liquid and gas phase fractions are also assumed constant along the packed
height since the evaporation and condensation rates are less than 5% of the feed
seawater in HDH. This assumption is extremely important for model simplification
otherwise another moving boundary between liquid and gas phases should be
traced which renders the numerical solution extremely difficult to be attainable.
Operating temperatures are below 85°C, and are therefore not high enough to
appreciate radiation effects.
Axial dispersion effects in the fluid which arise due to the mixing action within the
fluid as a result of eddy currents created as the fluid flows through the complex
porous passages are neglected.
The mathematical model is greatly simplified with these assumptions and leads to
time dependent equations in one spatial dimension. In addition, the 1-dimensional
formulation not only reduces the computational efforts, but also ensures more
stability of the simulation model as any small perturbations in the transverse
direction may cause large errors in the numerical solution.
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