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

that form the study logical foundation. In reference to figures (3.2) and (3.3), three
levels of this foundation are of paramount importance: microscale level, macroscale
level, and coupling physics on these two levels along the packing height. Within the
simulation strategy, the dual phase change phenomena described in this chapter
(including the set of governing heat and mass balance equations together with the
apparent heat capacity formulation) can be treated in two ways or as a sequential
combination of the two: on a micro level, followed by a macro level.
4.6.2.1 Microscale level
At the microscale, the interfaces between all phases serve as particular locations
where boundary or flux conditions must be applied to capture the coupled interaction
between all phases in the form of source and sink terms (i.e. q ls , q gs , q lg , and q latent ).
Regarding the micro level, the physical phase change problem within PCM beads is
literally similar to the case of evaporation of a falling water or fuel droplet. Here, the
droplet, surrounded by air is gradually heated, giving rise to a change in evaporation,
which uses a latent heat formulation. For the PCM beads, the resultant heat transfer
from the surrounding water and gas phases is transferred to the beads, where at a
moment in time, the phase is changed from solid to liquid.
This can either be treated as local within the bead or as an integrated value at each
point along the packing height in the 1-D model. The later approach has been
adopted as mentioned earlier using the apparent heat capacity model. The dominant
heat transfer mechanism inside the PCM beads is assumed to be by conduction at
the thermal conductivity of the solid state including the phase change of
melting/freezing.
4.6.2.2 Macroscale level
At the macroscale, the wetting phase is described in terms of its average properties
within a small volume, i.e. the volume averaging technique. Thus, at each point, a
macroscale phase is characterized as occupying a fraction of the available volume
and to have a certain interface per unit volume with other phases. Each phase in the
system is described in a similar way. Precise definition of the interface shape is
neither required nor possible to obtain at the macroscale.
On the macro level, the continuous solid approach for modeling phase change
regenerators (PCR) is applied using the apparent heat capacity formulation. Here,
the latent heat is defined at the melting/freezing front, which moves in space and
time under the continuously updated apparent heat capacity. For the PCM phase
change, the jump in the heat capacity, which takes place at sharp melting points (i.e.
the singularity problem), is regularized by introducing a temperature range or mushy
region over which the phase change occurs.
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