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

liquid and solid phases, respectively. At steady state conditions, the energy flow from
gas to solid phase equilibrates with the energy flow from solid to liquid phase and the
local temperatures of all phases remain constant. Any change of the system
parameters will break steady state conditions, and the local temperatures will
change.
The condensation rate depends mainly on the vapor pressure gradient between the
bulk gas phase from one side and both the gas-liquid interface and the gas-solid
interface from the other side. The vapor pressure is a direct function of the
respective local temperatures, assuming saturation conditions in closed loop cycles.
However, the sensible energy flow components also affect the film temperature at
gas-liquid interface and gas-solid interface, which indirectly affects the condensation
rate. On the other hand, condensation contributes a considerable fraction of latent
heat to the liquid and solid phases and leads to rising their temperatures, which in
turn affects both heat and mass balances. In fact, the microscopic analysis of the
condensation process is much more complicated than the described macroscopic
analysis, while the later is sufficiently accurate for the present application and range
of operation conditions in comparison with the experimental measurements as will
be presented later.
4.2.4 Closure relationships
Predictive models for packed column performance incorporate macroscopic
properties of the entire column based on volume or spatial averaging technique
which was developed by Slattery [26], rather than focusing rigorously on underlying
local variations of momentum, heat, and mass transfer processes. Hence, closure
models have to be provided in the numerical scheme to capture the information that
is lost in the averaging process. Careful selection of the appropriate closure
relationships from literature is therefore a fundamental factor for achieving high
accuracy of the simulation model. Modeling and design of a randomly packed
distillation column requires a reliable specification of effective interfacial areas,
phase fractions, heat and mass transfer coefficients, and pressure drop. The next
sections will be devoted to the adopted modeling procedures and calculations of
such critical parameters.
4.2.3.1 Evaporation and condensation rates
The evaporation rate, the condensation rates at the gas/liquid interface and the
gas/solid interface can be written respectively as a function of the difference
between the vapor pressure or vapor concentration at these interfaces and the vapor
pressure or vapor concentration at the bulk gas:
m
evap
k
g
a
e
c
inter
( T ) c
(4.36)
l
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