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

evaporation rate per unit volume of the packed column. It is noted that a, a ls , and a gs
are the total specific (per unit volume of the packed column), the wetted area (a w )
and the effective specific interfacial area (a e ) between liquid and gas respectively,
where a gs = a – a w is the specific gas-solid interfacial area. The symbols ε s , ε l , and ε g
denote the solid fraction in the bed, the liquid holdup, and the gas holdup
respectively. From definition, ε s + ε l + ε g = 1, the total porosity in the bed ε = ε l + ε g , and
the solid fraction ε s =1- ε.
In the above heat balance equations of fluid phases (i.e. equations (4.12) and
(4.13)), the last term stands for latent heat transfer in the same direction of heat
transfer from liquid to gas side assuming evaporation is the only mechanism of mass
transfer in the evaporator chamber. All other terms can be described similarly to
equations (4.7) and (4.8), for solid and fluid phases respectively.
The term Q, which appears on figure (4.4b) represents the energy flow by convection
heat transfer between each pair of phases due to the temperature difference
between them, and is represented in the energy equations by the last two terms for
the solid phase and both second and third terms on the right hand side of equations
(4.12)-(4.13) for liquid and gas phases respectively. The mass diffusion takes place
at the gas/liquid interface. The evaporation rate m evap is expressed in (mol.s -1 .m -3 ).
The corresponding latent heat of evaporation is absorbed by the gas phase. At
steady state conditions, the energy flow from liquid to solid phase equilibrates with
the energy flow from solid to gas phase and the local temperatures of all phases
remain constant. Any change of the operation and boundary conditions will break
steady state equilibrium, and the local temperatures will change correspondingly.
When the working fluid undergoes phase change (evaporation or condensation), a
rigorous model which couples the governing energy, mass and momentum balance
equations above together with state variables and thermodynamic relationships has
to be considered for simulating the system performance. Although it might be a
satisfactory approach for the liquid phase to be treated as incompressible fluid, it is
not so for the gas phase especially under natural draft operation or under high
pressures. Applying the Oberbeck-Boussinesq approximation in which all properties
of the gas mixture are assumed to be independent of the pressure and temperature
except for the density is applied in equation (4.13) to capture this effect will be
discussed in the momentum balance below. The solid-liquid phase change in PCM
beads is captured by introducing an apparent heat capacity c app in the one
dimensional form of the solid phase energy balance equation following the apparent
heat capacity approach [18].
Mass balance: The water vapor concentration gradient in the gas mixture at the
bulk of the packed bed along the axial direction (z) can be described by the equation:
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