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

4 Theoretical Analysis and Modeling
In this chapter, detailed thermodynamic and hydrodynamic modeling of various
components of the proposed HDH system has been developed. Pertinent theories,
several correlations, and closure models adopted from literature will be presented. A
mixed micro-macro balance transient simulation model in one spatial dimension for
capturing heat and mass transfer phenomena in the HDH plant as a whole has been
established. The model is fairly general to be applied as a design and optimization
tool for HDH plants with different types of packing and coupled to sensible or latent
thermal storage systems.
4.1 System variables
The system overall setup and operation processes which have been used for
developing the mathematical model are illustrated schematically in figure (4.1). The
setup is typically the same as that of figure (3.1) but the main operation parameters
of interest for the development of heat and mass balances in the following sections
are depicted on figure (4.1) for ease of referencing. As described previously, the
setup works on the same principle and contains two main sections; the distillation
(HDH) cycle and the solar water heater. The later consists of a solar collector and
PCM storage tank. A flat-plate solar collector (FPC) is proposed to provide the
thermal power supply to the system.
In figure (4.1), it is assumed that part of the outlet brine is blown down to keep the
salt concentration within a certain limit identified by the brine recirculation factor (r c ).
The other part is blended with the seawater makeup and re-circulated through a heat
exchanger (brine heater) downstream of the condenser where the latent heat of
condensation is partly recovered by the warm brine blend.
The warm brine flow is heated further through the solar water collector and then
passed through the external thermal storage and hence the cycle is repeated. The
collected solar energy during day time will then be divided between the load and the
storage tank. When solar energy is no longer available, the collector flow will be
bypassed and the load is handled by discharging the thermal storage until either it is
fully discharged (nightly part time operation) or solar energy again is available (24-
hour operation). The above description assumes no heat losses during the fluid
flows through piping and tube connections.
Existence of PCM packing (or any conductive medium) in the evaporator and
condenser creates a parallel path for heat and mass transfer between gas and liquid
through the packing elements due to partial wetting of the packing surfaces as
shown in figure (4.2). Let the subscript “s” identify the solid particles and subscripts
“l” and “g” designate the liquid water and humid air (air-water vapor gas mixture)
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