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Modelling the performance of a large area
plastic solar collector
S. Janjai*, A. Esper, W. Mu hlbauer
Institute for Agricultural Engineering in the Tropics and Subtropics, Hohenheim University, 70593
Stuttgart, Germany
Received 11 January 2000; accepted 30 March 2000
Abstract
A mathematical model for simulating the performance of a large area plastic solar
collector was developed. The collector was installed and used to supply hot water to a hotel
in Almeria, Spain. It consists of three main components, namely a plastic water bag, a UV-
stabilized plastic sheet cover and an insulated oor. The plastic materials were used in this
collector in order to reduce the investment cost. To develop the model, the various modes
of heat transfer in the collector were analysed. A system of equations representing the
model was simultaneously solved using the implicit nite dierence method. The data
obtained from the experiments were used to validate the model. It was found that the outlet
water temperature calculated using the model agreed well with the experimental data. The
model was then used to investigate the eect of various parameters on the performance of
the collector. The results were used as a guideline to improve the performance of the
existing collector. According to the investigation, the original design of the total collectorlength of 48.2 m was too long for the operational ow rate of 0.083 kg/s. From the
simulation, the new values of the water depth and the ow rate were also recommended in
order to increase the eciency of the collector. The time lags between the radiation peak
and the outlet water temperature peak were relatively large for all cases. It was also found
that wind speed slightly aects the outlet water temperature. 7 2000 Elsevier Science Ltd.
All rights reserved.
Keywords: Solar collector model; Large area plastic collector; Solar water heater
0960-1481/00/$ - see front matter 7 2000 Elsevier Science Ltd. All rights reserved.
P I I : S 0 9 6 0 -1 4 8 1 (0 0 )0 0 0 8 7 -2
Renewable Energy 21 (2000) 363376
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* Corresponding author. Physics Department, Silpakorn University, 73000 Nakhon Pathom, Thai-land. Fax: +66-34-255820.
E-mail address: [email protected] (S. Janjai).
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Nomenclature
Cpf specic heat of water, J/kg KD depth of water in the plastic bag, m
G mass ow rate per unit area perpendicular to the ow, kg/s m2
hk, ij heat transfer coecient between the collector component i and j, by
mode of heat transfer k, W/m2 K
hw heat transfer coecient from the cover to atmosphere due to wind, W/
m2 K
IT global solar radiation on the horizontal surface, W/m2
L length of the collector, m
m.
mass ow rate of water, kg/s
qs, i solar radiation absorbed by the component i of the collector, W/m2
t time, s
Ti temperature of the medium or component i, K
Ub heat loss coecient through the back insulator to ambient air, W/m2
K
V wind speed, m/s
W collector width, m
x distance along the length of the collector, m
Greek symbols
as, i solar radiation absorptance of the component i
ts, i solar radiation transmittance of the component i
tL, i long wave thermal radiation transmittance of the component i
eL, i emittance of the component i
rf density of water, kg/m3
s StefanBolzmann constant, W/m2 K4
Subscripts
a ambient air
b top layer of the plastic bag
c convection heat transfer, plastic cover
d conduction heat transfer
f water in the plastic bag
water at the inlet of the collector
L long wave radiation
p bottom layer of the plastic bag
r radiation heat transfer
s solar radiation, skyw wind
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1. Introduction
The solar collector is the main component of solar water heating systems. In
general, conventional at-plate solar collectors with a metal absorber plate and
glass covers are used to transform solar energy into heat [14]. Although many
types of conventional collectors have been commercialised, their investment costs
are still relatively high. To overcome this problem, we have developed a low cost
large area plastic solar collector using a plastic water bag to collect solar energy.
A research project on solar water heating systems employing this type of collector
was intensively conducted at Hohenheim University with support from the
German Federal Ministry for Education, Research and Technology [58].
Although the design concept of this collector is similar to that of shallow solar
ponds (SSP) [911], many new theoretical and technological aspects of this
collector were eectively developed at Hohenheim University [12]. In this research
project, a pilot-scale solar water heating system using a large area plastic solar
collector was constructed and used to supply hot water to a hotel in Almeria,Spain.
Like other solar energy systems, the performance of the collector depends
mainly on the weather conditions, design and operating parameters. However,
to estimate the optimum values of these parameters in dierent weather
conditions using full experiments is costly and time-consuming. So the
development of a simulation model oers a better alternative and has proven
to be a powerful tool in the evaluation of the performance of the system
[13]. Therefore, apart from our experimental work, a simulation model of a
large area plastic collector was developed and used as a tool for investigating
the performance of the collector. This paper is emphasised on the modelling
of this existing plastic solar collector.
Many at-plate solar collector analyses have been based on the Hottel, Whillier
and Bliss (HWB) model [14,15]. A few authors have proposed a dierent model
for the shallow solar pond collector [16,17]. Many models found in the literature
[18,19] were developed under the assumption that each component of the collector
has a uniform temperature. These models are not adequate for the detailed
investigation of a large area plastic collector. This is due to the relatively large
dimensions and thermal inertia of the plastic solar collector. Therefore, a more
basic model accounting for local heat transfer is needed for evaluating the
performance of this type of collector.
The objectives of this work are to develop a simulation model for evaluating the
performance of the existing large area plastic solar collector in Almeria and to
investigate the inuence of parameters aecting its performance using this model.
2. The solar water heating system using a large area plastic solar collector
The large area plastic collector in this investigation was part of a solar water
heating system installed in Almeria, Spain to supply hot water to a hotel. The
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system consists of a heat exchanger, a pump and two collectors connected in series
as shown in Fig. 1.
Each collector has a dimension of 1.25 m 24.1 m. Through a pump (3), cold
water from the heat exchanger (4) enters into the rst collector (1). It is heated up
as it passes through the collector. The water then ows via the connecting pipe (7)
to the second collector (2) where additional heating takes place. From this
collector (2), water is pumped to the heat exchanger (4) where heat is transferred
to the running cold water (5), thus increasing its temperature. This hot water (6)
then ows to the hot water storage tank.
3. Development of the model
The main structure of this collector comprises three basic components, namely,
a plastic bag, a UV-stabilised plastic sheet cover and an insulated oor as shown
in Fig. 2. The top layer of the bag (2) is made of a transparent plastic sheet andthe bottom layer (4) is made of a black plastic sheet to absorb solar radiation.
The insulated oor (5) is made of plastic foam sandwiched between two metal
sheets. Plastic materials were used in order to reduce the investment cost of the
Fig. 1. Solar water heating system using a large area plastic solar collector; 1. the rst collector; 2. the
second collector; 3. pump; 4. heat exchanger; 5. inlet cold water; 6. outlet hot water; 7. pipe connected
to the two collectors; 8. inlet of the rst collector; 9. outlet of the second collector; 10. concrete block
substructure.
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collector. All parts of the collector are designed as modular components which
facilitate the construction of the collector.
The dierent modes of heat transfer occurring in the collector are schematically
shown in Fig. 2. Incident solar radiation is rst transmitted through the plastic
cover (1) then the top layer of the water bag (2), the water in the bag (3) and
nally to the bottom layer of the bag (4). The incident radiation is mainly
absorbed by the bottom layer of the water bag and the water inside the bag.
The various modes of heat transfer in the collector are summarized as follows:
(1) forced convection heat transfer between the bottom layer of the bag and the
water, between the top layer of the bag and the water and the wind-related
convection heat loss from the plastic cover to the ambient air, (2) convection heat
transfer in the air gap between the top layer of the bag and the plastic cover, (3)
heat loss through the insulated oor to ambient air and (4) long wave thermal
radiation heat exchange between the water and the sky, between the water and the
plastic cover, between the top layer of the bag and the sky, between the top layer
of the bag and the plastic cover, and between the plastic cover and the sky. Thesethermal radiation exchanges between water in the bag and the sky were taken into
account because the plastic cover cannot completely protect against long wave
radiation losses.
Heat balance equations for each collector component were formulated as
follows:
1. Plastic cover
hc, bcTb Tc hr, bcTb Tc hr, cfTf Tc hr, csTs Tc
hwTa Tc qs, c 01
Fig. 2. Schematic diagram showing the cross section of the large area plastic solar collector and heat
transfers in the collector; 1. plastic sheet cover; 2. top transparent layer of the water bag; 3. water in
the bag; 4. bottom opaque layer of the water bag; 5. insulated oor; 6. side insulation; 7. metal frame.
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qs, c as, cIT 10
qs, b as, bts, cIT 11
qs, f as, fts, ctS, bIT 12
qs, p as, pts, cts, bts, fIT 13
The multiple reections of solar radiation in the collector were neglected to
simplify the calculation. The optical properties of water measured by Palmer and
Williams [23] were used to calculate the transmittance of water inside the bag. To
facilitate further calculations, an empirical equation representing the transmittance
as a function of the water depth was formulated as follows:
ts, f 0X814897 0X07223 ln100 D 14
Eqs. (1)(4) were numerically solved by using the implicit nite dierence method
[24]. The optical properties of the plastic cover and the plastic bag from
measurements reported by Linkh [25] were used for the calculations. Computer
simulation programs written in FORTRAN77 were developed to implement these
calculations.
4. Validation of the model
Since the collector operated regularly to supply hot water to the hotel and the
parameters aecting the performance of the system were constantly monitored,
these data were used to validate the model. The values of global solar radiation,
ambient temperature, wind speed, mass ow rate of water in the collector and
inlet water temperature of the collector were used as input data for the simulation
model. The outlet water temperature of the collector calculated from the
simulation model was compared to the measured data. The results are shown in
Fig. 3. It was found that the values of the temperature calculated from the model
agreed well with those obtained from the measurements.
5. Investigation of the performance of the collector
The simulation model discussed in the preceding section was used to investigate
the various parameters aecting the performance of the collector. These
parameters were water depth, water mass ow rate and collector length. Globalradiation measured on a clear day in Almeria, Spain was used in the simulations.
In this investigation the two collectors connected in series were considered as one
unit with the total length of 48.2 m.
For this type of collector, the water owing in the collector serves as both, the
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working uid for transporting energy and a radiation absorber. Incident solarradiation is absorbed by both, water and the bottom layer of the bag. According
to the simulation, the inuence of water depth on the outlet water temperature is
shown in Fig. 4. For a given value of ow rate, an increase in water depth
decreases the outlet water temperature, as expected. These results demonstrate
that the water depth plays an important role on the performance of the collector.
To select a suitable value of water depth, we have to consider not only the outlet
temperature required but also the eciency of the collector.
As the collector functions in a transient state with a high thermal inertia, it is
very dicult to determine its eciency using an experimental approach. Therefore,
the computer simulation oers a better alternative to overcome this diculty. In
this study, the performance of the solar collector was simulated with a constant
value of solar radiation. The eciency of the collector was calculated when the
outlet temperature reached a steady state value, as the results shown in Fig. 5. It
Fig. 3. Comparison of the calculated and measured values of outlet water temperature.
Fig. 4. Variation of the predicted outlet water temperature with time for dierent values of the water
depth.
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was found that the collector eciencies for the water depth of 3 cm and that for 5
cm were not signicantly dierent. However, the water depth of 3 cm oers an
advantage in terms of higher outlet temperature. Although, the eciency for the
case of water depth of 10 cm was higher than that of 3 cm, the outlet temperature
was too low.
In general, the mass ow rate of the working uid is one of the most important
parameters aecting the performance of solar collectors. For this collector, the
water ows in contact with the whole inner surface of the plastic bag. The
convection heat transfer between the bag and the water depends on the ow rate.
In this study, the inuence of the mass ow rate on the water outlet temperature
was investigated using this simulation model. The results in Fig. 6 show that the
peak of outlet temperature increases with the decrease of ow rate, as expected.
For the operational ow rate of 0.083 kg/s, the peak temperature was relatively
high. To choose the suitable ow rate, we also need to know the eect of the owrate on the eciency of the collector. The eciency was calculated employing the
method similar to that used for the case of water depth. Fig. 7 indicates that the
Fig. 5. Predicted eciency of the collector for dierent values of water depth.
Fig. 6. Variation of the predicted water outlet temperature for dierent values of the ow rate.
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operational ow rate of 0.083 kg/s results in relatively low eciency and that the
operational ow rate should be increased. However, the increase in the ow ratewill decrease outlet temperature. To select the optimum ow rate, the compromise
between the outlet temperature and the eciency has to be taken into account.
For this case, the ow rate of 0.167 kg/s was recommended.
Unlike the plate-tube conventional collector, the plastic collector has fewer
constrains in terms of materials used for construction. Although the length of the
collector can be chosen, the investigation of the eect of collector length on the
outlet water temperature was still needed. In this work, the outlet water
temperature for collectors having dierent lengths was calculated using the model.
Fig. 8 shows a typical example of the eect of length on the outlet temperature.
Under these conditions, the water outlet temperature of collectors with a length of
40 m or more does not dier at any given time.
An additional investigation on the eect of length on the outlet watertemperature was also conducted. Since the temperature of water along the length
of the collector varies with the time of the day, only the water temperature along
the length of the collector determined when the water outlet temperature was at a
Fig. 7. Predicted eciency of the collector for dierent values of the ow rate.
Fig. 8. Variation of the predicted water outlet temperature with dierent values of length.
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maximum, was plotted against the distance from the collector inlet. The results
are shown in Fig. 9. These show that at the mass ow rate of 0.083 kg/s, watertemperature increases rapidly along the rst 40 m and gradually becomes stable.
The distance from the inlet where the water temperature becomes stable, increases
with the increase of mass ow rate. Beyond 40 m, increasing the collector length
has no more eect on water outlet temperature. Therefore, this implies that for
future design the length of the collector should be limited to the point where the
water outlet temperature is stable.
From the investigation of the eect of the water depth, ow rate and
collector length, it was found that this collector exhibited a large time lag
between the solar radiation peak and outlet temperature peak. This is due to
the thermal inertia of the water in the collector. This inertia can be clearly
demonstrated when the collector is subjected to a step change of radiation, as
shown in Fig. 10.
The performance of the collector depends not only on the design and operating
parameters but also on the environmental conditions. In this work, the eect of
wind speed on the outlet temperature was also investigated. The results shown in
Fig. 9. Predicted temperature prole along the length of the collector as the water outlet temperature
reaches the peak value.
Fig. 10. Variation of the predicted water outlet temperature with time for dierent values of ow rate.
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Fig. 11 demonstrate that the outlet temperature was not sensitive to wind speed.
This is due to the fact that water owing in the collector is covered by both theupper layer of the bag and the plastic sheet cover.
6. Conclusion
A simulation model of a large-area plastic solar collector installed in Almeria,
Spain was developed. The model was validated and found to t well to the
experimental data. Using the model, the simulation results indicate that water
depth, mass ow rate and length of the collector signicantly aect the water
outlet temperature. First, the simulation results indicate that for the operational
ow rate of 0.083 kg/s, the original design of the collector length of 48.2 m was
too long because the outlet water temperature was stable at the distance of about
40 m from the inlet of the collector. Next, both the outlet temperature and the
eciency are sensitive to the water ow rate. The operational ow rate of 0.083
kg/s should be increased to 0.167 kg/s in order to increase the eciency. In this
case, the original collector length was still suitable for this new ow rate. Finally,
the simulation results also demonstrate that the water depth of 0.03 m gives good
compromise between the outlet temperature and the eciency. In addition, It was
found that the outlet water temperature was not sensitive to wind speed.
The model developed in this work performed well in terms of accuracy when
compared with the experimental results and showed that it could be used for
further investigation and optimization of the solar water heating system using this
large area plastic collector.
Acknowledgements
The authors would like to thank the German Federal Ministry for Education,
Research and Technology for nancially supporting the project. The rst author
Fig. 11. Predicted eect of wind speed on the outlet water temperature.
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carried out the modelling part of the project under the Marie Curie Post-doctoral
fellowship program of the European Commission. The authors gratefully
acknowledge the European Commission for this support. The authors would also
like to thank Dr. M. Schwarz for supplying some useful data.
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