Janjai Etal 2000

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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

www.elsevier.com/locate/renene

* 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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