Thermal performance of combined solar systems with different collector efficiencies

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Solar Energy Vol. 72, No. 4, pp. 299–305, 2002  2002 Elsevier Science Ltd S 0 0 3 8 – 0 9 2 X ( 0 1 ) 0 0 0 7 9 – 2 All rights reserved. Printed in Great Britain 0038-092X / 02 / $ - see front matter

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THERMAL PERFORMANCE OF COMBINED SOLAR SYSTEMS WITH DIFFERENT COLLECTOR EFFICIENCIES L. HENDEN, J. REKSTAD † and M. MEIR Department of Physics, University of Oslo, P.O. Box 1048 Blindern, N-0316 Oslo, Norway Received 10 August 2000; revised version accepted 27 June 2001 Communicated by ERICH HAHNE

Abstract—The performance of two kinds of solar systems for space- and domestic hot water heating has been compared by computer simulations. One system is a conventional radiator-based heating system with collectors of ‘ideal’ collector coefficients. The second system is a low temperature heating system with solar collectors of moderate efficiency. The investigation shows that the difference in performance of the two systems is in the order of 1–6%.  2002 Elsevier Science Ltd. All rights reserved.

transfer the necessary power. In low temperature heating systems, e.g. floor heating systems with large heating surfaces, the temperature in the heat distribution system can be reduced to approximately 5–78C above the room temperature. A low system temperature will generally increase the solar gain of the collectors and extend the buffer store’s thermal range of utilization (Rekstad et al., 1998). The aim of the present paper is to compare the performance of two kinds of solar systems. The solar gain will give a basis for evaluating the payback of the ‘investment in the collector efficiency’ and in the complete heating system. Few investigations of this kind have been carried out. The effect of collector efficiency on solar gain in small and medium-sized DHW systems has been investigated by Furbo and Shah (1997). The study concludes that the system performance is only weakly linked to the collector efficiency. The question whether larger collector area or higher collector efficiency meet the heat demand of a solar combisystem is studied by Fischer (1999), while the performance of solar combisystems in the German market has been tested, and their theoretical potential of performance has been studied by Pauschinger et al. (1998). These investigations referred, however, to heat distribution systems with high forward temperatures only. The influence of the heat distribution temperature in small solar combisystems has further been investigated by measurements and computer simulations (Neumann et al., 1996; Dahm, 1998).

1. INTRODUCTION

The main barrier for a large-scale introduction of thermal solar systems is the high costs compared to conventional heating systems. Solar systems for domestic hot water (DHW) preparation require collector areas in the range of 3–5 m 2 for a typical single family household. The collector area for combined systems for DHW preparation and space heating (solar combisystems) is considerably larger. Hence the costs of the collectors gain more importance, and the need of less expensive collectors that are adjusted to this field of application becomes evident. Normally the collector costs are related to the efficiency at high operating temperatures. Conventional solar systems operate at a temperature which is significantly higher than the temperature in demand from the user’s side. The latter temperature is in the range of 20–238C for space heating and approximately 508C for DHW preparation. The line of development shows that solar collectors have been introduced as an additional component to standard radiator-based heating systems with oil, gas, biomass or electricity as auxiliary heating source. Radiator systems require a temperature that is approximately 30–508C above the desired room temperature in order to

†

Author to whom correspondence should be addressed. Tel.: 147-22-856-475; fax: 147-22-856-422; e-mail: [email protected] 299

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2. SYSTEM CONFIGURATION

We study the total thermal performance of two solar system designs, shown in Fig. 1. System (A) is a radiator-based heating system with a highly efficient collector specified by almost ‘ideal’ collector coefficients (collector (a)). System (B) is a low temperature heating system with a nonselective collector of moderate efficiency (collector (b)). In order to carry out a fair comparison, the systems are made as similar as possible. In the design of the buffer store we allow free transport of the heat carrier between store volume and solar circuit, and between store volume and heat distribution system, both for system (A) and (B). The elimination of heat exchangers enables the utilization of solar heat at temperatures as close as possible to the required forward temperature in the radiator system (A) and the low temperature heating system (B). The buffer store includes an immersed tank for DHW pre-heating of 200 l volume. As shown in Fig. 1, the auxiliary heat for DHW preparation Q AUX( 1) and for space heating Q AUX( 2) is provided by an external heating source. The total auxiliary heat is the sum of these contributions, and presents the total power required in order to obtain the desired temperatures for space heating and DHW preparation. We assume that the systems (A) and (B) have the

remaining system parameters in common: the annual demand of space and DHW heating, the collector area, the tilt angle, the DHW pre-heater store volume and the heat buffer store volume. One basic difference between the two system designs is the lower threshold temperature for the supply of auxiliary heat to space heating. This threshold temperature, in the following named ‘characteristic’ temperature, is for the radiator system (A) 608C and for the floor heating system (B) 258C. The second difference lays in the collectors’ efficiency. The collector efficiency may in the first order be approximated by a linear function in DT /I, DT h 5 h0 2 k ? ] I where DT 5 (T collector 2 T ambient ) and I is the intensity of incident solar radiation. The coefficients characterising the two collectors are:

h0 5 0.81, k 5 3.0 Wm 22 K 21 Collector (b): h0 5 0.81, k 5 5.8 Wm 22 K 21 . Collector (a):

The efficiency curves of (a) and (b) are shown in Fig. 2. The difference in the system performances will give a basis for evaluating the payback of investment in ‘the collector efficiency’ and in the complete system. The collector with moderate efficiency has similar characteristics as the polymer-based collector described in (Henden, 2000; Norwegian Patent, 1994; Meir et al., 1997; Rekstad et al., 1999). 3. THE SIMULATION PROGRAM

Fig. 1. The two different solar combisystems that we compare: Radiator based heating system (A) with a collector of ‘ideal’ collector coefficients (a), and a low temperature heating system (B) with a collector of moderate efficiency (b).

The performance of the systems was modelled by a simulation program developed at the University of Oslo (Ingebretsen, 1992). The program calculates the solar gain for the specified system, based on the insolation, the ambient temperature, the latitude, the parameters specifying the solar collector system, the total energy demand for DHW preparation and space heating and their daily and annual load profiles. The time step for the calculation is set to 1 h, the results are given with monthly resolution. Instead of using standard Test Reference Years, the weather data are generated by a Monte Carlo-type simulation. Few parameters need to be adjusted in order to obtain representative data for the local climate to the extent necessary for modelling the performance of solar systems. The relations used for modelling the solar irradiation and the ambient temperature are presented in Sections (3.1) and (3.2). The

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Fig. 2. Efficiency of the ‘ideal’ collector (a) and the moderately efficient collector (b).

typical CPU consumption of a 1-year calculation with 1-h time steps is about 1.5 s using a single node 300 MHz PC. The simulation program is thus an efficient tool to study the effects of various design and weather parameters.

locations this distribution is assumed to have a similar functional form. The solar irradiation I on a horizontal plane can be described by the following empirical formula (Meinel and Meinel, 1977; Sørensen, 1979):

3.1. The insolation model

I 5 S ? exp[2[a ? (c´ 1 c 1 1 c 2 cos( r ))] c 3 ]

The simulation program uses a semi-empirical relation in order to generate the ‘weather’ and herewith the solar irradiation during a year. The weather is characterised as either ‘good’ or ‘bad’, defined by the clearness index K (Duffie and Beckman, 1991): K 5 H /Ho . 0.5 K 5 H /Ho , 0.55

for ‘good weather’, and for ‘bad weather’.

From this the number of succeeding days with good or bad weather can be determined, as well as their frequency distribution. The present model was developed on the basis of weather statistics from the southern part of Norway. For these data the frequency of observed period lengths can be described by an exponential function (Ingebretsen, 1992): P(n d ) 5 1 2 exp(2n d / kn d l),

(1)

where P(n d ) is the probability that the number of succeeding days with ‘good’ or ‘bad’ weather is n d days or less, and kn d l is the mean period length. The simulation program selects the actual period length from this distribution. For other

(2)

S is the Solar constant, a the atmospheric thickness, c 1 , c 2 , c 3 , are empirical parameters dependent on the declination, time-angle and latitude. The term cos( r ) 5 cos(2p ? (d / 181) / 365) compensates for the mean seasonal variation and the parameter ce describes the absorption in the atmosphere. Typical simulation input values for ce are 0.4 for climates with mainly clear sky and 0.9 for mainly overcast sky. The diffuse component of the solar radiation is not calculated explicitly, but absorbed in the normalisation of the radiation flux. In order to verify the weather data generated by the program, simulated and measured period length distributions have been compared for various insolation intensities, and are illustrated in Fig. 3. The frequency distribution shows a satisfactory agreement between simulated and measured data for high insolation intensities. The frequency of the lowest intensities is underestimated by the model. This effect is, however, of minor importance when the thermal performance of solar systems is calculated, because such low solar intensities are below the threshold insolation for the solar system operation.

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Fig. 3. Simulated and measured period length distribution for different solar irradiation intensities for the location Oslo.

3.2. Ambient temperature The model generates the ambient temperature in terms of daily mean values which are modified such that it represents the ambient temperature during sunshine hours, T a . This temperature is representative for the periods in which the solar system is active. It has the following seasonal variation:

S

d 2 d w 1 91 T a (d) 5 T¯ a 2 DT¯ a ? sin 2p ? ]]]] 365

D

(3)

where T¯ a is the annual mean value, DT¯ a the amplitude of annual variation of T a , and d w is the day number of the warmest day of the year. A relation similar to Eq. (3) determines the variation of the cold tap water temperature T c during the year.

3.3. Program validation Simulations with the present program have been compared with TRNSYS simulations (Rømen, 1992) and with results obtained from

in-situ measurements (Rekstad et al., 1981). The comparison is shown in Table 1. The present simulation gave about 8% lower performance than the corresponding TRNSYS simulation, case 4. This deviation is in the same order as the difference between measured and simulated solar gain for case 3. For cases 1 and 2 the monitoring periods were short, so that the uncertainty of the results are larger. We conclude that the present simulation program gives satisfactory results, both compared to the in-situ measurements and to the results of the TRNSYS simulations. 4. SYSTEM PERFORMANCE STUDIES

The thermal performance was determined for the system configurations (A,a), (A,b), (B,a), (B,b). The influence of collector area (10 m 2 , 20 m 2 , 30 m 2 ) and buffer store volume (1 m 3 , 2 m 3 , 3 m 3 ) were studied. Each configuration was analysed for northern European climate (Oslo, Norway, 59.98 N) and middle European climate (Stuttgart, Germany, 48.88 N). The mean annual

Table 1. Simulated solar gain compared to results from in-situ measurements Case

Measuring / simulation period

Collector area [m 2 ]

Heat store volume [m 3 ]

Measured solar gain [kWh]

Simulated solar gain [kWh]

TRNSYS simulation [kWh]

1 2 3 4

Feb.–May 98 May–Aug. 98 1 year 1 year

31.7 21.1 28.0 100.0

3.0 2.0 3.0 6.0

3040 2590 6550 –

3070 3930 6150 19 720

– – – 21 460

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Fig. 4. Influence of collector area and heat store volume on the annual solar gain for different kind of solar systems: The performance of ‘ideal’ flat plate collectors (a) and collectors of moderate efficiency (b) are studied in combination with radiator-based heating (A) and with a system with low temperature heating (B). The performance was calculated for Oslo. The uncertainty of 690 kWh / a is due to the Monte Carlo weather generator for a 10 years period.

insolation on a horizontal surface is 1139 kWh / m 2 for Stuttgart and 985 kWh / m 2 for Oslo (Meteonorm, 1997). The collector tilt angle is 458 and the orientation of the collector field is direct south. For each configuration the mean value of a ten-years simulation was calculated. The reference case is an average single-family household in Europe with a daily hot water consumption of 250 litres at a temperature of 528C. The annual heat demand for space heating is 12 000 kWh and for DHW preparation 4600 kWh. Fig. 4 illustrates the dependency of solar gain on collector area and buffer store volume for location Oslo. The left part of the figure shows the performance of the ‘ideal’ collector in different system configurations, the right part that of the collector with moderate efficiency. The uncertainty of 690 kWh / a is related to the fact that the weather in the simulation program is generated by a Monte Carlo-type simulation and refers to a 10 years simulation. The delivered energy increases with increasing collector area. The dependency of the heat store volume is small, particularly for the smallest collector area. For the 10 m 2 collector, the difference in delivered energy between the three buffer store volumes is less than 7%. However, the collector of moderate efficiency is less dependent on the buffer store volume than the ‘ideal’ collector. For a given collector area, buffer store volume and system type the solar gain of the ‘ideal’ collector is always larger. For system (A) the difference is 2563%, for system (B) 1462%. The performance of the collectors in a low

temperature heating system (B) exceeds in all cases the performance in a radiator-based heating system (A). Table 2 compares the annual solar gain of the system configuration (A,a) and (B,b) for the location Oslo and Stuttgart based on the same reference case. The presented results are again annual mean values over a 10 years simulation period with an uncertainty of 690 kWh / a. The solar gain does not differ more than 6% between configuration (A,a) and (B,b) (Oslo: 1–5%, Stuttgart: 1–6%). Hence the solar gain of a combisystem with collectors of moderate efficiency in a system with a low temperature heating is almost the same as with the gain obtained from high efficient collectors with a radiator based heating system. Fig. 5 shows the results of Table 2 in terms of

Fig. 5. The influence of the collector area on the annual solar fraction for system (A,a) and (B,b) for the locations Oslo and Stuttgart. The buffer store volume is 1 m 3 per 10 m 2 collector area.

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Table 2. Influence of collector area and heat store volume on the annual solar gain of combined solar systems in northern European climate (Oslo) and middle European climate (Stuttgart). The annual solar gain in kWh, obtained in a system with an ‘ideal’ collector and a radiator-based heating system (config. (A,a)), and in a system with a collector of moderate efficiency and low temperature heat distribution system (config. (B,b)). The uncertainty is 690 kWh / a for all values Collector aperture area [m 2 ]

Store volume [litres]

Annual solar gain, OSLO [kWh a 21 ] (A,a)

(B,b)

(A,a)

(B,b)

10

1000 2000 3000

3780 3870 3910

3610 3800 3860

4450 4710 4760

4410 4420 4600

20

1000 2000 3000

4980 5200 5300

4850 5140 5220

6170 6430 6480

6140 6350 6530

30

1000 2000 3000

5420 6020 6210

5390 6020 5910

6980 7440 7630

6880 7790 7880

solar fraction as a function of the collector area for a buffer store volume of 1 m 3 per 10 m 2 collector area. The uncertainty of the calculated values due to the weather simulation is shown. For the configuration (A,a) the solar fraction ranges from 23 to 37% in Oslo and from 27 to 46% in Stuttgart. For the configuration (B,b) the solar fraction lays between 22 and 36% for Oslo and between 27 and 48% for Stuttgart.

NOMENCLATURE a ci ce d dw H H0

5. CONCLUSION

The thermal performance of different solar combisystem designs have been investigated: The collector was either almost ideal or with moderate efficiency, while the heat distribution system was either based on high or low temperature distribution. When we compared the combination ‘ideal’ collector efficiency and radiator-based heating (A,a) to the combination moderate collector efficiency and low temperature distribution system (B,b), the following conclusions were drawn: • The solar fractions of the systems (A,a) and (B,b) did not reveal significant differences in the various cases investigated. • The heat distribution temperature is crucial to the total performance of the solar system. • The collector efficiency is less important when the temperature in the heat distribution system is low. • The results could motivate a reconsideration of the strong focus on collector efficiency, which has been ruling for test institutions and governmental subsidy programs until today.

Annual solar gain STUTTGART [kWh a 21 ]

I K k nd kn d l P(n d ) Q AUX(i ) S T a (d)

Tc T SYS

h h0

atmospheric thickness dependent on solar position, 5unity at zenith empirical parameters dependent on declination, time-angle, latitude; i51, 2, 3 empirical parameter, describing the atmospheric absorption day number (1, 356) day number of the warmest day of the year daily mean solar irradiation at ground level (Wm 22 ) maximum solar radiation at ground level on a clear day (Wm 22 ) intensity of incident solar radiation (Wm 22 ) clearness index overall heat loss coefficient (Wm 22 K 21 ) period length5number of succeeding days of same clearness index K mean period length probability for a period of succeeding days n d of same clearness index K auxiliary heat; i51: space heating; i52: DHW preparation Solar constant (Wm 22 ) ambient temperature during sunshine hours of day d (8C) amplitude of annual variation of T a (K) mean annual ambient temperature during sunshine hours (8C) cold tap water temperature (8C) system temperature (8C) cos( r )factor compensating for seasonal variation of I solar collector efficiency solar collector efficiency at DT 5 (T collector 2 T ambient ) 5 0

Acknowledgements—Financial support from the Norwegian Research Council under the R&D frame program NYTEK — Efficient, Renewable Energy Technologies is acknowledged. The authors wish to thank Dr. Ole Martin Løvvik for proofreading this manuscript.

Thermal performance of combined solar systems with different collector efficiencies

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