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Experimental and theoretical study of the efficiency of a dual-function solar collector
Applied Thermal Engineering 31 (2011) 1751e1756
Contents lists available at ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Experimental and theoretical study of the efficiency of a dual-function solar collector Jinwei Ma, Wei Sun*, Jie Ji*, Yang Zhang, Aifeng Zhang, Wen Fan Department of Thermal Science and Energy Engineering, University of Science and Technology of China, Hefei, Anhui 230026, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 10 November 2010 Accepted 11 February 2011 Available online 23 February 2011
A design of solar collector that is able to provide both hot water and hot air has been proposed to increase annual thermal conversion ratio of solar energy. By modifying the conventional flat-plate solar water heater, the collector with L-shape fins can also function as a double-flow solar air heater. Experiments have been conducted to investigate the dual functions of the collector. It is shown that the thermal efficiency of the collector reached 50% in water heating, and varied from 41% to 55% in air heating depending on the ambient condition and flow rate. Mathematical model has been presented for the collector working in air heating mode. The theoretical results are in good agreement with the experiment results. Theoretical results show that the air flow rate is a dominant factor to determine the efficiency. The enhancement of the L-shape fins on the performance of the collector in air heating is also proved from the theoretic results. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Solar collector Dual function Double-flow L-shape fins
1. Introduction Among the solar thermal technology, the flat-plate solar collectors have been widely used as air heaters or water heaters. The solar air heaters have been applied to space heating [1] and crop drying [2] for energy savings. However the facilities can be left unused in some seasons of the year because the demand of hot air is normally seasonal. In order to increase the annual application of solar energy, a dual-function solar collector is introduced in this paper. The collector can generate not only hot air for spacing heating in winter or crop drying in harvest season, but also hot water in other seasons while the hot air is no longer required. Such integrated design makes it more cost-effective than those conventional systems solely for solar air heating. The principal types of solar air heaters are: the single pass with air flow above the absorber, air flow below the absorber, double air flow above and below the absorber, and double-pass [3]. It has been observed that among single pass, double-flow is superior to the other two [4e6]. Experimental and simulation studies on the double-flow solar air heater have shown that significant improvement in the performance can be obtained with an appropriate choice of the collector parameters and the top to bottom channel depth ratio of the two ducts [7]. Solar air heaters are relatively
limited in their thermal performance due to the low density, volumetric heat capacity and heat conductivity of air. Roughnessinducing wires and wavy passage have been used in collector to augment heat transfer [8e10]. Obstacles like aluminum cans have been inserted into the air channel to enhance the thermal performance of solar air heaters [11]. Many kinds of fins such as offset strip fins [12,13] and continuous fins [14] have been studied extensively. From theoretic analysis it has shown that continuous fins provided higher net energy gain than offset strip fins because of lower pressure losses [15]. The efficiency of the double-flow solar heater with fins has been investigated experimentally and theoretically [16]. In the present work, the dual-function collector is modified from the conventional solar water collector by adjusting the interior air gap and changing the shape of the absorber, as shown in Fig. 1. Besides water heating, the collector can also function as a double-flow air heater. The absorber fins of the collector are bended as L-shape to increase the heat transfer in air heating. Experiments have been conducted to investigate the collector performance in air heating and water heating. Mathematic model has been developed to analyze the factors affecting on the performance of the collector in air heating.
2. Experimental procedure 2.1. Description of the collector
* Corresponding authors. Tel.: þ86 551 3601641; fax: þ86 551 3606459. E-mail addresses: [email protected] (W. Sun), [email protected] (J. Ji). 1359-4311/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2011.02.019
The structure of the dual-function collector is shown in Fig. 1. A copper tube is welded at the bottom of each L-shape aluminum fin.
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J. Ma et al. / Applied Thermal Engineering 31 (2011) 1751e1756
Fig. 2. Test setup of air heating system.
Fig. 1. Schematic illustration of dual-function solar collector.
The fins of total 13 are arranged side by side within the gap between the cover glass and the back plate. Hence the gap is divided by the fins into up and down channels where the air flows through in the working mode of air heating, similarly as a in a double-flow solar air collector [3]. While in the working mode of water heating, water flows in the copper tubes, and the air channels are closed at inlet and outlet. The inlet and outlet of water tubes are also closed in air heating. The fins are coated with selective material to absorb incident solar radiation and heat working fluid (air or water) flowing by. The cover glass is of 4 mm thickness with the aperture of 1.94 m in length and 0.93 m in width. The heights of up and down air channel in the collector are of 0.0375 m and 0.0175 m, respectively. The vertical part of the fins is 0.026 m. The glass fiber with the thickness of 0.02 m is in the back panel and at sides of the collector for thermal insulations.
temperatures. Two additional thermocouples were put at the entrance and exit of the water route of the collector. The experimental setup of the solar air heating is schematized in Fig. 3. A vortex pump was used to drive the air flow. The air flow rate was measured by the thermal mass flowmeter (SG101D1), of which the percent error is of 10% calibrated by Anhui Institute of Metrology. The temperatures of the air at inlet and outlet, and the temperatures of at the exterior surface of glass cover and back panel were measured. The performance of the dual-function collector has been tested in the outdoor environment. The collector was mounted southfacing at an inclination angle of 35.5 that is around the degree of
2.2. Experimental setup The experiments for the air heating and water heating have been conducted separately. The experimental setup of water heating system is shown in Fig. 2. The copper tubes in the collector were connected to a tank of 100 l with the pipes and associated valves. In the experiment, water in the tank and tubes was refilled in the early morning. Natural circulation of water route took place because of thermosyphon effect while the collector received solar radiation and the water in the tubes was heated up. Four thermocouples were arranged equidistantly in the tank to measure water
Fig. 3. Photo of water heating system.
J. Ma et al. / Applied Thermal Engineering 31 (2011) 1751e1756
the local latitude. The incident solar radiation and wind speed were measured by Pyranometer (TBQ-2) and deflecting vane anemometer, respectively. The temperatures were measured by type T (coppereconstantan) thermocouples. The measurement data were recorded by data acquisition unit at an interval of one minute.
In water heating mode, the thermal energy gain is the heat accumulated by the water in the tank. The daily average efficiency can be calculated as the following,
h¼
Ztexp
(1)
0
where mw is the mass of water in the tank, Cpw is heat capacity of water, DT is the temperature increase of water in the tank, and 4, texp are time and the time duration of the experiment, respectively. In air heating mode, the thermal energy gain is the enthalpy increase of the flow air between outlet and inlet, expressed as
(2)
The instantaneous efficiency of the collector is the heat gain of the air divided by incident solar radiation as
Q h¼ u ¼ SAg
_ p mC Tf;o Tf ;i SAg
(4)
where the coefficient of the heat loss via glass
UT ¼ hw þ hrs
(5)
UB ðTb Ta Þ ¼ hrpb Tp Tb þ hcbf2 Tf 2 Tb
(6)
where the coefficient of the heat loss via back panel
1 H UB ¼ 1= þ R hw kR
(7)
For the absorber of L-shape fins
SAg d4
_ p Tf;o Tf;i Qu ¼ mC
A UT Tg Ta þ hrpg ab Tg Tp þ hcgf 1 Tg Tf1 ¼ 0 Ac
For the back plate,
2.3. Performance evaluation
mw Cpw DT
1753
(3)
_ is the mass flow rate of air flowing through the collector, where m Cp is the specific heat capacity of the air, Tf,o, and Tf,i are the air temperatures at the outlet and inlet, respectively. The uncertainty analysis has been carried out on the basis of the measured data. The propagation of uncertainty in estimating efficiencies is within 3.5% and 10.6% relative error for water heating and air heating, respectively. 3. Theoretic modeling of the collector in air heating In air heating, the essential components of the collector are the glass cover, the back plate and the absorber that is consisted with the 13 fins. Fig. 4 shows schematic diagram of the heat-transfer coefficients in the collector. Under the assumption that the temperatures of the glass cover, absorber and the back plate vary only in the direction of air flow, the energy balance equations are established as follows: For the glass cover,
Aab A Tp Tg þ hrpb Tp Tb þ hcpf 1 ab Tp Tf 1 Ac Ac þ hcpf2 Tp Tf 2 ¼ Ssg ap
hrpg
(8)
where Aab and Ac are the exposal area of the L-shape fins in the up channel and down channel, respectively; For the air stream in the up channel,
_ p dTf1 mrC A ¼ hcpf1 ab Tp Tf 1 þ hcgf1 Tg Tf 1 w dx Ac
(9)
where r is the ratio of the flow rate in the up channel to the total flow rate, and x is the direction of air flow; For the air stream in the down channel,
_ mð1 rÞCp dTf2 ¼ hcpf2 Tp Tf2 þ hcbf2 Tb Tf 2 w dx
(10)
The air flows through the upper and lower channel simultaneously, and meets at joint exit. Hence the pressure drops in the two channels are balanced at the exit. The pressure drop Dp is calculated via the apparent Fanning friction factor fapp:
Dp ¼ fapp
4L ru2 De 2
(11)
where the hydraulic diameter
De;i ¼ 4Hi wi =ð2ðwi þ Hi ÞÞ;
i ¼ 1; 2
(12)
H1 and H2 are the height of the up and down channels, respectively; w1 refers the fin spacing in up channel, and w2 refers the width of the down channel. The calculation of friction factor fapp adopts the method given in Ref. [15]. From balancing the pressure drops at exit that Dp1 ¼ Dp2, the ratio r of mass flow rate can be obtained. The convective heat-transfer coefficients in Eqs. (4)e(10) are calculated from dimensionless Nusselt number, as:
hc ¼ Nuk=De
(13)
where Nu number is calculated with the method in Ref. [15] for the air flows in fined channel and between parallel plates. The connective heat-transfer coefficient for air flowing over the exterior surface of the collector in Eqs. (5) and (7) is calculated by the following empirical equation [17].
hw ¼ 2:8 þ 3:0V
(14)
The irradiative heat-transfer coefficient of the glass cover is estimated by: Fig. 4. Schematic diagram of heat exchange coefficients in the dual-function collector in air heating mode.
hrs ¼ 3g s Tg þ Ta Tg2 þ Ta2
(15)
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J. Ma et al. / Applied Thermal Engineering 31 (2011) 1751e1756
Fig. 5. Water temperatures at the inlet and outlet of the solar collector.
Fig. 6. Variation of water temperatures in the tank with time.
The irradiative heat-transfer coefficients between absorber and glazing/back plate are obtained by:
from 28 C to 63 C. The average water heating efficiency of the dual-function collector was 50.1% calculated by Eq. (1). The daily heat gain is 8.0 MJ/m2, above the requirement of 7.5 MJ/m2 (under 17 MJ/m2 daily incident solar energy) in the Chinese National Standard of specification of domestic solar water heating systems [18]. In the air heating mode, the air is sucked into the inlet of the collector from ambient and heated up while passing the absorber. Fig. 7 shows the variation of the temperature at outlet with time in the experiment of one day. The mean wind speed was 3 m/s during the experiment. The air mass flow rate was adjusted as 0.025 kg/s. The air temperature changed at the outlet followed the trend of the solar radiation as expected. The air was heated up to nearly 49 C with the maximum temperature increase of 34 C at noon. The daily average thermal efficiency was 47.9%. The instantaneous thermal efficiencies of the collector at noon of four different days are listed in Table 1. The efficiencies varied from 40.8% to 55.0% under the flow rate from 0.007 kg/s m2 to 0.016 kg/ s m2. Although the ambient conditions were different, the flow rate showed as a dominant factor in the efficiency change. It is difficult to compare the performance of solar air collectors of different design if the size and operating conditions are different as presented in Ref. [11]. Nevertheless near the upper bound of the air flow rate in the present study, the efficiency has been reported around 53% and 59% of v-groove collector under 0.016 kg/s m2 [10] and cans collector under 0.017 kg/s m2 [11], respectively.
hrpg
s Tp þ Tg Tp2 þ Tg2 ¼ 1=3p þ 1=3g 1
hrpb
s Tp þ Tb Tp2 þ Tb2 ¼ 1=3p þ 1=3b 1
(16) (17)
By solving the energy equations (4), (6), and (8)e(10) under the boundary conditions:
x ¼ 0;
Tf1 ¼ Tf2 ¼ Ta
The temperature of the air streams can be obtained
ED C2 D1 Tf1 ¼ K1 el1 x þ K2 el2 x 22 þ Ta E C1 C2
(18)
ED C1 D2 þ Ta Tf2 ¼ K3 el1 x þ K4 el2 x 21 E C1 C2
(19)
where the coefficients C1, C2, D1, D2, E, K1, K2, K3, K4, l1 and l2 are given in Appendix A. Hence the temperatures of the air streams at outlet (Tf1,o, Tf2,o) can be obtained by substituting L (the length of the channel) for x in Eqs. (18) and (19). Then the thermal efficiency of the collector is the heat gain divided by the incident solar radiation, expressed as:
h¼
i h Qu _ p =SAc rTf1;o þ ð1 rÞTf2;o Ta ¼ mC SAc
(20)
4. Results and discussions The experimental test of water heating was carried out in good weather conditions during May 2009. Figs. 5 and 6 show the experimental results of one day with the temperature values averaged every thirty minutes. Because of the natural circulation of water between the collector and the tank, water temperatures at inlet and outlet kept rising during the test time as shown in Fig. 5. The legends ‘a’, ‘b’, ‘c’, ‘d’ in Fig. 6 stand for the measure points in the tank from top to bottom. It shows that water temperature was higher at higher position, but tends to be equal in the tank at the end of the test. The mean water temperature in the tank increased
Fig. 7. Air temperatures at outlet and inlet air temperatures versus time.
J. Ma et al. / Applied Thermal Engineering 31 (2011) 1751e1756
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Table 1 Air heating efficiency of the collector under different operating conditions (Expdexperimental; Theodtheoretical). Wind speed (m/s)
Ambient temperature ( C)
Radiation (W/m2)
Flow rate (kg/s)
Exp efficiency
Theo efficiency
3.0 2.0 2.0 1.9
12.5 21.3 21.0 11.1
744.35 801.03 681.59 705.61
0.013 0.018 0.024 0.029
0.408 0.446 0.496 0.550
0.418 0.464 0.504 0.553
The mathematical model has been tested with the experiment results. In the calculation, the coefficients of ap, 3p, s, 3g, 3b, kR were set as 0.9, 0.2, 0.8, 0.9, 0.94 and 0.1 W/(m K), respectively, according to the thermal properties of the material used in the collector. The efficiency from the theoretic calculation is in well consistency with that from the experiment as shown in Table 1. The relative deviation of the efficiency is less than 4%. Mathematical calculation has been performed to investigate the influence of the flow rate under the same ambient conditions: S ¼ 800 W/m2, V ¼ 2 m/s, and Ta ¼ 10 C. With the rise of the air flow rate, the heating efficiency increases, but the outlet temperature decreases, as shown in Fig. 8. The variation trend is the same as in Table 1. The increase of efficiency at higher air flow rate is because the whole collector is of lower temperature and less heat losses. Considering the collector has two working modes, double channels and L-shape fins are used, which is different from the traditional solar water heaters. The influence of the arrangement of the channels heights and fins of L-shape on the performance in air heating is studied theoretically. In the calculation, S ¼ 800 W/m2, _ ¼ 0:02 kg=s, the height of the whole air V ¼ 2 m/s, Ti ¼ Ta ¼ 10 C, m duct is fixed, but the ratio of the up channel to the whole duct varies. For comparison, a collector with an absorber of flat plate without vertical fins is also been studied. Fig. 9 shows influence of the channel height ratio and the shape of the absorber on the efficiency. The highest efficiency is at the height ratio 0.5 and 0.6 for the collector with the absorber of flat plate and L-shape fins, respectively. When the ratio is no larger than 0.5, which means the up channel is no higher than the down channel, collector performs better with the absorber of flat plate. It is caused by two reasons: the convective heat-transfer coefficient between the air stream and glazing is higher with L-shape fins; at the mean time, the higher friction factor from the L-shape fins results in less flow rate and higher temperature in the up channel. Hence the collector with the L-shape fins loses more heat via the glass cover when the ratio is no larger than 0.5. As the height ratio increases above 0.5, the flow rate
Fig. 9. Effect of the height ratio of up channel to the whole duct on the efficiency of collectors with flat-plat absorber and L-shape fins.
in the up channel is relatively increased, which diminishes the negative effect of L-shape fins and makes its higher convective heat transfer more pronounced, then the collector shows better performance with L-shape fins. Considering the collector’s another function as water heating, in which the down channel is better of smaller height to prevent natural convective air flow, the dual-function collector with L-shape fins is advantageous in air heating. The dualfunction collector with L-shape fins is convenient to produce for the factories manufacturing flat panel solar water heaters. 5. Conclusions The performance of a dual-function solar collector has been investigated by experiments. Mathematic model has been developed and validated by the experiment for the collector in air heating mode. Theoretical investigation has been carried out to analyze the effect of the flow rate and the structure parameters on the collector performance. The experiment results show that the collector can increase the temperature of 100 l water by more than 30 C after absorbing solar radiation for a whole day. The daily efficiency in water heating mode reached 50%. While in air heating mode, the daily mean and instantaneous efficiency reached 52% and 55%, respectively. The study shows that in air heating, although the efficiency increases with the flow rate, the temperature of the outlet air decreases with the flow rate. The L-shape fins in the dual-function collector have proved to have positive effect on the efficiency in air heating mode from the theoretic results. Acknowledgements This work was supported by the National Natural Science Foundation of China (No. 50876098) and the National Key Technology R&D Program of China (No. 2006BAA04B04). Nomenclature
Fig. 8. Effect of air flow rate on efficiency and air temperature increases.
A Aab Cp De H hc hr
area, m2 total exposed absorbing plate surface, m2 specific heat capacity of air, J/(kg K) hydraulic diameter, m height or thickness, m convective heat-transfer coefficient, W/(m2 K) irradiative heat-transfer coefficient, W/(m2 K)
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J. Ma et al. / Applied Thermal Engineering 31 (2011) 1751e1756
k L _ m Nu Dp Qu r
thermal conductivity, W/(m K) length air channel, m mass flow rate of air, kg/s dimensionless Nusselt number pressure drop in the channel, Pa useful energy gain, J ratio of the mass flow rate in up channel to the total flow rate dimensionless Reynolds number solar radiation, W/m2 temperature, K time, s loss coefficient from the glass to the ambient, W/(m2 K) loss coefficient from the bottom of lower air channel to the ambient, W/(m2 K) velocity of air flow, m/s velocity of ambient wind, m/s width of air channel, m fin spacing in the up channel, m direction of air flow
Re S T t UT UB u V w w1 x
Greek symbols absorptivity emissivity thermal efficiency viscosity of air, kg/(m s) density of air, kg/m3 StefaneBoltzman constant, 5.67 108 J s1 m2 K4 transmissivity time variable
a 3 h m r s s 4
Subscripts a ambient b back plate f air flow g glass cover i inlet o outlet p absorbing plate R back insulation 1 up channel 2 lower channel
_ p mrC w
_ mð1 rÞCp w UT þ hrpg Aab =Ac þ hcgf1 A ¼ hrpg Aab =Ac
W2 ¼
(A.1)
(A.2) (A.3)
B ¼ hrpb = UB þ hrpb þ hcbf2
(A.4)
G ¼ hrpg Aab =Ac ð1AÞþhrpb ð1BÞþhcpf1 Aab =Ac þhcpf2
(A.5)
. C1 ¼ hcpf1 Aab =Ac þ hcgf 1 A $ hcpf1 Aab =Ac þ hcgf 1 A G 1 AUT =hrpg
D1 ¼ D1 ¼ E ¼
(A.7)
hcpf 1 Aab =Ac þ hcgf 1 A S=G
(A.8)
hcpf 2 þ hcbf2 B S=G
(A.9)
. hcpf1 Aab =Ac þ hcgf1 A hcpf 2 þ hcbf2 B G
(A.10)
K1 ¼ ðW2 l1 C2 Þ=EK3
(A.11)
K2 ¼ ðW2 l2 C2 Þ=EK3
(A.12)
K3 ¼
l2 ðC2 þ EÞW2 ðTin Ta Þ l2 l1 l2 ED1 C1 D2 D2 þ l2 l1 E2 C1 C2 W2 ðl2 l1 Þ l1 ðC2 þ EÞW2 ðTin Ta Þ l2 l1 l1 ED1 C1 D2 D2 þ l2 l1 E2 C1 C2 W2 ðl2 l1 Þ
(A.13)
K4 ¼
l1 ¼
l2 ¼
ðC1 W2 þC2 W1 Þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðC1 W2 C2 W1 Þ2 þ4E2 W1 W2 2W1 W2
ðC1 W2 þC2 W1 Þþ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðC1 W2 C2 W1 Þ2 þ4E2 W1 W2 2W1 W2
(A.14)
(A.15)
(A.16)
References
Appendix A
W1 ¼
. C2 ¼ hcpf 2 þhcbf2 B hcpf2 þhcbf2 B G1 BUB =hrpb
ðA6Þ
[1] X.Q. Zhai, Y.J. Dai, R.Z. Wang, Comparison of heating and natural ventilation in a solar house induced by two roof solar collectors, Appl. Therm. Eng. 25 (2005) 741e757. [2] C. Tiris, M. Tiris, I. Dincer, Experiments on a new small-scale solar dryer, Appl. Therm. Eng. 16 (1996) 183e187. [3] K.S. Ong, Thermal performance of solar air heaters: mathematical model and solution procedure, Sol. Energy 55 (1995) 93e109. [4] I.C. Macedo, C.A.C. Altemani, Experimental evaluation of natural convection solar air heaters, Sol. Energy 20 (1978) 367e369. [5] K.S. Ong, Results of investigation into forced and natural convection solar air heater and crop dryers, Reg. J. Energy Heat Mass Transfer 4 (1982) 29e45. [6] D.J. Close, Solar air heaters for low and moderate temperature applications, Sol. Energy 7 (1963) 117e124. [7] F.K. Forson, M.A.A. Nazha, H. Rajakaruna, Experimental and simulation studies on a single pass, double duct solar air heater, Energy Convers. Manage. 44 (2003) 1209e1227. [8] B.N. Prasad, J.S. Saini, Effect of artificial roughness on heat transfer and friction factor in a solar air heater, Sol. Energy 41 (1988) 555e560. [9] Y. Piao, E.G. Hauptmann, M. Iqbal, Forced convective heat transfer in crosscorrugated solar air heaters, J. Sol. Energy Eng. 116 (1994) 212e214. [10] Md A. Karim, M.N.A. Hawlader, Performance investigation of flat plate, V-corrugated and finned air collectors, Energy 31 (2006) 452e470. [11] F. Ozgen, M. Esen, H. Esen, Experimental investigation of thermal performance of a double-flow solar air heater heaving aluminium cans, Renew. Energy 34 (2009) 2391e2398. [12] A. Hachemi, Experimental study of thermal performance of offset rectangular plate fin absorber-plates, Renew. Energy 17 (1999) 371e384. [13] S. Karsli, Performance analysis of new-design solar air collectors for drying applications, Renew. Energy 32 (2007) 1645e1660. [14] N. Moummi, S. Youcef-Ali, A. Moummi, J.Y. Desmons, Energy analysis of a solar air collector with rows of fins, Renew. Energy 29 (2004) 2053e2064. [15] K. Pottler, C.M. Sippel, A. Beck, J. Fricke, Optimized finned absorber geometries for solar air heating collectors, Sol. Energy 67 (1999) 35e52. [16] H.M. Yeh, C.D. Ho, J.Z. Hou, Collector efficiency of double-flow solar air heaters with fins attached, Energy 27 (2002) 715e727. [17] J.H. Watmuff, W.W.S. Charters, D. Proctor, Solar and wind induced external coefficients for solar collectors, COMPLES 2 (1977) 56. [18] Chinese National Standard GB/T 19141-2003, Specification of domestic solar water heating systems, Beijing, 2003.
Contents lists available at ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Experimental and theoretical study of the efficiency of a dual-function solar collector Jinwei Ma, Wei Sun*, Jie Ji*, Yang Zhang, Aifeng Zhang, Wen Fan Department of Thermal Science and Energy Engineering, University of Science and Technology of China, Hefei, Anhui 230026, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 10 November 2010 Accepted 11 February 2011 Available online 23 February 2011
A design of solar collector that is able to provide both hot water and hot air has been proposed to increase annual thermal conversion ratio of solar energy. By modifying the conventional flat-plate solar water heater, the collector with L-shape fins can also function as a double-flow solar air heater. Experiments have been conducted to investigate the dual functions of the collector. It is shown that the thermal efficiency of the collector reached 50% in water heating, and varied from 41% to 55% in air heating depending on the ambient condition and flow rate. Mathematical model has been presented for the collector working in air heating mode. The theoretical results are in good agreement with the experiment results. Theoretical results show that the air flow rate is a dominant factor to determine the efficiency. The enhancement of the L-shape fins on the performance of the collector in air heating is also proved from the theoretic results. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Solar collector Dual function Double-flow L-shape fins
1. Introduction Among the solar thermal technology, the flat-plate solar collectors have been widely used as air heaters or water heaters. The solar air heaters have been applied to space heating [1] and crop drying [2] for energy savings. However the facilities can be left unused in some seasons of the year because the demand of hot air is normally seasonal. In order to increase the annual application of solar energy, a dual-function solar collector is introduced in this paper. The collector can generate not only hot air for spacing heating in winter or crop drying in harvest season, but also hot water in other seasons while the hot air is no longer required. Such integrated design makes it more cost-effective than those conventional systems solely for solar air heating. The principal types of solar air heaters are: the single pass with air flow above the absorber, air flow below the absorber, double air flow above and below the absorber, and double-pass [3]. It has been observed that among single pass, double-flow is superior to the other two [4e6]. Experimental and simulation studies on the double-flow solar air heater have shown that significant improvement in the performance can be obtained with an appropriate choice of the collector parameters and the top to bottom channel depth ratio of the two ducts [7]. Solar air heaters are relatively
limited in their thermal performance due to the low density, volumetric heat capacity and heat conductivity of air. Roughnessinducing wires and wavy passage have been used in collector to augment heat transfer [8e10]. Obstacles like aluminum cans have been inserted into the air channel to enhance the thermal performance of solar air heaters [11]. Many kinds of fins such as offset strip fins [12,13] and continuous fins [14] have been studied extensively. From theoretic analysis it has shown that continuous fins provided higher net energy gain than offset strip fins because of lower pressure losses [15]. The efficiency of the double-flow solar heater with fins has been investigated experimentally and theoretically [16]. In the present work, the dual-function collector is modified from the conventional solar water collector by adjusting the interior air gap and changing the shape of the absorber, as shown in Fig. 1. Besides water heating, the collector can also function as a double-flow air heater. The absorber fins of the collector are bended as L-shape to increase the heat transfer in air heating. Experiments have been conducted to investigate the collector performance in air heating and water heating. Mathematic model has been developed to analyze the factors affecting on the performance of the collector in air heating.
2. Experimental procedure 2.1. Description of the collector
* Corresponding authors. Tel.: þ86 551 3601641; fax: þ86 551 3606459. E-mail addresses: [email protected] (W. Sun), [email protected] (J. Ji). 1359-4311/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2011.02.019
The structure of the dual-function collector is shown in Fig. 1. A copper tube is welded at the bottom of each L-shape aluminum fin.
1752
J. Ma et al. / Applied Thermal Engineering 31 (2011) 1751e1756
Fig. 2. Test setup of air heating system.
Fig. 1. Schematic illustration of dual-function solar collector.
The fins of total 13 are arranged side by side within the gap between the cover glass and the back plate. Hence the gap is divided by the fins into up and down channels where the air flows through in the working mode of air heating, similarly as a in a double-flow solar air collector [3]. While in the working mode of water heating, water flows in the copper tubes, and the air channels are closed at inlet and outlet. The inlet and outlet of water tubes are also closed in air heating. The fins are coated with selective material to absorb incident solar radiation and heat working fluid (air or water) flowing by. The cover glass is of 4 mm thickness with the aperture of 1.94 m in length and 0.93 m in width. The heights of up and down air channel in the collector are of 0.0375 m and 0.0175 m, respectively. The vertical part of the fins is 0.026 m. The glass fiber with the thickness of 0.02 m is in the back panel and at sides of the collector for thermal insulations.
temperatures. Two additional thermocouples were put at the entrance and exit of the water route of the collector. The experimental setup of the solar air heating is schematized in Fig. 3. A vortex pump was used to drive the air flow. The air flow rate was measured by the thermal mass flowmeter (SG101D1), of which the percent error is of 10% calibrated by Anhui Institute of Metrology. The temperatures of the air at inlet and outlet, and the temperatures of at the exterior surface of glass cover and back panel were measured. The performance of the dual-function collector has been tested in the outdoor environment. The collector was mounted southfacing at an inclination angle of 35.5 that is around the degree of
2.2. Experimental setup The experiments for the air heating and water heating have been conducted separately. The experimental setup of water heating system is shown in Fig. 2. The copper tubes in the collector were connected to a tank of 100 l with the pipes and associated valves. In the experiment, water in the tank and tubes was refilled in the early morning. Natural circulation of water route took place because of thermosyphon effect while the collector received solar radiation and the water in the tubes was heated up. Four thermocouples were arranged equidistantly in the tank to measure water
Fig. 3. Photo of water heating system.
J. Ma et al. / Applied Thermal Engineering 31 (2011) 1751e1756
the local latitude. The incident solar radiation and wind speed were measured by Pyranometer (TBQ-2) and deflecting vane anemometer, respectively. The temperatures were measured by type T (coppereconstantan) thermocouples. The measurement data were recorded by data acquisition unit at an interval of one minute.
In water heating mode, the thermal energy gain is the heat accumulated by the water in the tank. The daily average efficiency can be calculated as the following,
h¼
Ztexp
(1)
0
where mw is the mass of water in the tank, Cpw is heat capacity of water, DT is the temperature increase of water in the tank, and 4, texp are time and the time duration of the experiment, respectively. In air heating mode, the thermal energy gain is the enthalpy increase of the flow air between outlet and inlet, expressed as
(2)
The instantaneous efficiency of the collector is the heat gain of the air divided by incident solar radiation as
Q h¼ u ¼ SAg
_ p mC Tf;o Tf ;i SAg
(4)
where the coefficient of the heat loss via glass
UT ¼ hw þ hrs
(5)
UB ðTb Ta Þ ¼ hrpb Tp Tb þ hcbf2 Tf 2 Tb
(6)
where the coefficient of the heat loss via back panel
1 H UB ¼ 1= þ R hw kR
(7)
For the absorber of L-shape fins
SAg d4
_ p Tf;o Tf;i Qu ¼ mC
A UT Tg Ta þ hrpg ab Tg Tp þ hcgf 1 Tg Tf1 ¼ 0 Ac
For the back plate,
2.3. Performance evaluation
mw Cpw DT
1753
(3)
_ is the mass flow rate of air flowing through the collector, where m Cp is the specific heat capacity of the air, Tf,o, and Tf,i are the air temperatures at the outlet and inlet, respectively. The uncertainty analysis has been carried out on the basis of the measured data. The propagation of uncertainty in estimating efficiencies is within 3.5% and 10.6% relative error for water heating and air heating, respectively. 3. Theoretic modeling of the collector in air heating In air heating, the essential components of the collector are the glass cover, the back plate and the absorber that is consisted with the 13 fins. Fig. 4 shows schematic diagram of the heat-transfer coefficients in the collector. Under the assumption that the temperatures of the glass cover, absorber and the back plate vary only in the direction of air flow, the energy balance equations are established as follows: For the glass cover,
Aab A Tp Tg þ hrpb Tp Tb þ hcpf 1 ab Tp Tf 1 Ac Ac þ hcpf2 Tp Tf 2 ¼ Ssg ap
hrpg
(8)
where Aab and Ac are the exposal area of the L-shape fins in the up channel and down channel, respectively; For the air stream in the up channel,
_ p dTf1 mrC A ¼ hcpf1 ab Tp Tf 1 þ hcgf1 Tg Tf 1 w dx Ac
(9)
where r is the ratio of the flow rate in the up channel to the total flow rate, and x is the direction of air flow; For the air stream in the down channel,
_ mð1 rÞCp dTf2 ¼ hcpf2 Tp Tf2 þ hcbf2 Tb Tf 2 w dx
(10)
The air flows through the upper and lower channel simultaneously, and meets at joint exit. Hence the pressure drops in the two channels are balanced at the exit. The pressure drop Dp is calculated via the apparent Fanning friction factor fapp:
Dp ¼ fapp
4L ru2 De 2
(11)
where the hydraulic diameter
De;i ¼ 4Hi wi =ð2ðwi þ Hi ÞÞ;
i ¼ 1; 2
(12)
H1 and H2 are the height of the up and down channels, respectively; w1 refers the fin spacing in up channel, and w2 refers the width of the down channel. The calculation of friction factor fapp adopts the method given in Ref. [15]. From balancing the pressure drops at exit that Dp1 ¼ Dp2, the ratio r of mass flow rate can be obtained. The convective heat-transfer coefficients in Eqs. (4)e(10) are calculated from dimensionless Nusselt number, as:
hc ¼ Nuk=De
(13)
where Nu number is calculated with the method in Ref. [15] for the air flows in fined channel and between parallel plates. The connective heat-transfer coefficient for air flowing over the exterior surface of the collector in Eqs. (5) and (7) is calculated by the following empirical equation [17].
hw ¼ 2:8 þ 3:0V
(14)
The irradiative heat-transfer coefficient of the glass cover is estimated by: Fig. 4. Schematic diagram of heat exchange coefficients in the dual-function collector in air heating mode.
hrs ¼ 3g s Tg þ Ta Tg2 þ Ta2
(15)
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J. Ma et al. / Applied Thermal Engineering 31 (2011) 1751e1756
Fig. 5. Water temperatures at the inlet and outlet of the solar collector.
Fig. 6. Variation of water temperatures in the tank with time.
The irradiative heat-transfer coefficients between absorber and glazing/back plate are obtained by:
from 28 C to 63 C. The average water heating efficiency of the dual-function collector was 50.1% calculated by Eq. (1). The daily heat gain is 8.0 MJ/m2, above the requirement of 7.5 MJ/m2 (under 17 MJ/m2 daily incident solar energy) in the Chinese National Standard of specification of domestic solar water heating systems [18]. In the air heating mode, the air is sucked into the inlet of the collector from ambient and heated up while passing the absorber. Fig. 7 shows the variation of the temperature at outlet with time in the experiment of one day. The mean wind speed was 3 m/s during the experiment. The air mass flow rate was adjusted as 0.025 kg/s. The air temperature changed at the outlet followed the trend of the solar radiation as expected. The air was heated up to nearly 49 C with the maximum temperature increase of 34 C at noon. The daily average thermal efficiency was 47.9%. The instantaneous thermal efficiencies of the collector at noon of four different days are listed in Table 1. The efficiencies varied from 40.8% to 55.0% under the flow rate from 0.007 kg/s m2 to 0.016 kg/ s m2. Although the ambient conditions were different, the flow rate showed as a dominant factor in the efficiency change. It is difficult to compare the performance of solar air collectors of different design if the size and operating conditions are different as presented in Ref. [11]. Nevertheless near the upper bound of the air flow rate in the present study, the efficiency has been reported around 53% and 59% of v-groove collector under 0.016 kg/s m2 [10] and cans collector under 0.017 kg/s m2 [11], respectively.
hrpg
s Tp þ Tg Tp2 þ Tg2 ¼ 1=3p þ 1=3g 1
hrpb
s Tp þ Tb Tp2 þ Tb2 ¼ 1=3p þ 1=3b 1
(16) (17)
By solving the energy equations (4), (6), and (8)e(10) under the boundary conditions:
x ¼ 0;
Tf1 ¼ Tf2 ¼ Ta
The temperature of the air streams can be obtained
ED C2 D1 Tf1 ¼ K1 el1 x þ K2 el2 x 22 þ Ta E C1 C2
(18)
ED C1 D2 þ Ta Tf2 ¼ K3 el1 x þ K4 el2 x 21 E C1 C2
(19)
where the coefficients C1, C2, D1, D2, E, K1, K2, K3, K4, l1 and l2 are given in Appendix A. Hence the temperatures of the air streams at outlet (Tf1,o, Tf2,o) can be obtained by substituting L (the length of the channel) for x in Eqs. (18) and (19). Then the thermal efficiency of the collector is the heat gain divided by the incident solar radiation, expressed as:
h¼
i h Qu _ p =SAc rTf1;o þ ð1 rÞTf2;o Ta ¼ mC SAc
(20)
4. Results and discussions The experimental test of water heating was carried out in good weather conditions during May 2009. Figs. 5 and 6 show the experimental results of one day with the temperature values averaged every thirty minutes. Because of the natural circulation of water between the collector and the tank, water temperatures at inlet and outlet kept rising during the test time as shown in Fig. 5. The legends ‘a’, ‘b’, ‘c’, ‘d’ in Fig. 6 stand for the measure points in the tank from top to bottom. It shows that water temperature was higher at higher position, but tends to be equal in the tank at the end of the test. The mean water temperature in the tank increased
Fig. 7. Air temperatures at outlet and inlet air temperatures versus time.
J. Ma et al. / Applied Thermal Engineering 31 (2011) 1751e1756
1755
Table 1 Air heating efficiency of the collector under different operating conditions (Expdexperimental; Theodtheoretical). Wind speed (m/s)
Ambient temperature ( C)
Radiation (W/m2)
Flow rate (kg/s)
Exp efficiency
Theo efficiency
3.0 2.0 2.0 1.9
12.5 21.3 21.0 11.1
744.35 801.03 681.59 705.61
0.013 0.018 0.024 0.029
0.408 0.446 0.496 0.550
0.418 0.464 0.504 0.553
The mathematical model has been tested with the experiment results. In the calculation, the coefficients of ap, 3p, s, 3g, 3b, kR were set as 0.9, 0.2, 0.8, 0.9, 0.94 and 0.1 W/(m K), respectively, according to the thermal properties of the material used in the collector. The efficiency from the theoretic calculation is in well consistency with that from the experiment as shown in Table 1. The relative deviation of the efficiency is less than 4%. Mathematical calculation has been performed to investigate the influence of the flow rate under the same ambient conditions: S ¼ 800 W/m2, V ¼ 2 m/s, and Ta ¼ 10 C. With the rise of the air flow rate, the heating efficiency increases, but the outlet temperature decreases, as shown in Fig. 8. The variation trend is the same as in Table 1. The increase of efficiency at higher air flow rate is because the whole collector is of lower temperature and less heat losses. Considering the collector has two working modes, double channels and L-shape fins are used, which is different from the traditional solar water heaters. The influence of the arrangement of the channels heights and fins of L-shape on the performance in air heating is studied theoretically. In the calculation, S ¼ 800 W/m2, _ ¼ 0:02 kg=s, the height of the whole air V ¼ 2 m/s, Ti ¼ Ta ¼ 10 C, m duct is fixed, but the ratio of the up channel to the whole duct varies. For comparison, a collector with an absorber of flat plate without vertical fins is also been studied. Fig. 9 shows influence of the channel height ratio and the shape of the absorber on the efficiency. The highest efficiency is at the height ratio 0.5 and 0.6 for the collector with the absorber of flat plate and L-shape fins, respectively. When the ratio is no larger than 0.5, which means the up channel is no higher than the down channel, collector performs better with the absorber of flat plate. It is caused by two reasons: the convective heat-transfer coefficient between the air stream and glazing is higher with L-shape fins; at the mean time, the higher friction factor from the L-shape fins results in less flow rate and higher temperature in the up channel. Hence the collector with the L-shape fins loses more heat via the glass cover when the ratio is no larger than 0.5. As the height ratio increases above 0.5, the flow rate
Fig. 9. Effect of the height ratio of up channel to the whole duct on the efficiency of collectors with flat-plat absorber and L-shape fins.
in the up channel is relatively increased, which diminishes the negative effect of L-shape fins and makes its higher convective heat transfer more pronounced, then the collector shows better performance with L-shape fins. Considering the collector’s another function as water heating, in which the down channel is better of smaller height to prevent natural convective air flow, the dual-function collector with L-shape fins is advantageous in air heating. The dualfunction collector with L-shape fins is convenient to produce for the factories manufacturing flat panel solar water heaters. 5. Conclusions The performance of a dual-function solar collector has been investigated by experiments. Mathematic model has been developed and validated by the experiment for the collector in air heating mode. Theoretical investigation has been carried out to analyze the effect of the flow rate and the structure parameters on the collector performance. The experiment results show that the collector can increase the temperature of 100 l water by more than 30 C after absorbing solar radiation for a whole day. The daily efficiency in water heating mode reached 50%. While in air heating mode, the daily mean and instantaneous efficiency reached 52% and 55%, respectively. The study shows that in air heating, although the efficiency increases with the flow rate, the temperature of the outlet air decreases with the flow rate. The L-shape fins in the dual-function collector have proved to have positive effect on the efficiency in air heating mode from the theoretic results. Acknowledgements This work was supported by the National Natural Science Foundation of China (No. 50876098) and the National Key Technology R&D Program of China (No. 2006BAA04B04). Nomenclature
Fig. 8. Effect of air flow rate on efficiency and air temperature increases.
A Aab Cp De H hc hr
area, m2 total exposed absorbing plate surface, m2 specific heat capacity of air, J/(kg K) hydraulic diameter, m height or thickness, m convective heat-transfer coefficient, W/(m2 K) irradiative heat-transfer coefficient, W/(m2 K)
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J. Ma et al. / Applied Thermal Engineering 31 (2011) 1751e1756
k L _ m Nu Dp Qu r
thermal conductivity, W/(m K) length air channel, m mass flow rate of air, kg/s dimensionless Nusselt number pressure drop in the channel, Pa useful energy gain, J ratio of the mass flow rate in up channel to the total flow rate dimensionless Reynolds number solar radiation, W/m2 temperature, K time, s loss coefficient from the glass to the ambient, W/(m2 K) loss coefficient from the bottom of lower air channel to the ambient, W/(m2 K) velocity of air flow, m/s velocity of ambient wind, m/s width of air channel, m fin spacing in the up channel, m direction of air flow
Re S T t UT UB u V w w1 x
Greek symbols absorptivity emissivity thermal efficiency viscosity of air, kg/(m s) density of air, kg/m3 StefaneBoltzman constant, 5.67 108 J s1 m2 K4 transmissivity time variable
a 3 h m r s s 4
Subscripts a ambient b back plate f air flow g glass cover i inlet o outlet p absorbing plate R back insulation 1 up channel 2 lower channel
_ p mrC w
_ mð1 rÞCp w UT þ hrpg Aab =Ac þ hcgf1 A ¼ hrpg Aab =Ac
W2 ¼
(A.1)
(A.2) (A.3)
B ¼ hrpb = UB þ hrpb þ hcbf2
(A.4)
G ¼ hrpg Aab =Ac ð1AÞþhrpb ð1BÞþhcpf1 Aab =Ac þhcpf2
(A.5)
. C1 ¼ hcpf1 Aab =Ac þ hcgf 1 A $ hcpf1 Aab =Ac þ hcgf 1 A G 1 AUT =hrpg
D1 ¼ D1 ¼ E ¼
(A.7)
hcpf 1 Aab =Ac þ hcgf 1 A S=G
(A.8)
hcpf 2 þ hcbf2 B S=G
(A.9)
. hcpf1 Aab =Ac þ hcgf1 A hcpf 2 þ hcbf2 B G
(A.10)
K1 ¼ ðW2 l1 C2 Þ=EK3
(A.11)
K2 ¼ ðW2 l2 C2 Þ=EK3
(A.12)
K3 ¼
l2 ðC2 þ EÞW2 ðTin Ta Þ l2 l1 l2 ED1 C1 D2 D2 þ l2 l1 E2 C1 C2 W2 ðl2 l1 Þ l1 ðC2 þ EÞW2 ðTin Ta Þ l2 l1 l1 ED1 C1 D2 D2 þ l2 l1 E2 C1 C2 W2 ðl2 l1 Þ
(A.13)
K4 ¼
l1 ¼
l2 ¼
ðC1 W2 þC2 W1 Þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðC1 W2 C2 W1 Þ2 þ4E2 W1 W2 2W1 W2
ðC1 W2 þC2 W1 Þþ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðC1 W2 C2 W1 Þ2 þ4E2 W1 W2 2W1 W2
(A.14)
(A.15)
(A.16)
References
Appendix A
W1 ¼
. C2 ¼ hcpf 2 þhcbf2 B hcpf2 þhcbf2 B G1 BUB =hrpb
ðA6Þ
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