- Email: [email protected]
Mathematical modelling of unglazed solar collectors under extreme operating conditions
Available online at www.sciencedirect.com
ScienceDirect Solar Energy 118 (2015) 547–561 www.elsevier.com/locate/solener
Mathematical modelling of unglazed solar collectors under extreme operating conditions M. Bunea a,⇑, B. Perers b, S. Eicher a, C. Hildbrand a, J. Bony a, S. Citherlet a a
Laboratory of Solar Energetics and Building Physics (LESBAT), Avenue des Sports 20, CH-1400 Yverdon-les-Bains, Switzerland b Departement of Civil Engineering, Technical University of Denmark, Brovej, Building 118, DK-2800 Kgs. Lyngby, Denmark Received 30 January 2015; received in revised form 11 May 2015; accepted 7 June 2015
Communicated by: Associate Editor Ursula Eicker
Abstract Combined heat pumps and solar collectors got a renewed interest on the heating system market worldwide. Connected to the heat pump evaporator, unglazed solar collectors can considerably increase their efficiency, but they also raise the coefficient of performance of the heat pump with higher average temperature levels at the evaporator. Simulation of these systems requires a collector model that can take into account operation at very low temperatures (below freezing) and under various weather conditions, particularly operation without solar irradiation. A solar collector mathematical model is developed and evaluated considering, the condensation/frost effect and rain heat gains or losses. Also wind speed and long wave irradiation on both sides of the collector are treated. Results show important heat gains for unglazed solar collectors without solar irradiation. Up to 50% of additional heat gain was found due to the condensation phenomenon and up to 40% due to frost under no solar irradiation. This work also points out the influence of the operating conditions on the collector’s characteristics. Based on experiments carried out at a test facility, every heat flux on the absorber was separately evaluated so that this model can represent a valuable tool in optimising the design or the thermal efficiency of the collector. It also enables the prediction of the total energy yield for solar thermal collectors under extreme operating conditions. Ó 2015 Elsevier Ltd. All rights reserved.
Keywords: Mathematical modelling; Solar thermal collector; Long wave irradiation; Condensation; Frost; Rain
1. Introduction Solar thermal collectors are originally designed to convert solar irradiation into useful heat. They have been adopted all over the world as a way to reduce fossil fuel consumption for space heating and domestic hot water production. Two main categories of solar collectors have
⇑ Corresponding author. Tel.: +41 (0)245572817.
E-mail address: [email protected] (M. Bunea). http://dx.doi.org/10.1016/j.solener.2015.06.012 0038-092X/Ó 2015 Elsevier Ltd. All rights reserved.
been developed depending on the existence or absence of a transparent cover on the absorber. This cover reduces the heat losses and therefore makes the solar collector more efficient at higher temperatures levels. On the other hand, uncovered collectors provide a higher solar energy yield at temperatures close to the ambient. The most important differences between these types of collectors are described by Keller (1985). The performance of these two categories of collectors is substantially different as that of the glazed collectors depends primarily on two factors (solar
548
M. Bunea et al. / Solar Energy 118 (2015) 547–561
Nomenclature Q_ collector thermal power supplied by the solar collector (W) Q_ rad;S short wave radiation heat exchange (W) convective heat exchange (W) Q_ conv Q_ rad;L long wave radiation heat exchange (W) conductive heat exchange (W) Q_ cond heat exchange with rain water (W) Q_ rain latent energy heat exchange (W) Q_ lat Q_ lat;C latent energy from condensation/evaporation heat exchange (W) latent energy from frost/melting heat exchange Q_ lat;F (W) F 0 ðfaÞen zero loss efficiency of the collector at normal incidence angle for the solar radiation onto the collector surface (–) g0 zero loss efficiency of the collector (–) Khb(h) incidence angle modifier for beam radiation (–) Khd(h) incidence angle modifier for diffuse radiation (–) G solar radiation (W/m2) Gb beam solar radiation (W/m2) Gd diffuse solar radiation (W/m2) EL long wave radiation (W/m2) c1 thermal heat loss/gain coefficient (W/m2/K) c2 temperature dependence of thermal heat losses/ gains coefficient (W/m2/K2) c3 wind velocity dependence of thermal heat losses/gains coefficient (J/m3/K) c4 long wave radiation dependence of the heat losses/gains coefficient – front side (–) c5 effective thermal capacitance of the solar collector (ccoll) (J/m2/K) c6 wind velocity dependence of the zero loss efficiency coefficient (s/m)
irradiance and ambient temperature) and for the unglazed collectors several other factors can also strongly influence their performance. These are the long wave irradiation, wind velocity, rain, condensation or frost. Solar energy is sometimes used indirectly through the evaporator of a heat pump. This configuration may increase the coefficient of performance of the heat pump but also shifts the operating range of the solar collectors to temperature levels below ambient. In this case, heat is no longer lost to the ambient air, but it becomes a gain. Therefore, the increasing demand for this type of systems, forces manufactures to use more frequently unglazed and sometimes non-insulated collectors in their installations. The purpose of the proposed solar thermal collector model is to best represent their behaviour under extended operating conditions and to quantify all energy inputs and/or losses as well as their influence on the total energy supplied by the solar collector.
c7
condensation/evaporation dependence coefficient (J/kg) c8 long wave radiation dependence of the heat losses/gains coefficient – rear side (–) c9 rain dependence of thermal heat losses/gains coefficient (–) u wind velocity (m/s) r Stefan–Boltzmann constant (W/m2/K4) va absolute humidity of the ambient air (kg/m3) vsat(tm) saturated absolute humidity of the ambient air at temperature tm (kg/m3) twat rain water temperature (°C) cp wat effective thermal capacitance of the rain water (J/kg/K) mwat rain water flow rate (kg/s) tm arithmetic mean temperature of the collector (tcoll) = (tin + tout)/2 (°C) Tm arithmetic mean temperature of the collector (Tcoll) = (Tin + Tout)/2 (K) ta ambient temperature (°C) thumide wet bulb temperature of the ambient air (°C) tsec dry temperature of the ambient air (°C) Ta ambient temperature (K) Tb building temperature (K) hr relative humidity of the ambient air (%) Rt total thermal resistance of a wall (m2 K/W) RSI internal superficial thermal resistance of a wall (m2 K/W) RSE external superficial thermal resistance of a wall (m2 K/W) U heat flow through a wall (W/m2 K)
2. Previous developments In the past, several studies contributed to a better characterisation of solar collector performance. In particular, Task III from the International Energy Agency (IEA), Solar Heating and Cooling Programme (SHC), and EN 12975 (2006) where work was done focused on the testing of glazed solar collectors. For unglazed collectors, a very comprehensive work was undertaken by Keller (1985) that shows the influence of the wind velocity, air humidity and long wave irradiation on the thermal performance of these collectors. Morrison and Gilliaert (1992) evaluated the difference between a three coefficient and a four coefficient form of the characteristic equation for the unglazed collectors. In IEA-SHC Task 44 several types of solar collectors, essentially unglazed, have been tested and modelled in combination with heat pumps.
M. Bunea et al. / Solar Energy 118 (2015) 547–561
549
condensation/evaporation Q_ lat;C or frost formation/melting Q_ lat;F . The latent energy becomes a heat gain for the collector in case of condensation or frost formation and a heat loss in case of evaporation or frost melting. Therefore, the total energy supplied by a solar collector is the addition of all these terms:
A mathematical model based on the heat balance and rate equations for unglazed transpired collectors was developed by Augustus Leon and Kumar (2006) where wind velocity was found to have an important effect on the collector effectiveness. The influence of the wind speed on the convection coefficient has also been presented by Palyvos (2008) and Keller (1985). For the climate of Limburg in Germany, Bertram et al. (2008) found that 4% of the annual unglazed collector yield was due to condensation when combined to a heat pump system. The condensation effect under no solar irradiation has also been reported by Keller (1985) and Philippen et al. (2011). For characterisation under any climate, condensation heat gains have been taken into account in several collector models reported by Keller (1985), Soltau (1992), Morrison (1994), Eisenmann et al. (2006), Perers (2011) and Bertram (2011). Still, no references were found in the literature on the influence of the rain, frost or rear side long wave irradiation. It is the purpose of this study to extend the modelling capabilities of current available solar thermal collectors to include these effects.
Q_ collector ¼ Q_ rad;S þ Q_ conv þ Q_ rad;L þ Q_ cond þ Q_ rain þ Q_ lat
It is important to notice that some of these phenomena may occur not only on the front side of the collector, but also on its rear side, see Fig. 1. The internal energy change should also be taken into account in the dynamic calculation. This term is as a function of the time derivative of the collector temperature and the thermal capacitance of the collector: dTdcoll ccoll
3.1. The standard model equation The EN 12975 (2006) standard provides a definition of the total heat gain for a collector under outdoor testing conditions.
3. Heat balance of a solar thermal collector Under low temperature conditions, all possible energy flow rates that may contribute to the collector energy balance are the absorbed solar irradiation Q_ rad;S , the convective heat exchange with the ambient air Q_ conv , the long wave irradiation, Q_ rad;L , the heat conduction through the ambient air or the collector’s support Q_ cond , the heat exchange with rain Q_ rain and the latent energy exchange Q_ lat . This latter can be divided into two terms:
optical efficiency:beam radiation
Q_ collector ¼
zfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflffl{ F 0 ðfaÞen K hb ðhÞGb
optical efficiency:diffuse radiation
þ
zfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflffl{ F 0 ðfaÞen K hd ðhÞGd
Heat lossngain at no wind
Wind dependence on optical efficiency
zffl}|ffl{ c6 uG
c2 ðtm ta Þ2 |fflfflfflfflfflfflffl{zfflfflfflfflfflfflffl}
Temperature dependence of the heat lossngain
þ c4 ðEL rT 4a Þ |fflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflffl} Long wave radiation
̇
dtm c5 dtffl} |fflffl{zffl
Thermal capacitance
,
̇ ̇ ̇ ̇
̇
,
̇ ̇
̇
ð1Þ
,
Fig. 1. Schematic representation of heat flow rates on the solar thermal collector.
zfflfflfflfflfflffl}|fflfflfflfflfflffl{ c1 ðtm ta Þ
þ
c3 uðtm ta Þ |fflfflfflfflfflfflffl{zfflfflfflfflfflfflffl}
Wind velocity dependence of the heat lossngain
ð2Þ
550
M. Bunea et al. / Solar Energy 118 (2015) 547–561
This standard has been adopted worldwide as a reference methodology for solar thermal collectors testing. Nevertheless, this model has not been designed to cope with very low temperature operating conditions such as the case of solar collectors combined with heat pumps. In this kind of application, the typical operating range of a solar collector is extended to include energy under no solar irradiation and at temperatures below ambient air and its dew point. As a consequence, additional terms have been introduced to the model presented in the standard along with some other modifications. For the condensation effect, Perers (2011) have already proposed an additional term so that Eq. (2) becomes: Q_ collector ¼ F 0 ðfaÞen K hb ðhÞGb þ F 0 ðfaÞen K hd ðhÞGd c6 uG c1 ðtm ta Þ c2 ðtm ta Þ2 þ c3 uðtm ta Þ dtm c7 ð2:8 3:0uÞðva vsat ðtm ÞÞ þ c4 ðEL rT 4a Þ c5 dt |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
Fig. 2. Incidence angle modifier for the unglazed collectors (see Footnote 3).
ð3Þ
Condensation
3.2. Considerations on the standard equation Based on this Eq. (3), a detailed analysis of each term was performed and a number of considerations were made. 3.2.1. Long wave radiation term The ðEL rT 4a Þ term is the calculation term of heat transfer by infrared irradiation between the sky and the collector. It is proposed to replace it by ðEL rT 4m Þ in order to have the sky radiation as a correction term by equating the average temperature Tm of the collector and not the ambient temperature Ta. 3.2.2. Condensation term (2.8 3u)(va vsat(tm)) corresponds to evaporation/ condensation term. Beckman and Duffie (1991) proposes to amend this term into (2.8 + 3u)(va vsat(tm)). This change will be retained, as in the basic equation, depending on the wind speed, this term could be negative or positive for the same value of (va vsat(tm)) (term giving the condition of condensation or evaporation). In addition, for the same term of condensation, it was decided to reverse the sign so that it adds a positive value to the total power when there is condensation and a negative value when there is evaporation. Thereby, the term becomes +(2.8 + 3u) (va vsat(tm)) instead of (2.8 3u)(va vsat(tm)). The calculation of the absolute humidity is done with:
3.2.4. Optical efficiency: beam and diffusion terms The incidence angles are not taken into account due to the position of the collectors in relation to the surrounding buildings. Direct solar radiation reaches the absorber with relatively small angles of incidence (<60°) where the IAM coefficients are almost constant (cf. Fig. 2). The F0 (fa)enKhb(h)Gb + F0 (fa)enKhd(h)Gd terms can be simplified to form a single term g0G where G includes direct and diffuse irradiation. Although solar irradiation is, generally, the most influential parameter in the energy balance of a solar thermal collector, the purpose of this work is to investigate conditions where this term is of less importance. For this reason, only the total solar irradiation is used, with no distinction between diffuse or direct irradiation. The influence of the angular solar absorptance and incident angles modifier was reported in literature (Tesfamichael and Wackelgard (2000)) where important decreases of the solar absorptance at high angles of incidence were found for two different coatings.
ð5Þ
3.2.5. Long wave radiation on the rear of the collector As some unglazed collectors have no insulation on rear side, one term was added to represent gains/losses by long wave (infrared) radiation exchange on the rear side of the collector. Calculation of this term is similar to that for the front side of the collector. The difference consists on the sky temperature that is replaced by the temperature of the body behind the collector, in this case it is the building and the flat roof where the collector is situated (cf. Fig. 7). The surface temperature of the building (Tb) is defined by:
3.2.3. Temperature dependence of heat The [(tm ta)|tm ta|] term is replacing the (tm ta)2. Indeed, when the collector temperature is lower than the ambient, there is a power supplied by the collector.
The room temperature under the roof set as a constant at 20 °C. The outside temperature. U value of the flat roof calculated at 0.24 W/m2K, see below.
V sat ðtÞ ¼ 0:001ð4:85 þ 0:347t þ 0:00945t2 þ 0:000158t3 þ 0:00000281t4 Þ v ¼ vsat ðtÞ hr
ð4Þ
M. Bunea et al. / Solar Energy 118 (2015) 547–561
The calculation of the thermal resistance of the flat roof is done using the following equations: X Ri þ RSE Rt ¼ RSI þ ð6Þ and U ¼ 1=Rt
ð7Þ
with RSI = 0.13 (m2 K)/W, RSE = 0.04 (m2 K)/W and Ri corresponds to the thermal resistance of each layer composing the roof.1 3.2.6. Rain term One term was added to account for the energy exchanged between the collector and the rain. The rainwater temperature is considered equal to the wet bulb temperature of the air, calculated with Heinrich Gustav Magnus-Tetens.2 No measurements on the test bench were capable to give a better approach of this temperature and no other approximations were found in the literature. thumide ¼ b aðtsec ; hr Þ=ða aðtsec ; hr ÞÞ
ð8Þ
with : aðtsec ; hr Þ ¼ a tsec =ðb þ tsec Þ þ lnðhr Þ
ð9Þ
a ¼ 17:27 ðÞ
b ¼ 237:7 ð CÞ The rain water mass is calculated from the data of the rain gauge installed next to the collectors. 3.3. Proposed model equation With the changes outlined above, Eq. (3) becomes Q_ collector ¼ g0 G c6 uG c1 ðtm ta Þ c2 ðtm ta Þjtm ta j þ c3 uðtm ta Þ
551
Table 1 system instrumentation and accuracy. Sensor
Manufacturer
Type
Accuracy
Temperature Flow rate
Transmettra Krohne
0.1 K 0.3%
Solar radiation Relative humidity Wind velocity
Kipp & Zonen Rotronic
Pt100 A class Electromagnetic flowmeter Pyranometer Hygromer humidity sensor Weather vane
Adolf Thies GmbH
1.4% 1% 3%
inlet collector temperatures varying from 10 °C to 5 °C. Sensor description and their accuracy is given in Table 1. Bunea et al. (2012) have shown that for glazed collectors without solar irradiance no significant additional benefits were obtained from condensation effect, frost or rain. Therefore, only unglazed solar collectors will be addressed in this article. For the standard collector (insulated), the parameters g0, c1, c2, c3 and c5 were taken from the documentation provided by the collector’s test report30. Parameters for the non-insulated collector including (c4, c6, c7, c8, c9) for which no values are documented were initially approximated by theoretical values and then refined in order for the simulations to be closest to the measurements and this for all climatic conditions encountered. These parameters are summarized in Tables 2 and 3. Briefs explanations on the process to arrive to these values will be presented in this section as well as the assumptions made in the laboratory. The absorber area of both collectors is 1.85 m2. Changes of the coefficient value from one test to another will be explained further down. 5. Results
Rear side long wave irradioation
þ
zfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflffl{ c8 ðrT 4b rT 4m Þ
þc4 ðEL rT 4m Þ
dtm þ c7 ð2:8 þ 3:0uÞðva vsat ðtm ÞÞ dt þ c9 mwat cp wat ðtwat tm Þ |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
c5
ð10Þ
Rain
4. Experimental setup A testing facility comprising four solar thermal collectors (flat plate collector, evacuated tube collector, insulated unglazed collector and non-insulated unglazed collector) equipped with different sorts of sensors was developed for collector monitoring purposes (see Fig. 3). Several tests under different real weather conditions in Yverdon-les-Bains, Switzerland, have been performed with 1 SIA 180 (1999) Isolation thermique et protection contre l’humidite´ dans les baˆtiments. 2 Barenbrug, A.W.T., Psychrometry and Psychrometric Charts, Le Cap, Afrique du Sud, Cape and Transvaal Printers Ltd., 1974, 3e e´d.
The analysis was made in terms of the net power and energy provided by the collectors. In fact, under these extended operating conditions, the classical definition of the efficiency of a solar collector (output power divided by the solar irradiation) is no longer relevant. Eq. (10) has been implemented in a spreadsheet to compare the calculated power against the measured power for several days under different weather conditions. This spreadsheet can also be used to estimate the values of various parameters of each collector. 5.1. Sunny periods The collector total power obtained with the mathematical Eq. (10) is close to that measured for a sunny day (cf. Fig. 4). However, some deviations (15%) are observed at certain times such as 12.5 h, but for a short duration.
3 Institut fur solartechnik, Collectors test reports, Factsheet – SPF-Nr.420.
Unglazed flat plate with rear insulation
Evacuated tube
Unglazed flat plate without rear insulation
M. Bunea et al. / Solar Energy 118 (2015) 547–561
Glazed flat plate
552
Weather Station
Temperature sensor Flow rate Pump Heat exchanger
C
Regulation valve C
Chiller
Fig. 3. Set-up diagram of the testing facility.
For these weather conditions, the parameters used in the equation correspond to the values given by the manufacturer or found in the literature. These values will be named “standards” for the remaining of this article. 5.2. Condensation periods To maximise condensed water vapour on the surface of the absorber, tests were made during the night (no solar irradiation) with an inlet temperature of the collectors close to 0 °C. In this case, the main energy sources are convection, long-wave irradiation and condensation on the surface of the collector. To experimentally estimate the amount of condensation on the unglazed collectors, a large bucket was placed underneath the collectors in order to recover the condensed water (see Fig. 5a). A lid with a narrow slot for the passage of the condensed water limits evaporation during the test (see Fig. 5b). The uncertainty of the condensation heat gains measurements was determined to be 8% by night. The measured yield for the conducted tests varied from 0.5 kW h to 3.3 kW h for the insulated solar collector and from 1.3 kW h to 4.8 kW h for the non-insulated solar collector. It was observed that condensation can represent 23– 55% of the total collector’s yield for these tests depending on the weather conditions.
As a consequence of the condensation phenomena, the collector becomes wet, leading to changes in the physical properties of its selective surface. Thus, the specific parameters of the collector were changed so that the power given by the equation would closely represent the new conditions as shown in Fig. 6. The most important change concerns the infrared emissivity of the absorber (c4 and c8) going from 0.05 with a dry surface (selective surface in small wavelengths) to a 0.9 (water effective emissivity) when the surface is wet because the selective layer of the absorber is no longer operative. The value of emissivity for thin water layers is given by Wolfe and Zissis (1993). Another important modification is the disruption of the convective transfer between the air and the collector through the film condensation, resulting in a decrease of parameter c1. Finally, parameter c7 related to condensation. The dependence of the air pressure or the inclination of the collector on the condensation phenomena were not tested in this work. Keller (1985) found negligible the influence of the air pressure on the condensation effect while Philippen et al. (2011) has not detected larger condensation gains for larger inclinations of the collector under outdoor conditions. Increased heat gains were principally due to higher long wave irradiance from the field of view of the unglazed collector.
Table 2 Parameters for non-insulated solar collector under different testing conditions. Testing conditions
Parameters for non-insulated unglazed solar collector g0 (–)
Sunny Condensation Frost Rain Mixed conditions
Optical efficiency
c1 (W/ (m2 K)) Convection at no wind
0.959 0.959 0.8 0.959 0.959
12 8.5 16.5 12 12
c2 (W/(m2 K2))
c3 (J/(m3 K))
c4 (–)
c5 (J/(m2 K))
c6 (s/m)
c7 (J/kg)
c8 (–)
c9 (–)
Temperature dependence on heat loss/gain
Wind dependence on heat loss/gain
Front side emissivity for long wave radiation
Thermal capacitance
Wind dependence on optical efficiency
Condensation
Rear side emissivity for long wave radiation
Rain
0 0 0 0 0
4 4 4 6 4
0.05 0.9 0.9 0.9 0.5
18,000 18,000 18,000 18,000 18,000
0.03 0.03 0.03 0.03 0.03
0 2,000 2,300 2,000 2,000
0.05 0.9 0.9 0.9 0.5
0 0 0 0.5 0.5
Testing conditions
Parameters for insulated unglazed solar collector g0 (–)
Sunny Condensation Frost Rain Mixed conditions
Optical efficiency
c1 (W/ (m2 K)) Convection at no wind
0.959 0.959 0.8 0.959 0.959
8.91 6.5 12.5 8.91 8.91
c2 (W/(m2 K2)]
c3 (J/(m3 K))
c4 (–)
c5 (J/(m2 K))
c6 (s/m)
c7 (J/kg)
c8 (–)
c9 (–)
Temperature dependence on heat loss/gain
Wind dependence on heat loss/gain
Front side emissivity for long wave radiation
Thermal capacitance
Wind dependence on optical efficiency
Condensation
Rear side emissivity for long wave radiation
Rain
0.047 0.047 0.047 0.047 0.047
2.26 2.26 2.26 4 2.26
0.05 0.8 0.9 0.9 0.5
18,000 18,000 18,000 18,000 18,000
0.03 0.03 0.03 0.03 0.03
0 1,300 1,500 1,300 1300
0 0 0 0 0
0 0 0 0.5 0.5
M. Bunea et al. / Solar Energy 118 (2015) 547–561
Table 3 Parameters for insulated solar collector under different testing conditions.
553
554
M. Bunea et al. / Solar Energy 118 (2015) 547–561
Non-insulated unglazed solar collector
Insulated unglazed solar collector
Fig. 4. Measured vs. calculated power of unglazed collectors – sunny day.
Fig. 5. (a) Buckets under solar collectors; (b) lid on the bucket.
Non-insulated unglazed solar collector
Insulated unglazed solar collector
Fig. 6. Measured vs. calculated power of unglazed collector – mild temperatures night conditions.
5.3. Frost periods If the supplied energy by an unglazed collector is lower than the one requested by the consumer (e.g. heat pump), the collector’s temperature will drop and reach negative values. In this case, the water vapour contained in ambient air will freeze on the surface of the collector as shown in Fig. 7. This phenomenon brings, as in the case of condensation, energy to the collector. A test with an inlet temperature of the collector at about 5 °C was made. The measured collector power was compared to that calculated by the mathematical model. The results are shown in Fig. 8. Some differences between
the measurements and the calculations are observed with little impact on the cumulated energy during the test. It is to notice the significant thermal power delivered by the non-insulated solar collector under no solar irradiation. An experiment was also carried out to attempt to quantify the amount of frost formed. However, this is very difficult to perform. A first estimation was made using a similar approach as performed for the condensation. The collector temperature was kept stable for several hours, which contributed to the formation of frost. Then, the fluid was heated at 20 °C melting the ice and the water was collected in buckets beneath the collector.
M. Bunea et al. / Solar Energy 118 (2015) 547–561
Rear side insulated
Non-insulated
555
5.4. Rainy periods The unglazed collectors are able to recover the energy contained in rainwater, whenever they operate at low temperatures. Conversely, they can lose energy when their temperature is higher than the rainwater. In Switzerland, the maximum energy gain from the rainwater was estimated at about 5 kW h/m2 per year, representing 2% of the average annual energy yield of an unglazed collector under normal operation. The unglazed collectors were tested during a rainy period of 7 h (total 4.8 mm). Fig. 9 shows the results obtained following some adjustments of the standard parameters. The results are slightly worse than those for tests with sunny periods. Still, the deviations do not exceed 15%. Modified parameters are:
Fig. 7. Unglazed solar collectors with frost on the surface.
The amount of water collected was close to that found in the case of condensation. However, the supplied energy to the collector is higher because the latent heat of solidification is added to the latent heat of condensation. Simulation results were obtained by modifying some standard parameters to cope with the above effects: The efficiency of the optical collector (g0) decreases because frost causes reverberation. The parameter c1 (convection + radiation) increases as the frost layer has a higher surface of exchange due to ice crystals. As for condensation, the infrared emissivity of the absorber (c4 and c8) increases, because the selective surface is no longer operational. The parameter c7 is related to the presence of frost and condensation. This value is higher than the one during condensation (15%), which corresponds approximately to the addition of the latent heat of solidification to the condensation latent heat.
Noninsulated unglazed solar collector
The dependence on heat loss/gain (c3) increases. It is assumed that this increase is due to an increased convective movements related to the rain. The c9 parameter related to the presence of rainwater on the surface of the absorber.
5.4.1. Long periods with changing conditions A test of 136 h from 15 to 21 of May was performed with varying weather conditions in order to validate the model for solar collectors under different conditions (rain, wind, condensation and sunlight) (cf. Fig. 10). During this test, the set-point temperature of the collector input was fixed to 0 °C. In practice, this temperature changes slightly depending on the weather conditions, especially for high solar irradiation, when the output temperature increases considerably. The chosen parameters for this configuration are the “standards” parameters except for: The effective emissivity parameters (c4 and c8); average values for sunny period and period with condensation (see Tables 2 and 3).
Insulated unglazed solar collector
Fig. 8. Measured and calculated power of unglazed collector – cold temperatures.
556
M. Bunea et al. / Solar Energy 118 (2015) 547–561
Non-insulated unglazed solar collector
Insulated unglazed solar collector
Fig. 9. Measured and calculated power of unglazed collector – rainy conditions.
Not insulated unglazed solar collector
Insulated unglazed solar collector
Fig. 10. Measured vs. calculated power for unglazed collectors – one week weather conditions (5 min average).
The parameters of condensation-frost (c7) and rain (c9) were added. Calculations (red lines) show a behaviour close to the measured power (blue) of the collector when there is no sudden change in climate conditions, such as during the night or during the second day (May 17). However, on days with variable solar irradiation, differences are observed between the measured and the calculated power as shown in Fig. 11. A detailed analysis of these periods shows that the average difference is 32 W for non-insulated collector and 34 W for the insulated collector. Also, standard deviations are 110 W for the non-insulated collector and 107 W for the insulated one (front or rear side area 2 m2). Important differences, as observed on the encircled zones in Fig. 11, occur in the morning because of the solar irradiation getting partially on the surface of the solar collector and not yet on the pyranometer. Differences outside these zones are explained by the very short time step calculations (10 s). For such time steps, a single node model as this mathematical equation, encounters difficulties in managing the thermal inertia of the solar collector during sudden changes in the climatic conditions. The temperature measurements recorded show very rapid changes that can be out of phase with those calculated. Perers (1997) revealed that this approximation is satisfying when the time
steps for measurements are long compared with the time for the fluid to pass through collector. Thus, especially for small mass flow rates and in the absence of solar irradiation, the simplifying assumption of a linear increase of the inlet fluid temperature and the outlet has to be checked carefully. The thermal capacitance of the collector should be in this case separated into several control volumes or a different approach may have to be chosen. Nevertheless, most of the weather data available are mean hourly values which is generally longer than the dwell time for the fluid in the collector. Kong et al. (2012) have already shown the sensitivity of this parameter and implemented a two-node method called “transfer function method” in which the collector was separated into the solid part and the fluid part in order to be more precise. He also added a new parameter to take into account the heat transfer between the solid to the fluid part of the collector. Possible remedies would be to incorporate the modifications suggested by Kong et al. (2012). Because the main objective of this work is to represent the behaviour of the collector under certain conditions, not necessary for long periods and to estimate the heat flows through the collector, these considerations were not integrated into the mathematical equation. Nevertheless, even if these differences may seem important in terms of absolute power output during these
M. Bunea et al. / Solar Energy 118 (2015) 547–561
Non-insulated unglazed solar collector
557
Insulated unglazed solar collector
Fig. 11. Differences between measured and calculated power (5 min average).
Not insulated unglazed solar collector
Insulated unglazed solar collector
Fig. 12. Evolution of measured and calculated energies for unglazed collectors – one week weather conditions.
changing periods, they have positive value at one time step and then negative value at the following time step with same amplitude. This gives a simulated energy yield very close to the measured energy as seen in Fig. 12. The maximum deviation on the energy calculation during the 136 h test is 5% for the insulated collector and 2% for non-insulated collector. 6. Discussion For classical operation of a solar thermal collector, simple models, as described in EN12975, have been tested for years and give fairly accurate estimations of the output power of the collector. Still, they have not been designed to cope with operating conditions such as night time or with temperatures below ambient. The analysis presented in this work shows that for these extended weather conditions additional parameters are needed in order to correctly account for the different phenomena occurring on the unglazed solar collector. On the other side, significant variation of the standard parameters was observed for different operating conditions, leading to the conclusion that optimal parameter sets are not universal. The additional power due to condensation was found relatively low (100 W/m2 maximum). More important heat gains up to 400 W/m2 were measured during frost
formation for the non-insulated unglazed collector and the frost was estimated to contribute to about 40% of this energy. Notwithstanding, special attention must be paid on damages that the condensation or frost can create in long-term operation especially for the selective coating or insulation. Accelerated aging tests with repeated uses under these conditions should be made to observe the evolution of their performance in time. When collector’s temperatures are negative for longer periods, there is also the risk of ice block development, so once detached from the collector are likely to fall and cause damage. The opposite phenomena of condensation (evaporation) and frost (thaw) are not treated in this manuscript. Still, what was observed during these tests is that, depending on the collector’s tilt, most of the water accumulated on the collector surface falls down and therefore the impact of the evaporation should be very small. A more important influence on the collector output power should be observed by the frost melting, for example on a sunny morning after a night of very low temperature operation. The energy needed for this phenomena should be in the same range as the energy for frost. The difficulty lies in the choice of these parameters for testing over periods with changing weather conditions. A setting that may give very good results during sunny periods, may produce unreliable results during the night. Therefore, the use of a static model as presented in this
62.51 69.29 65.97 62.31 76.72 80.8 72.09 76.76 136 Mixed conditions
15–21.05.2012
3.07 3.34 3.27 3.8 3.11 3.87 3.28 3.61 2.86 3.03 3.05 3.44 2.72 3.03 3.00 3.07 4 5.5 Sunny
23.05.2011 25.05.2011
3.33 1.34 3.21 1.18 3.28 1.17 3.41 1.00 4.53 1.99 4.45 1.65 4.07 1.49 5.32 1.76 13 11 Condensation (night time testing)
15–16.09 2011 27–28.10.2011
8.07 6.85 4.34 4.22 4.26 4.21 7.13 8.5 11.23 9.64 6.06 6.39 5.6 6.08 10.06 11.62 15.5 15 Frost
15.12.2011 16.12.2011
1.37 1.23
Type 136 Type 202
1.09 1.65
Measurements Eq. (10)
1.9 1.65
Type 136 Type 202
1.36 2.11 7.5 Rain
Testing date
Table 4 and Fig. 13 shows the operating conditions of the various tests and the total energy supplied by each collector during the entire test while the average meteorological conditions of each test are presented in Table 5. The proposed mathematical equation was also integrated into TRNSYS and then compared to the results obtained with the TRNSYS models. Parameters, excepted c5 and c6, are adapted to the weather conditions as in Table 2. Figs. 14 and 15 give the percent difference between the energy obtained in the experimental measurements and the simulation results, for the non-insulated collector and the insulated one, respectively. The test between 15 and 21 of May includes various operating conditions (sunny, rain, condensation and frost). In general, the proposed mathematical equation provides less differences than the TRNSYS models, thanks to the added terms for rain, condensation/frost and infrared radiation behind the collector, but also because the parameters vary with the operating conditions. For all
Test duration (h)
Inlet temperature. Mass flow rate. Solar irradiance. Ambient temperature. Wind velocity. Sky temperature. Relative humidity. Precipitation.
Table 4 Operating conditions for each test and energy yield measured and simulated.
Measurements
Perers (2011) and Bertram (2011) have developed and validated models of unglazed collectors which also include operation under condensation conditions. These have been translated into TRNSYS components (Type 136 and Type 202, respectively). In order to have a global view on the behaviour of these models under various conditions (rain, frost, condensation or sunny) a comparison was performed against the measurements and the mathematical equation. The required model parameters were taken from the manufacturer and the inputs were set as the measured values on the test bench and kept constant for each model:
Energy yield insulated collector (kW h)
7. Comparison between the proposed mathematical equation and other available models
Energy yield non-insulated collector (kW h)
work is of interest mainly for analysis with a given weather pattern. With variable conditions, it is essential to have a dynamic model that allows changing the parameters values according to the weather conditions in order to simulate all these effects. The influence of the rear side long wave emissivity and the relative humidity of the ambient air on the total performance of the absorber was not found significant and therefore is not detailed in this work. Keller (1985) found an important difference on the heat transfer coefficient when the air humidity is 100% compared to 80%, but almost no difference between a relative humidity of 80% and 60%.
07.12.2011
Eq. (10)
M. Bunea et al. / Solar Energy 118 (2015) 547–561
Testing conditions
558
M. Bunea et al. / Solar Energy 118 (2015) 547–561
Rain
Fig. 13. Energy yield measured or simulated during each test. Values for the first seven tests should be read on left axis while the last one on the right axis.
models, the most significant differences are observed for tests with frost (40%) and rain. For the TRNSYS models these differences can be explained by the non-account of these phenomena. Results also show a large relative difference for tests with little quantity of condensed water (27–28 October) for the insulated collector. Still, in terms of absolute values, the difference is very small because the energies involved are small, see Table 4. At this stage, on the basis of the above comparison, the mathematical model seems to be the best alternative for numerical modelling under the specified conditions. However, a performance analysis based only on the total energy is not enough. In fact, the evolution of the difference between the measurement and simulation at each time step must also be taken into consideration. For this an integration of the absolute value of the difference was performed continuously. The obtained sum gives an indication of the behaviour of the model during the entire test. Figs. 16 and 17 show the values of this integration: These figures completes the information given by energy charts as shown in Fig. 12 by summing differences between measurements and simulations weather the value is negative or positive. It can be seen that:
559
Frost
Condensation
Sunny
Fig. 14. Relative differences between measured and simulated energy on several tests for the non-insulated collector.
Condensation
Rain
Frost
Sunny
Fig. 15. Relative differences between measured and simulated energy on several tests for the insulated collector.
The proposed equation provides better results under frost and rain conditions when compared to alternative models. In times of condensation and sunny periods, results from the three models are similar and no significant difference is observed when compared to measurements. During the sequence of several days with changing weather conditions and particularly for the non-insulated collector, the equation has a much higher dispersion, due to the single node model and the short time steps than the two models of TRNSYS, which are more stable during sudden changes in irradiation.
Table 5 Average meteorological conditions during each test. Testing conditions
Testing date
Rain
07.12.2011
Frost
15.12.2011 16.12.2011
Condensation (night time testing)
Ambient temp. (°C)
Relative humidity (%)
Solar radiation (W/m2)
6.5
84.9
18.1
4.2
4.8
5.5 7.0
75.9 84.1
26.7 2.7
1.3 4.6
0 0
15–16.09 2011 27–28.10.2011
14.9 8.0
83.4 87.0
0 0
4.8 3.0
0 0
Sunny
23.05.2011 25.05.2011
27.1 26.6
45.1 38.3
884.2 899.1
20.2 18.8
0 0
Mixed conditions
15–21.05.2012
14.0
89.3
170.2
6.4
Sky temperature (°C)
Precipitation (mm)
5.0
560
M. Bunea et al. / Solar Energy 118 (2015) 547–561
Rain
Frost
Condensation
phase of a solar collector working under particular conditions.
Sunny
8. Conclusions
Fig. 16. Integrated difference between measured and simulated energy on several tests for the non-insulated collector.
Rain
Frost
Condensation
Sunny
Fig. 17. Integrated difference between measured and simulated energy on several tests for the insulated collector.
Rain
Frost
Condensation
Sunny
Fig. 18. Heat flows for unglazed non-insulated collector during several tests.
An advantage of the proposed mathematical equation is that, unlike the TRNSYS models, it allows quantifying and to distinguish the different energy gains/losses of the solar collector, as shown in Fig. 18. For example it can be seen that the convective effect represents an important part of the heat gains during night time periods and greatly contributes to heat losses during sunny periods. This comparison has shown the limits of the proposed mathematical model when simulated periods of changing weather conditions. On the other side, this tool allows quantifying the different inputs and losses of a solar collector. Moreover, this model could be of use in the selection
In this article, a mathematical model is developed able to simulate unglazed collectors operating under specific weather conditions like condensation, frost and rain. A number of simulations have been conducted in order to compare the model predictions against other available models already translated into the TRNSYS simulation tool. The model results were also validated against measurements performed on a collectors test bench. Based on Figs. 16 and 17, it can be argued that the proposed mathematical model is not better for modelling long and changing weather conditions, but was able to better predict the heat delivered from the new terms taken into account for unglazed solar collectors when compared to the available models. The latter give satisfying results for cases with variable weather conditions including night condensation (10% deviation from the measurements). In addition, they are fairly stable during sudden changes in weather parameters. In comparison to the proposed model, the main drawback of these models lies in the non-integration of energy inputs due to frost, rain and gains/losses of long wave radiation behind the collector. However, the proposed equation is relatively unstable when considerable changes in operating conditions occur. Heat gains up to 50% of the total heat power of the solar collector were found due to the condensation effect while frost was estimated to contribute for 40% of the collector’s power during very low operating temperatures and no solar irradiation. Non-negligible thermal power can be exchanged between the unglazed solar collector and the rain water. The rainwater temperature is very difficult to define according to climatic conditions. A measurement of this temperature seems very complicated to implement. However, even if a solution is found, these results are interesting only for regions with high rainfall. For the Swiss climate, the potential energy recovered by an unglazed solar collector in rainwater was estimated at only 2% of the annual energy yield. The proposed correction terms validated in this article could be integrated into the TRNSYS types with quite little effort and therefore this mode can be used under extreme operating conditions with good accuracy. The proposed method of modelling solar collectors can also provide a tool for determining the strengths or weaknesses of a given collector. It could help choosing the best use of a solar collector under specific weather conditions and/or on the type of chosen system. Acknowledgement The Swiss Federal Office of Energy is gratefully acknowledged for the financial support of this work through the AquaPacSol project.
M. Bunea et al. / Solar Energy 118 (2015) 547–561
References Augustus Leon, M., Kumar, S., 2006. Mathematical modelling and thermal performance analysis of unglazed transpired solar collectors. Sol. Energy. Beckman, W., Duffie, J., 1991. Solar Engineering of Thermal Processes, ISBN: 0-471-51056-4. Bertram, E., 2011. Model of an Unglazed Solar Thermal Collector for TRNSYS 16 (documentation), ISFH. Bertram, E., Glembin, J., Schueren, J., Rockendorf, G., Zienterra, G., 2008. Unglazed Solar Collectors in Heat Pump Systems: Measurement, Simulation and Dimensioning. Bunea, M., Eicher, S., Hildrand, C., Bony, J., Perers, B., Citherlet, S., 2012. Performance of solar collectors under low temperature conditions: measurements and simulations results. Eurosun. DIN EN 12975-2, 2006. Thermal Solar System and Components – Solar Collectors – Part 2: Test Methods. Eisenmann, W., Mu¨ller, O., Pujiula, F., Zienterra, G., 2006. Metal roofs as unglazed solar collectors, coupled with heat pump and ground storage: gains from condensation, basics for system concepts. In: Proc. of the EuroSun 2006 Conference, Glasgow, Scotland, Paper 256. Keller, P., 1985. Characterization of the Thermal Performance of Uncovered Solar Collectors by Parameters Including the Dependence on Wind Velocity, Humidity and Infrared Sky Radiation as Well as on Solar Irradiance.
561
Kong, W., Wang, Z., Fan, J., Bacher, P., Perers, B., Chen, Z., Furbo, S., 2012. An improved dynamic test method for solar collectors. Sol. Energy. Morrison, G.L., 1994. Simulation of packaged solar heat-pump water heaters. Sol. Energy 53 (3), 249–257. Morrison, G.L., Gilliaert, D., 1992. Unglazed solar collector performance characteristics. J. Sol. Energy Eng. Palyvos, J., 2008. A survey of wind convection coefficient correlations for building envelope energy systems’ modeling. Appl. Therm. Eng. 28 (8– 9), 801–808. Perers, B., 1997. An improved dynamic solar collector test method for determination of non-linear optical and thermal characteristics with multiple regression. Sol. Energy. Perers, B., 2011. An Improved Dynamic Solar Collector Model Including Condensation and Asymmetric Incidence Angle Modifiers. Philippen, D., Haller, M.Y., Frank, E., 2011. Einfluss der Neigung auf den a¨usseren konvektiven Wa¨rmeu¨bergang unabgedeckter Absorber. In: 21. Symposium Thermische Solarenergie, 11. – 13. Mai, OTTI Regensburg, Bad Staffelstein, Germany, CD. Soltau, H., 1992. Testing the thermal performance of uncovered solar collectors. Sol. Energy 49 (4), 263–272. Tesfamichael, T., Wackelgard, E., 2000. Angular solar absorptance and incident angle modifier of selective absorbers for solar thermal collectors. Sol. Energy. Wolfe, W.L., Zissis, G.J., 1993. The Infrared Handbook, revised edition, 4th printing, pp. 3–104 to 3–109.
ScienceDirect Solar Energy 118 (2015) 547–561 www.elsevier.com/locate/solener
Mathematical modelling of unglazed solar collectors under extreme operating conditions M. Bunea a,⇑, B. Perers b, S. Eicher a, C. Hildbrand a, J. Bony a, S. Citherlet a a
Laboratory of Solar Energetics and Building Physics (LESBAT), Avenue des Sports 20, CH-1400 Yverdon-les-Bains, Switzerland b Departement of Civil Engineering, Technical University of Denmark, Brovej, Building 118, DK-2800 Kgs. Lyngby, Denmark Received 30 January 2015; received in revised form 11 May 2015; accepted 7 June 2015
Communicated by: Associate Editor Ursula Eicker
Abstract Combined heat pumps and solar collectors got a renewed interest on the heating system market worldwide. Connected to the heat pump evaporator, unglazed solar collectors can considerably increase their efficiency, but they also raise the coefficient of performance of the heat pump with higher average temperature levels at the evaporator. Simulation of these systems requires a collector model that can take into account operation at very low temperatures (below freezing) and under various weather conditions, particularly operation without solar irradiation. A solar collector mathematical model is developed and evaluated considering, the condensation/frost effect and rain heat gains or losses. Also wind speed and long wave irradiation on both sides of the collector are treated. Results show important heat gains for unglazed solar collectors without solar irradiation. Up to 50% of additional heat gain was found due to the condensation phenomenon and up to 40% due to frost under no solar irradiation. This work also points out the influence of the operating conditions on the collector’s characteristics. Based on experiments carried out at a test facility, every heat flux on the absorber was separately evaluated so that this model can represent a valuable tool in optimising the design or the thermal efficiency of the collector. It also enables the prediction of the total energy yield for solar thermal collectors under extreme operating conditions. Ó 2015 Elsevier Ltd. All rights reserved.
Keywords: Mathematical modelling; Solar thermal collector; Long wave irradiation; Condensation; Frost; Rain
1. Introduction Solar thermal collectors are originally designed to convert solar irradiation into useful heat. They have been adopted all over the world as a way to reduce fossil fuel consumption for space heating and domestic hot water production. Two main categories of solar collectors have
⇑ Corresponding author. Tel.: +41 (0)245572817.
E-mail address: [email protected] (M. Bunea). http://dx.doi.org/10.1016/j.solener.2015.06.012 0038-092X/Ó 2015 Elsevier Ltd. All rights reserved.
been developed depending on the existence or absence of a transparent cover on the absorber. This cover reduces the heat losses and therefore makes the solar collector more efficient at higher temperatures levels. On the other hand, uncovered collectors provide a higher solar energy yield at temperatures close to the ambient. The most important differences between these types of collectors are described by Keller (1985). The performance of these two categories of collectors is substantially different as that of the glazed collectors depends primarily on two factors (solar
548
M. Bunea et al. / Solar Energy 118 (2015) 547–561
Nomenclature Q_ collector thermal power supplied by the solar collector (W) Q_ rad;S short wave radiation heat exchange (W) convective heat exchange (W) Q_ conv Q_ rad;L long wave radiation heat exchange (W) conductive heat exchange (W) Q_ cond heat exchange with rain water (W) Q_ rain latent energy heat exchange (W) Q_ lat Q_ lat;C latent energy from condensation/evaporation heat exchange (W) latent energy from frost/melting heat exchange Q_ lat;F (W) F 0 ðfaÞen zero loss efficiency of the collector at normal incidence angle for the solar radiation onto the collector surface (–) g0 zero loss efficiency of the collector (–) Khb(h) incidence angle modifier for beam radiation (–) Khd(h) incidence angle modifier for diffuse radiation (–) G solar radiation (W/m2) Gb beam solar radiation (W/m2) Gd diffuse solar radiation (W/m2) EL long wave radiation (W/m2) c1 thermal heat loss/gain coefficient (W/m2/K) c2 temperature dependence of thermal heat losses/ gains coefficient (W/m2/K2) c3 wind velocity dependence of thermal heat losses/gains coefficient (J/m3/K) c4 long wave radiation dependence of the heat losses/gains coefficient – front side (–) c5 effective thermal capacitance of the solar collector (ccoll) (J/m2/K) c6 wind velocity dependence of the zero loss efficiency coefficient (s/m)
irradiance and ambient temperature) and for the unglazed collectors several other factors can also strongly influence their performance. These are the long wave irradiation, wind velocity, rain, condensation or frost. Solar energy is sometimes used indirectly through the evaporator of a heat pump. This configuration may increase the coefficient of performance of the heat pump but also shifts the operating range of the solar collectors to temperature levels below ambient. In this case, heat is no longer lost to the ambient air, but it becomes a gain. Therefore, the increasing demand for this type of systems, forces manufactures to use more frequently unglazed and sometimes non-insulated collectors in their installations. The purpose of the proposed solar thermal collector model is to best represent their behaviour under extended operating conditions and to quantify all energy inputs and/or losses as well as their influence on the total energy supplied by the solar collector.
c7
condensation/evaporation dependence coefficient (J/kg) c8 long wave radiation dependence of the heat losses/gains coefficient – rear side (–) c9 rain dependence of thermal heat losses/gains coefficient (–) u wind velocity (m/s) r Stefan–Boltzmann constant (W/m2/K4) va absolute humidity of the ambient air (kg/m3) vsat(tm) saturated absolute humidity of the ambient air at temperature tm (kg/m3) twat rain water temperature (°C) cp wat effective thermal capacitance of the rain water (J/kg/K) mwat rain water flow rate (kg/s) tm arithmetic mean temperature of the collector (tcoll) = (tin + tout)/2 (°C) Tm arithmetic mean temperature of the collector (Tcoll) = (Tin + Tout)/2 (K) ta ambient temperature (°C) thumide wet bulb temperature of the ambient air (°C) tsec dry temperature of the ambient air (°C) Ta ambient temperature (K) Tb building temperature (K) hr relative humidity of the ambient air (%) Rt total thermal resistance of a wall (m2 K/W) RSI internal superficial thermal resistance of a wall (m2 K/W) RSE external superficial thermal resistance of a wall (m2 K/W) U heat flow through a wall (W/m2 K)
2. Previous developments In the past, several studies contributed to a better characterisation of solar collector performance. In particular, Task III from the International Energy Agency (IEA), Solar Heating and Cooling Programme (SHC), and EN 12975 (2006) where work was done focused on the testing of glazed solar collectors. For unglazed collectors, a very comprehensive work was undertaken by Keller (1985) that shows the influence of the wind velocity, air humidity and long wave irradiation on the thermal performance of these collectors. Morrison and Gilliaert (1992) evaluated the difference between a three coefficient and a four coefficient form of the characteristic equation for the unglazed collectors. In IEA-SHC Task 44 several types of solar collectors, essentially unglazed, have been tested and modelled in combination with heat pumps.
M. Bunea et al. / Solar Energy 118 (2015) 547–561
549
condensation/evaporation Q_ lat;C or frost formation/melting Q_ lat;F . The latent energy becomes a heat gain for the collector in case of condensation or frost formation and a heat loss in case of evaporation or frost melting. Therefore, the total energy supplied by a solar collector is the addition of all these terms:
A mathematical model based on the heat balance and rate equations for unglazed transpired collectors was developed by Augustus Leon and Kumar (2006) where wind velocity was found to have an important effect on the collector effectiveness. The influence of the wind speed on the convection coefficient has also been presented by Palyvos (2008) and Keller (1985). For the climate of Limburg in Germany, Bertram et al. (2008) found that 4% of the annual unglazed collector yield was due to condensation when combined to a heat pump system. The condensation effect under no solar irradiation has also been reported by Keller (1985) and Philippen et al. (2011). For characterisation under any climate, condensation heat gains have been taken into account in several collector models reported by Keller (1985), Soltau (1992), Morrison (1994), Eisenmann et al. (2006), Perers (2011) and Bertram (2011). Still, no references were found in the literature on the influence of the rain, frost or rear side long wave irradiation. It is the purpose of this study to extend the modelling capabilities of current available solar thermal collectors to include these effects.
Q_ collector ¼ Q_ rad;S þ Q_ conv þ Q_ rad;L þ Q_ cond þ Q_ rain þ Q_ lat
It is important to notice that some of these phenomena may occur not only on the front side of the collector, but also on its rear side, see Fig. 1. The internal energy change should also be taken into account in the dynamic calculation. This term is as a function of the time derivative of the collector temperature and the thermal capacitance of the collector: dTdcoll ccoll
3.1. The standard model equation The EN 12975 (2006) standard provides a definition of the total heat gain for a collector under outdoor testing conditions.
3. Heat balance of a solar thermal collector Under low temperature conditions, all possible energy flow rates that may contribute to the collector energy balance are the absorbed solar irradiation Q_ rad;S , the convective heat exchange with the ambient air Q_ conv , the long wave irradiation, Q_ rad;L , the heat conduction through the ambient air or the collector’s support Q_ cond , the heat exchange with rain Q_ rain and the latent energy exchange Q_ lat . This latter can be divided into two terms:
optical efficiency:beam radiation
Q_ collector ¼
zfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflffl{ F 0 ðfaÞen K hb ðhÞGb
optical efficiency:diffuse radiation
þ
zfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflffl{ F 0 ðfaÞen K hd ðhÞGd
Heat lossngain at no wind
Wind dependence on optical efficiency
zffl}|ffl{ c6 uG
c2 ðtm ta Þ2 |fflfflfflfflfflfflffl{zfflfflfflfflfflfflffl}
Temperature dependence of the heat lossngain
þ c4 ðEL rT 4a Þ |fflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflffl} Long wave radiation
̇
dtm c5 dtffl} |fflffl{zffl
Thermal capacitance
,
̇ ̇ ̇ ̇
̇
,
̇ ̇
̇
ð1Þ
,
Fig. 1. Schematic representation of heat flow rates on the solar thermal collector.
zfflfflfflfflfflffl}|fflfflfflfflfflffl{ c1 ðtm ta Þ
þ
c3 uðtm ta Þ |fflfflfflfflfflfflffl{zfflfflfflfflfflfflffl}
Wind velocity dependence of the heat lossngain
ð2Þ
550
M. Bunea et al. / Solar Energy 118 (2015) 547–561
This standard has been adopted worldwide as a reference methodology for solar thermal collectors testing. Nevertheless, this model has not been designed to cope with very low temperature operating conditions such as the case of solar collectors combined with heat pumps. In this kind of application, the typical operating range of a solar collector is extended to include energy under no solar irradiation and at temperatures below ambient air and its dew point. As a consequence, additional terms have been introduced to the model presented in the standard along with some other modifications. For the condensation effect, Perers (2011) have already proposed an additional term so that Eq. (2) becomes: Q_ collector ¼ F 0 ðfaÞen K hb ðhÞGb þ F 0 ðfaÞen K hd ðhÞGd c6 uG c1 ðtm ta Þ c2 ðtm ta Þ2 þ c3 uðtm ta Þ dtm c7 ð2:8 3:0uÞðva vsat ðtm ÞÞ þ c4 ðEL rT 4a Þ c5 dt |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
Fig. 2. Incidence angle modifier for the unglazed collectors (see Footnote 3).
ð3Þ
Condensation
3.2. Considerations on the standard equation Based on this Eq. (3), a detailed analysis of each term was performed and a number of considerations were made. 3.2.1. Long wave radiation term The ðEL rT 4a Þ term is the calculation term of heat transfer by infrared irradiation between the sky and the collector. It is proposed to replace it by ðEL rT 4m Þ in order to have the sky radiation as a correction term by equating the average temperature Tm of the collector and not the ambient temperature Ta. 3.2.2. Condensation term (2.8 3u)(va vsat(tm)) corresponds to evaporation/ condensation term. Beckman and Duffie (1991) proposes to amend this term into (2.8 + 3u)(va vsat(tm)). This change will be retained, as in the basic equation, depending on the wind speed, this term could be negative or positive for the same value of (va vsat(tm)) (term giving the condition of condensation or evaporation). In addition, for the same term of condensation, it was decided to reverse the sign so that it adds a positive value to the total power when there is condensation and a negative value when there is evaporation. Thereby, the term becomes +(2.8 + 3u) (va vsat(tm)) instead of (2.8 3u)(va vsat(tm)). The calculation of the absolute humidity is done with:
3.2.4. Optical efficiency: beam and diffusion terms The incidence angles are not taken into account due to the position of the collectors in relation to the surrounding buildings. Direct solar radiation reaches the absorber with relatively small angles of incidence (<60°) where the IAM coefficients are almost constant (cf. Fig. 2). The F0 (fa)enKhb(h)Gb + F0 (fa)enKhd(h)Gd terms can be simplified to form a single term g0G where G includes direct and diffuse irradiation. Although solar irradiation is, generally, the most influential parameter in the energy balance of a solar thermal collector, the purpose of this work is to investigate conditions where this term is of less importance. For this reason, only the total solar irradiation is used, with no distinction between diffuse or direct irradiation. The influence of the angular solar absorptance and incident angles modifier was reported in literature (Tesfamichael and Wackelgard (2000)) where important decreases of the solar absorptance at high angles of incidence were found for two different coatings.
ð5Þ
3.2.5. Long wave radiation on the rear of the collector As some unglazed collectors have no insulation on rear side, one term was added to represent gains/losses by long wave (infrared) radiation exchange on the rear side of the collector. Calculation of this term is similar to that for the front side of the collector. The difference consists on the sky temperature that is replaced by the temperature of the body behind the collector, in this case it is the building and the flat roof where the collector is situated (cf. Fig. 7). The surface temperature of the building (Tb) is defined by:
3.2.3. Temperature dependence of heat The [(tm ta)|tm ta|] term is replacing the (tm ta)2. Indeed, when the collector temperature is lower than the ambient, there is a power supplied by the collector.
The room temperature under the roof set as a constant at 20 °C. The outside temperature. U value of the flat roof calculated at 0.24 W/m2K, see below.
V sat ðtÞ ¼ 0:001ð4:85 þ 0:347t þ 0:00945t2 þ 0:000158t3 þ 0:00000281t4 Þ v ¼ vsat ðtÞ hr
ð4Þ
M. Bunea et al. / Solar Energy 118 (2015) 547–561
The calculation of the thermal resistance of the flat roof is done using the following equations: X Ri þ RSE Rt ¼ RSI þ ð6Þ and U ¼ 1=Rt
ð7Þ
with RSI = 0.13 (m2 K)/W, RSE = 0.04 (m2 K)/W and Ri corresponds to the thermal resistance of each layer composing the roof.1 3.2.6. Rain term One term was added to account for the energy exchanged between the collector and the rain. The rainwater temperature is considered equal to the wet bulb temperature of the air, calculated with Heinrich Gustav Magnus-Tetens.2 No measurements on the test bench were capable to give a better approach of this temperature and no other approximations were found in the literature. thumide ¼ b aðtsec ; hr Þ=ða aðtsec ; hr ÞÞ
ð8Þ
with : aðtsec ; hr Þ ¼ a tsec =ðb þ tsec Þ þ lnðhr Þ
ð9Þ
a ¼ 17:27 ðÞ
b ¼ 237:7 ð CÞ The rain water mass is calculated from the data of the rain gauge installed next to the collectors. 3.3. Proposed model equation With the changes outlined above, Eq. (3) becomes Q_ collector ¼ g0 G c6 uG c1 ðtm ta Þ c2 ðtm ta Þjtm ta j þ c3 uðtm ta Þ
551
Table 1 system instrumentation and accuracy. Sensor
Manufacturer
Type
Accuracy
Temperature Flow rate
Transmettra Krohne
0.1 K 0.3%
Solar radiation Relative humidity Wind velocity
Kipp & Zonen Rotronic
Pt100 A class Electromagnetic flowmeter Pyranometer Hygromer humidity sensor Weather vane
Adolf Thies GmbH
1.4% 1% 3%
inlet collector temperatures varying from 10 °C to 5 °C. Sensor description and their accuracy is given in Table 1. Bunea et al. (2012) have shown that for glazed collectors without solar irradiance no significant additional benefits were obtained from condensation effect, frost or rain. Therefore, only unglazed solar collectors will be addressed in this article. For the standard collector (insulated), the parameters g0, c1, c2, c3 and c5 were taken from the documentation provided by the collector’s test report30. Parameters for the non-insulated collector including (c4, c6, c7, c8, c9) for which no values are documented were initially approximated by theoretical values and then refined in order for the simulations to be closest to the measurements and this for all climatic conditions encountered. These parameters are summarized in Tables 2 and 3. Briefs explanations on the process to arrive to these values will be presented in this section as well as the assumptions made in the laboratory. The absorber area of both collectors is 1.85 m2. Changes of the coefficient value from one test to another will be explained further down. 5. Results
Rear side long wave irradioation
þ
zfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflffl{ c8 ðrT 4b rT 4m Þ
þc4 ðEL rT 4m Þ
dtm þ c7 ð2:8 þ 3:0uÞðva vsat ðtm ÞÞ dt þ c9 mwat cp wat ðtwat tm Þ |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
c5
ð10Þ
Rain
4. Experimental setup A testing facility comprising four solar thermal collectors (flat plate collector, evacuated tube collector, insulated unglazed collector and non-insulated unglazed collector) equipped with different sorts of sensors was developed for collector monitoring purposes (see Fig. 3). Several tests under different real weather conditions in Yverdon-les-Bains, Switzerland, have been performed with 1 SIA 180 (1999) Isolation thermique et protection contre l’humidite´ dans les baˆtiments. 2 Barenbrug, A.W.T., Psychrometry and Psychrometric Charts, Le Cap, Afrique du Sud, Cape and Transvaal Printers Ltd., 1974, 3e e´d.
The analysis was made in terms of the net power and energy provided by the collectors. In fact, under these extended operating conditions, the classical definition of the efficiency of a solar collector (output power divided by the solar irradiation) is no longer relevant. Eq. (10) has been implemented in a spreadsheet to compare the calculated power against the measured power for several days under different weather conditions. This spreadsheet can also be used to estimate the values of various parameters of each collector. 5.1. Sunny periods The collector total power obtained with the mathematical Eq. (10) is close to that measured for a sunny day (cf. Fig. 4). However, some deviations (15%) are observed at certain times such as 12.5 h, but for a short duration.
3 Institut fur solartechnik, Collectors test reports, Factsheet – SPF-Nr.420.
Unglazed flat plate with rear insulation
Evacuated tube
Unglazed flat plate without rear insulation
M. Bunea et al. / Solar Energy 118 (2015) 547–561
Glazed flat plate
552
Weather Station
Temperature sensor Flow rate Pump Heat exchanger
C
Regulation valve C
Chiller
Fig. 3. Set-up diagram of the testing facility.
For these weather conditions, the parameters used in the equation correspond to the values given by the manufacturer or found in the literature. These values will be named “standards” for the remaining of this article. 5.2. Condensation periods To maximise condensed water vapour on the surface of the absorber, tests were made during the night (no solar irradiation) with an inlet temperature of the collectors close to 0 °C. In this case, the main energy sources are convection, long-wave irradiation and condensation on the surface of the collector. To experimentally estimate the amount of condensation on the unglazed collectors, a large bucket was placed underneath the collectors in order to recover the condensed water (see Fig. 5a). A lid with a narrow slot for the passage of the condensed water limits evaporation during the test (see Fig. 5b). The uncertainty of the condensation heat gains measurements was determined to be 8% by night. The measured yield for the conducted tests varied from 0.5 kW h to 3.3 kW h for the insulated solar collector and from 1.3 kW h to 4.8 kW h for the non-insulated solar collector. It was observed that condensation can represent 23– 55% of the total collector’s yield for these tests depending on the weather conditions.
As a consequence of the condensation phenomena, the collector becomes wet, leading to changes in the physical properties of its selective surface. Thus, the specific parameters of the collector were changed so that the power given by the equation would closely represent the new conditions as shown in Fig. 6. The most important change concerns the infrared emissivity of the absorber (c4 and c8) going from 0.05 with a dry surface (selective surface in small wavelengths) to a 0.9 (water effective emissivity) when the surface is wet because the selective layer of the absorber is no longer operative. The value of emissivity for thin water layers is given by Wolfe and Zissis (1993). Another important modification is the disruption of the convective transfer between the air and the collector through the film condensation, resulting in a decrease of parameter c1. Finally, parameter c7 related to condensation. The dependence of the air pressure or the inclination of the collector on the condensation phenomena were not tested in this work. Keller (1985) found negligible the influence of the air pressure on the condensation effect while Philippen et al. (2011) has not detected larger condensation gains for larger inclinations of the collector under outdoor conditions. Increased heat gains were principally due to higher long wave irradiance from the field of view of the unglazed collector.
Table 2 Parameters for non-insulated solar collector under different testing conditions. Testing conditions
Parameters for non-insulated unglazed solar collector g0 (–)
Sunny Condensation Frost Rain Mixed conditions
Optical efficiency
c1 (W/ (m2 K)) Convection at no wind
0.959 0.959 0.8 0.959 0.959
12 8.5 16.5 12 12
c2 (W/(m2 K2))
c3 (J/(m3 K))
c4 (–)
c5 (J/(m2 K))
c6 (s/m)
c7 (J/kg)
c8 (–)
c9 (–)
Temperature dependence on heat loss/gain
Wind dependence on heat loss/gain
Front side emissivity for long wave radiation
Thermal capacitance
Wind dependence on optical efficiency
Condensation
Rear side emissivity for long wave radiation
Rain
0 0 0 0 0
4 4 4 6 4
0.05 0.9 0.9 0.9 0.5
18,000 18,000 18,000 18,000 18,000
0.03 0.03 0.03 0.03 0.03
0 2,000 2,300 2,000 2,000
0.05 0.9 0.9 0.9 0.5
0 0 0 0.5 0.5
Testing conditions
Parameters for insulated unglazed solar collector g0 (–)
Sunny Condensation Frost Rain Mixed conditions
Optical efficiency
c1 (W/ (m2 K)) Convection at no wind
0.959 0.959 0.8 0.959 0.959
8.91 6.5 12.5 8.91 8.91
c2 (W/(m2 K2)]
c3 (J/(m3 K))
c4 (–)
c5 (J/(m2 K))
c6 (s/m)
c7 (J/kg)
c8 (–)
c9 (–)
Temperature dependence on heat loss/gain
Wind dependence on heat loss/gain
Front side emissivity for long wave radiation
Thermal capacitance
Wind dependence on optical efficiency
Condensation
Rear side emissivity for long wave radiation
Rain
0.047 0.047 0.047 0.047 0.047
2.26 2.26 2.26 4 2.26
0.05 0.8 0.9 0.9 0.5
18,000 18,000 18,000 18,000 18,000
0.03 0.03 0.03 0.03 0.03
0 1,300 1,500 1,300 1300
0 0 0 0 0
0 0 0 0.5 0.5
M. Bunea et al. / Solar Energy 118 (2015) 547–561
Table 3 Parameters for insulated solar collector under different testing conditions.
553
554
M. Bunea et al. / Solar Energy 118 (2015) 547–561
Non-insulated unglazed solar collector
Insulated unglazed solar collector
Fig. 4. Measured vs. calculated power of unglazed collectors – sunny day.
Fig. 5. (a) Buckets under solar collectors; (b) lid on the bucket.
Non-insulated unglazed solar collector
Insulated unglazed solar collector
Fig. 6. Measured vs. calculated power of unglazed collector – mild temperatures night conditions.
5.3. Frost periods If the supplied energy by an unglazed collector is lower than the one requested by the consumer (e.g. heat pump), the collector’s temperature will drop and reach negative values. In this case, the water vapour contained in ambient air will freeze on the surface of the collector as shown in Fig. 7. This phenomenon brings, as in the case of condensation, energy to the collector. A test with an inlet temperature of the collector at about 5 °C was made. The measured collector power was compared to that calculated by the mathematical model. The results are shown in Fig. 8. Some differences between
the measurements and the calculations are observed with little impact on the cumulated energy during the test. It is to notice the significant thermal power delivered by the non-insulated solar collector under no solar irradiation. An experiment was also carried out to attempt to quantify the amount of frost formed. However, this is very difficult to perform. A first estimation was made using a similar approach as performed for the condensation. The collector temperature was kept stable for several hours, which contributed to the formation of frost. Then, the fluid was heated at 20 °C melting the ice and the water was collected in buckets beneath the collector.
M. Bunea et al. / Solar Energy 118 (2015) 547–561
Rear side insulated
Non-insulated
555
5.4. Rainy periods The unglazed collectors are able to recover the energy contained in rainwater, whenever they operate at low temperatures. Conversely, they can lose energy when their temperature is higher than the rainwater. In Switzerland, the maximum energy gain from the rainwater was estimated at about 5 kW h/m2 per year, representing 2% of the average annual energy yield of an unglazed collector under normal operation. The unglazed collectors were tested during a rainy period of 7 h (total 4.8 mm). Fig. 9 shows the results obtained following some adjustments of the standard parameters. The results are slightly worse than those for tests with sunny periods. Still, the deviations do not exceed 15%. Modified parameters are:
Fig. 7. Unglazed solar collectors with frost on the surface.
The amount of water collected was close to that found in the case of condensation. However, the supplied energy to the collector is higher because the latent heat of solidification is added to the latent heat of condensation. Simulation results were obtained by modifying some standard parameters to cope with the above effects: The efficiency of the optical collector (g0) decreases because frost causes reverberation. The parameter c1 (convection + radiation) increases as the frost layer has a higher surface of exchange due to ice crystals. As for condensation, the infrared emissivity of the absorber (c4 and c8) increases, because the selective surface is no longer operational. The parameter c7 is related to the presence of frost and condensation. This value is higher than the one during condensation (15%), which corresponds approximately to the addition of the latent heat of solidification to the condensation latent heat.
Noninsulated unglazed solar collector
The dependence on heat loss/gain (c3) increases. It is assumed that this increase is due to an increased convective movements related to the rain. The c9 parameter related to the presence of rainwater on the surface of the absorber.
5.4.1. Long periods with changing conditions A test of 136 h from 15 to 21 of May was performed with varying weather conditions in order to validate the model for solar collectors under different conditions (rain, wind, condensation and sunlight) (cf. Fig. 10). During this test, the set-point temperature of the collector input was fixed to 0 °C. In practice, this temperature changes slightly depending on the weather conditions, especially for high solar irradiation, when the output temperature increases considerably. The chosen parameters for this configuration are the “standards” parameters except for: The effective emissivity parameters (c4 and c8); average values for sunny period and period with condensation (see Tables 2 and 3).
Insulated unglazed solar collector
Fig. 8. Measured and calculated power of unglazed collector – cold temperatures.
556
M. Bunea et al. / Solar Energy 118 (2015) 547–561
Non-insulated unglazed solar collector
Insulated unglazed solar collector
Fig. 9. Measured and calculated power of unglazed collector – rainy conditions.
Not insulated unglazed solar collector
Insulated unglazed solar collector
Fig. 10. Measured vs. calculated power for unglazed collectors – one week weather conditions (5 min average).
The parameters of condensation-frost (c7) and rain (c9) were added. Calculations (red lines) show a behaviour close to the measured power (blue) of the collector when there is no sudden change in climate conditions, such as during the night or during the second day (May 17). However, on days with variable solar irradiation, differences are observed between the measured and the calculated power as shown in Fig. 11. A detailed analysis of these periods shows that the average difference is 32 W for non-insulated collector and 34 W for the insulated collector. Also, standard deviations are 110 W for the non-insulated collector and 107 W for the insulated one (front or rear side area 2 m2). Important differences, as observed on the encircled zones in Fig. 11, occur in the morning because of the solar irradiation getting partially on the surface of the solar collector and not yet on the pyranometer. Differences outside these zones are explained by the very short time step calculations (10 s). For such time steps, a single node model as this mathematical equation, encounters difficulties in managing the thermal inertia of the solar collector during sudden changes in the climatic conditions. The temperature measurements recorded show very rapid changes that can be out of phase with those calculated. Perers (1997) revealed that this approximation is satisfying when the time
steps for measurements are long compared with the time for the fluid to pass through collector. Thus, especially for small mass flow rates and in the absence of solar irradiation, the simplifying assumption of a linear increase of the inlet fluid temperature and the outlet has to be checked carefully. The thermal capacitance of the collector should be in this case separated into several control volumes or a different approach may have to be chosen. Nevertheless, most of the weather data available are mean hourly values which is generally longer than the dwell time for the fluid in the collector. Kong et al. (2012) have already shown the sensitivity of this parameter and implemented a two-node method called “transfer function method” in which the collector was separated into the solid part and the fluid part in order to be more precise. He also added a new parameter to take into account the heat transfer between the solid to the fluid part of the collector. Possible remedies would be to incorporate the modifications suggested by Kong et al. (2012). Because the main objective of this work is to represent the behaviour of the collector under certain conditions, not necessary for long periods and to estimate the heat flows through the collector, these considerations were not integrated into the mathematical equation. Nevertheless, even if these differences may seem important in terms of absolute power output during these
M. Bunea et al. / Solar Energy 118 (2015) 547–561
Non-insulated unglazed solar collector
557
Insulated unglazed solar collector
Fig. 11. Differences between measured and calculated power (5 min average).
Not insulated unglazed solar collector
Insulated unglazed solar collector
Fig. 12. Evolution of measured and calculated energies for unglazed collectors – one week weather conditions.
changing periods, they have positive value at one time step and then negative value at the following time step with same amplitude. This gives a simulated energy yield very close to the measured energy as seen in Fig. 12. The maximum deviation on the energy calculation during the 136 h test is 5% for the insulated collector and 2% for non-insulated collector. 6. Discussion For classical operation of a solar thermal collector, simple models, as described in EN12975, have been tested for years and give fairly accurate estimations of the output power of the collector. Still, they have not been designed to cope with operating conditions such as night time or with temperatures below ambient. The analysis presented in this work shows that for these extended weather conditions additional parameters are needed in order to correctly account for the different phenomena occurring on the unglazed solar collector. On the other side, significant variation of the standard parameters was observed for different operating conditions, leading to the conclusion that optimal parameter sets are not universal. The additional power due to condensation was found relatively low (100 W/m2 maximum). More important heat gains up to 400 W/m2 were measured during frost
formation for the non-insulated unglazed collector and the frost was estimated to contribute to about 40% of this energy. Notwithstanding, special attention must be paid on damages that the condensation or frost can create in long-term operation especially for the selective coating or insulation. Accelerated aging tests with repeated uses under these conditions should be made to observe the evolution of their performance in time. When collector’s temperatures are negative for longer periods, there is also the risk of ice block development, so once detached from the collector are likely to fall and cause damage. The opposite phenomena of condensation (evaporation) and frost (thaw) are not treated in this manuscript. Still, what was observed during these tests is that, depending on the collector’s tilt, most of the water accumulated on the collector surface falls down and therefore the impact of the evaporation should be very small. A more important influence on the collector output power should be observed by the frost melting, for example on a sunny morning after a night of very low temperature operation. The energy needed for this phenomena should be in the same range as the energy for frost. The difficulty lies in the choice of these parameters for testing over periods with changing weather conditions. A setting that may give very good results during sunny periods, may produce unreliable results during the night. Therefore, the use of a static model as presented in this
62.51 69.29 65.97 62.31 76.72 80.8 72.09 76.76 136 Mixed conditions
15–21.05.2012
3.07 3.34 3.27 3.8 3.11 3.87 3.28 3.61 2.86 3.03 3.05 3.44 2.72 3.03 3.00 3.07 4 5.5 Sunny
23.05.2011 25.05.2011
3.33 1.34 3.21 1.18 3.28 1.17 3.41 1.00 4.53 1.99 4.45 1.65 4.07 1.49 5.32 1.76 13 11 Condensation (night time testing)
15–16.09 2011 27–28.10.2011
8.07 6.85 4.34 4.22 4.26 4.21 7.13 8.5 11.23 9.64 6.06 6.39 5.6 6.08 10.06 11.62 15.5 15 Frost
15.12.2011 16.12.2011
1.37 1.23
Type 136 Type 202
1.09 1.65
Measurements Eq. (10)
1.9 1.65
Type 136 Type 202
1.36 2.11 7.5 Rain
Testing date
Table 4 and Fig. 13 shows the operating conditions of the various tests and the total energy supplied by each collector during the entire test while the average meteorological conditions of each test are presented in Table 5. The proposed mathematical equation was also integrated into TRNSYS and then compared to the results obtained with the TRNSYS models. Parameters, excepted c5 and c6, are adapted to the weather conditions as in Table 2. Figs. 14 and 15 give the percent difference between the energy obtained in the experimental measurements and the simulation results, for the non-insulated collector and the insulated one, respectively. The test between 15 and 21 of May includes various operating conditions (sunny, rain, condensation and frost). In general, the proposed mathematical equation provides less differences than the TRNSYS models, thanks to the added terms for rain, condensation/frost and infrared radiation behind the collector, but also because the parameters vary with the operating conditions. For all
Test duration (h)
Inlet temperature. Mass flow rate. Solar irradiance. Ambient temperature. Wind velocity. Sky temperature. Relative humidity. Precipitation.
Table 4 Operating conditions for each test and energy yield measured and simulated.
Measurements
Perers (2011) and Bertram (2011) have developed and validated models of unglazed collectors which also include operation under condensation conditions. These have been translated into TRNSYS components (Type 136 and Type 202, respectively). In order to have a global view on the behaviour of these models under various conditions (rain, frost, condensation or sunny) a comparison was performed against the measurements and the mathematical equation. The required model parameters were taken from the manufacturer and the inputs were set as the measured values on the test bench and kept constant for each model:
Energy yield insulated collector (kW h)
7. Comparison between the proposed mathematical equation and other available models
Energy yield non-insulated collector (kW h)
work is of interest mainly for analysis with a given weather pattern. With variable conditions, it is essential to have a dynamic model that allows changing the parameters values according to the weather conditions in order to simulate all these effects. The influence of the rear side long wave emissivity and the relative humidity of the ambient air on the total performance of the absorber was not found significant and therefore is not detailed in this work. Keller (1985) found an important difference on the heat transfer coefficient when the air humidity is 100% compared to 80%, but almost no difference between a relative humidity of 80% and 60%.
07.12.2011
Eq. (10)
M. Bunea et al. / Solar Energy 118 (2015) 547–561
Testing conditions
558
M. Bunea et al. / Solar Energy 118 (2015) 547–561
Rain
Fig. 13. Energy yield measured or simulated during each test. Values for the first seven tests should be read on left axis while the last one on the right axis.
models, the most significant differences are observed for tests with frost (40%) and rain. For the TRNSYS models these differences can be explained by the non-account of these phenomena. Results also show a large relative difference for tests with little quantity of condensed water (27–28 October) for the insulated collector. Still, in terms of absolute values, the difference is very small because the energies involved are small, see Table 4. At this stage, on the basis of the above comparison, the mathematical model seems to be the best alternative for numerical modelling under the specified conditions. However, a performance analysis based only on the total energy is not enough. In fact, the evolution of the difference between the measurement and simulation at each time step must also be taken into consideration. For this an integration of the absolute value of the difference was performed continuously. The obtained sum gives an indication of the behaviour of the model during the entire test. Figs. 16 and 17 show the values of this integration: These figures completes the information given by energy charts as shown in Fig. 12 by summing differences between measurements and simulations weather the value is negative or positive. It can be seen that:
559
Frost
Condensation
Sunny
Fig. 14. Relative differences between measured and simulated energy on several tests for the non-insulated collector.
Condensation
Rain
Frost
Sunny
Fig. 15. Relative differences between measured and simulated energy on several tests for the insulated collector.
The proposed equation provides better results under frost and rain conditions when compared to alternative models. In times of condensation and sunny periods, results from the three models are similar and no significant difference is observed when compared to measurements. During the sequence of several days with changing weather conditions and particularly for the non-insulated collector, the equation has a much higher dispersion, due to the single node model and the short time steps than the two models of TRNSYS, which are more stable during sudden changes in irradiation.
Table 5 Average meteorological conditions during each test. Testing conditions
Testing date
Rain
07.12.2011
Frost
15.12.2011 16.12.2011
Condensation (night time testing)
Ambient temp. (°C)
Relative humidity (%)
Solar radiation (W/m2)
6.5
84.9
18.1
4.2
4.8
5.5 7.0
75.9 84.1
26.7 2.7
1.3 4.6
0 0
15–16.09 2011 27–28.10.2011
14.9 8.0
83.4 87.0
0 0
4.8 3.0
0 0
Sunny
23.05.2011 25.05.2011
27.1 26.6
45.1 38.3
884.2 899.1
20.2 18.8
0 0
Mixed conditions
15–21.05.2012
14.0
89.3
170.2
6.4
Sky temperature (°C)
Precipitation (mm)
5.0
560
M. Bunea et al. / Solar Energy 118 (2015) 547–561
Rain
Frost
Condensation
phase of a solar collector working under particular conditions.
Sunny
8. Conclusions
Fig. 16. Integrated difference between measured and simulated energy on several tests for the non-insulated collector.
Rain
Frost
Condensation
Sunny
Fig. 17. Integrated difference between measured and simulated energy on several tests for the insulated collector.
Rain
Frost
Condensation
Sunny
Fig. 18. Heat flows for unglazed non-insulated collector during several tests.
An advantage of the proposed mathematical equation is that, unlike the TRNSYS models, it allows quantifying and to distinguish the different energy gains/losses of the solar collector, as shown in Fig. 18. For example it can be seen that the convective effect represents an important part of the heat gains during night time periods and greatly contributes to heat losses during sunny periods. This comparison has shown the limits of the proposed mathematical model when simulated periods of changing weather conditions. On the other side, this tool allows quantifying the different inputs and losses of a solar collector. Moreover, this model could be of use in the selection
In this article, a mathematical model is developed able to simulate unglazed collectors operating under specific weather conditions like condensation, frost and rain. A number of simulations have been conducted in order to compare the model predictions against other available models already translated into the TRNSYS simulation tool. The model results were also validated against measurements performed on a collectors test bench. Based on Figs. 16 and 17, it can be argued that the proposed mathematical model is not better for modelling long and changing weather conditions, but was able to better predict the heat delivered from the new terms taken into account for unglazed solar collectors when compared to the available models. The latter give satisfying results for cases with variable weather conditions including night condensation (10% deviation from the measurements). In addition, they are fairly stable during sudden changes in weather parameters. In comparison to the proposed model, the main drawback of these models lies in the non-integration of energy inputs due to frost, rain and gains/losses of long wave radiation behind the collector. However, the proposed equation is relatively unstable when considerable changes in operating conditions occur. Heat gains up to 50% of the total heat power of the solar collector were found due to the condensation effect while frost was estimated to contribute for 40% of the collector’s power during very low operating temperatures and no solar irradiation. Non-negligible thermal power can be exchanged between the unglazed solar collector and the rain water. The rainwater temperature is very difficult to define according to climatic conditions. A measurement of this temperature seems very complicated to implement. However, even if a solution is found, these results are interesting only for regions with high rainfall. For the Swiss climate, the potential energy recovered by an unglazed solar collector in rainwater was estimated at only 2% of the annual energy yield. The proposed correction terms validated in this article could be integrated into the TRNSYS types with quite little effort and therefore this mode can be used under extreme operating conditions with good accuracy. The proposed method of modelling solar collectors can also provide a tool for determining the strengths or weaknesses of a given collector. It could help choosing the best use of a solar collector under specific weather conditions and/or on the type of chosen system. Acknowledgement The Swiss Federal Office of Energy is gratefully acknowledged for the financial support of this work through the AquaPacSol project.
M. Bunea et al. / Solar Energy 118 (2015) 547–561
References Augustus Leon, M., Kumar, S., 2006. Mathematical modelling and thermal performance analysis of unglazed transpired solar collectors. Sol. Energy. Beckman, W., Duffie, J., 1991. Solar Engineering of Thermal Processes, ISBN: 0-471-51056-4. Bertram, E., 2011. Model of an Unglazed Solar Thermal Collector for TRNSYS 16 (documentation), ISFH. Bertram, E., Glembin, J., Schueren, J., Rockendorf, G., Zienterra, G., 2008. Unglazed Solar Collectors in Heat Pump Systems: Measurement, Simulation and Dimensioning. Bunea, M., Eicher, S., Hildrand, C., Bony, J., Perers, B., Citherlet, S., 2012. Performance of solar collectors under low temperature conditions: measurements and simulations results. Eurosun. DIN EN 12975-2, 2006. Thermal Solar System and Components – Solar Collectors – Part 2: Test Methods. Eisenmann, W., Mu¨ller, O., Pujiula, F., Zienterra, G., 2006. Metal roofs as unglazed solar collectors, coupled with heat pump and ground storage: gains from condensation, basics for system concepts. In: Proc. of the EuroSun 2006 Conference, Glasgow, Scotland, Paper 256. Keller, P., 1985. Characterization of the Thermal Performance of Uncovered Solar Collectors by Parameters Including the Dependence on Wind Velocity, Humidity and Infrared Sky Radiation as Well as on Solar Irradiance.
561
Kong, W., Wang, Z., Fan, J., Bacher, P., Perers, B., Chen, Z., Furbo, S., 2012. An improved dynamic test method for solar collectors. Sol. Energy. Morrison, G.L., 1994. Simulation of packaged solar heat-pump water heaters. Sol. Energy 53 (3), 249–257. Morrison, G.L., Gilliaert, D., 1992. Unglazed solar collector performance characteristics. J. Sol. Energy Eng. Palyvos, J., 2008. A survey of wind convection coefficient correlations for building envelope energy systems’ modeling. Appl. Therm. Eng. 28 (8– 9), 801–808. Perers, B., 1997. An improved dynamic solar collector test method for determination of non-linear optical and thermal characteristics with multiple regression. Sol. Energy. Perers, B., 2011. An Improved Dynamic Solar Collector Model Including Condensation and Asymmetric Incidence Angle Modifiers. Philippen, D., Haller, M.Y., Frank, E., 2011. Einfluss der Neigung auf den a¨usseren konvektiven Wa¨rmeu¨bergang unabgedeckter Absorber. In: 21. Symposium Thermische Solarenergie, 11. – 13. Mai, OTTI Regensburg, Bad Staffelstein, Germany, CD. Soltau, H., 1992. Testing the thermal performance of uncovered solar collectors. Sol. Energy 49 (4), 263–272. Tesfamichael, T., Wackelgard, E., 2000. Angular solar absorptance and incident angle modifier of selective absorbers for solar thermal collectors. Sol. Energy. Wolfe, W.L., Zissis, G.J., 1993. The Infrared Handbook, revised edition, 4th printing, pp. 3–104 to 3–109.