MODEL OF A PV/THERMAL UNGLAZED TRANSPIRED SOLAR COLLECTOR Veronique Delisle, and Michael R. Collins University of Waterloo, Waterloo, Canada
1
200 University Avenue West, Waterloo, ON, N2L 3G1 Phone: 519-888-4567 ext 33885, Fax: 519-885-5862 Email:
[email protected]
ABSTRACT In the last few years, unglazed transpired solar collectors (UTC) have demonstrated as being an effective and viable method of reducing HVAC load and building energy consumption. With the growing interest in combined photovoltaic-thermal collectors (PV/Thermal), the potential of PV/Thermal unglazed transpired solar collectors is currently being studied intensively. This paper presents a model to predict the performance of a PVT unglazed transpired corrugated solar collector with PV cells mounted on the absorber plate. The mathematical model developed to predict the performance of this collector is to be implemented as a component in TRNSYS, and is based on an actual TRNSYS UTC flat plate collector model. Changes were made to this model to account for both the corrugated shape of the plate, and the addition of PV cells on some surfaces.
INTRODUCTION In the last few years, unglazed transpired solar collectors (UTC) have demonstrated as being an effective and viable method of reducing HVAC load and building energy consumption. With their capacity to directly preheat outside air, UTC’s are a costeffective option for buildings requiring a large amount of hot fresh air or for solar crop drying applications. A well-known UTC, the Solarwall®, appeared in the 1990’s and has been installed in 25 different countries on commercial, industrial, institutional and multiresidential buildings (Conserval Engineering Inc.). In this analysis the PV cells are mounted directly on some surfaces of the collector, leaving the holes uncovered. The model, formulated as a TRNSYS component, predicts the performance of a PV/Thermal unglazed transpired solar collector with a trapezoidal corrugated shape. Figure 2 presents the two different configurations studied in this analysis. In configuration a), only the top of the corrugations are covered with PV cells while in configuration b), PV cells are deposited on the whole surface of the collector.
Figure 1. PV/Thermal collector configurations
MODEL DEVELOPMENT Literature Review Several models of thermal UTC were developed over the years to facilitate their design. SWift and Retscreen are the most well-known ones and predict similar results even though they use quite different approaches (Carpenter et al., 2002). The main difference between the two programs is that SWift uses equations derived from basic thermodynamics principles such as Fourier’s law, while Retscreen uses empirical correlation. In addition to these two programs, a TRNSYS model has also been developed by Summers (Summers, 1995), but has not been incorporated yet to the main TRNSYS library. His model solves a set of energy balances to predict the performance of the collector. However, it does not account for any wind effects or for the corrugated shape of the absorber plate. Assumptions In order to minimize the computing time of the model, the following assumptions were made. • The temperature of the plate is assumed to be uniform. This is a common assumption for UTC that is used in SWift, Retscreen and Summers’ models. In reality, there is a temperature gradient around the perforations where the convective heat transfer is greater. However, as shown by Gawlik et al. (Gawlik et al., 2005) this non-isothermality does not have a great effect on the collector performance. The uniformity of the absorber temperature was
also verified by Gogakis (Gogakis, 2005), who performed an outdoor experiment on an UTC with trapezoidal corrugated shape. • The calculations performed at every time step are assumed to have reached steady-state, since the response time of UTC to a change in solar radiation is very fast. In his experiment, Gogakis (Gogakis, 1995) found that the response time was approximately 1 minute. Therefore, for a simulation performed hourly, this is a valid assumption. • The PV cells are assumed to work at maximum power point. • The suction and porosity (σ) are assumed to be uniform at the surface of the collector, and the perforations are considered to be circular on a square pitch. Theory In order to predict the performance of the PV/Thermal collector, a set of energy balances are performed on the collector. These equations are similar to the ones used by Summers (Summers, 1995), but few changes were made to account for the wind effect and the fact that PV is on the absorber plate. Figure 3 presents the different terms associated with the heat transfer occurring in the transpired collector. On this figure, the collector is assumed to be mounted on a vertical wall, but it could also be installed on an inclined roof.
Tamb. The correlation developed by Van Decker (Van Decker et al., 2001) is used to obtain εHX as a function of the wind velocity Uw, the suction velocity Vs, the pitch P and the diameter D of the perforations. It takes into account the convective heat transfer occurring in all three regions of the hole: the back, the sides of the hole, and the front. It was found to be in agreement with a model developed earlier by Kutscher et al. (Kutscher et al., 1994), but is valid for a wider range of plate thicknesses and hole pitches. Equations (2), (3) and (4) are obtained by performing energy balances on the absorber plate, on the wall located at the back of the collector, and on the holes, respectively. In these equations, Qabs is the total solar radiation absorbed by the collector, Qrad,wall-col is the radiation heat transfer between the wall/roof and the collector, Qconv,col-plen is the convective heat transfer from the collector (front, side and back) to the plenum, Qwind is the wind heat loss, Qrad,col-sur is the radiation heat transfer from the collector to the surroundings, Qconv,wall-plen is the convective heat transfer from the wall to the plenum, Qcond,wall is the conductive heat transfer & is the mass flow rate through the building wall and m through the collector.
ε HX =
T plen − Tamb
(1)
Tcol − Tamb
Q abs + Q rad , wall − col = Qconv ,col − plen + Q wind + Q rad ,col − sur Tout εcol
εcol,back
Qconv , wall − plen + Qrad , wall −col = Qcond , wall
Qconv,col − plen = m& Acol , proj (T plen − Tamb )
εwall
Qrad,wall-col Qrad,col-sur Qabs
Tplen Qconv,col-plen
Tamb Qcond,back Qwind Tcol
Qconv,back-air Twall
Twall,in
Figure 2. PV/Thermal collector The first equation (eq.(1) was developed by Kutscher et al. (Kutscher et al., 1993) for an isothermal UTC. It expresses the collector as a heat exchanger of effectiveness εHX. The maximum temperature rise possible corresponds to the difference between the collector temperature Tcol and the ambient temperature Tamb, while the actual temperature rise occurring is the difference between the plenum temperature Tplen and
(2) (3) (4)
The next equations are obtained by expressing the terms of equations (2) and (3) as a function of temperature. Assuming the view factor between the wall and the back of the collector to be one, i.e. neglecting the sides of the plenum, the radiation losses from the wall to the collector Qrad,wal-col can be expressed as eq. (5 where σsb is the Stefan-Boltzmann constant, εwall is the emissivity of the outdoor surface of the building wall and εcol,back is the emissivity of the back surface of the collector.
Qrad ,wall −col =
4 σ sb Acol , proj (Twall − Tcol4 )
1
ε wall
+
1
ε col ,back
(5)
−1
Because of the corrugated shape of the collector, Qrad,col-sur is the summation of the radiation losses of the three portions k of the collector surface shown on Figure 4: the grooves (k=1), the top of the corrugations (k=2), and the side grooves (k=3).
Figure 3. Collector representation In eq. (6, Fcol-sur,k is the view factor between the collector and the surroundings which corresponds to 1 for k=2. εk is either the emissivity of the PV cells or the emissivity of the collector depending on the configuration.
(
4 Qrad ,col − sur = σ sb Tcol4 − Tsur
)∑ ε 3
k =1
k
Ak Fcol − sur ,k
(6)
However, none of them seem to apply directly for plates with trapezoidal corrugations. Gawlik et al. (Gawlik et al., 2002) developped a correlation for hwind for corrugated transpired plates, and found that the wind heat losses could be as much as 17 times greater for corrugated plates compared to flat plates. However, this correlation couldn’t be applied to this analysis, because the plate studied had sinusoidal corrugations. Consequently, it was decided to use eq. (11, which is the correlation used by the SWift software based on empirical results from testing at the National Solar Test Facility (Enermodal, 1994). This relation is also in agreement with the correlation developed by Kutscher for flat transpired collectors (Kutscher et al. 1993). Q wind = hwind Acol , proj (Tcol − Tamb )
The convective heat losses from the wall to the plenum, Qconv,wall-plen, is expressed as eq. (7), where the convective heat transfer coefficient hconv,wall-plen is calculated as a function of the mean velocity in the plenum. The average Nusselt number in the plenum Nu L is obtained with eq.(8 for laminar flow and with eq.(9 for mixed boundary layer conditions (Incropera and DeWitt, 2002). During the summer months, or at nightime, the UTC is usually bypassed to let fresh air enter the building. However, it is still interesting to know the temperature of the collector during bypass conditions, since the PV cells will continue producing electricity during summer. Maurer (Maurer, 2004) tried to find an approximation of hconv,wall-plen for two different bypass conditions. In the first scenario, the air enters the plenum at the bottom of the collector due to the plate getting heated, rises as it flows along the wall driven by natural convection, and exits at the top of the plenum. In the second scenario, she assumed that there was no flow induced in the plenum and that only natural convection was taking place. For the first case, she obtained a value for hconv,wall-plen of 0.1W/m2K and for the second case, her simulations predicted a value between 0.1 and 1W/m2K. Therefore, the value of hconv,wall-plen was set to 0.1W/m2K during bypass conditions. Qconv , wall − plen = hconv , wall − plen Acol , proj (Twall − T plen ) Nu L = 0.664 Re
1/ 2 L
Re L ≤ 5 × 10 5
(
Pr
(8)
)
Nu L = 0.037 Re 4L / 5 − 871 Pr 1 / 3 5 × 10 < Re L ≥ 10 5
8
(7)
1/ 3
(9)
The convective heat losses from the collector to the wind, Qwind can be expressed as eq. (10) where hwind is the wind heat transfer coefficient. There are several correlations available in the literature to calculate hwind.
hwind
⎡ ⎤ U = min ⎢0.02 wind ,2.8 + 3.0U w ⎥ Vs ⎣ ⎦
(10) (11)
The last equation is for the conduction through the wall or roof on which the collector is mounted, Qcond, wall. It can be expressed as eq. (12 where Uwall is the U-value of the wall or roof. Qcond , wall = U wall Acol , proj (Twall ,in − Twall )
(12)
Absorbed Radiation on the Collector In the models available in the litterature, the calculation of the total absorbed solar radiation Qabs is straightfoward. It does not account for the shading or the multiple reflections that can occur on the surfaces located in the grooves. For thermal collectors, both phenomena can be neglected since they are not expected to play significant roles in the prediction of the collector performance. In this analysis however, they have to be taken into account because PV cells can be located in the grooves. If shading occurs on the cells, the electrical performance of the collector will be significantly affected. Also, if the grooves are very deep, the multiple reflections can lead to a considerable increase in the irradiation of certain surfaces. In order to account for these two phenomena, the total irradiation of the collector is calculated considering each surface of the absorber plate separately. Assuming the corrugations to be identical along the collector, the absorber plate can be divided in 8 different types of surfaces i as shown on Figure 5. The number of surfaces corresponding to each type of surface i will vary depending on the total width of the collector.
as 1-αd(i), where αd(i) is the absorptance of the surface at the incidence angle of the diffuse radiation θd(i) on the wall or roof behind the collector. It can be obtained using eq.(16 (Beckman et al., 1977) where θd(i) is calculated as a function of the collector slope β with eq.(17 (Loutzenheiser et al., 2007).
Figure 4. Surface Numbering The total radiation falling on a surface i, GT(i), has a beam and a diffuse component. When the beam component of the incident radiation hits a surface in the groove, it is reflected on the other surfaces as diffuse radiation. Therefore, the diffuse radiation component for surfaces 2,3, and 4 is not only due to sky diffuse (Gdd(i)) and ground reflected radiation (Gdg(i)), but also to the beam radiation reflected diffusely (Gdb(i)) as shown in eq.(13. The beam radiation,Gb(i), is obtained in a straightforward manner knowing the inclination of the collector and the sun’s position, but the three other terms are obtained by performing a solar optical analysis on each surface.
GT (i ) = Gb (i ) + Gdb (i ) + Gdd (i ) + Gdg (i )
(13)
As shown in Incroprera and Dewitt (Incropera and Dewitt, 2002), the radiation falling on a surface i, G(i), located in an enclosure of N surfaces, can be expressed as eq.(14), where Fi-j is the view factor between a surface i and a surface j and J(j) is the radiosity of the jth surface. N
G( i ) = ∑ Fi − j J ( j )
J d ( d − g )(i ) = Gd (d − g )(i ) ρ d (i ) α i (θ ) −3 α
(15)
= 1 + 2.0345 ∗10 θ − 1.99 ∗10 − 4 θ 2
+ 5.324 ∗10 − 6 θ 3 − 4.799 ∗10 −8 θ 4
0 0 ≤ θ ≤ 80 0 α i (θ ) = −0.064θ + 5.76 α 80 0 ≤ θ ≤ 90 0
θ d ( i ) = 59.68 − (0.1388 β + 0.001497 β 2 )
(16)
(17)
In the case of the radiosity for the beam radiation reflected diffusely, Jdb(i), the surfaces in the grooves can be shaded and not receive direct beam radiation. Depending on the geometry of the plate, the shaded proportion of the surfaces in the grooves will be more or less significant on the thermal energy absorbed, but it will certainly have an effect on the electrical output of the collector. Consequently, each surface in the groove is split into two surfaces, one that does not receive beam radiation due to shading noted is and one that does, noted i. Surface 3 is split into three surfaces because it can be shaded from each side as shown on Figure 7.
(14)
j =1
In order to calculate Gdd(i) and Gdg(i) for the surfaces located in the grooves, a fictitious surface is added at the top of the groove to simulate the area from which the diffuse radiation is coming, as shown on Figure 6.
Figure 5. Groove representation for calculation of Gdd(i) and Gdg(i) For each surface i, the radiosities Jdd(i) and Jdg(i) can be expressed as the product of the reflectance and the incoming diffuse radiation as shown in eq.(15. For surface 5F, the reflectance is 1, and the radiosity corresponds to the diffuse radiation (sky or ground) since it is a fictitious surface. Using Kirchoff’s law, the diffuse reflectance of the surface ρd(i) can be expressed
Figure 6. Groove representation for calculation of Gdb(i) Following the same principle used to calculate Jdd(i) and Jdg(i), Jdb(i) can be expressed as the summation of both reflected beam radiation and beam radiation reflected diffusely (eq.(18). The reflectance of a surface i, ρb(i), is taken at the incidence angle of the beam radiation on that particular surface. It can be obtained with Kirchoff’s law and eq. (16 using the incidence angle of the beam radiation on the surface i, θb(i).
J dg (i ) = ρ b (i ) Gb (i ) + ρ d (i )Gdb (i )
(18)
Using eq. (14 in equations (15 and (18, the following set of equations ((19, (20, (21) can be written for each surface in a matrix form. Once the values of J’s are
obtained, Gdd(i), Gdg(i) and Gdb(i) can be calculated using equations (15 and (18. N
J dd ( i ) − ρ d (i ) ∑ Fd ,i − j J dd ( j ) = 0
(19)
j =1 N
J dg (i ) − ρ d (i ) ∑ Fd ,i − j J dg ( j ) = 0
(20)
j =1 N
J db ( i ) − ρ d (i ) ∑ Fb,i − j J db ( j ) = ρ b (i ) Gb (i )
(21)
j =1
Then, the absorbed radiation on a surface, Qabs(i) can be expressed as eq. (22 where Psh(i) is the shaded proportion of the surface obtained with the method described in the next section. The total absorbed radiation by the collector Qabs is exprresed as eq. (23, where ηPV is the efficiency of the PV cells. For simplicity, the PV efficiency is assumed to depend linearly on the temperature as shown in eq. (24 (Sandnes and Rekstad, 2002), where ηr is the PV efficiency at the reference temperature Tref and μ is the PV temperature coefficient . Qabs ( i ) = α b (i ) A( i ) (1 − σ )(1 − Psh (i ) )Gb (i ) + (22) α d (i ) A( i ) (1 − σ ) Gdb (i ) Psh ( i ) + Gdd (i ) + Gdg (i )
[
]
cells move on their operating I-V curve closer to the open-circuit voltage. While trying to increase the current at which they are operating, the voltage of the shaded cells can then be driven in the negtive voltage range. This result in the formation of a hot-spot which will reduces the PV output or in worst cases, damage the module. To avoid this, bypass diodes are usually used to isolate groups of cells from each other so that when shading occurs, the group of cells containing the shaded cell is bypassed. However, a reduction of the PV performance still occurs. The power output on such cases is difficult to predict because it will depend on how the cells are linked together. A 50% shading will not necessarily results in a 50% reduction of the power production. Nevertheless, to simplify the calculations, a conservative approximation similar to the one used by the TRNSYS Type 551 (TESS, 2005) is employed to estimate the power production. When the collector is partially shaded, the whole PV on the collector is assumed to see the minimum of the diffuse radiation seen by any of the surfaces i (eq. (28). When the collector is unshaded, the whole PV is assumed to see the minimum of the total radiation seen by any of the surfaces i (eq. (29). This method is however, very approximative and could certainly be improved.
Qe = η PV (Gb (1) + Gd (1) + G g (1) )(1 − σ )A(1)
(27)
Qe = η PV ⋅ MIN (Gdd (u ) + Gdg ( i ) )⋅ (1 − σ )∑ A(i )
(28)
8
Qabs = Qabs (1) (1 − η PV ) + ∑ Qabs (i )
(23)
8
Qabs = ∑ Qabs (i ) (1 − η PV )
4
Conf. a)
i =2
Conf. b) (24)
The 3 unknown temperatures and the 7 unknown heat transfer terms are obtained by solving the 10 equations ((1, (2, (3, (4, (5, (6, (7, (10, (12, and (23) using a matrix solver. The collector outlet temperature Tout and the useful thermal energy obtained Qu are obtained with eq. (25 and (26 by performing an energy balance in the plenum of the collector.
m& c p (Tout − Tamb ) = Qconv,wall − plen + Qconv,col − plen
Qu = m& c p (Tout − Tamb )
Qe = η PV ⋅ MIN (Gb (i ) + Gdd (i ) + Gdg (i ) + Gdb (i ) )⋅ (1 − σ )∑ A(i ) 4
i=1
η PV = η r + μ (Tcol − Tref )
i =1
(25) (26)
For configuration a), the PV cells will never be shaded by the collector and the calculation of the electrical power output, Qe is simple (eq.(27). However, in the case of configuration b), the calculation is more complex because of the shading of the cells. Typically, when a PV module is partially shaded, the shaded cell current drops. In order to compensate, the non-shaded
i =1
(29)
Collector Shading In order to find the shaded portion of a surface Psh(i), a two-step method is followed. First, the shading case is identified by comparing the comparison angle θc to each one of the 5 shading cases. The comparison angle is the projection of the sun incidence angle on the cross-section plane of the collector. The second step consists in calculating the shaded area of each surface by using the geometric parameters of the collector.
The method used to find the comparison angle is based on the work of Lee, Chung and Park (Lee et al., 1987), assuming an hypothetical surface of slope β and azimuth angle γ on which the collector is mounted (Figure 8). The orientation of the surface relative to the cardinal points can be expressed with three unit vectors
v v v U 1 , U 2 and U 3 that can be expressed respectively as
equations (30), (31), and (32). The sun ray is represented by the vector
v S and is developed in eq.
v v v (33). By projecting the vector S in the ( U 1 , U 3 ) plane, the angle θc is calculated (eq.(34). v v v U 1 = − cos γi + sin γj v v v v U 2 = − sin γ cos β i − cos β cos γj + sin β k
v v v v v v U 3 = U 1 × U 2 = sin γ sin β i + sin β cos γj + cos βk v v v v S = cosα s sin γ s i + cosα s cos γ s j + sin α s k v v ⎛ S ⋅U ⎞ tan θ c = ⎜⎜ v v3 ⎟⎟ ⎝ S ⋅ U1 ⎠
(30 ) (31 ) (32 ) (33 ) (34 )
Figure 8. 5 Shading Cases
SIMULATION In order to compare the effect of adding PV cells on the collector, TRNSYS simulations were performed for configuration a) and b) and for the stand-alone thermal UTC. The geometry of the SW100 Solarwall® profile was considered in the calculations and the parameters and inputs were set to the value listed in Table 1 in the simulations. Type 109 was used as the Weather Data Reader and Processor in combination with the Meteonorm weather data files of the TRNSYS library. Table 1. Parameters and Inputs to the TRNSYS model PARAMETER/INPUT Acol,proj P D β
m&
αcol εcol,back εcol αwall εwall Uwall μ Tref ηref Tbypass Twall,in Night Bypass
Figure 7. Sun’s position relative to the collector
Figure 10 presents a comparison of the performance of a standard UTC and of a PV/Thermal collector with the PV mounted according to configuration a) and b). The simulations were performed with the weather data for the city of Toronto. Thermal and PV/Thermal collector performance 1.6 1.4 Energy [GJ/m2 of UTC]
There are 5 different shading cases, each delimited by a minimum and a maximum angle that are function of the geometric parameters of the collector. The 5 cases, the limit angles where they apply as well as how the shading fraction is calculated are illustrated on Figure 9.
VALUE 5 m2 0.0256 m 0.00159 m 45o 210 kg/h (constant) 0.94 0.9 0.9 0.4 0.9 2 kJ/hm2K -0.5%/K 25oC 0.15 18oC 21 oC Yes
1.2 1 QE
0.8
QU
0.6 0.4 0.2 0 THERMAL
CONF. A)
CONF. B)
Figure 9. Thermal and PV/Thermal collector performance for different configurations
In order to evaluate the thermal and electrical output of the PV/Thermal collector for different climates, simulations were performed for the configuration a) of the collector for 3 different Canadian cities. The results are shown on Figure 11. PV/Thermal collector (Conf. A) performance at different locations 2
Energy [GJ/m2 of UTC]
1.8 1.6 1.4 1.2
QE
1
QU
0.8 0.6 0.4 0.2 0 TORONTO
MONTREAL
EDMONTON
Figure 10. PV/Thermal Collector Performance at different locations
DISCUSSION AND RESULT ANALYSIS As shown in Figure 10, the addition of PV cells on the transpired collector results in a minor decrease in the thermal energy collected. For the case of configuration b), the increase in electrical energy collected is only of 20% even though the surface covered by the PV cells is almost doubled. The assumption that a PV partially shaded does not see any beam radiation explains why such poor electrical output are obtained with the PV covering the whole collector. However, one can still consider that configuration a) would be more costeffective since the maximum possible power is always obtained from the PV cells. Figure 11 shows that a collector located in Edmonton would provide more thermal energy than in cities like Montreal and Toronto. This can be explained by the fact that the difference between the ambient temperature in Edmonton is generally lower than in the two other cities.
CONCLUSION REFERENCES Carpenter, S., Meloche N. 2002. The Retscreen Model for Simulating the Performance of Solar Air Heating Systems, Proceedings of e-sim 2002. Conserval Engineering Inc. 2006. http://www.solarwall.com (Consulted on April 20, 2007)
Enermodal. 1994. Performance of the PerforatedPlate/Canopy Solarwall at GM Canada, Oshawa, Report prepared for CANMET, Natural Resources Canada, Ottawa. Gawlik, K.M., Kutscher, C.F. 2002. Wind Heat Loss from Corrugated Transpired Solar Collectors, Transactions of the ASME, V.124, pp.256-261. Gawlik, K.M, Kutscher, Christensen, C., Kutscher C.F. 2005. A Numerical and Experimental Investigation of Low-conductivity Unglazed, Transpired Solar Air Heaters, Journal of Solar Energy Engineering, V. 127, pp.153-155. Gogakis, C. 2005. Theoretical and Experimental Analysis of Solarwall® Technology, M.S. Thesis. University of Reading, UK. Hollick J. 1998. Solar Cogeneration Panels, Renewable Energy, 15, pp.195-200. Incroprera, F.P., Dewitt, D.P. 2002. Fundamentals of Heat and Mass Transfer, 5th ed, New York, John Wiley & Sons. Kutscher, C.F., Christensen, C.B., Barker G.M. 1993. Unglazed Transpired Solar Collectors: Heat Losss Theory, Transactions of the ASME, V.115, August, 1993. Lee, J.H., Chung, M., Park, W-H. 1987. An Experimental and Theoretical Study on the Corrugated Water-Trickle Collector, Solar Energy, V. 38(2), pp.113-123. Loutzenheiser P.G., Hanz. H., Felsmann, C., Strachan, P.A., Frank, T., Maxwell, G.M. 2007. Empirical Validation of Models to Compute solar Irradiance on Inclined Surfaces for Building Energy Simulation, Solar Energy, V.81, pp.254-267. Maurer, C.C. 2004. Field Study and Modeling of an Unglazed Transpired Solar Collector System. M.S. Thesis, North Carolina Sate University, Raleigh. Naveed, A.T., Kang, E.C., Lee, E.J. 2006. Effect of Unglazed Transpired Collector on the Performance of a Polycrystalline Silicon Photovoltaic Module, Solar Energy, V.128, pp.349-353. Saidov, M.S., Abdul’nabi, Z.M., Bilyalov, R.R., Saidov, A.S. 1995. Temperature Characteristics of Silicon Solar Cells, Appl Solar Energy, V.31(6), pp.84-88. Sandnes, B., Rekstad, J. 2002. A Photovoltaic/Thermal (PV/T) Collector with a Polymer Absorber Plate, Experimental Study and Analytical Model, Solar Energy, V.72(1), p.63-73. Summers, D. 1995. Thermal Simulation and Economic Assessment of Unglazed Transpired Collectors
Systems. M.S. Thesis, University of Wisconsin at Madison, Madison, WI. TESS. 2005. TESS Libraries Version 2.02, Reference Manuals (13 Volumes), Thermal Energy Systems Specialists, Madison, WI. http://tess-inc.com. Van Decker G.W.E., Hollands, K.G.T., Brunger A.P. 2001. Heat Exchange Effectiveness of Unglazed Transpired-Plate Solar Collector in 3D Flow, Solar Energy, V.71 (1), pp.33-45.
NOMENCLATURE Tplen Tamb Tcol
σ
Temperature of the plenum [K] Ambient temperature [K] Average temperature at the surface of the collector [K] Wall temperature [K] Wall temperature inside the building [K] Surrounding temperature [K] Total solar radiation absorbed by the collector [kJ/hr] Radiation heat transfer from the wall to the collector [kJ/hr] Radiation heat transfer from the collector to the plenum [kJ/hr] Wind heat losses from the collector [kJ/hr] Radiation heat transfer from the collector to the surroundings [kJ/hr] Convection heat transfer from the wall the plenum [kJ/hr] Conduction from the wall/roof inside the building to the outside wall behind the collector [kJ/hr] Stefan-Boltzmann constant [5.6697x108 W/m2K] 2 Plate porosity π D
Acol,proj Ai
Collector projected area W*L [m2] Surface area [m2]
Twall Twall,in Tsur Qabs Qrad,wall-col Qconv,col-plen Qwind Qrad,col-sur Qconv,wall-plen Qcond,wall σsb
4 P2
A1 = aLNb c (1 − σ )
A2 , 3, 4 = (2t t + d − a )L ( Nbc − 1)(1 − σ )
A5, 6, 7 ,8 = (2t t + Wend )L(Nbc − 1)(1 − σ )
εHX W L εwall εcol,back α ReL
Collector effectiveness Collector width [m] Collector length [m] Emissivity of the wall or roof behind the collector Emissivity of the back of the collector Absorptance Reynolds number based on plenum velocity and length of the collector
Re l =
ρ Vs Cp Fcol-sur,k hconv,wall-plen NuL hwind Uw Uwall G J Psh μ ηr Tref γ β αs γs
1 ρVs LAcol , proj 2 μAcross−sec tion
Air density [kg/m3] Suction velocity [m/hr] Air constant specific heat [kJ/kgK] Configuration factor Convective heat loss coefficient from the wall to the plenum [kJ/hr m2K] Nusselt number Wind heat loss coefficient [kJ/hr m2K] Wind velocity [m/hr] Wall U-value [kJ/hr m2K] Irradiation Radiosity Shading proportion PV temperature coefficient (1/oC) PV reference efficiency PV reference temperature Surface azimuth angle on which the collector is mounted[o] Slope of the wall or roof on which the collector is mounted [o] Solar altitude angle [o] Solar azimuth angle [o]
