t he yield of different combined pv-thermal …solar energy 74 (2003) 253–269 t he yield of...

Solar Energy 74 (2003) 253–269

T he yield of different combined PV-thermal collector designsa , a b c*H.A. Zondag , D.W. de Vries , W.G.J. van Helden , R.J.C. van Zolingen ,

aA.A. van SteenhovenaEindhoven University of Technology, P.O. Box 513, 5600MB Eindhoven, The Netherlands

bEnergy Research Centre of the Netherlands ECN, P.O. Box 1, 1755ZG Petten, The NetherlandscShell Solar Energy B.V, P.O. Box 849, 5700AV Helmond, The Netherlands

Accepted 6 March 2003

Abstract

Various concepts of combined PV-thermal collectors are possible. These concepts differ in their approach to obtain themaximum yield and it is not easy to say whether the yield of a complicated design will be substantially higher than the yieldof a simpler one. In order to obtain a clearer view on the expected yield of the various concepts, nine different designs wereevaluated. The channel-below-transparent-PV design gives the best efficiency, but since the annual efficiency of thePV-on-sheet-and-tube design in a solar heating system was only 2% worse while it is easier to manufacture, this design wasconsidered to be a good alternative. 2003 Elsevier Ltd. All rights reserved.

1 . Introduction systems, the literature on combined photovoltaic-thermalcollector design is very limited. Research in this field was

A combined PV-thermal collector, henceforth to be carried out in the late 1970s and early 1980s in the USA. Acalled a PVT-collector, consists of a PV-laminate that systematic investigation was made at the MIT in whichfunctions as the absorber of a thermal collector. In this way several new designs were suggested (Hendrie, 1982), whilea device is created that converts solar energy into both a further optimisation study was carried out at Brownelectrical and thermal energy. The main advantages of a University (Russell et al., 1981). Since then, the effortPVT-collector are as follows. invested in optimising the overall design of the PVT-1. An area covered with PVT-collectors produces more collector has been limited; with respect to flat-plate PVT-

electrical and thermal energy than a corresponding area liquid almost all the work focuses on the optimisation ofpartially covered with conventional PV systems and sheet-and-tube designs. Theoretical work in this area waspartially covered with conventional thermal collectors. carried out byBergene and Løvvik (1995)while a largeThis is particularly useful when the amount of space on amount of experimental work, also covering the possi-a roof is limited, which will become increasingly bilities of booster reflectors, was carried out at the uni-important in the future. versity of Patras (Tripanagnostopoulos et al., 2002). In

2. PVT-collectors provide architectural uniformity on a Germany and Denmark, where also commercial partiesroof, in contrast to a combination of separate PV- and were involved in the research, the focus was likewise onthermal-systems. sheet-and-tube (see e.g.Rockendorf et al., 1999; Sørensen,

3. Due to the fact that only one type of system has to be 2001). Exceptions were the work ofSandnes and Rekstadinstalled instead of two, a reduction of installation costs (2002), examining a PV-thermal collector based on ais possible. polymer channel absorber plate and the work ofBakker etIn contrast to the situation for conventional thermal al. (2002),examining a two-absorber PV-thermal collector.

With respect to the optimisation of PV for PVT, earlytheoretical investigations were carried out byCox and*Corresponding author. Tel.:131-224-564941; fax:131-224-Raghuraman (1985),while more recently experimental568966.

E-mail address: [email protected](H.A. Zondag). work was carried out byAffolter et al. (2000)andPlatz et

0038-092X/03/$ – see front matter 2003 Elsevier Ltd. All rights reserved.doi:10.1016/S0038-092X(03)00121-X

mailto:[email protected]

254 H.A. Zondag et al. / Solar Energy 74 (2003) 253–269

Nomenclature

2A collector surface area (m )c specific heat (J /kg K)D tube diameter (m)

2D mass diffusion coefficient (m /s)AB

F view factor (–)2g gravitational acceleration (m /s)

2G irradiation (W/m )2h coefficient of heat transfer (W/m )

h coefficient of mass transfer (m/s)AB

I current (A)H height of insulation air layer (m)

21K extinction coefficient (m )k thermal conductivity (W/m K)L length of collector surface (m)c

2~m mass flow (kg/s m )Nu Nusselt number (–)n refractive index (–)Pr Prandtl number (–)

2q heat flux (W/m )Q latent heat (J /kg)latent

R reflection coefficient (–)Ra Rayleigh number (–)Re Reynolds number (–)Sh Sherwood number (–)Sc Schmidt number (–)T temperature (K)

2T reduced temperature (Km /W)red

v velocity (m/s)2U overall loss coefficient (W/m K)loss

V voltage (V)W tube spacing (m)X vapour mass fraction (–)b coefficient of expansion of air (–)d thickness of layer (m)´ coefficient of emissivity (–)h efficiency (–)h electrical efficiency at standard conditions (–)0

u angle to perpendicular of collector2

n viscosity (m /s)t transmission absorption coefficient (–)a

t transmission coefficient for layers above PV (–)PV

f collector angle with the horizontal

Subscriptsa ambientabs absorberba from back to ambientca from cells to absorberconv convectioncrit criticalel electricalevap evaporationg glassin inflowmpp maximum power pointrad radiationth thermaltopglass↑ upper surface topglasstopglass↓ lower surface topglassvap vapour

H.A. Zondag et al. / Solar Energy 74 (2003) 253–269 255

al. (1997).Overviews of the literature on PVT-collectors standard photovoltaic panel and integrate it into a thermalare presented byLeenders et al. (2000)and Bazilian and collector without any modification. The sheet-and-tubePrasad (2000). PVT-collector, that is shown inFig. 1a, is an example of

The aim of this paper is to make a comparison of the such an approach. The thermal insulation of such a designefficiency of seven different design types of PVT-collec- can be improved by increasing the number of top covers.tors to make clear what the effects of design choices are on However, since each cover creates additional reflections,the electrical and thermal efficiency of the design. The this strategy reduces the electrical yield of the PVT-efficiency curves will be compared. In addition, a com- collector. Sheet-and-tube PVT-collectors are examinedparison will be made of the annual yield of the PVT- with zero, one and two covers. Designs with more thancollectors for one specific application: a solar heater in a two glass covers do not seem to have practical applica-domestic hot water system in the Dutch climate. tions, since the electrical efficiency is reduced too much.

2 .3. Channel PVT-collector2 . Design concepts

Fig. 1bshows a channel PVT-collector with the channel2 .1. Introduction on top of the PV. Such a configuration imposes constraints

on the choice of the collector fluid; for a PVT-collectorNine design concepts for water-type PVT-collectors are design the absorption spectrum of the fluid should be

evaluated here, which can be classified in four groups. An sufficiently different from the absorption spectrum of theexample of each group is given inFig. 1. PV in order to allow the PV to receive the incomingA. Sheet-and-tube PVT-collectors. radiation. In the present design water is used, which has aB. Channel PVT-collectors. small overlap in absorption with the PV, resulting in 4%C. Free flow PVT-collectors. relative decrease in the electrical performance. A dis-D. Two-absorber PVT-collectors. advantage of this design is that, if a wide channel is used

that is covered by one large glass plate, very thick glass2 .2. Sheet-and-tube PVT-collector may be necessary to withstand the water pressure, resulting

in a heavy but fragile construction (Bakker et al., 2002). AThe simplest way to construct a PVT-collector is to rely variation of the channel design is obtained by letting the

entirely on well-known available technology by taking a water flow underneath the PV panel. Two cases are

Fig. 1. Various collector concepts: (A) sheet-and-tube PVT, (B) channel PVT, (C) free flow PVT, (D) two-absorber PVT (insulated type).


examined: a channel below a conventional opaque PV concept level. Of course, other materials could have beenpanel and a channel below a transparent PV panel with a chosen, such as transparent plastics instead of glass orseparate black thermal absorber underneath the channel. other types of PV. Highly transparent plastics wouldThe latter can be expected to have a higher thermal probably give a small increase in optical efficiency, butefficiency, but it should be kept in mind that transparent their material properties, such as sensitivity to UV or highPV laminates are at present substantially more expensive. temperatures as well as limited watertightness, wouldIn addition, the PV panel should be able to withstand the probably limit their application in PV-thermal. A differentpressure of the water. In the case of the opaque PV this type of PV would change the ratio of heat production overmight be less of a problem since the backside could be electricity production (due to a different electrical ef-strengthened with a metal back. Care should be taken that ficiency) and change the optical efficiency of the laminatethe backside of the PV laminate is sufficiently watertight. (due to different reflection losses). In addition, a small

effect of temperature on PV-efficiency would be present, as2 .4. Free flow PVT-collector e.g. the yield of amorphous silicon PV is less sensitive to

temperature.In a free flow panel unrestrained fluid flows over the

absorber, as shown inFig. 1c. In comparison to thechannel case, this design eliminates one glass layer. Thusreflections and material costs are reduced, while the 3 . Optical efficiencymechanical problem of breaking the glass cover is avoided.A disadvantage is the increased heat loss due to evapora- In order to determine the thermal efficiency of thetion. As in the case of the channel PVT-collector, the fluid PVT-collector, two models are required. Whereas a thermalflowing over the PV panel has to be transparent for the model is required to determine the heat flows within thesolar spectrum. Water seems a natural choice, but, since itsPVT-collector, an optical model is required to determineevaporation pressure is not very low, evaporation will be how much irradiation is absorbed by the PVT-collector.shown to create problems at higher temperatures. The optical model is used to calculate the transmission–

absorption factor of the PVT-collectort , and this value isa

2 .5. Two-absorber PVT-collector then inserted as a constant into the thermal model.The optical model presently used is based on the net

The two-absorber panel uses a transparent PV laminate radiation method. This method solves the energy fluxas a primary absorber and a black metal plate as a balance at each interface in the PVT-collector configura-secondary absorber. The panel contains two water channelstion. As an example, the reflection at the glass cover ison top of each other. The water flows in through the upper given inFig. 2.The energy flux equations for this examplechannel and is returned through the lower channel. This are now presented bydesign was also examined as part of the PV-thermalcollector development program of the MIT (Hendrie, q 5Gi,1

1982), which indicated a high thermal efficiency for this q 5R q 1 12R qs do,1 1,2 i,1 1,2 i,2design. However, the disadvantage of the heavy channel (1)q 5 12R q 1R qs do,2 1,2 i,1 1,2 i,2cover—indicated previously for the channel PVT—appliesq 5 q exp 2Kd /cosuf geven more strongly for the two-absorber PVT (Bakker et i,2 o,3 topglass

al., 2002). Several variations can be applied in the design.The efficiency of the design could be improved by an The values for the coefficients of reflectionR are1,2

additional transparent insulating layer between the primary determined from the Fresnel equations:and the secondary channel to reduce the heat loss further.On the other hand, this reduces the robustness of the

collector. This insulated version is shown inFig. 1d.Another possible variation is obtained by replacing thechannel under the secondary absorber by a sheet-and-tubeconstruction, but this option is not examined here.

2 .6. Materials selection

In the calculation of the various concepts, we have usedmaterials that are routinely applied in conventional PVlaminates and thermal collectors. In addition, we decidedto use the same materials for all concepts as much as Fig. 2. The numbering of the radiative flux densities in the netpossible, in order to be able to make a valid comparison on radiation method.


For each of the different design concepts, a different1 ↑ →]R5 sR 1R d value is found for the absorption of the PV-combi collec-2

tor. In particular, for the concepts in which water flows2 2sin u 2u tan u 2u1 f g f gi r i r over the PV laminate, both the transmission–absorption] ]]]] ]]]]5 1 (2)S D2 22 coefficient of the laminate,t , and the transmission–ab-sin u 1u tan u 1uf g f g ai r i r

sorption coefficient of the water,t , have to bea,waterin which the angles are determined using Snell’s law: distinguished. The latter represents the relative amount ofthe incoming energy that is absorbed by the water layer,sinu /sinu 5 n /n (3)r i i r

while the former represents the relative amount of energyThis method is applied to all the interfaces in the collectively absorbed by the solid material layers in the

PVT-collector, which generates a set of equations that is PVT-collector. Similarly, for the determination of thesolved by a matrix-solving procedure. Since both the electrical yield, the amount of radiation received by thecoefficient of extinctionK and the index of refractionn PV-laminate is determined by the number of glass anddepend on the wavelength, the equations are solved for water layers above the PV-laminate, the combined trans-each wavelength interval separately and then integrated mission of which is given byt . The calculated values forPV

over the solar spectrum. The solar radiation is assumed to normal incidence are presented inTable 1. Fig. 3indicateshave no nett polarisation, so the incoming light is split in the normalised angular dependence oft and t . Thisa PV

50% parallel and 50% transverse polarisation,t is de- figure shows that the curves for the one- and two-covera

termined for each mode separately and the results are designs are almost the same, while the values for the zeroadded. The calculation is based on the assumption of cover case are somewhat larger in the interval between 50specular reflection, so diffuse reflection is not taken into and 80 degrees. The value oft (u ) can be obtained bya

account. A complication is presented by the fact that a multiplying the value fromTable 1 with the angularPV-laminate does not present a homogeneous surface but dependence factor inFig. 3.consists of different parts (active PV-area, the top grid andthe spacing between the cells). For each part the value fort is calculated separately and thent of the entire PVT- 4 . Thermal efficiencya a

collector is determined by taking the average of thesevalues, weighed with the respective surface areas. This The thermal model is steady-state, based on solving themethod results in a slight underestimation oft due to the heat balance for all the layers in the PVT-collector. Fora

fact that no exchange of light between the different more information on the model, seeZondag et al. (2002).material surfaces is possible; light reflected by the top grid The transmission–absorption factor of the PVT-collectorarea cannot be reflected back by the glass on the PV area. was calculated with the optical model and the calculatedIn the analysis, reference is made to two types of PV- values are indicated inTable 1.The value of this parameterpanels: either opaque or transparent. The opaque PV-panel is inserted into the corresponding thermal-yield model.is a standard Shell Solar multi-crystalline PV-panel consist- With respect to the effect of the electrical energy pro-ing of a sandwich of glass/EVA/TiO /Si /EVA/PE-Al- duction, the electrical efficiency, which is a function of2

tedlar. The transparent PV-panel is essentially the same but temperature, is subtracted from the transmission–absorp-the PE-Al-tedlar layer at the back has been exchanged for tion factor to find the amount of thermal energy that wasa glass plate. absorbed in the system, according tot 5 t 2t h .h ja,eff a PV el

T able 1Transmission–absorption factors for the various design concepts (AM 1.5 spectrum)

Design concept t t ta a,water PV

Uncovered sheet-and-tube PVT-collector 0.78 – 1One-cover sheet-and-tube PVT-collector 0.74 – 0.92Two-cover sheet-and-tube PVT-collector 0.71 – 0.84Channel above PV 0.62 0.16 0.87Channel underneath opaque PV 0.74 – 0.92Channel underneath transparent PV 0.55 first absorber 0.10 0.92

0.12 second absorberFree flow PVT-collector 0.62 0.17 0.88Two-absorber PVT-collector (insulated type) 0.52 first absorber 0.16 0.87

0.12 second absorberTwo-absorber PVT-collector (non-insulated type) 0.52 first absorber 0.14 upper channel 0.87

0.11 second absorber 0.013 lower channel


Fig. 3. The normalised angular dependence oft andt .a PV

Here,t is obtained fromTable 1.In this way one obtains equations relating the heat flows and the temperatures ofPV

the amount of absorbed energy that contributes to the the various layers in the PVT-collector. These equationsthermal yield. are given in Appendix A (Eqs. (A.1)–(A.10)) since they

The results of the measurements and the calculations are are the same for all designs. These general equations arethe yield and the efficiency of the collector. The yield of related to each other through the heat balance equations,the collector is defined as the amount of useful energy which depend on the specific design that is examined.produced by it, while the efficiency is defined as the yield Therefore, they will be presented below in separatedivided by the amount of solar energy received by the paragraphs for each design.collector. In this way, both an electrical and a thermalefficiency are defined

4 .1. Sheet-and-tube collectorc T 2Ts dout in]]]]~h ;m (4)th G The heat flows in the sheet-and-tube PVT-collector are

indicated schematically inFig. 4. For the sheet-and-tubeV IMPP MPP]]] PVT-collector, the heat balance is represented by theh ; (5)el GA

following equations:V and I represent the voltage and the current in theMPP MPP

q 5 q 2 q (8)maximum power point,A is the panel area,c is the heat water ca ba

~capacity of the collector medium (water),m the mass flow2 2per square meter in kg/s /m ,G the irradiation in W/m q 5 t 2t h G 2 q (9)s dca a PV el PVglass

andT andT are the inflow temperature and the outflowin out

temperature in8C, respectively. The thermal efficiency is T able 2Values of coefficients used in simulationsconventionally shown as a function of reduced tempera-

ture, which is defined as Collector length L 1.776 mc

Emissivity of glass ´ 0.9 –gT 2 Tin a]]T ; (6) Emissivity of PV ´ 0.9 –red PVG

Heat capacity of water c 4200 J/kg KHeat conduction through air k 0.025 W/m Kin which T represents the ambient temperature. aira

Heat conduction through glass k 0.9 W/m KIn the presented models, Eq. (7) is used for the electrical glass

Heat conduction through water k 0.6 W/m Kwaterefficiency of the PV2Heat transfer to water for channelh 650 W/m Kabstowater2Heat transfer to absorber for sheet-h 500 W/m Kh 5h 120.0045 T 2 25 8C (7)s f gd cael 0

and-tube2in whichh 5 0.097 for both conventional and transparent Heat transfer through back of theh 1 W/m K0 back

PV. Table 2shows the values that are used in the models collectorThickness of cover glass d 3.2 mmfor the characteristic collector parameters that are used in topglass

Thickness of PV glass d 3.0 mmthe calculations. The values for the heat conduction PVglass

Tube diameter D 0.01 mthrough air and water in this table are the values at 208C;Tube spacing W 0.095 min the simulations the temperature dependence of theseWidth of air layer H 0.02 mquantities is taken into account as well. The quantitiesWidth of water channel d 5 mmwaterindicated in Table 2 appear in the general heat flow


Fig. 4. The heat flows in the sheet-and-tube PVT-panel, together with the temperature distribution according to the Hottel–Whillierequations.

q 5 q 1 q (10) T ) while the set of Eqs. (8)–(12) consists of onlyPVglass air,conv air,rad topglass↑

five equations. Therefore, one more equation is required. Inorder to solve this, the average absorber temperatureTq 1 q 5 q (11) absair,conv air,rad topglass

for the sheet-and-tube design is calculated from thetemperature distribution indicated by the Hottel–Whillerq 5 q 1 q (12)topglass sky,conv sky,rad

equations (Duffie and Beckman, 1991,pp. 252–283). ThisThe set of equations (8)–(12) presented above is for the temperature distribution is also shown inFig. 4. It resultscase of the panel with one cover. For the zero cover case from the fact that a temperature gradient over the absorberEqs. (10) and (11) are left out, while in Eq. (12) the is required to drive the absorbed heat to the tubes. Aq is changed intoq . For the panel with two mathematical representation of this temperature distribu-topglass PVglass

covers, Eqs. (10) and (11) are repeated. tion is given by Eq. (16)In contrast to the case of the channel collector designs,

for the sheet-and-tube combi collector the PV is connected t 2t h Gs da PV el]]]]T x 5T 1s dto a separate thermal absorber plate by means of an abs a Ulossadhesive layer. Therefore, the heat transfer between the PV

T 2 T 2 t 2t h G /Us dcells and the absorber plate should be modelled as well. bond a a PV el loss]]]]]]]]]1 cosh mxs dThis is taken into account by using Eqs. (13) and (14) cosh m W2D /2f s d g

indicated below instead of Eq. (A.8) (in Appendix A) (16a)¯q 5 h T 2 T (13)s dca ca cell abs

with¯q 5 h T 2 T (14)s dba ba abs a ]]]

m ; U /kd (16b)œ loss absIt is assumed that the heat resistance is minimised by theapplication of a highly conductive glue ofk50.85 W/Km in which the heat loss coefficient and the bond temperaturein a layer of 50mm thickness. With respect to the PV- are given bylaminate, a PE-Al-tedlar layer of 0.1 mm with conductionk 5 0.2 W/Km and an EVA layer of 0.5 mm and a con- q 1 q 1 qsky,rad sky,conv baductivity of k 5 0.35 W/Km are assumed (Krauter, 1993). ]]]]]]U 5 (17)loss T 2TPVglass aThe heat resistance of the PV-laminate can now bedetermined:

T 5 T 1 q /hbond water water tube21h 5 R 1R 1Rs dca EVA tedlar glue

5 T 1 qD/Nu k (18)water tube water24 24 25 2153 10 13 10 53 10S]]] ]]] ]]]D5 1 10.35 0.2 0.85 Re , 2300⇒ Nu 54.364tube

W 0.8 0.4Re . 2300⇒ Nu 50.023Re Pr (19)]]5500 (15) tube2Km (Dittus2Boelter equation)The equations for the heat flows as given in Appendix A,

Eq. (16) is numerically integrated with respect tox intogether with Eqs. (13) and (14) contain six unknownorder to provide the average absorber temperature.temperatures (T , T , T , T , T andout cell PVglass abs topglass↓


Fig. 5. The heat flows in the PVT-panel with the channel above the PV.

4 .2. Channel PVT-collector T , T and T ) and no additionaltopglass1↑ topglass2↓ topglass2↑

equation is required for the temperature. The heat transferThe heat flows in the channel PVT-collector are indi- between the PVglass and the water is determined from

cated schematically inFig. 5 for the case of the channelkwaterabove the PV. For this concept a similar approach as for ]]Nu 5 5.385⇒ h 5Nu 5 650 (27)channel dthe sheet-and-tube PVT-collector can be followed. How- water

ever, in the set of equations for the channel, in contrast toThis value of the Nusselt number is valid for a rectangularthe case of the sheet-and-tube absorber, the water presentschannel that is insulated at one side (Bejan, 1993,p. 298).a layer through which part of the heat absorbed by the PV

The case for the channel-below-transparent-PV (which isis lost to the collector surface again. Part of the incomingassumed to consist of the package glass/EVA/PV-cell /heat q will be retained in the water and drawn offwater,inEVA/glass) is similar to the case for the channel-above-PV.(q ), while another part will be transferred from thewaterHowever, the heat flow from the PV upwards is nowwater layer to the glass plate on top of the water channelentirely a loss flow, while the heat flow downwards(q ). In addition, the water now absorbs solar energywater,outcontributes to the collected heat. In addition, the additionaldirectly as well, according to the transmission–absorptioncover glass on top of the channel disappears. The heat flowcoefficient for the watert . The heat balance isa,waterdiagram is shown inFig. 6.presented by

The heat balance is now presented byt 2t h G 5 q 1 q (20)s da PV el PVglass ba

t 2t h G 5 q 1 q (28)s da PV el PVglass1 PVglass2

q 5 q (21)PVglass water,in

q 5 q (29)PVglass2 water,in

q 1 q 5 q 1t G (22)water water,out water,in a,water

q 1 q 5 q 1t G (30)water water,out water,in a,water

q 5 q (23)water,out topglass1

q 1t G 5 q (31)water,out a,abs2 baq 5 q 1 q (24)topglass1 air,conv air,rad

q 5 q 1 q (32)PVglass air,conv air,radq 5 q 1 q (25)topglass2 air,conv air,rad

q 5 q 1 q (33)topglass air,conv air,radq 5 q 1 q (26)topglass2 sky,rad sky,conv

The presence of the additional glass layer which acts as q 5 q 1 q (34)topglass sky,rad sky,conv

the ceiling of the water channel presents two additionalBoth q and q are determined from Eq. (27),equations when compared to the sheet-and-tube case, so water,in water,out

while q is defined by Eq. (A.9).the full set of equations is increased to seven. Similarly, PVglass2

For the case with the opaque PV, due to the fact that thethe additional cover increases the number of temperaturesPV is not transparent, the terms representing the absorptionby two, but the absence of a heat transfer between cellsby the water and the secondary absorber disappear fromand absorber reduces the number of temperatures again byEqs. (30) and (31). However, the base set of heat balanceone. Therefore, the amount of unknown temperatures isequations is the same as for the case with transparent PV.increased to seven (T , T , T , T ,out cell PVglass topglass1↓


Fig. 6. The heat flows in the PVT-panel with the channel below the PV.

4 .3. Free flow PVT-collector equations are retained. However, the fact that air is presentabove the fluid introduces a new heat transfer mechanism

The heat flows in the free flow PVT-collector are due to evaporation. The equation for the correspondingindicated schematically inFig. 7. In the free flow concept q is derived in Appendix B.evap

the solving procedure is much like the PVT-collectort 2t h G 5 q 1 q (35)s da PV el PVglass backdesign with the channel above the PV. However, in the free

flow panel evaporative heat transfer takes place. The modelq 5 q (36)PVglass water,inassumes that the evaporation process at the water film on

the PV laminate and the subsequent condensation processq 1 q 1 q 1 q 5 q 1t Gwater air,rad air,conv air,evap water,in a,waterat the top glass layer are much faster than the actual

transport of the water vapour through the air /vapour (37)mixture due to concentration differences. Therefore, thisdiffusion process determines the evaporative heat transfer q 1 q 1 q 5 q (38)air,rad air,conv air,evap topglasscoefficient. The natural convection due to the temperaturedifference over the air layer enhances this process but this q 5 q 1 q (39)topglass sky,rad sky,conveffect is not accounted for in the present calculations.

Similar to the case of the channel design, the heat transferFirstly, the natural convection is calculated as if nobetween the PVglass and the water is again provided bydiffusion of vapour is present. Next, the mass flux ofEq. (27). Since only five temperatures have to be calcu-vapour is calculated that also represents a heat flux due tolated explicitly (T , T , T , T andthe latent heat of the vapour. out cell PVglass topglass↑

T ), no additional equations are required.Because of the similarity of the free flow design with the topglass↓

PVT-collector design with the channel above the PV, theequations are largely the same as in the latter case. The4 .4. Two-absorber PVT-collectordifference is the absence of the topglass1, so that thermalradiation and convection take place directly between the The heat flows in the insulated version of the two-water layer and the topglass2, which leads to the dis- absorber PVT-collector are indicated schematically inFig.appearance of Eqs. (23) and (24). Therefore, only five 8. The equations are similar to those for the channel

Fig. 7. The heat flows in the free flow PVT-panel.


Fig. 8. The heat flows in the two-absorber PVT-panel.

PVT-collector. However, an additional set of equations direction of the flow and since the situation downstreamappears that is related to the second water channel. does not influence the situation upstream, the calculation isTherefore, we now also getq , q andq straightforward. However, in the two-absorber panel thewater2,in water2,out water2

that are related to the heat flow from the second absorber two water layers cannot be treated independently, since theto the water temperature of the secondary layer influences the ef-

ficiency of the primary layer, which in its turn determinesq 5 q (40)ba water2,out the inflow temperature of the secondary layer. Because of

this extra interaction between the water layers, an estimateq 5 q 1 q (41)water2,in water2 water2,out of the temperatures of the water segments in the secondary

layer is required to calculate the temperature in the primaryt G 5 q 1 q 1 q (42)a2 air2,conv air2,rad water2,in layer and the top layer. With these calculated values of the

segment temperatures in the primary layer we can thenq 1 q 5 q (43)air2,rad air2,conv PVglass2 obtain a better approximation of the temperatures in the

secondary layer again. This iteration process is continuedt 2t h G 1 q 5 q (44)s d until the solution is sufficiently converged. For threea PV el PVglass2 PVglass1

segments in each channel 10 iterations are sufficient.q 5 q (45) For the non-insulated version of the two-absorber de-water1,in PVglass1

sign, the equations are almost the same. However, Eqs.q 1 q 5 q 1t G (46) (42) and (43) merge due to the absence of the insulatingwater1 water1,out water1,in a,water

layer, while the absorption term moves from Eq. (42) toEq. (41) due to the fact that the secondary absorber is nowq 5 q (47)water1,out topglass1

no longer on top of the secondary water channel butunderneath it. On the other hand, Eq. (41) is split due toq 5 q 1 q (48)topglass1 air1,conv air1,rad

the presence of the secondary absorber at the bottom of thechannel. This results in Eqs. (51)–(53) coming in place ofq 5 q 1 q (49)topglass2 air1,conv air1,radEqs. (41)–(43)

q 5 q 1 q (50)topglass2 sky,rad sky,conv q 1t G 5 q 1 q (51)water2,in a,water2 water2 water2,out

In the equations 11 unknown temperatures appear (T ,back

t G 1 q 5 q (52)T , T , T , T , T , T , T , a2 water2out backout1 out2 abs2 PVglass2 PVglass1 cell topglass1↑

T , T , T ). Since the heat balancetopglass1↓ topglass2↑ topglass2↓

consists of 11 equations, no additional equations are q 5 2 q (53)PVglass2 water2,in

required.The solving procedure for this set of equations is more Note that q , as defined inFig. 8, has becomePVglass

complex than for the previous cases. In the previous panels negative due to the fact that the heat flows from the PV tothe system is divided into a number of segments in the the water in the secondary channel.


Fig. 9. Thermal efficiency for the case with production of electricity of the various PVT-panels.

Fig. 10. Electrical efficiency of the various PVT-panels. The lines for the electrical efficiency of the channel beneath opaque and transparentPV coincide in the figure.


T able 3 higher reduced temperatures, water is not a good choice forAmbient conditions used in simulations a free flow collector. An extra complication is caused by

the fact that the condensate on the top glass layer willAmbient temperature T 20 8Camb2 cause additional reflection of the radiation (not taken intoIrradiance G 800 W/m

Wind speed v 1 m/s account in the numerical model), which will reduce thewind2~Mass flow m 76 kg/m h efficiency at high reduced temperatures even faster than

Sky temperature (clear sky) T 4 8Csky shown inFig. 9. An advantage of the free flow concept isCollector angle w 458 its intrinsic prevention against overheating because of the

strong increase in the rate of evaporation towards highertemperatures.

5 . Results5 .2. Experimental verification of the results for the one

5 .1. Efficiency curves cover sheet-and-tube PVT-collector

With the set of equations obtained in paragraph 3, the In order to be able to verify the results, a test facilityefficiency of the various designs is calculated as a function was built (de Vries, 1998). Since it was not feasible toof the reduced temperature. The thermal efficiency curves build all the designs described, a choice had to be madeare shown inFig. 9 and the electrical efficiencies inFig. which design would be realised. The single cover sheet-10. The ambient conditions used in the simulations are and-tube design was chosen. It was preferred over thepresented inTable 3. Table 4shows the thermal and channel designs because it could be built entirely fromelectrical efficiencies at zero reduced temperature. components that were based on well-known technology

The uncovered sheet-and-tube collector is obviously and that were commercially available. The single coverperforming poorest at zero reduced temperature because of sheet-and-tube was preferred over the other two sheet-and-its large heat losses. The sheet-and-tube collectors with tube designs because, as can be seen inFig. 9, the thermalone or two covers have a substantially larger efficiency at performance strongly decreases if the number of covers isthese conditions. It seems that a sheet-and-tube collector less, while the electrical performance decreases too muchwith two covers is only useful for high temperature if more than one cover is used.applications since the electrical efficiency strongly de- A non-optimised first prototype was constructed byteriorates due to the second cover, while the thermal connecting a conventional PV-laminate, containing multi-efficiency does not show a significant increase at modest crystalline silicon cells, to the absorber plate of a conven-values of the reduced temperature. In addition, it can be tional glass-covered sheet-and-tube collector, as shownobserved that the channel concepts (the channel concept, previously inFig. 1. The panel was then integrated into athe free flow panel concept and the two-absorber concept) test rig, next to a conventional sheet-and-tube thermalall have a substantially higher efficiency than the sheet- collector and a multi-crystalline silicon PV-panel of theand-tube collectors because of the excellent heat transfer same length and width. A photograph of the test rig isproperties of a channel. shown inFig. 11. For more extensive information on the

For the case of the free flow panel,Fig. 9 shows that experiments and experimental conditions, the reader isevaporation strongly reduces the thermal efficiency at referred tode Vries (1998)and Zondag et al. (1999).higher reduced temperatures. It can be concluded that, at The results of the measurements are presented inFig.

T able 4Thermal efficiency at zero reduced temperature with simultaneous production of electricity and corresponding electrical efficiency at zeroreduced temperature for various PVT-collector design concepts

Panel type Thermal Electricalefficiency efficiency

PV laminate – 0.097Sheet and tube PVT-collector 0 cover 0.52 0.097Sheet and tube PVT-collector 1 cover 0.58 0.089Sheet and tube PVT-collector 2 covers 0.58 0.081PVT-collector with channel above PV 0.65 0.084PVT-collector with channel below opaque PV 0.60 0.090PVT-collector with channel below transparent PV 0.63 0.090Free flow PVT-collector 0.64 0.086Two-absorber PVT-collector (insulated type) 0.66 0.085Two-absorber PVT-collector (non-insulated type) 0.65 0.084Thermal collector 0.83 –


Fig. 11. The test rig. Left to right: a conventional thermal collector, the PVT-collector and a conventional PV-laminate.

12, together with the results of the simulations. The 5 .3. Annual yield of a PV-thermal domestic hot watertemperature difference over the laminate was measured system

2and for h a value of 45 W/Km was found, which wasca

substantially below the expected value. The low heat For the calculation of the annual yield, a shell is builttransfer coefficient between cells and absorber was found around the program for the calculations of the efficiencyto be due to air enclosure in the glue layer, as well as a curves, in which the meteorological data and the systemheat conduction coefficient of the glue that turned out to be characteristics are specified. The meteorological data aresubstantially below the specified value. The value of 45 W/ obtained from the KNMI test reference year. In addition,

2Km is used in the simulations shown inFig. 12. The the sky temperature is calculated for every hour withthermal efficiency was determined as a function of reduced TRNSYS by means of a correlation that determines thetemperature for the 2D steady state model. The agreement cloudiness factor and the clear sky emittance from thebetween the model and the experiments is considered to be parameters in the test reference year. The system consists

2well within the range of the experimental data. of two 1.75 m PVT-collectors connected in parallel

Fig. 12. Left, measured thermal efficiency (3) thermal collector, (s,1) PVT-collector either without or with electricity production. Theuncertainties (least square fits) in the measurements are presented by the bar lengths.Right, least squares fit of the measurements of thethermal efficiency (solid) compared to the results obtained with the 2D model (dashed). Upper line, conventional thermal collector; middleline, PVT-collector not producing electricity; lower line, PVT-collector producing electricity.


T able 5ISSO warm water withdrawal schedule, (2) no withdrawal, (1) 175/8 l withdrawal

Hour 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Tapping 2 2 2 2 2 2 2 1 2 2 2 2 1 1 2 2 2 1 1 1 2 1 1 2

together with a storage vessel of 175 l. A conventional respect to the thermal yield are the non-insulated two-2mass flow of 50 l /(m h) is assumed, leading to a total absorber design and the channel-below-transparent-PV

mass flow of 175 l per hour. It is assumed that tapping design. The lower electrical efficiency of the first fourtakes place every day of the year according to the same designs makes the channel-below-transparent-PV designpattern. For the tapping during the day the ISSO tapping the most attractive from the efficiency point of view.scheme is used, that is displayed inTable 5. However, the basic one-cover sheet-and-tube design per-

During a day, the angle of the irradiation changes. It was forms only 2% worse while it is substantially easier toassumed that all radiation (direct and diffuse) comes out of manufacture, which seems to make it the most promisingthe direction of the sun. InFig. 3 it was found that the scheme from a marketing point of view. The table alsonormalised angular dependence of the one-cover and the shows that the free-flow panel performs much poorer thantwo-cover panels is almost the same. Since the new the channel designs for the present configuration, althoughdesigns can be expected to have an absorption that follows it has roughly the same thermal efficiency as the channelthe absorption of the one-cover case even more closely designs at zero reduced temperature. This is due to thethan the two-cover panel, the one-cover normalised angu- large thermal loss at higher temperatures due to evapora-lar dependence curve is used to determine the angular tion.dependence of the channel-, free flow- and two-absorber The presented thermal efficiencies show a substantialdesigns as well. reduction when compared to the thermal efficiency at zero

In the calculation of the thermal yield, heat losses from reduced temperature. In order to understand this reduction,the storage vessel and the tubing to the ambient are the efficiency was simulated again in which the lossincluded in the model. For the calculation of the heat loss, mechanisms were removed one by one. The results area constant local temperature of 108C is assumed around summarised inTable 7.With respect to the thermal losses,the vessel and the tubing. The heat loss coefficients for the the largest loss is due to the reduced efficiency of the

2vessel and the combined tubing are taken to be 0.4 W/Km PVT-collector at higher reduced temperatures. However,and 3 W/K, respectively. Mixing within the vessel is not the tubing heat loss also gives a substantial contribution oftaken into account. The vessel is replenished with water of 5%. Small losses result from the vessel heat loss and the10 8C. These calculations led to the results presented in increased reflection losses due to oblique radiation.Table 6. With respect to the calculation of the electrical yield, a

This table shows that the insulated two-absorber design, similar procedure can be followed. The results are indi-the two-cover sheet-and-tube design and the channel- cated inTable 8. The largest losses are those due toabove-PV design have the highest thermal yield for this inverter losses (0.9%) and top cover reflection (0.8%).domestic heating configuration, while the uncovered sheet- This again underscores the importance of the glass cover inand-tube design performs poorest. Second in line with reducing the PV-efficiency. The next largest losses are

T able 6Annual average efficiencies for the presented PVT-collector design concepts

System Annual Annualthermal electricalefficiency efficiency

PV – 0.072Sheet and tube PVT-collector uncovered 0.24 0.076Sheet and tube PVT-collector 1 cover 0.35 0.066Sheet and tube PVT-collector 2 covers 0.38 0.058PVT-collector with channel above PV 0.38 0.061PVT-collector with channel below opaque PV 0.35 0.067PVT-collector with channel below transparent PV 0.37 0.065Free flow PVT-collector 0.34 0.063Two-absorber PVT-collector (insulated type) 0.39 0.061Two-absorber PVT-collector (non-insulated type) 0.37 0.061Thermal collector 0.51 –


T able 7 design. However, the electrical performance of these threeLoss mechanisms affecting the annual thermal yield (values for systems is somewhat lower due to the additional glass andone cover sheet-and-tube PVT-collector) water layers on top of the PV. Taking this into account, it

seems that the channel-below-transparent-PV seems theLoss mechanism Thermalefficiency best option from the efficiency point of view, while the

one-cover sheet-and-tube design is a good alternative sinceBase case: one cover sheet-and-tube 0.35its efficiency is only 2% less. Since the latter design is byNo oblique irradiation loss 0.37far the easiest to manufacture, the single cover sheet-and-No vessel heat loss 0.38tube design seems the most promising of the examinedNo tubing heat loss 0.43

No reduced efficiency at increasing 0.58 concepts for domestic hot water production.reduced temperature However, a low-temperature application may show a

different picture. For this case, the uncovered PVT-collec-tor will probably come out better, since the reflection

those due to low (0.6%) and oblique irradiation (0.4%). losses at the cover are foregone in this design, while theThe increased laminate temperature accounts for only heat losses will remain low because of the low temperature0.2%. However, one should realise that this accounts for level required. This gives an interesting perspective for thethe present solar heater configuration only and is linked to combination of an uncovered PVT-collector with a heat-the fact that the average water outflow temperature is only pump.28 8C.

6 . Concluding discussion A ppendix A. Overview of the heat transportequations

The presented numerical analysis shows that for acombined photovoltaic-thermal collector, the total ef-

~q 5mc T 2 T (A.1)s dficiency at zero reduced temperature is over 50%. There- water out in

fore, it produces a higher yield per unit area than a thermal4 4collector and a PV laminate placed next to each other q 5F ´ s T 2 Ts dsky,rad sky g topglass↑ sky

under these conditions.4 4

1F ´ s T 2 T (A.2)s dearth g topglass↑ aFirstly, efficiency curves were calculated and it wasshown that for zero reduced temperature the thermal

q 5 h T 2 Tefficiency of the uncovered collector is 52% and the s dsky,conv wind topglass↑ a

thermal efficiency of the single cover sheet-and-tube Nu kwind air]]]design is 58%, while the channel above PV design 5 T 2 T (A.3)s dtopglass↑ aLctypically has 65% thermal efficiency.

Next, a prototype PVT-collector was built for the single 0.333 0.3330.25Nu 50.56 Ra sinw 1 0.13 Ra 2Ras ds dwind crit critcover sheet-and-tube collector. The measurements indi-3gb T 2T Ls dtopglass↑ a ccated that the model agreed with the experimental results -]]]]]]Ra 5Pr 2well within the range of the experimental data. n

8Finally, the annual yield was calculated for a domestic Ra 5 10 (Fujii and Imura, 1972)crithot water system. The best thermal annual yield is

(A.4)provided by the channel-above-PV design, the two-coversheet-and-tube design and the insulated two-absorber ´ ´g pv 4 4]]]]q 5 s T 2T (A.5)s dair,rad PVglass topglass↓´ 1´ 2´ ´T able 8 g pv g pv

Loss mechanisms affecting the annual electrical yield (values forq 5 h T 2Tone cover sheet-and-tube PVT-collector) s dair,conv air PVglass topglass↓

Loss mechanism Electrical Nu kair air]]5 T 2 T (A.6)s dPVglass topglass↓efficiency H

Base case: one cover sheet-and-tube 0.0661.61708 sin 1.8ws dNo increased laminate temperature 0.068 ]]]]]Nu 5 11 1.44 12F Gair Ra coswNo low irradiation 0.074

No oblique irradiation 0.078 1 10.3331708 Ra cosw]]] ]]]No inverter losses 0.087 3 12 1FS D 21G (A.7)F GRa cosw 5830

Ideal power-point tracking 0.089No top cover reflection 0.097

q 5 h T 2 T (A.8)s dba ba cell a


T able B.1Temperature dependency of properties in the air–water vapour mixture

Property of saturated mixture Least squares fit for property as a function oftemperature in8C

207 205 2 21Binary mass diffusion coefficientD D 51.5310 T 1 2.23 10 m s208 205 2 21Kinematic viscosityn n 5 8.13 10 T 1 1.353 10 m s204 202 21 21Thermal conductivityk k 5 1.03 10 T 1 2.453 10 W m K

2 21 21Specific heatc c 5 0.1T 2 3T 11057 J kg K203 23Density r r 5 2 5.33 10 T 1 1.297 kg m

203 202Water vapour mass fractionX X 54.76310 T 3exp [5.573 10 T ]03 06 21Latent heat of water vapourQ Q 5 22.43310 T 1 2.503 10 J kg

205 2 203Prandtl numberPr Pr 5 2.483 10 T 2 1.303 10 T 1 0.732204Schmidt numberSc Sc 5 2 3.233 10 T 1 0.612

assumed that the vapour at both sides of the layer is fullykglass]]q 5 T 2 T (A.9) saturated. The Sherwood numberSh is determined froms dPVglass cell PVglassdPVglass the empirical relation

k 1 / 3glass Sc]]q 5 T 2 T (A.10)s d ]topglass topglass↓ topglass↑ Sh ¯NuS D (B.5)dtopglass Pr

In Eq. (A.7), the correlation found by Hollands (Duffie and which is valid over the range 0.6,Pr , 60 and 0.6, Sc ,Beckman, 1991,p. 160), the1 signs indicate that these 3000. In this equation the Schmidt number and the Prandtlterms have the indicated value only if they are positive. If number appear, which are defined asthe term between the brackets assumes a negative value

n nthese terms become zero. ] ]Sc ; Pr ; (B.6)D aAB

Here, n represents the momentum diffusivity (viscosity)A ppendix B. Evaporation loss

anda the thermal diffusivity. Tabulated values ofQ ,latent

D and r can be found in various handbooks. TheAB vapIn order to calculated the evaporation loss, the diffusivequantities are evaluated for a mixture of vapour and air.

mass flow is determined byFirstly, the mass fraction of the vapour is determined and

≠X then the mixture properties can be found. For all the]M 5 2rD 5rh DX. (B.1)vap AB AB quantities involved the temperature dependence is taken≠y

into account by fitting the data to a function over theHere,DX is the difference in mass fraction of the vapour required temperature range. The fits are presented inTableover the air layer,d is the width of the air layer andD isAB B.1. In the calculation, the equations are evaluated at thethe mass diffusion coefficient. Introducing the Sherwood average layer temperature.number, which is defined as

h dAB]]Sh ; (B.2) R eferencesDAB

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