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The multiple layer solar collector
Solar Energy, Vol. 30. No. 3, pp. 225-235, 1983
0038-092X/83/030225-11503.00/0 Pergamon Press Ltd.
Printed in Great Britan.
THE MULTIPLE LAYER SOLAR COLLECTOR J. P. KENNA Solar Energy Unit, University College, Cardiff CF2 ITA, Wales (Received 4 December 1981; accepted 22 April 1982)
Abstract--The Multiple Layer Solar Collector is a proposed design in which the working liquid passes through several successive transparent layers. It has low reflection losses and operates in a once-through mode thereby ensuring that the outer layer is near ambient temperature. A mathematical model of this collector is developed. It is shown that the performance depends on three parameters (a) the number of layers (b) the heat transfer coefficientacross each layer (c) the absorption properties of the working fluid. Thermal performance predictions are made and compared with a selective flat plate collector operating in a once-through mode. For all practical designs the multiple layer collector is inferior to the selective surface collector. A further design is considered in which two liquid layers are insulated with an air gap. Computer predictions show that this design cannot improve on the flat plate collector. These predictions are confirmedwith experimental tests carried out on flat plate and two layer solar collectors. It is concluded that the multiple layer solar collector is not a viable design. 1. INTRODUCTION Several novel solar collector designs have been considered in recent years[l-3]. The objective of these studies has been to develop a more efficient or cost effective design then the conventional flat plate collector, An analysis of energy losses from a flat plate collector shows two areas for an improvement in performance. (a) Increasing the proportion of incident radiation absorbed by the working fluid. (b) Reducing the thermal Losses from the outer surface of the collector. If the solar collector steady state efficiency is given by the Hottel-Whillier equation[4]: = 77° - U T *
(1)
with T * = (T,,, - Ta)/G, then (a) can be identified with increasing o and (b) with reducing the collector loss coefficient U. Generally, attempting to improve one of these parameters results in a reduction in the other one. For example reducing the outer cover temperature (and hence thermal losses) by use of several glazings also increases the reflection and absorption losses. The proportion reflected depends on the incidence angle of the solar radiation. For cloudy environments, such as the U.K., with a large percentage of the radiation at high angles of incidence this proportion can be high. Two glass covers have a reflectance of 24 per cent at an incidence angle of 60° (which is an approximation to the reflectance for diffuse radiation[5]), To overcome this increased reflection loss a novel solar collector was proposed by Caouris et a/.[l]. This design attempts to reduce the heat losses from the front cover without increasing reflection losses. The heat transfer liquid circulates between the inner glazings (Fig. 1). Since the refractive indices of the working fluid (e.g. water n = 1.33) is close to that of the transparent plate (e.g. acrylic n = 1.5) the reflection from each liquid/plate
interface is minimal. The collector operates in a oncethrough mode, the cold liquid entering at the outermost layer, thereby keeping the cover at a temperature close to ambient. A mathematical model of this collector has been reported by Caouris et a/.[1] but this makes the assumption that each layer can be characterised by a single nodal temperature. While this assumption is perfectly adequate for collectors operating in a conventional mode (high flow rate with small temperature rise across the collector) it may not be reasonable for collectors operating in a once-through mode where the flow rate is reduced to obtain high outlet temperatures. Consequently a more detailed model has been developed which solves numerically the differential equations describing each layer. The model has been used to identify the most important design parameters of this collector and compare its performance with flat plate collector characteristics. 2. THEMULTIPLELAYERCOLLECTOR The design of Caouris et a/.[1] is shown in Fig. 1. Several transparent plates are placed above an absorber plate. The working liquid enters into the top (outermost layer) and travels down to the absorber through successive layers. Solar radiation enters the collector and is partially transmitted by the outer liquid layers. Any radiation absorbed by the working liquid has not been lost. The transmitted radiation is absorbed by the blackened plate, which then transfers heat to the inner liquid layer by convection and conduction. The absorbing surface does not have to be selective because any infra red radiation emitted will be absorbed by the inner liquid layer. Each transparent plate acts as a thermal barrier between adjacent liquid layers thus reducing the transfer of heat from the absorber to the outer cover. Since the liquid is in complete contact with the absorber there are
225
226
J.P. KENNA
] T+n
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I/
II
Transparent Plates j=1
~/
y'
j =2
/
/ J
t
/
/ /,
/ / #
To
/,,
ilatJon
//~?
'////
j =n-1
j=n-2
i
/ /
//////t///// Fluid Layers
- "
Absorber
Fig. l. Vertical section of the multiple layer solar collector.
no fin effects. The multiple layer collector can be cornpared to a solar pond with thermal statification achieved by physical separation of the layers. 3. ANALYSIS Several assumptions are made to simplify the analysis. (1) Radiation transfer between adjacent liquid layers is neglected. This is a good approximation if glass or suitable plastics are used for the transparent plates because these are opaque to thermal radiation, (2) The heat transfer liquid is considered to be opaque to thermal radiation since water and most organic fluids are highly absorbing in this region. (3) Conduction in the counter flow direction is neglected because the thermal diffusion velocity of the working liquid is typically much lower than the flow velocity. (Compare the diffusion velocity of water 1.4 x 10 7 ms-~ with a typical flow velocity of 1.4 × 10-4 ms 1). (4) Absorption of solar radiation by the transparent plates is neglected. While this may not be true in practice it simplifies the analysis considerably and indicates operating conditions that bear further investigation. (5) Heat transfer across the transparent plates is assumed to be described by a single coefficient h. This heat transfer coefficient will be dependent primarily on the thermal conductivity and thickness of the plate and to a lesser exten[ on boundary layer heat transfer coefficients between plate and working fluids. [1]. (6) The temperature distribution is assumed to be one dimensional in the flow direction. (7) The absorptance of the blackened plate is taken as 100 per cent. This assumption together with assumption[4] will lead to higher efficiencies than possible practically but should not affect the thermal loss coefficient. It has been shown by Duffle and Beckman[6] that the effect of absorption of solar radiation by flat plate collector covers is to modify the cover transmittance whilst having no effect on the collector loss coefficient, (8) Radiative and convective losses from the outer cover occur with a constant loss coefficient hL.
(9) The working fluid enters the collector at a ternperature equal to ambient. Consider a collector of n layers and of unit width. An energy balance for each layer gives the following three sets of equations of any point x: 1st layer (j = 1)
ranG + h(T2- TI) + hL(Ta
-
dTl T1) -'~--x ?~lcp = 0
(5)
2nd layer to (n - 1) layer (j = 2, n - 1)
rajG + h(Tj+l + Tj_~ - 2Tj)- u.+ rhcv = 0
(6)
nth layer j=n- 1 ( =~' ) r I-' ai G + h ( T , ~ - T , ) dT, ' c + hB(T, - T,) - ~ m p = 0.
(7)
Applying the boundary condition TI = Ta at x = 0, the set of equations can be solved numerically, to yield the outlet temperature (To) and hence the efficiency:
rt
rncp(To-T.) G
(8)
Analysis is simplified if eqns (5)-(8) are re-written in terms of the reduced temperature. T-T, T* = - -G
The multiple layer solar collector to become: j= 1
ra~+h(T*-T*)-hLT*-
df~
rh% = 0
(9)
227
Although the solution of eqns (9)-(11) is possible analytically, it is tedious and instead the equations have been solved numerically to yield thermal performance curves as a function of: (1) Number of layers n. (2) Absorptance of each layer aj. (3) Heat transfer coefficient h. The back loss and top loss coefficients hB and hL were held constant for these calculations. The results, shown in Figs. 2-7 will be discussed later.
j = 2, n - 1
,;.aj+h(T*+,+,v* ,~,v*, dT~ . lj_~--~lj)-- d--~-mcp= 0
(10)
4. PERFORMANCEOF FLATPLATECOLLECTORS OPERATING IN A ONCE THROUGH MODE
j= n T,,(1 ,=.-ti~=,a,/~+ h(T,_,-T*)*
-
, _.
dT*.
- n B l , - d x - x rn% = 0 (11)
and
= rhcpT*.
(12)
Solution of eqns (9)-(11) will give the reduced temperature distribution T* as a function of n, r, a, h, hE, hB, rhcp. Thus for a given collector design (with constant n, r, a, h, he) and a given outer cover loss coefficient hL, the reduced temperature distribution T*, and hence reduced outlet temperature T~, depend only on the thermal mass flow rate m%. From eqn (12) the collector efficiency is then seen to be dependent on thermal mass flow rate only and by varying the, a performance characteristic of the collector can be obtained. Each thermal mass flow rate corresponds to a different reduced outlet temperature. For comparison with a fiat plate collector (see next section) it is instructive to present the thermal performance characteristic in terms of collector efficiency and reduced outlet temperature.
i.e., =/(r*o).
In order to compare multiple layer with flat plate solar collectors the performance of flat plate collectors operating in a once-through mode must be predicted. This could be done by solving the differential equations describing the absorber and cover but a much simpler analytic solution can be derived from the Hottel-Whillier equation. Using the derivation given in Appendix 1 the final solution is UT~ = - ln(1 - UT*I~o)
where 0 < T* < U/rh). Here, the efficiency of the flat plate collector has been expressed in terms of reduced outlet temperature and can therefore be compared directly with the multiple layer collector efficiency. A physical interpretation of eqn (14) can be given by expanding the log term to give: U( ~ ='0o-
,,, o /,io 1 U T ~-1/UT~\ , 2 ) I + Z - W - + 5 [ - - £ - - ] . . . . . T~
"q= ~,,- U~T*
(16)
where IT;
(13)
~
(15)
or
1UT*
I [ U T~o~ 2
Vo =~-(1 + ~ - ~ - o + ~ \ - ~ - o ]
0.6 a 0./,
(14)
-.''"'"
0"21/ Thmkness(mm)
Fig. 2. Solar absorptance of water (A M2 spectrum).
.
.
.
.
.
.
! .
(17)
228
J.P. KENNA 1
-
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,,
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Flat Rate C_~lector 2 Layers
-....
5
.... i"
Layers
i
o02
I I
0-o~
I
i
J
j
oo6
oos
OlO
o12
(TooTaI/G(K m2 w - l )
Fig.3. Effectofincreasinglayers.
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Flat Plate Collector I Wm-2K-1 J h=lO I h: 5 Win_2 K_~ . . . . . . . . . h=30 W m-2K l I ~ 0-02 0.0/. 0.06 (To -Ta )IG(K m2 W -1) Fig. 4. Effect of h for 2 layers.
I
j 008
i 0.10
I 032
The multiple layer solar collector
229
1.(]
0.~
0,6
",,
c
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ill
0./.
02 h=5 W m -2 K "1 . . . . h=lO W m-2K -1 . . . . .
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Fk~ Pklle Collectc~ h=30 W m-2 K -1 . . . . . . 0
I 0 02
' 0.04
' 006
A 008
, 0.10
,. 012
(To-To)/O ( K m 2 W -1 )
Fig, 5. Effect of h for 5 layers.
10
o6
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~,
\,
.~
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\.
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=
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o~
\,
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0.2
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h=10 W m-2K "1 No Absorption . . . . h=lO W m - 2 K -1 Water .... !
0.02
1
I
O.04 04)5 {To-To)IG(K m2K I )
I
0.08
Fig. 6. Effect of liquid absorption (2 layers).
I
I,
0.10
012
230
J.P. KENNA lo~
0.8
" ~
0.6
0.~
0.2 h:lO W m-2K-1 h:lO W m'-2K°1 I
0.02
No Absorption Woter I
I
I
004 0.06 (To-Tol/G (K m2 W"1)
0.08
I
0-10
I
0.12
Fig. 7. Effect of liquid absorption (5 layers). and is an effective loss coefficient which is dependent on the reduced outlet temperature To*. It can be seen from eqn (17) that for UT*/'~o'~6 the effective loss coefficient reduces to - U / 2 which implies that flat plate collectors operate more efficiently in a once-through mode than in their conventional operating mode. For this reason the multiple layer collector should be compared with a flat plate collector in a once-through mode and not the conventional fixed flow rate-variable inlet temperature mode. An equation of the form of eqn (16) is general to any collector operating with an inlet temperature equal to ambient. Thus the performance characteristics of the multiple layer collector can be examined by assuming an effective 7o and an effective loss coefficient in just the same way as for a conventional flat plate collector, 5. MATERIALS It is instructive to survey the materials that are available for a multiple layer collector so that appropriate values of liquid absorptance and heat transfer coefficients can be used for performance predictions, 5.1 Heat transfer fluids. For practical reasons the most suitable liquid is water, since for most applications solar collectors are used to heat water. The multiple layer collector, operating in a once-through mode, would have to be used in a direct system, so water is the obvious choice. Assuming the solar absorption properties of water used by Rabl[7], the solar absorptance of water is shown as a function of thickness in Fig. 2. If heat transfer oils are used in a water heating system the major disadvantage is that the collector must operate in an indirect system, and with a multiple layer collector
there would also be the additional expense of a very efficient heat exchanger, to cool the outlet fluid back down to ambient temperature. Organic oils tend to be slightly coloured and consequently have excessive solar absorption. 5.2 Transparent Plates. The thermal conductivity and thickness of the plates in a multiple layer collector are the prime factors governing the heat transfer coefficient between adjacent layers (h). Clearly h should be as small as possible to reduce heat transfer from the bottom of the collector to the top. Glass has a relatively high thermal conductivity (1 W m-~K 5, so to achieve a reasonably low h value say 1 0 W m - / K -~, a 100ram thickness of glass would be required. Transparent plastics typically have thermal conductivities which are five or six times lower than that of glass, so approximately 20mm of plastic would be required to achieve h = 10 W m -2 K 1. The plate thickness must have to be a compromise because the large thicknesses which are required to minimise "h" result in high solar absorption in the plates and also in high collector materials cost. If plastics are selected then attention needs also to be paid to their compatability with the heat transfer fluid and their resistance to temperature. For example acrylic sheets are unsuitable for use at temperatures greater than 90°C and polycarbonate sheets should not be used at temperatures above 120°C. 6. PERFORMANCEPREDICTIONSFORMULTIPLE LAYERCOLLECTORS The predictions discussed below have been made assuming a top loss coefficient (hD of 25 W m 2 K - ' and
The multiple layer solar collector a back loss coefficient (hB) of 0.5 W m-2K 1. The collector performance characteristics are presented as a plot of efficiency against reduced outlet temperature, (T~)and to examine the performance it has been assumed that each curve can be described by an equation of the form: = rlo- U,T~
(18)
where ~0ois the intercept on the efficiency axis and Ue is the effective loss coefficient, 6.1 Effect of number of layers (n). Figure 3 shows the effect of increasing the number of liquid layers from 2 to 5 for an "h" value of 3 0 W m - 2 K -~ (corresponding to 5 mm thick plates with conductivity 0.15Wm 1K-l). Each water layer was assumed to be 5 mm thick resulting in solar absorptances of a~= 0.22, ~2 = 0.05, a3 = 0.03, a4= 0.02 and a5 = 0.02. Also shown in Fig. 3 is the performance curve for a flat plate collector operating in a once-through mode calculated from eqn (14). The flat plate collector parameters were taken as U = 4.67 W m K -1 (i.e. corresponding to a selective surface collector) and "0o = 0.92 (i.e. a single cover with no absorption, and a sandwich type absorber with 100 per cent absorptance. The same absorber assumptions were used for the multiple layer collector.) Despite the generous assumption concerning the absorptive properties of the plates, it can be seen from Fig. 3 that the performance of the multiple layer collector is inferior to that of the flat plate collector, The gradients of the curves for the multiple layer collector are steeper than the gradient of the flat plate collector curve, indicating that with the assumptions made above the effective loss coefficient for the multiple layer collectors is larger than that for the flat plate collector. 6.2 Effect of heat transfer coel~cient "h". Figures 4 and 5 show the effect of decreasing h from 30 to 5 W m 2 K-l, for both 2 and 5 layer collectors. Again it has been assumed that water is the heat transfer fluid and a comparison is made with the same flat plate collector, It can be seen that decreasing "h" is more significant than increasing the number of layers. With h = 10Wm 2K-1 the five layer collector has an effective
loss coefficient approaching that of the flat plate coltector. With h = 5 W m -2 K -1 there is an improvement at high To*. However to achieve these low values of h would require glass plates of thickness 100-200mm or plastic plates with a thickness of 20--40 ram. For a two layer collector it is necessary to reduce h below 5 W m-2K 1, and the only practical way to achieve this would be to have an air gap between adjacent layers. This solution is unattractive, however, since it increases the reflection losses from the collector. 6.3 Effect of liquid absorption. The third parameter which influences the performance of a multiple layer collector is the solar absorptance of the working liquid. Decreasing the absorptance will improve the thermal performance because the temperature of the outer liquid layers will be reduced. To examine this effect real collector performance has been compared with that for an ideal collector containing a heat transfer fluid with zero absorptance, all solar radiation being absorbed by the blackened plate and transferred to the liquid by conduction and convection. Figures 6 and 7 allow a comparison of performance between that of the ideal collector and that of 2 and 5 layer collectors using water as the working fluid. A value of h = 10W m 2 K-, was assumed for these collectors. For both the 2 and 5 layer collectors the effect is to decrease the effective loss coefficient, whilst the intercept ('0o) remains the same. The decrease in collector performance due to solar absorption in the fluid becomes larger as the number of layers is increased, but for the two layer collector, performance is still not comparable with that of a flat plate collector. 7. COLLECTORSWITHAIR GAPS In the previous section it has been shown that using materials that are available at the present time the multiple layer collector has a thermal performance that is inferior to a typical selective surface flat plate collector. Comparable performance is achieved only when the conductive transfer coefficient between adjacent layers is too low to be achieved by transparent plates. This suggests the use of an air gap to insulate adjacent layers. In this case there might be no improvement in reflection
1 OI Tin
V
231
1
II
Transparent plates ~--~/'"//
/ /
AIR GAP
To
~'/
~.
~
Absorber Fig. 8. Vertical section of the two layer collector.
lotion
232
J.P. KENNA Table 1. Optical properties of flat plate and two layer collectors Flat Plate
Two Layer
Cover transmittance
0.84
0.70
Cover absorptance
0.08
0.22
Absorber absorptance
1.0
1.0
losses but the outer cover could be cooled by the incomingfluid at ambienttemperature, To examine this idea a comparison has been made between a single glazed flat plate collector and a two layer collector, a sketch of which is shown in Fig. 8. The significant parameter here is the heat transfer coefficient between the absorber and outer layer. Two values have been chosen, h = 2 and 5 W m -2K -L, corresponding respectively to an evacuated air gap with a selective absorber and a selective absorber alone. For the fiat plate collector, assuming a cover loss coefficient of 2 5 W m - 2 K -t and the back loss coefficients of 0.5Wm -l K -t, this leads to overall loss coefficients (U) of 2.35 and 4.67 W m 2K '. The optical properties of each collector are shown in Table 1. A comparison between the thermal performance of these collectors is shown in Fig. 9. Two points can be noted from this graph: (i) The intercept (~7o) for the two layer collector is higher than the intercept for the flat plate collector. This is because all radiation absorbed by the two layer outer cover is assumed to be due to water absorption only, a situation unlikely to be achieved in
practice. (ii) The effective loss coefficient for the two layer collector is greater than the effective loss coefficient for the flat plate collector. In practice the intercept (~0o) is likely to be similar for both collectors because the cover materials will have a similar solar absorptance. In this case the two layer collector will not match the thermal performance of the flat plate collector. 7.1 Experimental results. To confirm the computer prediction a modular collector has been designed where different absorber types and different cover systems can be accommodated in the same case. This comprises a wooden case with an aperture area of dimension 1.18 × 1.04 m, insulated with 35 mm of isocyanurate foam and 55 mm of rockwool. A two layer collector was assembled consisting of a copper fin and tube absorber with a Maxorb (Trademark M.P.D. Technology Ltd., U.K.) selective foil coating and a twin walled polycarbonate outer layer with 4mm wide channels (Trade name Qualex). Polypropylene headers were attached to the outer layer. Water entered at the top header and was transfer-
1.0
:~':. :~ . . . . . . . . . . . .
- ~ -."c~.
0.1.
0.2 Two Two Flat FI~ 0
Layer h=5 W m-2 K-1 - - - Loyer h = 2 Win-2 K -1 - - ' Plate U =4.67 W m-2 K-1 . . . . . Rdm U=235 W m-2 K-1 . . . . . . . i
0.02
I
I
0-0/. 0.06 (To-T~/G (K rn2 K -1 )
I
I
I
008
O10
0-12
Fig. 9. Comparison of two layer collector with a flat plate collector.
The multiple layer solar collector red from the lower header to the selective absorber by means of a well insulated plastic hose. The spacing between outer and inner layer was 40 mm. The collector was tested in the S.R.C. Solar Simulator at Cardiff[8]. A 4 m high constant head tank was used to provide a steady flow rate. The inlet temperature was held constant and close to ambient with an in line ternperature controller. Both inlet and outlet temperatures were measured with platinum resistance thermometers, Mass flow rate was measured at the outlet with a timer and weighing tank. The test was carried out under a nominal irradiance of 900 W m -2, a collector tilt of 450 and an air speed parallel to the outer layer of 4ms 1. Collector test results obtained in a simulator differ from those obtained outdoors due to the higher thermal radiation indoors. It is possible to correct the simulator results to give equivalent outdoor results[8]. For selective flat plate collectors the correction to the collection efficiency is usually 2-3 per cent, but results reported here are uncorrected, To obtain the performance characteristic whilst maintaining the inlet temperature close to ambient the mass flow rate was changed. Steady state conditions were established for a range of flow rates and measurements made to give the collector efficiency:
and the reduced outlet temperature: T* = (To- T,) G Figure 10 shows a comparison between the two layer collector and a flat plate collector operating in a once through mode. The flat plate collector was formed by replacing the outer layer of the two layer collector with 4 mm float glass. A once-through test was carried out to give the thermal performance characteristic shown in Fig. 10. The experimental point with no wind indicates that the performance is very sensitive to the outer cover loss coefficient (hL). This could be reduced by adding a cover to protect the outer water layer. To test this idea a 3 mm acrylic cover was added to the two layer collector and a further once-through test carried out. The results are shown in Fig. 11. No improvement in performance was found however, because the decrease in loss coefficient was balanced by the increase in reflection loss. s. CONCLUSION Reduction in thermal losses from a flat plate collector can be achieved by multiple glazings. However, this results in increased optical losses. A novel collector was proposed by Caouris et al.[1] which overcame this by passing the heat transfer fluid in between the transparent glazings. A mathematical model of this has been
rhcp(To- T~,) ~/-
233
G
1.0
O8 :~'~"~""o
[] No Wind
.~ W
r'l\
04
0.2
0
. Simulator [] S~mulator
Result Flat Plate Result Two Layer Collector I
0.02 (To - T a ) / G
I
OOZ.,
I
0.06
(K m 2 W -1)
Fig. 10. Experimental performance of two layer and flat plate collectors.
234
J.P. KENNA 1.0
0.8
¢O
rn
1.1.1
Or.
0.2
0
a Simulator Result Two Layers Simulator Result Two Layers and I I 0.02 O.OZ, ITo-To)/G(Km2 K -1 )
Ac~Iic Cov~r 006
Fig. ll. Experimental performance of two layers and outer cover.
developed. The model indicated that three parameters determined the thermal performance of the collector. (1) No of layers n. (2) Heat transfer coefficient between adjacent layers"h". (3)Absorptanceoftheheattransfer fluid a. The sensitivity of thermal performance to these parameters has been examined and the most sensitive parameter was found to be the heat transfer coefficient (h). In comparing this collector with a flat plate collector it is necessary to make the comparison with both collectors operating in the once-through mode. If this is done then to equal the performance of a typical flat plate collector with a selective surface it is necessary to have a five layer collector with an "h" value below 10 W m-2K ~. To achieve this h value with existing materials is not practicable because a thickness of plates separating the layers of over 20 mm would be required. A second collector was examined consisting of two liquid layers separated by an air gap. It was found that at high operating temperatures (TD the thermal performance was inferior to the performance of flat plate collector with a selective absorber. To achieve high outlet temperatures very low flow rates are necessary and the outer layer becomes almost stagnant. Under this condition the outer cover resembles the cover of a flat
plate collector but with a much larger absorptance (22 per cent compared with 8 per cent). This results in higher heat losses. The results of the computer studies have been confirmed by experimental tests on a two layer collector and a fiat plate collector. It was further shown experimentally that an additional cover on a two layer collector does not improve the performance. This study has lead to the conclusion that the multiple layer collector is not a viable proposition.
Acknowledgements--Thanksare given to Dr. W. B. Gillett for many helpful comments and discussions.
a c~ G h hc hB m n r/ "00 r
NOMENCLATURE solar absorptance specific heat, J kg t K-t solar irradiance, W m-2 heat transfer coefficient between a:ijacent layers, Wm-ZK-1 heat transfer coefficientfrom outer cover, W m 2 Kheat transfer coefficient from back and sides of collector, W m-2K mass flow rate, kgs refractive index collectorefficiency collector efficiencyfor mean fluid temperature at ambient solar transmittance
The multiple layer solar collector
T*~ (Tm-T~)/G, KW-~m 2 T~, (Tin- T~)/G, K W -~ m2 T~ (To- T)/G, K W -~ m 2 Tj Tm T~. To Ta U Ue
235
For collectors operating in a once-through mode the inlet temperature will be at or close to ambient temperatures giving T~ = 0. Equation (A2) then becomes:
temperature of jth layer at distance x, K mean fluid temperature, K temperature of fluid at collector inlet, K temperature of fluid at collector outlet, K ambient temperature, K collector loss coefficient, W m - 2 K -1 effective loss coefficient, W m -2 K -1
"o = F"r/o
(A5)
The steady state efficiency is also given by: r/= mco(To- T~)/G
(A6)
when Tin = Ta. Defining T~ = (To - Ta)/G the eqn (A6) becomes REFERENCES
1. Y. Caouris et al., A novel solar collector. Solar Energy 21, 157-160 (1978). 2. J. E. Minardi and H. N. Chuang, Performance of a "Black" liquid flat plate solar collector. Solar Energy 17, 17%184 (1975). 3. P. R. Smith et al., Parametric Studies of the Thermal Trap Hat Plate Collector. A.I.Ch.E. Syrup. Series 73. No. 164, pp. 164-170 (1977). 4. H. C, Hottel and A. Whillier, Evaluation of Hat Platg Collector Performance. Trans. of the Conference on the Use of Solar Energy. 2. Part 1. University of Arizona Press (1958). 5. M. J. Brandemuehl and W. A. Beckman, Transmission of diffuse radiation through CPC and flat plate collector glazings. Solar Energy 24, 511-513 (1980). 6. J. A. Duffle and W. B. Beckman, Solar Energy Thermal Processes. Wiley, New York (1974). 7. A. Rabl and C. E. Nielsen, Solar ponds for space heating, Solar Energy 17, 1(1975). 8. W. B. Gillett et al., Collector Testing Using Solar Simulators. UK-ISES Conference C22 Solar Energy Code of Practices and Test Procedures (1980).
r/= inepT*.
(A7)
By substitution of (A7) into (A4) the flow factor can be expressed in terms of efficiency and reduced outlet temperature (To*).
"11 {.
{ - UT*\\
F" =~-~o~ l - e x p ~ ) ) .
(A8)
Equation (A5) then becomes
( r/= " 0 o \ ~
(
- UT~ 1
(A9)
or re-arranging
UT* r/=
(A10) - l n ( 1 - UT'~" r/o /
A restriction which must be imposed on (A10) is that the thermal mass flow rate must be positive and finite.
APEENDIX 1
~ > rhcp > 0
Performance of a solar collector operating in a once-through mode. Under steady state conditions the thermal performance of
or from (AT)
a solar collector is given by the Hottel-WhiUier equation: ~>r//T*>0 "11= r/o- UT*~
(A1) which leads to the restriction on (A10) that:
If eqn (A1) is assumed to hold for any mass flow rate then two assumptions are implicit: The collector loss coefficient U is independent of fluid temperature. The heat transfer from the absorber to working fluid is independent of mass flow rate, i.e. r/o is constant. Following a method given by DutSe and Beckman[6] (A1) can be rewritten in its T~, form:
r~= F"r/o- F" UT*,
(A2)
where T*, = (T~n- T,)IG
(A3)
mep( F " = - - U-
SE Vo130,No. 3--D
1 - exp
(~.~cpU)) .
(A,t)
oo< - l n ( l - UT*/r/o) > O. This imposes limitations on T* of 0 < T* < ~U which can be interpeted physically as: (1) T~' >0. If T~' = 0 then the outlet temperature is equal to ambient. This is only possible with an infinite flow rate. (2) To*< r/o/U. If the mass flow rate is zero then the collector reaches a stagnation temperature defined by ~o/U. Thus temperatures above "0o/U are impossible to achieve.
0038-092X/83/030225-11503.00/0 Pergamon Press Ltd.
Printed in Great Britan.
THE MULTIPLE LAYER SOLAR COLLECTOR J. P. KENNA Solar Energy Unit, University College, Cardiff CF2 ITA, Wales (Received 4 December 1981; accepted 22 April 1982)
Abstract--The Multiple Layer Solar Collector is a proposed design in which the working liquid passes through several successive transparent layers. It has low reflection losses and operates in a once-through mode thereby ensuring that the outer layer is near ambient temperature. A mathematical model of this collector is developed. It is shown that the performance depends on three parameters (a) the number of layers (b) the heat transfer coefficientacross each layer (c) the absorption properties of the working fluid. Thermal performance predictions are made and compared with a selective flat plate collector operating in a once-through mode. For all practical designs the multiple layer collector is inferior to the selective surface collector. A further design is considered in which two liquid layers are insulated with an air gap. Computer predictions show that this design cannot improve on the flat plate collector. These predictions are confirmedwith experimental tests carried out on flat plate and two layer solar collectors. It is concluded that the multiple layer solar collector is not a viable design. 1. INTRODUCTION Several novel solar collector designs have been considered in recent years[l-3]. The objective of these studies has been to develop a more efficient or cost effective design then the conventional flat plate collector, An analysis of energy losses from a flat plate collector shows two areas for an improvement in performance. (a) Increasing the proportion of incident radiation absorbed by the working fluid. (b) Reducing the thermal Losses from the outer surface of the collector. If the solar collector steady state efficiency is given by the Hottel-Whillier equation[4]: = 77° - U T *
(1)
with T * = (T,,, - Ta)/G, then (a) can be identified with increasing o and (b) with reducing the collector loss coefficient U. Generally, attempting to improve one of these parameters results in a reduction in the other one. For example reducing the outer cover temperature (and hence thermal losses) by use of several glazings also increases the reflection and absorption losses. The proportion reflected depends on the incidence angle of the solar radiation. For cloudy environments, such as the U.K., with a large percentage of the radiation at high angles of incidence this proportion can be high. Two glass covers have a reflectance of 24 per cent at an incidence angle of 60° (which is an approximation to the reflectance for diffuse radiation[5]), To overcome this increased reflection loss a novel solar collector was proposed by Caouris et a/.[l]. This design attempts to reduce the heat losses from the front cover without increasing reflection losses. The heat transfer liquid circulates between the inner glazings (Fig. 1). Since the refractive indices of the working fluid (e.g. water n = 1.33) is close to that of the transparent plate (e.g. acrylic n = 1.5) the reflection from each liquid/plate
interface is minimal. The collector operates in a oncethrough mode, the cold liquid entering at the outermost layer, thereby keeping the cover at a temperature close to ambient. A mathematical model of this collector has been reported by Caouris et a/.[1] but this makes the assumption that each layer can be characterised by a single nodal temperature. While this assumption is perfectly adequate for collectors operating in a conventional mode (high flow rate with small temperature rise across the collector) it may not be reasonable for collectors operating in a once-through mode where the flow rate is reduced to obtain high outlet temperatures. Consequently a more detailed model has been developed which solves numerically the differential equations describing each layer. The model has been used to identify the most important design parameters of this collector and compare its performance with flat plate collector characteristics. 2. THEMULTIPLELAYERCOLLECTOR The design of Caouris et a/.[1] is shown in Fig. 1. Several transparent plates are placed above an absorber plate. The working liquid enters into the top (outermost layer) and travels down to the absorber through successive layers. Solar radiation enters the collector and is partially transmitted by the outer liquid layers. Any radiation absorbed by the working liquid has not been lost. The transmitted radiation is absorbed by the blackened plate, which then transfers heat to the inner liquid layer by convection and conduction. The absorbing surface does not have to be selective because any infra red radiation emitted will be absorbed by the inner liquid layer. Each transparent plate acts as a thermal barrier between adjacent liquid layers thus reducing the transfer of heat from the absorber to the outer cover. Since the liquid is in complete contact with the absorber there are
225
226
J.P. KENNA
] T+n
i
I/
II
Transparent Plates j=1
~/
y'
j =2
/
/ J
t
/
/ /,
/ / #
To
/,,
ilatJon
//~?
'////
j =n-1
j=n-2
i
/ /
//////t///// Fluid Layers
- "
Absorber
Fig. l. Vertical section of the multiple layer solar collector.
no fin effects. The multiple layer collector can be cornpared to a solar pond with thermal statification achieved by physical separation of the layers. 3. ANALYSIS Several assumptions are made to simplify the analysis. (1) Radiation transfer between adjacent liquid layers is neglected. This is a good approximation if glass or suitable plastics are used for the transparent plates because these are opaque to thermal radiation, (2) The heat transfer liquid is considered to be opaque to thermal radiation since water and most organic fluids are highly absorbing in this region. (3) Conduction in the counter flow direction is neglected because the thermal diffusion velocity of the working liquid is typically much lower than the flow velocity. (Compare the diffusion velocity of water 1.4 x 10 7 ms-~ with a typical flow velocity of 1.4 × 10-4 ms 1). (4) Absorption of solar radiation by the transparent plates is neglected. While this may not be true in practice it simplifies the analysis considerably and indicates operating conditions that bear further investigation. (5) Heat transfer across the transparent plates is assumed to be described by a single coefficient h. This heat transfer coefficient will be dependent primarily on the thermal conductivity and thickness of the plate and to a lesser exten[ on boundary layer heat transfer coefficients between plate and working fluids. [1]. (6) The temperature distribution is assumed to be one dimensional in the flow direction. (7) The absorptance of the blackened plate is taken as 100 per cent. This assumption together with assumption[4] will lead to higher efficiencies than possible practically but should not affect the thermal loss coefficient. It has been shown by Duffle and Beckman[6] that the effect of absorption of solar radiation by flat plate collector covers is to modify the cover transmittance whilst having no effect on the collector loss coefficient, (8) Radiative and convective losses from the outer cover occur with a constant loss coefficient hL.
(9) The working fluid enters the collector at a ternperature equal to ambient. Consider a collector of n layers and of unit width. An energy balance for each layer gives the following three sets of equations of any point x: 1st layer (j = 1)
ranG + h(T2- TI) + hL(Ta
-
dTl T1) -'~--x ?~lcp = 0
(5)
2nd layer to (n - 1) layer (j = 2, n - 1)
rajG + h(Tj+l + Tj_~ - 2Tj)- u.+ rhcv = 0
(6)
nth layer j=n- 1 ( =~' ) r I-' ai G + h ( T , ~ - T , ) dT, ' c + hB(T, - T,) - ~ m p = 0.
(7)
Applying the boundary condition TI = Ta at x = 0, the set of equations can be solved numerically, to yield the outlet temperature (To) and hence the efficiency:
rt
rncp(To-T.) G
(8)
Analysis is simplified if eqns (5)-(8) are re-written in terms of the reduced temperature. T-T, T* = - -G
The multiple layer solar collector to become: j= 1
ra~+h(T*-T*)-hLT*-
df~
rh% = 0
(9)
227
Although the solution of eqns (9)-(11) is possible analytically, it is tedious and instead the equations have been solved numerically to yield thermal performance curves as a function of: (1) Number of layers n. (2) Absorptance of each layer aj. (3) Heat transfer coefficient h. The back loss and top loss coefficients hB and hL were held constant for these calculations. The results, shown in Figs. 2-7 will be discussed later.
j = 2, n - 1
,;.aj+h(T*+,+,v* ,~,v*, dT~ . lj_~--~lj)-- d--~-mcp= 0
(10)
4. PERFORMANCEOF FLATPLATECOLLECTORS OPERATING IN A ONCE THROUGH MODE
j= n T,,(1 ,=.-ti~=,a,/~+ h(T,_,-T*)*
-
, _.
dT*.
- n B l , - d x - x rn% = 0 (11)
and
= rhcpT*.
(12)
Solution of eqns (9)-(11) will give the reduced temperature distribution T* as a function of n, r, a, h, hE, hB, rhcp. Thus for a given collector design (with constant n, r, a, h, he) and a given outer cover loss coefficient hL, the reduced temperature distribution T*, and hence reduced outlet temperature T~, depend only on the thermal mass flow rate m%. From eqn (12) the collector efficiency is then seen to be dependent on thermal mass flow rate only and by varying the, a performance characteristic of the collector can be obtained. Each thermal mass flow rate corresponds to a different reduced outlet temperature. For comparison with a fiat plate collector (see next section) it is instructive to present the thermal performance characteristic in terms of collector efficiency and reduced outlet temperature.
i.e., =/(r*o).
In order to compare multiple layer with flat plate solar collectors the performance of flat plate collectors operating in a once-through mode must be predicted. This could be done by solving the differential equations describing the absorber and cover but a much simpler analytic solution can be derived from the Hottel-Whillier equation. Using the derivation given in Appendix 1 the final solution is UT~ = - ln(1 - UT*I~o)
where 0 < T* < U/rh). Here, the efficiency of the flat plate collector has been expressed in terms of reduced outlet temperature and can therefore be compared directly with the multiple layer collector efficiency. A physical interpretation of eqn (14) can be given by expanding the log term to give: U( ~ ='0o-
,,, o /,io 1 U T ~-1/UT~\ , 2 ) I + Z - W - + 5 [ - - £ - - ] . . . . . T~
"q= ~,,- U~T*
(16)
where IT;
(13)
~
(15)
or
1UT*
I [ U T~o~ 2
Vo =~-(1 + ~ - ~ - o + ~ \ - ~ - o ]
0.6 a 0./,
(14)
-.''"'"
0"21/ Thmkness(mm)
Fig. 2. Solar absorptance of water (A M2 spectrum).
.
.
.
.
.
.
! .
(17)
228
J.P. KENNA 1
-
0
~
\
0-8
,,,
"',%
\\\
,.,.
\\ 0-6
",, \
""
\
-
\ \
'"=1=
\
o.~.
,,
\
0.2
I
I 0
Flat Rate C_~lector 2 Layers
-....
5
.... i"
Layers
i
o02
I I
0-o~
I
i
J
j
oo6
oos
OlO
o12
(TooTaI/G(K m2 w - l )
Fig.3. Effectofincreasinglayers.
10 F
\
,~ \
"-... \
\\ \
0.6
o_
o~
......
"\.
"--..... \.\
\
\
=
LU
"--.
"\
\
"'-.......
\
\
\
\ \
\ \
02
0
\ t
\
I
Flat Plate Collector I Wm-2K-1 J h=lO I h: 5 Win_2 K_~ . . . . . . . . . h=30 W m-2K l I ~ 0-02 0.0/. 0.06 (To -Ta )IG(K m2 W -1) Fig. 4. Effect of h for 2 layers.
I
j 008
i 0.10
I 032
The multiple layer solar collector
229
1.(]
0.~
0,6
",,
c
\
ill
0./.
02 h=5 W m -2 K "1 . . . . h=lO W m-2K -1 . . . . .
"
Fk~ Pklle Collectc~ h=30 W m-2 K -1 . . . . . . 0
I 0 02
' 0.04
' 006
A 008
, 0.10
,. 012
(To-To)/O ( K m 2 W -1 )
Fig, 5. Effect of h for 5 layers.
10
o6
\-
~,
\,
.~
\
\.
",\
=
\
o~
\,
\
\
\ \
0.2
\
h=10 W m-2K "1 No Absorption . . . . h=lO W m - 2 K -1 Water .... !
0.02
1
I
O.04 04)5 {To-To)IG(K m2K I )
I
0.08
Fig. 6. Effect of liquid absorption (2 layers).
I
I,
0.10
012
230
J.P. KENNA lo~
0.8
" ~
0.6
0.~
0.2 h:lO W m-2K-1 h:lO W m'-2K°1 I
0.02
No Absorption Woter I
I
I
004 0.06 (To-Tol/G (K m2 W"1)
0.08
I
0-10
I
0.12
Fig. 7. Effect of liquid absorption (5 layers). and is an effective loss coefficient which is dependent on the reduced outlet temperature To*. It can be seen from eqn (17) that for UT*/'~o'~6 the effective loss coefficient reduces to - U / 2 which implies that flat plate collectors operate more efficiently in a once-through mode than in their conventional operating mode. For this reason the multiple layer collector should be compared with a flat plate collector in a once-through mode and not the conventional fixed flow rate-variable inlet temperature mode. An equation of the form of eqn (16) is general to any collector operating with an inlet temperature equal to ambient. Thus the performance characteristics of the multiple layer collector can be examined by assuming an effective 7o and an effective loss coefficient in just the same way as for a conventional flat plate collector, 5. MATERIALS It is instructive to survey the materials that are available for a multiple layer collector so that appropriate values of liquid absorptance and heat transfer coefficients can be used for performance predictions, 5.1 Heat transfer fluids. For practical reasons the most suitable liquid is water, since for most applications solar collectors are used to heat water. The multiple layer collector, operating in a once-through mode, would have to be used in a direct system, so water is the obvious choice. Assuming the solar absorption properties of water used by Rabl[7], the solar absorptance of water is shown as a function of thickness in Fig. 2. If heat transfer oils are used in a water heating system the major disadvantage is that the collector must operate in an indirect system, and with a multiple layer collector
there would also be the additional expense of a very efficient heat exchanger, to cool the outlet fluid back down to ambient temperature. Organic oils tend to be slightly coloured and consequently have excessive solar absorption. 5.2 Transparent Plates. The thermal conductivity and thickness of the plates in a multiple layer collector are the prime factors governing the heat transfer coefficient between adjacent layers (h). Clearly h should be as small as possible to reduce heat transfer from the bottom of the collector to the top. Glass has a relatively high thermal conductivity (1 W m-~K 5, so to achieve a reasonably low h value say 1 0 W m - / K -~, a 100ram thickness of glass would be required. Transparent plastics typically have thermal conductivities which are five or six times lower than that of glass, so approximately 20mm of plastic would be required to achieve h = 10 W m -2 K 1. The plate thickness must have to be a compromise because the large thicknesses which are required to minimise "h" result in high solar absorption in the plates and also in high collector materials cost. If plastics are selected then attention needs also to be paid to their compatability with the heat transfer fluid and their resistance to temperature. For example acrylic sheets are unsuitable for use at temperatures greater than 90°C and polycarbonate sheets should not be used at temperatures above 120°C. 6. PERFORMANCEPREDICTIONSFORMULTIPLE LAYERCOLLECTORS The predictions discussed below have been made assuming a top loss coefficient (hD of 25 W m 2 K - ' and
The multiple layer solar collector a back loss coefficient (hB) of 0.5 W m-2K 1. The collector performance characteristics are presented as a plot of efficiency against reduced outlet temperature, (T~)and to examine the performance it has been assumed that each curve can be described by an equation of the form: = rlo- U,T~
(18)
where ~0ois the intercept on the efficiency axis and Ue is the effective loss coefficient, 6.1 Effect of number of layers (n). Figure 3 shows the effect of increasing the number of liquid layers from 2 to 5 for an "h" value of 3 0 W m - 2 K -~ (corresponding to 5 mm thick plates with conductivity 0.15Wm 1K-l). Each water layer was assumed to be 5 mm thick resulting in solar absorptances of a~= 0.22, ~2 = 0.05, a3 = 0.03, a4= 0.02 and a5 = 0.02. Also shown in Fig. 3 is the performance curve for a flat plate collector operating in a once-through mode calculated from eqn (14). The flat plate collector parameters were taken as U = 4.67 W m K -1 (i.e. corresponding to a selective surface collector) and "0o = 0.92 (i.e. a single cover with no absorption, and a sandwich type absorber with 100 per cent absorptance. The same absorber assumptions were used for the multiple layer collector.) Despite the generous assumption concerning the absorptive properties of the plates, it can be seen from Fig. 3 that the performance of the multiple layer collector is inferior to that of the flat plate collector, The gradients of the curves for the multiple layer collector are steeper than the gradient of the flat plate collector curve, indicating that with the assumptions made above the effective loss coefficient for the multiple layer collectors is larger than that for the flat plate collector. 6.2 Effect of heat transfer coel~cient "h". Figures 4 and 5 show the effect of decreasing h from 30 to 5 W m 2 K-l, for both 2 and 5 layer collectors. Again it has been assumed that water is the heat transfer fluid and a comparison is made with the same flat plate collector, It can be seen that decreasing "h" is more significant than increasing the number of layers. With h = 10Wm 2K-1 the five layer collector has an effective
loss coefficient approaching that of the flat plate coltector. With h = 5 W m -2 K -1 there is an improvement at high To*. However to achieve these low values of h would require glass plates of thickness 100-200mm or plastic plates with a thickness of 20--40 ram. For a two layer collector it is necessary to reduce h below 5 W m-2K 1, and the only practical way to achieve this would be to have an air gap between adjacent layers. This solution is unattractive, however, since it increases the reflection losses from the collector. 6.3 Effect of liquid absorption. The third parameter which influences the performance of a multiple layer collector is the solar absorptance of the working liquid. Decreasing the absorptance will improve the thermal performance because the temperature of the outer liquid layers will be reduced. To examine this effect real collector performance has been compared with that for an ideal collector containing a heat transfer fluid with zero absorptance, all solar radiation being absorbed by the blackened plate and transferred to the liquid by conduction and convection. Figures 6 and 7 allow a comparison of performance between that of the ideal collector and that of 2 and 5 layer collectors using water as the working fluid. A value of h = 10W m 2 K-, was assumed for these collectors. For both the 2 and 5 layer collectors the effect is to decrease the effective loss coefficient, whilst the intercept ('0o) remains the same. The decrease in collector performance due to solar absorption in the fluid becomes larger as the number of layers is increased, but for the two layer collector, performance is still not comparable with that of a flat plate collector. 7. COLLECTORSWITHAIR GAPS In the previous section it has been shown that using materials that are available at the present time the multiple layer collector has a thermal performance that is inferior to a typical selective surface flat plate collector. Comparable performance is achieved only when the conductive transfer coefficient between adjacent layers is too low to be achieved by transparent plates. This suggests the use of an air gap to insulate adjacent layers. In this case there might be no improvement in reflection
1 OI Tin
V
231
1
II
Transparent plates ~--~/'"//
/ /
AIR GAP
To
~'/
~.
~
Absorber Fig. 8. Vertical section of the two layer collector.
lotion
232
J.P. KENNA Table 1. Optical properties of flat plate and two layer collectors Flat Plate
Two Layer
Cover transmittance
0.84
0.70
Cover absorptance
0.08
0.22
Absorber absorptance
1.0
1.0
losses but the outer cover could be cooled by the incomingfluid at ambienttemperature, To examine this idea a comparison has been made between a single glazed flat plate collector and a two layer collector, a sketch of which is shown in Fig. 8. The significant parameter here is the heat transfer coefficient between the absorber and outer layer. Two values have been chosen, h = 2 and 5 W m -2K -L, corresponding respectively to an evacuated air gap with a selective absorber and a selective absorber alone. For the fiat plate collector, assuming a cover loss coefficient of 2 5 W m - 2 K -t and the back loss coefficients of 0.5Wm -l K -t, this leads to overall loss coefficients (U) of 2.35 and 4.67 W m 2K '. The optical properties of each collector are shown in Table 1. A comparison between the thermal performance of these collectors is shown in Fig. 9. Two points can be noted from this graph: (i) The intercept (~7o) for the two layer collector is higher than the intercept for the flat plate collector. This is because all radiation absorbed by the two layer outer cover is assumed to be due to water absorption only, a situation unlikely to be achieved in
practice. (ii) The effective loss coefficient for the two layer collector is greater than the effective loss coefficient for the flat plate collector. In practice the intercept (~0o) is likely to be similar for both collectors because the cover materials will have a similar solar absorptance. In this case the two layer collector will not match the thermal performance of the flat plate collector. 7.1 Experimental results. To confirm the computer prediction a modular collector has been designed where different absorber types and different cover systems can be accommodated in the same case. This comprises a wooden case with an aperture area of dimension 1.18 × 1.04 m, insulated with 35 mm of isocyanurate foam and 55 mm of rockwool. A two layer collector was assembled consisting of a copper fin and tube absorber with a Maxorb (Trademark M.P.D. Technology Ltd., U.K.) selective foil coating and a twin walled polycarbonate outer layer with 4mm wide channels (Trade name Qualex). Polypropylene headers were attached to the outer layer. Water entered at the top header and was transfer-
1.0
:~':. :~ . . . . . . . . . . . .
- ~ -."c~.
0.1.
0.2 Two Two Flat FI~ 0
Layer h=5 W m-2 K-1 - - - Loyer h = 2 Win-2 K -1 - - ' Plate U =4.67 W m-2 K-1 . . . . . Rdm U=235 W m-2 K-1 . . . . . . . i
0.02
I
I
0-0/. 0.06 (To-T~/G (K rn2 K -1 )
I
I
I
008
O10
0-12
Fig. 9. Comparison of two layer collector with a flat plate collector.
The multiple layer solar collector red from the lower header to the selective absorber by means of a well insulated plastic hose. The spacing between outer and inner layer was 40 mm. The collector was tested in the S.R.C. Solar Simulator at Cardiff[8]. A 4 m high constant head tank was used to provide a steady flow rate. The inlet temperature was held constant and close to ambient with an in line ternperature controller. Both inlet and outlet temperatures were measured with platinum resistance thermometers, Mass flow rate was measured at the outlet with a timer and weighing tank. The test was carried out under a nominal irradiance of 900 W m -2, a collector tilt of 450 and an air speed parallel to the outer layer of 4ms 1. Collector test results obtained in a simulator differ from those obtained outdoors due to the higher thermal radiation indoors. It is possible to correct the simulator results to give equivalent outdoor results[8]. For selective flat plate collectors the correction to the collection efficiency is usually 2-3 per cent, but results reported here are uncorrected, To obtain the performance characteristic whilst maintaining the inlet temperature close to ambient the mass flow rate was changed. Steady state conditions were established for a range of flow rates and measurements made to give the collector efficiency:
and the reduced outlet temperature: T* = (To- T,) G Figure 10 shows a comparison between the two layer collector and a flat plate collector operating in a once through mode. The flat plate collector was formed by replacing the outer layer of the two layer collector with 4 mm float glass. A once-through test was carried out to give the thermal performance characteristic shown in Fig. 10. The experimental point with no wind indicates that the performance is very sensitive to the outer cover loss coefficient (hL). This could be reduced by adding a cover to protect the outer water layer. To test this idea a 3 mm acrylic cover was added to the two layer collector and a further once-through test carried out. The results are shown in Fig. 11. No improvement in performance was found however, because the decrease in loss coefficient was balanced by the increase in reflection loss. s. CONCLUSION Reduction in thermal losses from a flat plate collector can be achieved by multiple glazings. However, this results in increased optical losses. A novel collector was proposed by Caouris et al.[1] which overcame this by passing the heat transfer fluid in between the transparent glazings. A mathematical model of this has been
rhcp(To- T~,) ~/-
233
G
1.0
O8 :~'~"~""o
[] No Wind
.~ W
r'l\
04
0.2
0
. Simulator [] S~mulator
Result Flat Plate Result Two Layer Collector I
0.02 (To - T a ) / G
I
OOZ.,
I
0.06
(K m 2 W -1)
Fig. 10. Experimental performance of two layer and flat plate collectors.
234
J.P. KENNA 1.0
0.8
¢O
rn
1.1.1
Or.
0.2
0
a Simulator Result Two Layers Simulator Result Two Layers and I I 0.02 O.OZ, ITo-To)/G(Km2 K -1 )
Ac~Iic Cov~r 006
Fig. ll. Experimental performance of two layers and outer cover.
developed. The model indicated that three parameters determined the thermal performance of the collector. (1) No of layers n. (2) Heat transfer coefficient between adjacent layers"h". (3)Absorptanceoftheheattransfer fluid a. The sensitivity of thermal performance to these parameters has been examined and the most sensitive parameter was found to be the heat transfer coefficient (h). In comparing this collector with a flat plate collector it is necessary to make the comparison with both collectors operating in the once-through mode. If this is done then to equal the performance of a typical flat plate collector with a selective surface it is necessary to have a five layer collector with an "h" value below 10 W m-2K ~. To achieve this h value with existing materials is not practicable because a thickness of plates separating the layers of over 20 mm would be required. A second collector was examined consisting of two liquid layers separated by an air gap. It was found that at high operating temperatures (TD the thermal performance was inferior to the performance of flat plate collector with a selective absorber. To achieve high outlet temperatures very low flow rates are necessary and the outer layer becomes almost stagnant. Under this condition the outer cover resembles the cover of a flat
plate collector but with a much larger absorptance (22 per cent compared with 8 per cent). This results in higher heat losses. The results of the computer studies have been confirmed by experimental tests on a two layer collector and a fiat plate collector. It was further shown experimentally that an additional cover on a two layer collector does not improve the performance. This study has lead to the conclusion that the multiple layer collector is not a viable proposition.
Acknowledgements--Thanksare given to Dr. W. B. Gillett for many helpful comments and discussions.
a c~ G h hc hB m n r/ "00 r
NOMENCLATURE solar absorptance specific heat, J kg t K-t solar irradiance, W m-2 heat transfer coefficient between a:ijacent layers, Wm-ZK-1 heat transfer coefficientfrom outer cover, W m 2 Kheat transfer coefficient from back and sides of collector, W m-2K mass flow rate, kgs refractive index collectorefficiency collector efficiencyfor mean fluid temperature at ambient solar transmittance
The multiple layer solar collector
T*~ (Tm-T~)/G, KW-~m 2 T~, (Tin- T~)/G, K W -~ m2 T~ (To- T)/G, K W -~ m 2 Tj Tm T~. To Ta U Ue
235
For collectors operating in a once-through mode the inlet temperature will be at or close to ambient temperatures giving T~ = 0. Equation (A2) then becomes:
temperature of jth layer at distance x, K mean fluid temperature, K temperature of fluid at collector inlet, K temperature of fluid at collector outlet, K ambient temperature, K collector loss coefficient, W m - 2 K -1 effective loss coefficient, W m -2 K -1
"o = F"r/o
(A5)
The steady state efficiency is also given by: r/= mco(To- T~)/G
(A6)
when Tin = Ta. Defining T~ = (To - Ta)/G the eqn (A6) becomes REFERENCES
1. Y. Caouris et al., A novel solar collector. Solar Energy 21, 157-160 (1978). 2. J. E. Minardi and H. N. Chuang, Performance of a "Black" liquid flat plate solar collector. Solar Energy 17, 17%184 (1975). 3. P. R. Smith et al., Parametric Studies of the Thermal Trap Hat Plate Collector. A.I.Ch.E. Syrup. Series 73. No. 164, pp. 164-170 (1977). 4. H. C, Hottel and A. Whillier, Evaluation of Hat Platg Collector Performance. Trans. of the Conference on the Use of Solar Energy. 2. Part 1. University of Arizona Press (1958). 5. M. J. Brandemuehl and W. A. Beckman, Transmission of diffuse radiation through CPC and flat plate collector glazings. Solar Energy 24, 511-513 (1980). 6. J. A. Duffle and W. B. Beckman, Solar Energy Thermal Processes. Wiley, New York (1974). 7. A. Rabl and C. E. Nielsen, Solar ponds for space heating, Solar Energy 17, 1(1975). 8. W. B. Gillett et al., Collector Testing Using Solar Simulators. UK-ISES Conference C22 Solar Energy Code of Practices and Test Procedures (1980).
r/= inepT*.
(A7)
By substitution of (A7) into (A4) the flow factor can be expressed in terms of efficiency and reduced outlet temperature (To*).
"11 {.
{ - UT*\\
F" =~-~o~ l - e x p ~ ) ) .
(A8)
Equation (A5) then becomes
( r/= " 0 o \ ~
(
- UT~ 1
(A9)
or re-arranging
UT* r/=
(A10) - l n ( 1 - UT'~" r/o /
A restriction which must be imposed on (A10) is that the thermal mass flow rate must be positive and finite.
APEENDIX 1
~ > rhcp > 0
Performance of a solar collector operating in a once-through mode. Under steady state conditions the thermal performance of
or from (AT)
a solar collector is given by the Hottel-WhiUier equation: ~>r//T*>0 "11= r/o- UT*~
(A1) which leads to the restriction on (A10) that:
If eqn (A1) is assumed to hold for any mass flow rate then two assumptions are implicit: The collector loss coefficient U is independent of fluid temperature. The heat transfer from the absorber to working fluid is independent of mass flow rate, i.e. r/o is constant. Following a method given by DutSe and Beckman[6] (A1) can be rewritten in its T~, form:
r~= F"r/o- F" UT*,
(A2)
where T*, = (T~n- T,)IG
(A3)
mep( F " = - - U-
SE Vo130,No. 3--D
1 - exp
(~.~cpU)) .
(A,t)
oo< - l n ( l - UT*/r/o) > O. This imposes limitations on T* of 0 < T* < ~U which can be interpeted physically as: (1) T~' >0. If T~' = 0 then the outlet temperature is equal to ambient. This is only possible with an infinite flow rate. (2) To*< r/o/U. If the mass flow rate is zero then the collector reaches a stagnation temperature defined by ~o/U. Thus temperatures above "0o/U are impossible to achieve.