cpcs with segmented absorbers

Solar Energ), Vol. 47, No. 4, pp. 269-277. 1991 0038-092X/91 $3.00 + .00 Printed in the U.S.A. Copyright © 1991 Pergamon Press pie

CPCs WITH SEGMENTED ABSORBERS

MAMADOU KIEITA and HARRY S. ROBERTSON Department of Physics, University of Miami, Coral Gables, FL 33124, U.S.A.

Abstract~One of the most promising means of improving the performance of solar thermal collectors is to reduce the energy lost by the hot absorber. One way to do this, not currently part of the technology, is to recognize that since the absorber is usually not irradiated uniformly, it is therefore possible to construct an absorber of thermally isolated segments, circulate the fluid in sequence from low to high irradiance segments, and reduce loss by improving effective concentration. This procedure works even for ideal concentrators, without violating Winston's theorem. Two equivalent CPC collectors with single and segmented absorber were constructed and compared under actual operating conditions. The results showed that the daily thermal etficiency of the collector with segmented absorber is higher (about 13%) than that of the collector with nonsegmented absorber.

!. INTRODUCrlON

The object of concentration, in solar collectors, is to reduce the energy loss rate, which, for a given absorber temperature, is proportional to the area. As Winston has shown [ 1 ] there is a price to be paid for concentration. For a two-dimensional (trough-like) collector, the concentration ratio ~Y is related to the aperture 0,, (half the total acceptance angle) by

e _< 1/sin 0,,,, (1)

and for the three-dimensional collectors, the result is

(~ < 1/sin20m. (2)

The usual CPC troughs, though ideal in the sense that they satisfy the equality of eqn ( 1 ), are less than ideal for two reasons. They reject all radiation outside of the acceptance angle, and the radiation collected within the acceptance cannot be used as efficiently as possible when collected by a single segment absorber. The aim of this work is to show that by using infor- mation about the position of the sun and by segmenting the absorber, it is possible to waste less of the incoming irradiance and thereby to improve collector efficiency at usually high temperatures.

2. TEMPERATURE MEASUREMENT ALONG THE FLOP,' PATH

Strategies for using a system of collectors with different characteristics to optimize energy collection at a specified output temperature have been discussed in a recent article [ 2 ]. One of the results of that study is that maximum efficiency is attained, when output temperature is specified, by heating in a single pass through the collector system. As a corollary, it follows that the high-flow-rate, many-pass heating that is stan- dard procedure in a large part of the solar-fluid-heating community is not merely inefficient, but also precludes the use of any sequential-flow strategy to improve performance, because it circulates already-heated fluid through low irradiance parts of the absorber. In the

following analysis, we assume that heating takes place in a single pass through the collector. We assume, fur- ther, that the collector system is in a steady state, and that there is no heat transfer in the direction of the absorber transverse to the flow path.

The change in temperature per unit length of the i-th absorber segment is given by

rhCpdT~ / dx

= F ' [SWaf - W,,ULfTi(x) - T~)] (3)

where the symbols are defined in the final section of this paper. If we assume that F ' and UL are temperature independent in position, then the solution for the temperature at any position x (subject to the condition that the inlet fluid temperature is T.n) is

S To.,- T o - - - - - f W, tl~

W~ S r , . - r o - m - - f w.,u~

= exp( xWr, ULF' I /

If the collector has a length L in the direction of the flow, then the outlet fluid temperature To,, is found by substituting L for x in Eq. (4). The quantity LW,, = A,, is the area of the i-th absorber element so that

W, S T o . . - T ~ - m - - f W, t ; .

W~ S T, . - Ta f W. t1~

A~ULF' I = exp rhCp ] " (5)

We define the following quantities:

WQ =-----Aa ~i, and --=rn G, kl p,, At, A~

where ~ is the concentration ratio relative to the i-th absorber segment, and G is the mass flow rate per unit

269

270 M. K~ITA and H. S. ROBERTSON

surface area of collector ( k g / s m 2) of the working fluid. Equation (5) becomes

S To~, -- To -- e , -~LLL f

= exp( A~ULF'I ,nC. ] S

Ti. - T. - (g i -~z f

To., = To + 2T, .A + (To~ - T~ - 2T , .A)e -w2

= T~ + 2T.,( 1 - e -w2)

X ( f e -w2 +A) + t~e-',

( ":') = e x p - r n A . co = e x p G(9,C,/" (6)

A° A,~

(10)

where t~ = Ti. - T~. The increase in temperature is found to be

A T = Tout - Tin = 2Tin( 1 - e -'r/2)

×(Ae- ' /2 + A ) - ( 1 - e - ' ) ) t ~ . ( I 1 )

In order to apply these results to a two-segment absorber, we letf t andj~ be the fractions of the captured radiat ion absorbed respectively by the lower-temperature and the higher- temperature sections of the absorber.

We have

ft + A = 1, (7)

and

Wo/W,, = Ao/A,, = 2Ao/A, = 2(9, (8)

where W. = collector aperture width, IV,, = width of the ioth segment, Aa = collector aperture area, A,, = area of the i-th absorber segment, A, = absorber total area, and ~ = collector geometrical concentration ratio. We assume that the absorber has been split into two equal segments, so that A, = 2A,,.

Also let

A,~ULF'_ ULF' z~_ rhC. 2GeC. 2 '

where

UzF' "Y = G ( g G

The intermediate temperature Tot, i.e., the temperature of the fluid as it leaves the first segment and enters the second, is given by

The useful rate of energy collection is given by

Q. = rhCpAT

=rhC.( l -e - ' /2 )[2(9- l~L(A+Ae- ' /2)

- (1 + e-W2)t~]

_ UzF'A~ ( 1 - e-WZ)[2(9 I r ( r a ) e----T- (l -:

+ f t e -~/2) -- (1 + e-'r/2)ti]

ULF'Aa { Iv(rot) = e ~ ' (1 - e -w2) 2 e UL

× [ l - - f l ( l - e-W2)l - (1 + e-W2)ti} g

The efficiency is found to be

G = IrA~

ULF' e 7

(12)

( r a ) - - - ( l - e -w2) 2(9--~--L [ l - f t ( 1

- e - ' / 2 ) ] - ( 1 + e - ' / 2 ) ~r }

= rt(f~, ~, t~/Ir). (13)

For uniform irradiation, (f~ = ~ = ½ ), the useful rate of energy collection becomes

W S To , =

+ T i a - T o W.~U-'~L f exp - rhCp ]

( = T . + 2 0 ~ A + T i . - T o - 2 ( 9 f e -w2

= To + 2Tmf~ + (Ti. - Ta - 2T,,f~)e -'/~, (9)

S where T , . = ( 9 - - .

UL The final temperature To.t is obtaind by using the

intermediate temperature Tot as input:

ULF'Aa ( 1 - e-*/2)[(9 Ir(ra) , e_W2 ) Qu = e----U-

- (1 + e- ' /2) t~]

ULF'A°( l_e - , ) [ (9 Ir(ra) ] - (9--""~"- ~ - - t, . ( 1 4 )

The efficiency in this case will be

7 7 = m Qu UL F'

ITAa e T - - ( 1 - e - ~ ) I e ( r a ) U L ~t']

= rt(% t~/Ir). (15)

CPCs with segmented absorbers 271

The rate of energy collection and the efficiency found in these two equations, for uniform irradiation of the absorbers, are identical to those For unsegmented absorbers, as will be elaborated in the next section.

3. USEFUL HEAT TRANSFER FROM THE I-TH ABSORBER SEGMENT

TO compare the performance of a real collector with the thermodynamic optimum, it is convenient to define the heat-removal factor F~ as the ratio[3-5] of the actual useful gain of the collector to the useful gain if the whole collector surface were at the fluid inlet temperature. From its definition, the useful gain at the minimum temperature difference between the i-th absorber segment and the environment Fs, can be expressed as

The values of Fn, r, a, and F~Ut for each collector must be the values corresponding to the actual fluid flow rate through the pair. By eliminating Tm from these two equations the useful output heat-transfer rate of the combination can be expressed as

Q~.l+2 = [ A , , F ~ , f ( r a ) l ( l - K) + A.2FR2f2(rc~)2llr

- [A.,FR, Uz, ( I - K) +A,~F~U~2](TI . - T . ) ,

(19)

where K = A.~F~, U~,/rhC~. The form ofeqn (19) suggests that an absorber of

two segments is equivalent to a single-segment absorber with the following characteristics:

A~ = A., = A. 2, (20)

F~, m C . ( T<>o, - T i . ) AaS f - At, UUi

(m/&,)Cp(To.,- T~.)

GO~Cp( To~, - T~.)= GO,Cp

@ ~ S f - ULt~ U,

@ S i f ~ - (Tom - Ta)

X I S

e , f -~L - ( T i " - T . )

= UL 1 - exp G~?~Cp]J' (16)

where again the terms are defined in the last section of this paper. The rate of useful heat transfer from the i-th absorber segment can now be expressed in terms of the fluid inlet temperature, or

Q~ = FR, [ S A a f - At, Uz( Ti. - 7".)]

= AaFR~f l r ( ro t ) - Ar~FR, UL( Tin - Ta). (17)

For a two-segment absorber, seen in Fig. 1, the useful rate o f energy output is given by

Qu:+2 = Qu,, + Q..2

= [ A ~ , F R , f i l , ( r a ) , - A . , F R , U z , ( T i . - T.)]

+ [A. ,FRaAL(ra)2

- A,2FR, UL,(To, - T~)], (18)

where Tm = Ti + Q~,/rhCp.

fl f2

Qu.I Qu.2

fl : Fract ion of insolat ion on segment 1 f2 : Fraction o f insolat ion on segment 2

fl + f2 = I and fl <' f2-

Fig. 1. Schematic diagram of two-segment absorber.

F R ( r a ) =

and

FRUL =

A. = A., + A. 2, ( 2 1 )

(1 - K)Ao, FR , ( ra ) IA + A.2FR2(ra)2A aa

(22)

(1 - K)A, ,F~,UL, + A,,FR2UL2

A~ (23)

If the two segments are identical, i.e., A,, = A. 2 = A,, and A,, -- A,~= A , / 2 , then eqns (22) and (23) become

and

F R ( r a ) = FR,(ra)l[( 1 -- K)fl +J2], (24)

,2 , ,

where

Fs, 2eGCp [1 - e - * / 2 ] , UL,F' dl = UL, ~ = ~ G C p ' a n d G = ~ .

The output energy removal rate will be then

Qua+2 = F R ( r a ) A , l r - FRUI_A,ti

= m C , ( l - e - ' / 2 ) { 2 O U - ~ ( f z + f l e - ' / 2 )

- (1 + e-~/2)t i} (26) o

For the case of uniform irradiation, i.e., ft = J2 = ½, we get

Q ~ - - r h C , ( 1 - e - ' ) I d ~ U ~ . - t ' } " t L, (27)

If three or more segments are placed in series, then these equations can be used for the first two segments

272

tO define a new "equivalent first segment." The equations are applied again with this equivalent first segment and with the third segment becoming the second segment. The process can be iterated for as many segmentations as desired.

For N identical segments with non-uniform irradiation in series, repeated applications of eqns (22) and (23) yield

N

FR(ra) = FRt(ra)l ~ fi( 1 -- K) s-i, (28) i - I

and

FRUL = ERr Uz, ~ K)N_i N (1 - (29) i= l

Equations (28) and (29) can be used to compute the useful energy transport rate for any number of segments of the absorber.

Comparison of ideal efficiencies of collectors with and without segmented absorbers is difficult in general because of the number of parameters involved. There- fore, only selected examples will be considered. In the next section, we present experimental results for two far-from-ideal, but essentially identically-constructed examples of CPC collectors, with 2-segment collector designating the one with absorber divided into two equal segments, and 1-segment collector the one with entire, nonsegmented absorber. Accordingly, we denote by subscripts 1 and 2 the corresponding ideal collectors in the following comparisons. It is evident from eqns ( 13 ) and ( 15 ) that the efficiencies are equal when the irradiation is uniform, such that f~ = J~ for the segmented absorber. In the opposite extreme, when all of the incident radiation on the 2-segment collector falls on its segment 2, so thatf~ = 0 andj~ = 1, the maximum ideal advantage in absorber segmentation becomes evident. In order to simplify comparisons, we choose the input and ambient temperatures equal, so that t~ = 0. The most meaningful comparisons can be made by choosing equal output temperatures, and therefore different flow rates if the efficiencies are different.

From eqn ( I ! ), with ti = 0, the temperature rise in the 2-segment collector is found to be

AT2 = 2T,,( 1 - e-*a2)(J~ +f,e-~2/2),

where the subscript on 3' is necessary because 3'~ = A~ULF'/rh~eCp, and the th~ may be different for the two collectors. The corresponding result for the l- segment collector is found by setting f, = ]~ = ½ in the equation above, to get

ATI = T,,( 1 - e -~').

Evidently, under these conditions, the ratio of collector efficiencies is simply the ratio of the mass flow rates. or

,/~ = __rh2 = __3"~ (30) rh rht 3'2 '

M. KI~ITA and H. S. ROBERTSON

where the 7's can be determined by setting the temperatures equal. Table l shows the efficiency ratio in terms of the two parameters, AT~ Tm (the ratio of temperature rise to the stagnation temperature of the 1- segment collector), andf~ (the fraction of the radiation absorbed by the input segment of the absorber in the 2-segment collector). These results are universal, in that they are independent of concentration or other collector parameters for identically-constructed collectors.

Table l shows explicitly that for operation at temperature rises that approach the theoretical maximum for the single-absorber collector, there is a significant advantage in the segmented-absorber geometry. The application of these results to the design of a collector system requires determination of the operating conditions and construction costs of the various options.

4. EXPERIMENTAL PROCEDURES

In the proof-of-concept study, the procedure was to construct and compare, under actual operating conditions, two equivalent CPC collectors with single and segmented absorber [ 6 ]. The collector with segmented absorber is called 2-segment collector, and the one with single absorber is called 1-segment collector. The object of this study was to seek experimental verification that segmenting the absorber and establishing a proper flow sequence lead to a significant improvement factor in collector operation. Since the improvement in technology' based on segmented absorbers should be compoundable with other advances, it was not deemed necessary at this stage and budget level to strive for temperature records.

The two collectors under comparison were mounted side-by-side on the roof of the Physics Department re- search laboratory building. The principal characteristics of the collectors are • a gross length of 2 m, a gross width of 0.50 m, and

a gross depth of 0.30 m; • a geometric concentration factor of 2, i.e., an aperture

width of 20.32 cm for an absorber width of 10.16 cm. Let us recall here that the absorber of the 2-

Table I. Ideal efficiency ratios of segmented to single-piece absorbers for specified fractions jq of incoming irradiance

falling on the input absorber segment, and for temperature rise ATas a fraction of the maximum possible rise T,, for

an unsegmented absorber

AT/T~ f~=O.O 0.1 0.2 0.3 0.4 0.5 0.00 1.000 1.000 1.000 1.000 1.000 1.000

0.i0 1.027 1.022 1.016 1.011 1.006 1.000

0.20 1.059 1.048 1.036 1.024 1.012 1.000

0.30 1.097 1.079 1.060 1.041 1.021 1.000

0.40 1.145 1.118 1.091 1.062 1.032 1.000

0.50 1.205 1.169 1.131 1.091 1.047 1.000

0.60 1.284 1.237 1.185 1.130 1.069 1.000

0.70 1.397 1.334 1.265 1.189 1.102 1.000

0.80 1.575 1.489 1.395 1.287 1.161 1.000

0.90 1.926 1.801 1.661 1.498 1.296 1.000

0.95 2.325 2.101 1.976 1.757 1.476 1.000


segment collector is split longitudinally into two

equal segments, while that of I-segment collector is left intact:

• an angular acceptance (full angle) of 60 ° for direct sunlight collection o f 4 hours, i.e., approximately from l0 a.m. to 2 p.m. Figure 2 shows the profiles of the 2-segment and l-

segment collectors. It is worth ment ioning that full

CPC's are rather deep. This major drawback can be alleviated by truncation which will greatly reduce costs. Rabl has shown that a 50% truncat ion causes a con- centrat ion ratio reduct ion o f only 10% while reducing the average number of reflections by about 20%. Figure

3 shows the path of water for both collectors. The gap

between segments in the 2-segment collector is exaggerated for clarity.

The collectors, with a single cover glass, a copper plate painted black as absorber, and reflective surfaces made of polished sheet a luminum, were moun ted on a tilted platform oriented no r th - sou th for the purpose of this experiment . The tilt angle was about 26 ° which is the latitude o f Miami. In the normal eas t -west ori- entat ion, the flow reversal, which is function of the

nonuni form distribution ofirradiance on the absorbers,

might be seasonal, rather than daily. Flow reversal, in that case, is not often needed, and with occasional ad-

jus tmen t of the tilt angle, flow reversal can be elimi-

nated entirely. The irradiance was moni to red by two Eppley pyr-

anometers with the following geometries: the first was in the horizontal plane, and the second in the tilted collector plane, and by two photovoltaic cells mounted

on segmented absorbers of a similar miniature CPC (o f ratio 3.2). They were calibrated against a radi- ometer, so that we could record absolute instantaneous irradiances as well.

a) 2-segment collector

/ b) l-segment collector

Fig. 2. Collector profiles, showing an exaggerated separation of the two absorber segments in 2-segment collector.

In

a) 2-segment collector

Out

In

b) l-segment collector

Fig. 3. Flow paths through the collectors. The shaded areas on the absorbers are those of relatively low irradiance.

The photovoltaic cells are to permit compar ison of

local irradiances, particularly in selecting the flow path for 2-segment collector. Other guides to selection of

the flow path are ray tracing, with results in Table 2 and Fig. 4 and a sketch of the distribution of the incident i l lumination of the absorbers made every 15 minutes as shown in Fig. 5. Table 2 gives some results

Table 2. Distribution of radiation on the two absorber segments as determined by ray tracing of 41 equally spaced

parallel rays, for incidence angles between 0 ° and 30 °

Time Theta Left Segment Right Segment 10:00 AM 30.00 0 0.00 % 41 100.00 % 10:05 28.75 3 7.32 38 92.68 10:10 27.50 4 9.76 37 90.24 10:15 26.25 6 14.63 35 85.37 10:20 25.00 8 19.51 33 80.49 10:25 23.75 10 24.39 31 75.61 10:30 22.50 12 29.27 29 70.73 10:35 21.25 14 34.15 27 65.85 10:40 20.00 19 46.34 22 53.66 10:45 18.75 24 58.54 17 41.46 10:50 17.50 29 70.73 12 29.27 10:55 16.25 36 87.80 5 12.20 11:00 15.00 34 82.93 7 17.07 11:05 13.75 33 80.49 8 19.51 11:10 12.50 32 78.05 9 21.95 11:15 11.25 31 75.61 10 24.39 11:20 10.00 30 73.17 11 26.83 11:25 8.75 28 68.29 13 31.71 11:30 7.50 27 65.85 14 34.15 11:35 6.25 26 63.41 15 36.59 11:40 5.00 25 60.98 16 39.02 11:45 3.75 24 58.54 17 41.46 11:50 2.50 23 56.10 18 43.90 11:55 1.25 22 53.66 19 46.34 12:00 PM 0.00 21 51.22 20 48.78

274 M. KI~ITA and H.

' ' ' I ' ' ' [ ' ' ' I ' ' '

11, 12. 13. SOLAR TIME

Fig. 4. Plot from the ray-tracing data of Table 2. showing the percentage of irradiation on one of the segments vs. solar time.

S. R O B E R T S O N

abou t the nonun i fo rmi ty of the dis t r ibut ion of irra- d iance to the absorber segments. For example, the ray t racing of 41 incident equally-spaced parallel rays through the CPC at 10:30 gives the following irradiance distr ibut ion on the segmented absorber: 12 rays or 29% on the left segment and 29 rays or 71% on the right segment . This means that the left segment , the one tha t is receiving less insolation, has an optical concen- t ra t ion rat io of

~',,~ = 2 . 6 0 . 0 . 2 9 = 0.586 °, (31)

and the right segment , the one receiving more insolation, has an optical concen t ra t ion ratio of

~'ng,t = 2 . 6 0 . 0 . 7 1 = 1.4260. (32)

10:(30 10:i5

!1:00 11:i5

/ / / i 12:00

13:01)

14:01)

Reverse 12:i5

|

Reverse 13:15

Key for Irradiation

lj 10:30

10:30

12:30

13:30

Reverse 10:45

I 1 : 4 5

12:45

13:45

Fig. 5. Sketch of the distribution of the incident insolation on the absorbers of the collectors.

CPCs with segmented absorbers

Equations (31) and (32), in which, 2 represents the number of segmentations, lead to the following inter- esting result:

~'l~a < ~ < ~ ' . g . , . ( 3 3 )

Since there is no useful gain in circulating already- heated fluid through the low-irradiance part of the absorber, the fluid in its sequential single-pass flow will first pass through the part receiving less insolation (the left segment ) for preheating, and then through the part receiving more insolation (the right segment) for final heating. Therefore the result of the ray tracing can give us an idea about the direction of the path of the working fluid, as can be seen in Table 2. Figure 4 is an extended plot (from 10 a.m. to 2 p.m. instead of 10 a.m. to 12 noon) from Table 2.

Figure 4 shows that the flow has to be reversed three times a day, namely, approximately at 10:40 a.m., 12 noon, and 1:20 p.m., instead of once a day ( 12 noon) as anticipated. (As already noted, in the normal east- west orientation, these reversals might be seasonal, rather than daily.) When the percentage of incident radiation falling on the right-hand segment is greater than 50, the working fluid enters the left segment first and exits the right segment, and when the percentage is less than 50, the flow is from the right segment to the left. Note that the preceding optical analysis was based on idealized optics in that the sun was assumed to be a point source and the reflectors assumed to be perfect parabolas. In practice, surface imperfections and diffuse radiation must also be considered. Still, the results from the ray tracing are in good agreement with those from the sketch of the incident insolation on the absorbers.

Since the collectors to be compared, placed side- by-side, were equivalent except for the segmentation of the absorber in 2-segment collector, we assumed that they experience the same wind losses; therefore, we did not record wind speed, because it was not needed for simple comparisons. The input, output, and air temperatures, as well as intermediate temperature of the 2-segment collector, were monitored by use of thermistors. All these data were recorded every five minutes on a single chart by means of an Apple-Straw- berry microcomputer-based laboratory data acquisition and control system, except for the flow, which was physically measured every four minutes for the low flow range, and every two minutes for the high flow range. The collectors were tested under sunny and partly cloudy days, from 9:30 a.m. to 4:30 p.m., using mainly low flow rate (~0 .15 l / r a in ) but also on oc- casion high flow rate ( ~0 .50 l /m in ) .

The water, used as working fluid in this experiment, was heated in a single pass through the collectors, a procedure that offers the highest theoretical efficiency under most circumstances [ 2 ]. More complex strategies, such as preheating in the early morning and re- heating to temperature near midday, could improve overall efficiency of a total solar energy system, but

275

this initial study seeks to compare collector ef~ciencies, not overall strategies of operation.

5. E X P E R I M E N T A L R E S U L T S A N D D I S C U S S I O N

Different daily irradiance profiles are shown in Figs. 6-8. The flow rates were not constant, but varied over a small range, as shown by a typical high flow rate plotted in Figure 9. Figures 10-12 show respectively the instantaneous thermal efficiencies obtained for a low flow rate, (~0 .15 l /min ) , an intermediate flow rate, and a higher flow rate, (--~0.5 l / ra in) . Table 3 shows daily thermal efficiencies of the collectors. At low flow rates, there are higher losses because of the higher temperature outputs that result from longer heating times, and efficiency is sensitive to loss rate. As predicted, the 2-segment collector performs better (about 13%) than the l-segment collector in this re- gime, since the combination of its segmented absorber and the proper flow path with respect the nonuniform irradiation reduces losses by improving effective concentration. However, we expected the 2-segment collector to l-segment collector efficiency ratio to vary from 1, for uniform i!lumination, to 1.3 or 1.5, i.e., 30 to 50% for relatively small flow rates. In the limit of the rate approaching zero, the efficiency ratio becomes a maximum of 2 f o r f = 0 ( if the flow rate is the same in the two collectors).

It is worth mentioning that the collector temperatures are sensitive to the reverse of the flow because of the mixing of the cold and hot water. But this is only for the short period of time, usually the time for one reading as shown in Figs. 6 and 7. For the low (high) flow range, the difference in output and input temperatures is reduced (increased) abruptly during the flow-reversal period, resulting in a sharp drop (rise) in apparent efficiency, but this result is spurious because the transient behavior during flow reversal does not approximate steady flow.

For the high flow range, with input temperatures near ambient, we expected both collectors to yield the same higher efficiency, because there was little change in temperature along the flow path and the losses are

DATA OF W-r.DNESDAY, 17 FEBRUARY 1988 I I I I I

1000

800.

600.

, I , I , I , I , I , 10. 1L 12. 13. 14.

L O C A L T I M E

Fig. 6. Plots of the daily irradiance profiles.

276

N

Z

M. KI~ITA and H. S. ROBERTSON

t000

~ 0

600.

~0 .

DATA OF TUESDAY, 15 MARCH 1988

t I I I I

I , I , I , I , I , 10. 11. 12. 13. 14.

L O C A L "I'IME

Fig. 7. Plots of the daily irradiance profiles.

0.062

0,06(

~ I).11'32

II.C49

DATA OF WEDNESDAY, 23 MARCH 1988

1 I L ~ I

2-SEGMENT

, , I , I , I , I 10 11 12 13 14

TIME

Fig. 9. Plot of the instantaneous flow rates.

so small that segmenting the absorber should make little difference. We were surprised to see that the 2- segment collector still performed somewhat better than the l-segment collector. To confirm this unexpected result, we took data at very high flow, ( ~ 3 I /min) with similar outcome. One of the reasons for that seems to be that in 2-segment collector (the segmented one), since the width of each absorber segment is smaller than the full width of the absorber in l-segment collector, heat is transferred more efficiently from the plate to the working fluid than in 1-segment collector. How- ever, numerical estimates indicate that the part of the difference in collector efficiencies attributable to the fin efficiencies is very small.

6. CONCLUSION AND RECOMMENDATIONS

The combination of the segmentation (decreasing the area of the absorber at high temperature) and the proper flow path of the working fluid (from low to high irradiance) indeed increased the performance of concentrating collectors, which undeniably exhibited nonuniform irradiance distribution on the absorber. The results of our experiments showed that the segmented CPC performed better than the non-segmented one at low flow rate, under clear and partly cloudy skies, and surprisingly even at high flow rate.

This performance can be enhanced by more seg-

mentation, since the process is compoundable, and formulae in Section 3 dealing with the temperature measurement along the flow path should be tested. It should be noted, however, that a disadvantage of any segmentation can be the small loss in absorber area as a result of the space needed to provide thermal separation of the segments. This disadvantage can be over- come by proper design of the absorber. Even so, segmented absorbers with gaps between the segments will allow a small fraction of the radiation to pass through the gaps and be absorbed by other parts of the collector. But since the energy is misplaced within the collector, rather than lost, the fractional degradation should not be as large as the fractional loss in absorber area implies.

Some other factors exist that will tend to degrade the performance of segmented-absorber collectors be- low ideal expectations. These all involve practical considerations, several of which are common to most collectors[7]. First, reflection losses reduce the beam irradiance falling on the absorber. The radiation that is not reflected is nevertheless not all lost, since it is absorbed by the reflectors and mostly transferred to the air, where it reduces the convective losses from the absorber. The magnitude of this effect is not easy to calculate, but it is expected, for example, that a 90% reflectivity will not cause as much as a 10% degradation in collector performance.

Second, the radiation will sometimes strike the ab-

DATA OF WEDNESDAY, 23 MARCH 1988

I

A

600.

., J J I 10.

DATA OF WEDNESDAY, 17 FEBRUARy 1988 I I I I [ I

g -

1. MFA~

[ , I , I , [ , I I [ I1. 12. 13. 14. 10 I | 12 $3 14

T I M E TIME

Fig. 8. Plots of the daily irradiance profiles. Fig. 10. Plots of the instantaneous thermal efhciencies.


u E m

87

69. I

51

33

15 i

DATA OF TUESDAY. 15 M A R C H 1988

I

10 I1

I

2-SEGMENT

I , I , I , 12 13 14

T I M E

Fig. 11. Plots of the instantaneous thermal efficiencies.

sorber at large angles of incidence, resulting in poor absorption and higher-than-optimum reflection losses. This problem arises in almost all collectors to some extent, and it is not expected to be any worse for segmented-absorber collectors than for others. But it could affect the compounding of improvements. Again, as for any type of collector, use of selective coatings good for all angles of incidence should help.

Third, there will be heat transfer between the absorber segments, resulting in effects that have not been treated in our calculations. It is evident, nevertheless, that in the limit of perfect thermal contact between segments, the performance should degrade to that of an unsegmented absorber, so we expect the de facto poor thermal contact to result in only minimal reduc- tion of the expected improvement in efficiency.

By careful engineering analysis, the conflicting design criteria of minimum gaps between segments and good the rma l isolation can be resolved, and the flow- reversal procedure can be revised to min imize the small t rans ien t losses tha t occur when al ready-heated fluid in the col lector is sent back th rough the absorbers.

Finally, it should be no ted tha t a large array o f seg- men ted -abso rbe r collectors can be control led by a single m o n i t o r system, so tha t the flow direct ions in the individual collectors can be reversed s imul taneous ly when required by the changing i r radia t ion pat tern.

Table 3. Collectors daily thermal efficiencies

Flow ~i I"12 ~2/171

I/n-fin % %

0.15 37.06 41.92 1.13

0.50 49.00 59.60 1.22

3.00 49.46 62.69 1.27

NOMENCLATURE

Aa area of collector aperture, m 2 A,, area of i-th absorber segment, m 2 Cp specific heat capacity of fluid, J /kg *C tY concentration ratio

e i cone. ratio for i-th absorber segment ( =Aa/A,, ) Ei~: incident energy on collector planes ( =f[.'0 ~°" 1A dt) J E,~ energy absorbed by collector (=f~'.'o 3°°~ KnCp(To,1

- T~.)dt) J FR heat-removal factor

FR, heat-removal factor for i-th segment F ' collector efficiency factor ( =Uo/UL ~ 1 ) f fraction of entrant radiation incident on i-th absorber

segment G mass flow rate per unit surface area of aperture ( = m /

Ao), kg/s m2 lr incident solar irradiance, W / m : K heat removal number for segment 2 (=A,~F,~UL2/

me.) Q. rate ofenergy removal by fluid ( =mCp( To., - Ti.)). W Q., rate of energy removal by fluid from i-th segment, W

S total absorbed solar power per unit area of aperture (both beam and diffuse) ( = c a l f ) . W / m 2

To ambient temperature, °C T,, fluid input temperature, °C

To,, fluid exit temperature, °C Toi fluid exit temperature for i-th segment, °C

t~ relative input temperature (=T~, - To), °C UL heat transfer coefficient from collector to ambient air,

W/m: °C Uo heat transfer coefficient from fluid to ambient air, W/

m 2 ° C W~ width of collector aperture, m IV,, width of the i-th absorber segment

Greek a solar absorptance of the absorber plate 3' dimensionless constant (=ULF' /G~Cp)

AT temperature rise of fluid passing through collector, °C collector efficiency ( = Q J l r A , )

n~ efficiency of nonsegmented-absorber collector ( l-segment collector)

n2 efficiency of segmented-absorber collector (2-segment collector)

~'~ optical concentration ratio of i-th segment (=2C9f,) ¢ solar transmittance of collector cover

Z 50.

u

40.

D A T A O F W E D N E S D A Y , 23 M A R C H 1988

I I I I 2-SEGMENT

I , I , I , 10 II 12 13. 14.

S T A N D A R D T I M E

Fig. 12. Plots of the instantaneous thermal efficiencies.

R E F E R E N C E S

1. R. Winston, Light collection within the framework of geometrical optics, J. Opt. Soc. Am. 60, 245-247 (1970).

2. H. S. Robertson and R. P. Patera, Collection of solar energy at specified output temperuatre, Solar Energy 29, 331-337 (1982).

3. J. A. Duffle and W. A. Beckman, Solar engineering o/ thermal processes, Wiley, New York, ( 1980 ).

4. C. K. Hsieh, Thermal analysis of CPC collectors, Solar Energy 27, 19-29 ( 1981 ).

5. J. F. Kreider and F. Kreith, Principles of solar engineering, McGraw-Hill, New York, (1978).

6. M. Krita, Study of segmented absorbers of thermal solar compounds parabolic concentrators, Univ. of Miami, PhD Thesis ( 1988 ).

7. A. Rabl, N. B. Goodman, and R. Winston, Practical design considerations for CPC solar collectors, Solar Energy 22, 373-381 (1979).

cpcs with segmented absorbers

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