Stationary reflector-augmented flat-plate collectors

SolarEnergy.Vol.29,No.1,pp. 65--69,1982 PrintedinGreatBritain.

0038-092X/82/070065-.05503.00/0 © 1982PergamonPressLtd.

STATIONARY REFLECTOR-AUGMENTED FLAT-PLATE COLLECTORS H. F. CHIAM Division of EnergyTechnology,CommonwealthScientificand Industrial Research Organization,Higbett, Victoria 3190, Australia (Received 23 March 1981; revision accepted 2 June 1981)

Abstract--A general procedure for determining the optimum geometry of a reflector-augmentedsolar collector which produces a desired pattern of flux-augmentation is described. The example used for illustration is a stationary collectorwhose winter performanceis to be improved.Considerationof both a flat-plate collectorwith a bottom reflector and one with a top reflector led to distinct differences in their optimum configuration and performance being identified. Since either systems can be used to augmentwinter flux, a criterion for selectingthe appropriate system is given. This criterion is based on the displacement in collectortilt from latitude inclination. INTRODUCTION

The addition of a planar reflector to a flat-plate collector is often seen as an inexpensive means of increasing the solar energy collected per unit area of absorber. Whilst results presented in the literature are in general agreement that reflectors are beneficial, it is difficult to conclude which is the optimum configuration from the range analyzed. Take as an example the configurations suggested for boosted winter collection. They include the near horizontal reflector positioned below the receiver[l,2], and the alternative reflector-abovereceiver combination with the receiver tilted either above latitude inclination[3], or closer to the ground[4]. Although the reflector-above- and reflector-below-receiver systems have not been studied together, Larson[5] has suggested that their optimum geometries are symmetrical because of the analytical equivalence of the two systems. A reflector attached above the receiver is referred to in the current work as the top reflector, and the one below the receiver as the bottom reflector. Both reflector sys-

terns were thoroughly investigated, and significant differences in their performance were found. The performance characteristics have been summarized in a convenient graphical form[6]. It will be shown in this paper, by referring to a potential space heating application, that the appropriate system and system parameters can readily be determined with the performance curves. The resulting optimization of a stationary reflector-augmented collector also allows a rationalisation of geometries reported in the literature. ANALYSIS The planar reflector-receiver system studied (Fig. 1) consists of a specular reflector with an overhang of length L~, width WR, and positioned at an angle ~ to the plane of the cover of the receiver. The receiver has a length Lc, width We, and is tilted at an angle//to face the equator. A vectorial analysis is used to ray-trace the reflected beam irradiating the cover of the receiver. A detailed

REFLECTOR

RECEIVER

Lc Fig. I. Reflector-receivergeometry. 65

H. F. CreAM

66

width ratio, the reflector angle (relative to the plane of the cover), and the angle through which the collector is tilted from latitude inclination (Fig. 2). There is, for a given reflector width and collector tilt, an optimum reflector angular position. This optimum in the case where edge losses have been minimized, occurs when the reflected solar bean irradiance is fully utilized at noon. The optimum reflector positions approach the perpendicular to the collector cover as the reflector width is increased (dashed line), while the reflector must be repositioned to accommodate the changed solar-collector geometry as the collector tilt is altered (dotted line). The index of performance, Area Ratio, depends only on the geometrical relationship between the reflector, receiver, and the sun. Consequently, the curves shown for the bottom reflector configuration are equally applicable to the alternative top reflector arrangement for days on the other side of the equinox when the sun occupies the same relative position to the collector. For example, the bottom reflector curve of a collector at latitude tilt on 22 December is the same as the top reflector curve on 22 June, and vice versa.

description of the optical model involved is presented in [6]. The basic model which considers irradiance on the cover is used here. The extended model requires the radiative characteristics of the collector cover system to be specified. An index of performance, the Area Ratio, is used to evaluate the merits of mounting a reflector to a receiver which is at a tilt /~. It is defined as the ratio of the projected area of cover irradiated by the reflected bean to the projected area of cover under direct solar irradiation. (The projected area is given by the product [area illuminated] x [cosine of the angle of incidence].) A daily averaged value is used, and is derived by summing hourly values between 0800 and 1600 solar time. The index provides a measure of the additional effective receiver area which would have to be supplied to replace the reflector. RESULTS AND DISCUSSION

The computer simulation is based on the collection of beam irradiance over an 8-hr day. Clear sky radiation data are taken from [7], which gives hourly values for selected days at monthly intervals from the equinox. Whilst the solar data is specific for Melbourne, Australia (~b = 38°S), the performance characteristics obtained are, however, of a general nature and independent of locality. The performance curves have been generated using one receiver size (Lc/Wc = 2.5), and a reflector overhang (LR/Wc = 1.0) which minimizes end-losses. Provided that the overhang is similarly chosen, the curves can be applied to other receiver sizes [6]. (End-losses occur during the collection period unless the reflector length is sufficient to ensure that the reflected beam completely illuminates the cover.) However, the dimensions selected for the current work are the same as those used previously to generate the performance curves.

Configurationfor winterenhancement A top reflector is more effective in winter when the collector is tilted at the latitude angle (e = 0), but the collector should be tilted towards a more vertical inclination (e > 0) if a bottom reflector is used instead (Fig. 2). This suggests that should the two reflectors be utilized together to give a trough concentrator, then both cannot be optimized simultaneously for winter performance. It is desirable when selecting the geometry of a single reflector-receiver system, that the additional amount of solar energy received be known. An enhancementfactor may be defined by comparing the daily energy received by a solar flux-angmented collector at a given tilt,//, with that by a conventional flat-plate collector fixed at latitude tilt. Whilst the performance characteristics of the reflector-receiver system could equally have been evaluated by using either the enhancement factor or

Performance characteristics The principal parameters affecting the performance of a reflector-augmented collector are the reflector/cover

j

1.0 0,81

'

0.6I

"

,

,

MAR 21 or SEP 22

0 ~.~.

._J

~ : / ~ : o2-s L ~ / ~ :1.o

1.o

..--''".

L_ --

wR/Wc 1-0

c 0

1-0 1.5

25 0

.......

0,8

1

~ 0-4 ~

~

,o

5~

6~

?b

~

TOP REFLECTOR ANGLE

..j"

22

I L go 9o

i 80 BOTTOM

i 70

">.1 , 60

, "'" 50

REFLECTOR ANGLE

Fig. 2. Performancecurves for planar reflector-receivercombinations.

] 40

Stationary reflector-augmentedflat-platecollectors Area Ratio[6], the properties of the reflector must, however, be specified before the value of the enhancement factor can be determined, unlike the more general but less familiar Area Ratio. Accordingly, a specular reflectance of 0.8 has been assumed. Although the effect of weathering and dust is generally not known, some effect is allowed for by reducing the reflectance to a value below that for clean reflector materials. The enhancement factor is particularly useful for indicating the period of year over which the reflector provides meaningful flux-augmentation. The enhancement values presented in Table I illustrate the effect of reflector angle at a number of collector tilt angles. Winter collection can be improved markedly with a top reflector for a receiver tilted at around the latitude angle. The top reflector should be positioned as close as possible to its optimum angle at winter solstice on 22 June, because the degradation in performance at an off-optimum angle in June exceeds the gain near the equinox. This effect can clearly be seen in Fig. 2. Summer rather than winter enhancement results from the addition of a bottom reflector to a receiver at latitude tilt [6]. However, preferential winter enhancement can be produced by displacing the receiver towards a more

67

vertical tilt, since the winter solar rays now strike the cover at smaller angles of incidence which increases their effectiveness. Unlike the top reflector, a bottom reflector benefits from an off-optimum position at the winter solstice, as its improved performance at the equinox is off-set by a relatively smaller loss over the solstice period (Table 1). The more consistent enhancement values during the 2 months on either side of the winter solstice is noted. Use of the performance curves has thus yielded a criterion for selecting the reflector-above- or reflectorbelow-receiver system for winter enhancement, namely the collector tilt. The top reflector when positioned at its optimum winter configuration, and the receiver fixed at latitude tilt, produces the best overall seasonal performance. The bottom reflector can, however, be angled to give similar overall results over a wide range of off-latitude collector tilt angles, thus offering a choice of winter configurations. The limiting case is obviously a vertical receiver, which for Melbourne's latitude of 38°S, requires an off-latitude displacement of 52°. Placing constraints on the bottom reflector's position provides a means of resolving the extent the receiver is to be displaced from latitude inclination. A reflector tilt

Table 1. Effect of reflectorangle on seasonal solar beam enhancement(Lc[Wc= 2.5, Ls/Wc= 1.0, WRIWc= 1.0, p = 0.8, ~ = 38°S) ENHANCEMENT FACTOR Collector tilt, flo

Reflector angle, ~o

Mar 21 (Sep 22)

Apr 22 (Aug 22)

May 22 (Jul 22)

Jun 22

TOP REFLECTOR 38 (c=o °)

48

75*

1.20

1.40

1.50

1.49

70

1.27

1.44

1.39

1.35

70*

1.12

1.37

1.51

1.54

65

1.19

1.42

1.44

1.42

60*

0.97

1.29

1.48

1.53

65

1.11

1.41

1.48

1.47

70

1.24

1.43

1.41

1.40

70*

0.89

1.28

1.51

1.57

75

1.03

1.39

1.50

1.52

80

1.16

1.41

1.44

1.45

75*

0.78

1.19

1.46

1.54

80

0.91

1.30

1.50

1.53

85

1.03

1.37

1.44

1.46

(~=10 °)

BOTTOM REFLECTOR 63 (~=25 °)

78 (~=40 °)

88 (~=50 °)

*

Value at, or nearest to the optimum angle.

68

H. F. CHIAM

may be defined as the angle the reflector makes with the horizontal, It is calculated by subtracting the bottom reflector angle, ¢, from the collector tilt, /~, so that a positive value signifies a reflector inclined below the horizontal and facing the equator. Table 1 shows that the pattern of winter enhancement at a given collector tilt is affected significantly by whether the bottom reflector (of unity WR/Wc) is to be positioned above or below the horizontal. The winter enhancement results are, however, less sensitive to the collector tilt, as can be seen from the values corresponding to a bottom reflector tilt of 30 in the first, second, and third row of the results for ~ = 25, 40, and 500 respectively. It follows that this near horizontal reflector may be combined with a vertical receiver to boost winter collection between 65 and 400 latitude. That is, the near horizontal reflector/vertical receiver arrangement may be adopted over a range of latitude. The optimum bottom reflector configuration evaluated by Rudloff et al. [1] specifically for space heating has the angular values, using the nomenclature in this paper, of ~=25 °, ¢=70 °. This configuration has also been obtained using performance curves (Table 1). Whereas transmission losses caused by the cover system were considered by Rudloff et al., the performance curves have been derived from solar beam irradiance on the cover. Furthermore, the configurations found in [2, 3], in which solar transmittance was also considered, can readily be shown to be consistent with that obtainable with the approach used here. It is reasonable therefore to suggest that the performance curves can be applied to

the determination of optimum configuration, in particular when near normal reflector angles are involved. A stationary reflector cannot provide useful enhancement of solar beam energy on a year-round basis because of the wide separation of the optimum reflector angles. Provision must be made for adjusting of the reflector angle if flux-augmentation is required throughout the year. However, a stationary augmented collector may be well suited to domestic solar hot water systems since augmentation can be restricted to the cooler months of the year without adversely affecting summer performance. Its optimum geometry can, as in the space heating application, be determined directly from performance curves. A comprehensive set of curves has been presented in [6]. Listed in Section A of Table 2 are some configurations obtained by tilting the receiver to face the winter sun and attaching a bottom reflector to compensate for the reduced effective cover area under direct irradiation in summer. The relatively small influence of the collector tilt on the overall performance is again evident. Comparing Sections A and B reveals that the benefits of increasing the reflector/cover width (WR/Wc) ratio beyond unity is restricted to a fairly short period of the year. It has been suggested that the optimum orientation of reflector and receiver can be determined from an analysis of either the bottom or top reflector system [5], since the two systems have previously been shown to be analytically equivalent[3]. Caution must however be exercised in applying the optimum bottom reflector configuration to the alternative top reflector system.

Table 2. Performanceof stationary reflector-augmentedflat-platecollector in Melbourne(Lc/Wc= 2.5, LR/Wc 1.0, p 0.8, ~b 38°S) =

No.

A.

Off-latitude displacement eo

Reflector angle ~o

Bottom reflector,

=

=

ENHANCEMENT FACTOR Dec 22

Jan 22 (Nov 22)

Feb 22 (Oct 22)

Mar 21 (Sep 22)

Apr 22 (Aug 22)

May 22 (Jul 22)

J u n 22

WR/W C = 1.0

A1

I0

65

0.94

1.01

1.18

1.37

1.32

1.23

1.20

A2

25

80

0.95

1.04

1.24

1.36

1.31

1.26

1.25

A3

40

95

0.91

1.00

1.20

1.22

1.22

1.22

1.22

A4

14

69

0.95

1.02

1.21

1.41

1.32

1.24

-1.22

B.

Bottom reflector, WR/W c = 1.5

BI

I0

65

0.94

1.01

1.18

1.37

1.46

].32

1.26

B2

25

80

0.95

1.04

1.24

1.45

1.44

1.34

i .31

C.

Top reflector, WR/W C = 1.0

C1

-25

95

0.98

1.02

1.10

1.18

1.26

1.31

1.31

C2

-15

85

0.95

1.01

1.13

1.24

1.36

1.41

1.39

C3

0

65

0.94

1.02

1.17

1.33

1.35

1.24

1.20

C4

-14

69

1.21

1.24

1.33

1.41

1.18

1.02

0.96

Stationary reflector-augmented flat-plate collectors

69

Table 3. Effect of reflector overhang on seasonal solar beam enhancement (WR/Wc= 1.0, top reflector angle, ~=75°,p=0.8,~=~) ENHANCEMENT FACTOR

Collector length,

Reflector overhang

Lc/Wc

I~/W R

Har 21 (Sep 22)

Apr 22 (Aug 22)

Hay 22 ( J u l 22)

3un 22

0

1.14

1.27

1.34

1.35

0.5

1.19

1.36

1.46

1.46

1.0

1.20

1.39

1.49

1.49

0

1.19

1.37

1.47

1.46

0.5

1.20

1.39

1.49

1.48

1.0

1.21

1.40

1.50

1.49

1.0

5.0

Consider the bottom reflector configuration No. A4 (e = + 14°) recommended by Larson[5] as the optimum for year-round collection with unity width (W~I Wc) ratio, and the corresponding configuration No. C4 (e = - 14p) for the top reflector. While the yearly averaged enhancement is similar, the latter configuration produces higher flux-augmentation in summer because its receiver is tilted towards the summer sun. This contrasts with the preferential winter enhancement for the former configuration. However, the top reflector can be positioned to redirect more winter irradiation on to the cover, as indicated by configurations No. C1-C3. These values were derived by inspecting the bottom reflector curves at e > 0 over the summer-equinox period, since these performance curves are similar to those for the top reflector at e < 0 over the equinox-winter period [6]. Configuration No. CI is nearly the same as that recommended by Espy[4/ for maximum winter collection (namely, WR/Wc = 0.93, ~ = 90°, e = - 23.5°), but its performance in winter is inferior compared with that obtained with a bottom reflector at e = + 250 (Table 1). This can also be seen graphically [6], as the peak at 22 June, e = +25° is larger than that at e = - 25° (approximated by 22 December, e = + 25°). The simplicity and usefulness of the performance curve approach is again illustrated. The need to minimize end-effects is emphasized by the results shown in Table 3. A short reflector overhang is desirable for use with square receivers, although the overhang may possibly be dispensed with in an array of such receivers. CONCLUSION

The performance .curves can readily be used to determine whether a reflector should be mounted above or below a flat-plate solar collector. To obtain winter only enhancement, a top reflector should be used if the receiver is maintained at latitude tilt, but a bottom reflector is preferred if the receiver is in a more vertical position. An additional advantage of the bottom reflector

configuration is the greater flexibility in the selection of collector tilt. A top reflector can, however, be used with a receiver tilted closer to the ground, but this configuration produces a lower maximum winter flux-augmentation. It is suited more to solar hot water systems, and it can be used over a range of off-latitude tilts. A reflector/cover width ratio of around unity is suggested for a stationary reflector-receiver combination. Acknowledgement--Support was provided under the National Energy Research, Development and Demonstration Program administered by the Dept. of National Development, Australia. NOMENCLATURE

/~ collector tilt angular displacement from latitude tilt ( =/3 - 4) p surface reflectance 0 latitude angle 0 inclination of the reflector relative to the cover plane Lc length of cover LR lengthof reflector overhang Wc width of cover WK width of reflector RI~NCES

1. F. A. Rudloff, S. R. Swanson and R. F. Boehm, Computer simulation results for planar reflectors and flat-plate solar collectors. ASME Paper 79- WAISol-37, ASME WinterAnn. Meet., New York, December 1979. 2. S. Baker, D. K. McDaniels, H. D. Kaehn and D. H. Lowndes, Time integrated calculation of the insolation collected by a reflector-collector system. Solar Energy 20, 415-17 (1978). 3. S. L. Grassie and N. R. Sheridan, The use of planar reflectors for increasing the energy yield of flat-plate collectors. Solar Energy 19, 663-668 (1977). 4. P. N. Espy, Solar thermal collectors using planar reflector. In Proc. Int. Solar Energy Soc. Cong., 1038-1042, New Delhi, January 1978. 5. D. C. Larson, Optimization of flat-plate collector flat mirror systems. Solar Energy 24, 203--207(1980). 6. H. F. Chiam, Planar concentrators for flat-plate solar collectors. Solar Energy 26, 503-509 (1981). 7. J. W. Spencer, Melbourne Solar Tables. CSIRO Division of Building Research, Tech. Paper 7 (1974).