The influence of collector azimuth on solar heating of residential buildings and the effect of anisotropic sky-diffuse radiation

Solar Energy Vol. 26, pp. 249-257, 1981 0038~92X1030249~9502.0010 Printed in Great Britain. Pergamon Press Ltd.

THE INFLUENCE OF COLLECTOR AZIMUTH ON SOLAR HEATING OF RESIDENTIAL

BUILDINGS AND THE EFFECT OF ANISOTROPIC SKY-DIFFUSE RADIATION

M, IQBAL

Department of Mechanical Engineering, University of British Columbia, 2075 Wesbrook Mall, Vancouver, B.C., Canada V6T IW5

(Received 12 November 1979; revision accepted 12 November 1980)

Abstraet--A liquid-base active residential solar heating system employing flat-plate collectors was examined. The two particular objectives of this study were: (a) to determine the influence of the collector azimuth on the fraction of the total demand supplied by the solar system, and (b) to consider the effect of sky-diffuse radiation being non-isotropic and the hourly radiation being asymmetric around solar noon vs the symmetric-isotropic model.

The study showed that the influence of the collector azimuth varied with the collector slope. For low-sloped collectors, the collector azimuth had minimal effect on the energy supplied by the solar system. The azimuthal orientation had maximum effect when the collectors were vertically sloped. The maximum amount of energy supplied by the solar system was always obtained from collectors facing the equator.

The final results were obtained by using either the symmetric-isotropic model or the asymmetric-anisotropic radiation model. These results differed from each other only by about 5 per cent maximum. The former model produced conservative results.

The above calculations were carried out using meteorological data from three Canadian locations with different climates. Yearly heating loads of 10 5, 105 and 10 7 MJ were employed at each location. Ratios of space-heating to service-hot-water loads were varied from 5 to 15.

INTRODUCTION In the literature on flat-plate collectors, the effects of various material and environmental parameters on the useful heat delivered have been extensively analysed. The ground work on this subject was laid down by the classic studies of Hottel and Woertz[1], Hottel and Whillier[2], Bliss[3] and Liu and Jordan[4]. More recently, some special aspects of fiat-plate collectors, such as their transient considerations and response time, have been reported by Klien et al.[5] and Wijeysundra [6].

In addition to the material aspects of fiat-plate collectors, their slope and orientation are also among the design parameters. Garg and Gupta[7] and Kern and Harris [8] studied the influence of collector slope on the collector's useful heat gain. Lorsch and Niyogi[9], taking into account direct radiation only, investigated the influence of wall orientation on collectable energy from vertical collectors. They observed that the besi results are obtained from a due south orientation and that a 230 deviation from the exact southern orientation produces only' a 5 per cent energy penalty. Morse and Czarnecki[10] studied the effects of inclination and orientation on fiat-plate solar absorbers. They considered only direct radiation and reported that, except at high latitudes, both the collector inclination and its orientation have minimal influence on the yearly collectable energy. Janke and Boehm[ll], considering only direct radiation, studied short-period effects of surface orientation on the collectable energy. They reported that for some ap- plications, an off-south orientation for fixed fiat-plate

collectors may be more desirable. Felske [12] has reported the effect of azimuth on the performance of fiat-plate collectors at any inclination. He separately studied the effect of direct radiation only, as well as the effect of actual weather data. A surprising conclusion of Felske's study is that for vertical collectors, the yearly energy collected increases with the increase in collector azimuth.

Felske and some of the other investigators mentioned have examined the collector as a single component without taking into consideration the type and capacity of storage or the load function. Any study of the effect of collector slope and its azimuth on the energy collected has, of course, very little practical value when the collector is considered as a single item. In solar heating systems for residential buildings, for instance, in addition to the material considerations for fiat-plate collectors, their slope and azimuth, type and size of storage, collector area, ratio of space-heating to service-hot-water load and load function should be all considered simul- taneously. The objective in such an application is to obtain maximum fraction of the yearly load supplied by the solar energy system. In new buildings, optimum slope and orientation can be easily realized. However, in a retrofit application there may be little choice and the designer has to predict any penalties.

For active solar heating systems, Klein[13], Beckman et all14], and Klein and Beckman[15] have presented general design methods which can be readily used by engineers and architects. These methods are now being adopted as standard procedures for the sizing of solar

249

250 M. IQBAL

heating systems for residential buildings. Using the method (f-chart method) laid in [13,14], Iqbal[16] carried out a study of the optimum collector slope (for collectors facing the equator) for residential buildings. It was concluded that optimum collector slope is strongly tied to the fraction of yearly load to be supplied by the solar system. This conclusion was somewhat contrary to a widely held belief that for solar heating of residential buildings, the optimum collector slope is always lat.+ 15 °.

The present report has two main objectives. The first is to extend the study in [16] to include the effect of collector azimuth and to compare the results with other studies if possible. The second objective is to investigate the azimuth effect under two different types of radiation models: (a) symmetric-isotropic; and (b) asymmetric- anisotropic. Each of these is defined below.

(a) Symmetric-isotropic radiation model Computation of the energy-___weighted monthly average

transmittance-absorptance (~'a) requires separate values of the beam and diffuse radiation on inclined planes. A common approach is to adopt Liu and Jordan's procedure[17] which is to obtain the horizontal hourly global (beam plus diffuse) and diffuse radiation [ and [a respectively from the monthly average daily global value H. However, this procedure assumes symmetry around solar noon. To obtain the beam and diffuse radiation on inclined planes, it is assumed that the sky radiation is isotropic. It is because of the above two considerations that this model of radiation is called symmetric-isotropic.

(b) Asymmetric-anisotropic radiation model At many locations, the actual hourly radiation quan-

tities/~ and fd may not be symmetric around solar noon. Iqbal[18,19] has shown that in some cases, strong asymmetries may exist. It therefore seems that the collectors should be appropriately oriented to achieve maximum benefit. Ideally, the measured hourly global and diffuse radiation on horizontal surfaces should be known. At present, hourly global radiation is measured at many stations across North America. There are over 50 such stations in Canada alone. On the other hand, stations where hourly diffuse radiation is measured are very rare. However, from measured hourly global values, diffuse horizontal radiation could be estimated through Hay's procedure[20], which is well suited for such a purpose. Hay [21] has also presented a method to account for the anisotropy of sky-diffuse radiation on surfaces inclined

toward the south. Assuming that this method is applicable to other orientations, asymmetric-anisotropic radiation on oriented surfaces can be calculated.

Examination of the orientation effect under symmetric-isotropic and asymmetric-anisotropic radiation models is obviously very important. It is necessary to be sure of the accuracy of radiation input value to the f-chart method in order to obtain realistic final results. However, complicated radiation calculation procedures require a higher level of expertise, and are time-consum- ing and costly. Therefore, it is recommended to engineers and architects that they consistently use sim- pler procedures if the final results from them correspond well with those obtained through more complex routines.

In this report, the effect of collector orientation on the solar heating system at three locations in Canada is studied (Table 1). This table also lists the type and period of radiation data employed. Wind velocities and ambient temperatuees were obtained from [22].

Details of the system parameter are given below. Three loads of 105, 106 and 107 MJ/yr were treated.

Space-heating to service-hot-water load ratios of 5 and 15 were considered. Monihly load distributions were calculated assuming a constant service-hot-water load and assuming that the space-heating load followed the local degree-day distribution. Liquid-base storage of 75 kg of water per m 2 of collector area was used [23]. The solar system was assumed 1o have a 2-per cent energy drop in the heat exchanger between the collector fluid loop and storage. Tube-and-sheet type double glass flat-plate collectors with a flat black absorber surface were assumed to be used.

CALCULATION PROCEDURE

The f-chart method requires the calculation of essentially the following five quantities: L, the monthly average load; FR, the collector heat removal factor; UL, the collector overall energy loss coefficient; S, the monthly average insolation on the collector; and (To), the energy-weighted monthly average transmittance-absorptance. Calculation of the monthly average load has al- ready been discussed in the previous section. Procedures to evaluate the heat removal factor FR and the loss coefficient UL laid down in [1-3,24] were followed. Evaluation of the monthly average insolation, S. on collector surface and calculation of the energy-weighted transmittance-absorptance (7"a) requires careful atten- tion. The last two quantities have to be calculated for the two radiation models. Complete calculation details of the

Table 1. Canadian stations used in this study, with hourly measurement of solar radiation

Station Lat. ° (N)' Long. ° (W)'

Montreal, Jean de Brebeuft 45 30 73 37 Oct. l%4-Dec 1975 Edmonton:~ 53 34 113 31 July 1957-Dec 1975 Vancouver~t 49 15 123 15 Jan. 1959-Dec 1975

tStation with regular hourly measurement of diffuse and global solar radiation on horizontal surfaces.

~:Stations with regular hourly measurements of global solar radiation on horizontal surfaces.

Solar heating of residential buildings 251

symmetric-isotropic radiation field followed in this paper are given below.

(a) Symmetric-isotropic radiation model calculations In this model, global radiation H on a horizontal

surface is assumed to be known either from measured data or through estimates. The corresponding diffuse component Ha is obtained through the linear correlation.

Ha : 0.958 - 0.982 H (1) H Ho

on a tilted and oriented collector, it is necessary to calculate the sunrise hour angle tos~ and the sunset hour angle to,s for the collector surface. Klein[26] has given equations for tos~ and to,,. However, he has employed sign conventions for to and y which are different from those used in this study. Furthermore, because of some typographical errors [27] in his expressions, it is useful to rewrite them with the convention for signs used in this study.

y > O

where Ho is the monthly average extraterrestrial radiation on a horizontal surface. Iqbal [18] has shown that (1) gives better results compared to Liu and Jordan's correlation[17] for locations considered in this report. The hourly horizontal diffuse value [a is obtained from [17],

,%_[0 Ha /4o (2)

where/% is monthly average hourly extraterrestrial radiation on a horizontal surface. Hourly horizontal global radiation is also obtained from Liu and Jordan's[17] graphs, represented in mathematical form by Collares- Pereira and Rabl [25] as,

y < O

T U - X/(T 2 - U 2 + 1)} to~ = rain to~, arcos T 2 + 1 (6)

{ TU+~/(T2-U2+I)} (7) toss = - rain tos, arcos T 2 + 1

TU+X/(T 2- U2+ 1)} (8) to,r = min to~, arcos T 2 + t

TU-X/(T 2- U2+ 1)~ to, = - min to,, arcos - ~ 7 i j (9)

where

where

I Io, = _~:-ta + b cos to)

Ho

a = 0.409 + 0.5016 sin (tos - 60 °)

(3a) T = cos 0/tan/3 sin y + sin 0/tan y

U = tan ~{cos 0/tan y - sin 0/sin y tan/3}.

The beam radiation on collector surface can be written (3b) as

b = 0.6609 - 0.4767 sin (tos - 60°). (3c)

Equations (2) and (3) result in the hourly radiation values [a and [ being symmetric about solar noon.

Transmittance-absorptance (ra) was computed using eqn (A4.1) of [13], which can be written as,

- - d a y d a y

(ra) /qo`" (4)

[bo`" and [dO,, are the monthly average hourly beam and diffuse radiation respectively on oriented surfaces. Ho`" is the monthly average daily global radiation on oriented surfaces. In order to solve (4), it is necessary to write down the geometric relations between the collector glaz- ing surface and the sun vector. The angle between the beam radiation and the surface normal is given by,

cos O = (sin & cos/3 - cos & sin/3 cos y) sin 6

. , cos 0 /%~, = ( / - la)c--~ ~ z (10)

where Oz is the incidence angle for a horizontal surface. The diffuse radiation on a collector surface is com-

posed of the sky-diffuse and the ground-reflected. It is reasonable to accept that all radiation incident on the ground is reflected diffusely in the polar sense, and hence the portion arriving on the collector is isotropic. An exception to this would be if the radiation arriving at the earth's surface were composed of a strong beam component and the collector were exposed to a large specu- lar surface such as waterfront.

The sky-diffuse radiation is usually anisotropic. However, assuming it to be isotropic, the total diffuse radiation on the collector surface can be written as

(11)

+ (cos O cos/3 + sin O sin/3 cos 3') cos 6 cos to

+ cos 8 sin/3 sin a sin to). (5)

In order to evaluate actual day-length for direct radiation

The first term on the r.h.s, of ( l l ) represents the ground-reflected component and the second term represents the sky-diffuse portion.

To complete the computation of (4), /4or can be obtained by summing up eqns (lO) and ( l l ) for the

252

collector day-length. That is,

c.d.I.

where c.d.l, stands for collector day-length. It simply means that although [bo~ is calculated only during the period the collector "sees" the sun, the ground-reflected and the sky-diffuse radiation would be incident on the collector throughout the day. A similar concept of day- length is to be applied on eqn (4). /4t3~, can also be computed by employing the daily values as,

(13)

An expression for/~b for an oriented collector has been given by Klein[26]. However, again because of conflicting sign conventions between the two papers and for the sake of completeness, the equation for /~b is rewritten here,

/~b = cos/3 sin 8 sin d~lw, - oJ,rll-- ~

- sin 6 cos ~b sin/3 cos rl~Oss - o,,rli~ 6

M. IQBAL

calculation of sky-diffuse radiation. Instead of using the second term on the r.h.s, of (11), Hay's[29] equation

(12) given below was employed.

-{ g [ao,.sky = Ia \ ~ } cos 0

- l[m ~2 +[a 1 - ( , / ~ b ~ ] (cos 0z)](l + cos /3 (15) \&,- COS Oz / J

where [~,sky is the anisotropic sky-diffuse radiation on a tilted surface, and m is air mass. The air mass was obtained from Kasten [30],

m=(cosOz+O.15(93.885-O~) ~253)J. (15)

Where the measured values of/~ estimated [a and eqn (14), the hourly values of beam and diffuse radiation on inclined planes were computed. Subsequent evaluation of (~'a) and S followed the same procedure as outlined in the previous section. Although the sky-diffuse radiation is considered anisotropic, (ra)a was nevertheless calculated with the usual assumption that all diffuse radiation is incident at 60 o to the collector normal. The reason for this assumption is that while eqn (15) represents anisotropy, it does not give its directional distribution.

+ cos 4~ cos S cos/3]sin Ws, - sin w,,[

+ cos 6 cos y sin & sin/3[sin w~, - sin w,~l

+cos 8 sinfl sin yJcos o~,, -cos ~o,rl}

2 cos$cosSsinws+~-~o)ssinSsinS • (14)

For surfaces tilted toward the equator, Iqbal [28] has shown that an equation like (12) produces better results than one like (13), especially when actual horizontal data are employed. Consequently, in this paper, /'1o, was computed through (12).

The quantity S is equal to H~, multiplied by the number of days in a particular__month. This completes the procedure for calculating (ra) and S when hourly diffuse and beam radiations are assumed symmetric about solar noon and the sky-diffuse radiation on the collector is considered isotropic.

(b) Asymmetric-anisotropic radiation model calculations

From the measured global horizontal radiation Hay [20] has calculated the corresponding [,~ values for a number of cities in Canada, including the locations treated here. These quantities are available in the form of tables[29]. Thus, the asymmetric horizontal radiation values are available, fbt3,~ was calculated using (10). Ground-reflected radiation was assumed to be isotropic and was obtained from the first term on the r.h.s, of (11). The main difference between the two models lies in the

RESULTS

The effect of collector orientation was studied for three locations: Montreal, Edmonton and Vancouver. For Montreal, hourly measured diffuse and global radiation has been used throughout this study. Therefore, differences between the two radiation models were only with respect to the assumption of isotropy or anisotropy of sky-diffuse radiation. It is for this reason that all diagrams showing results for Montreal refer to the two models as actual data-isotropic or actual data-anisotropic. For Edmonton and Vancouver, the symmetric-isotropic model started with the daily measured horizontal global radiation H and proceeded with the calculation of slope radiation as described in the earlier section. For these two cities, the asymmetric-anisotropic model began with the hourly measured global radiation on horizontal surfaces L estimated [a and then slope radiation was calculated through the anisotropic model described earlier.

For each city, four slopes from the horizontal position were considered: vertical, lat.+ 15 °, latitude, and lat. - 15 °. Collector azimuths varied from 0 to + 90 °. It has been observed that for vertical collectors, orientation has maximum effect on the fraction of energy supplied by the solar system and obviously no effect at all when the collectors are in a horizontal position. Therefore, starting with the vertical position of collectors, various elements of the two radiation models which are used in the/-chart method are presented. Calculations with Montreal data follow.

The method of computing sky-diffuse radiation on inclined surfaces is the major difference between the two radiation models. Figure 1 contains plots of sky-diffuse radiation for vertical surfaces. Figure l(a) is a plot of the


0.6

0.4

E O.2

-3 ~0.0

- - 0.6

z o

~ o . 4

oE 02

U_ o.c

i >.- o.E v. t./)

0.4

0.2

0.0

I I I I I | I I I I I I I I

MONTREAL COLLECTOR SLOPE 90* -ACTUAL DATA- ISOTROPIC. ORIENTATION INDEPENDENT

( a ) ~!!

_MONTREAL COLLECTOR SLOPE 90 ACTUAL DATA-ANISOTROPIC. SOUTH FACING COLLECTOR

MONTREAL COLLECTOR SLOPE 90* "ACTUAL DATA-ANISOTROPIC. EAST FACING COLLECTOR " - -

(c) OCT

UL

! !

6 8 I0 12 14 16 18

HOUR

Fig. 1. Mean hourly sky-diffuse radiation on vertical surfaces.

20

hourly isotropic sky-diffuse radiation valid for all orientations. Figures I(b) and l(c) contain corresponding anisotrolSic plots for surfaces facing south and east, respectively. Comparing Fig. l(a) with Fig. t(b), it is evident that during the winter months, the anisotropic model gives higher values of sky-diffuse radiation. However, during the summer months--April-July--the differences between the two models are relatively small. In a strict sense, Hay's anisotropic model[21] is applic- ~ I.o able to south-facing surfaces only. However, extending it I-- <~ to other orientations, Fig. l(c) shows the anisotropic ~ oa sky-diffuse radiation on vertical surfaces facing east. o~ This diagram is substantially skewed. It shows higher z amounts of radiation before noon than in the afternoons. , o.e Comparing Fig. l(a) with Figs. l(b) and l(c), it is ap- parent that for vertical surfaces, there are substantial o, differences between the isotropic and anisotropic ~ 0.4 models. For west-facing vertical surfaces, sky-diffuse radiation curves are almost a mirror image of Fig. l(c).

The Montreal diagrams show that during the winter ~ 0.2 months, the level of anisotropic sky-diffuse radiation on ~- east-facing surfaces (Fig. lc) is substantially lower than co o.c' that on south-facing surfaces (Fig. lb). A similar trend o has been noticed for Vancouver, well known to be a very cloudy place during the winter. This result is somewhat disturbing. On a physical basis, under very cloudy con-

ditions, the sky-diffuse radiation should not vary substantially with surface orientation.

The ratio between sky-diffuse and global radiation has also been investigated. Maximum variations were for vertical surface. Figure 2 shows the monthly variation of

I I I I I I I

MONTREAL 45" :50 'N COLLECTOR SLOPE 90*

I I I I

ACTUAL DATA- ISOTROPIC - - - - ACTUAL DATA -- ANISOTROPIC

/ " / ~ I[ AS T FACING

~ FACINQ COLLECTOR ~ I I I I I I I I I I I

2 4 6 8 I0 12

MONTH Fig. 2. Ratio of sky-diffuse to global radiation on vertical sur-

faces.

254 M. IQBAL

this ratio for surfaces facing south and east. For south- m.c facing surfaces, the monthly variation of this ratio is substantial, especially in the isotropic model. Also, for

14£ the south-facing surfaces, differences between the two

"t, models are greater than those for the east-facing surfaces. This is in correspondence with Fig. 1. Figure 2 :~ tz.c essentially represents the area under the curves of Fig. 1 divided by the monthly global radiation. I:~

The /'-chart method requires computation of global 7 Io.o O

radiation on inclined surfaces. These calculations were V- carried out for a number of slopes and collector orien- ~ a.o rations. Maximum differences between the two models O were obtained for vertical surfaces. Figure 3 contains examples for Montreal of south-facing and east-facing ~ 6.o surfaces. For south-facing surfaces, the plots do not exhibit any clear pattern in the two models. However, for east-facing surfaces, maximum values are obtained 4,o from the isotropic model. Also for east-facing surfaces, maximum insolation is received during summer months. ~ 2.0 Calculations indicated that similar comments can be applied to west-facing vertical surfaces. This means that where the demand for energy is mainly during summer o.0 months, an off-south orientation could be an optimum one as far as vertical surfaces are concerned. This observation agrees with that of Janke and Boehm[ll].

A general variation of insolation with orientation for vertical surfaces is plotted in Fig. 4 and shows that for the month of July, for instance, maximum insolation is obtained when the collector azimuth is about 60 ° off south. This diagram is for Montreal; for the other two locations, the situation could be slightly different. For

I I I I I I I

MONTREAL 45* 30'N COLLECTOR SLOPE 90 °

I I I I

~ ~JUL

,, <.. 2--2 ~ x \ , ?AiR

/ V, Oc2 ACTUAL DATA- ISOTROPIC

-- -- ACTUAL DATA- ANISOTROPIC i i I I I i i I i i t

-I00 -60 -20 20 60 I00 140

COLLECTOR ORIENTATION,~ (DEGREES)

Fig. 4. Effect of collector orientation on daily global radiation of vertical surfaces.

solation during July is received when the surface is oriented at about 60 o toward the west.

The second critical parameter for the ]'-chart method is calculation of the energy-weighted transmittance ab-

instance, at Vancouver, for vertical surfaces studied sorptance (~a). This parameter was also examined in under the asymmetric-anisotropic model, maximum in- detail for a number of slopes and collector orientations.

East- or west-facing surfaces exhibited maximum 16.o ~ i i ~ i i , , , , , / differences betwee__n the two models (Fig. 5). For south-

~ MONTREAL 45 ° 30'N ..] facing surfaces, (ra) values were almost identical for the 14. COLLECTOR SLOPE 900 t two models. This is a fortuitous result. It demonstrates

that in spite of rather substantial differences between the s I" /~SOU, TH FAClile COLLECXO~ H,, values of the two radiation models, the (~-da) values

+ -i-S,/'x ~ 12. are least affected.

r I/ -4 , , , , , , , , , , , ~"rq" ~ I.O - MONTREAL 45"30'N"

'7 .- /,/" \X xt\ -I " o L / / ',X \ \ J 08

6. ~ 0.6 "1-

\I I " - - _A_C_TUAL DATA-ISOTROPIC 4 [ ]

0 0 2 4 6 8 I0 12 0 2 4 6 8 I0 12

MONTH MONTH

Fig. 3. Monthly variation of average daily global radiation on Fig. 5. Monthly variation of the energy-weighted (m)for vertical vertical surfaces, surfaces.

Solar heating of residential buildings

The collector heat removal factor F~ and the collector hd loss coefficient U~ were also investigated. They appear ~ Lo

to remain invariant with respect to the two radiation models. It therefore can be concluded that in calculating the fraction of yearly energy supplied by the solar sys- c~ oa tern, any differences between the two radiation models will be mainly due to the monthly insolation S. ~ o.s

Figures 6--11 show plots of the effect of collector orientation on the yearly fraction of energy supplied by the solar system. These are two diagrams for each of the three O.4 cities. The collector slopes are equal to latitude and vertical o u.

position. All these diagrams indicate that the maximum z O 02 fraction is obtained for south-facing colectors. This is in

agreement with the studies of Lorsch and Niyogi[9], Morse ,~ and Czarnecki[10], Janke and Boehm[ll] and Weiss[31]. ~ o.~ However, it is contrary to the results obtained by Felske[12]. These diagrams also show that when the solar system is designed to supply a small fraction of the

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a,, o£

I I I .... Ii m i m w v I I I MONTREAL 45 ° :50' N COLLECTOR SLOPE 45.5 ° _~

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- \ ' S O O m ' . Or ~,. . . , , , . ,,,,- ==" ~ ~ ',,~ ,,~. ,~. ~ ~, 4 0 0 m ~ .

oom,- ...... ACTUAL DATA - ISOTROPIC

m-- ACTUAL DATA - ANISOTROPIC "" I I I I I | m ! I I I

4 0 0 -60 -20 20 60 I00 140

C O L L E C T O R O R I E N T A T I O N , ~)~DEGREES)

Fig. 6. Effect of collector orientation on the fraction of yearly load supplied by the solar system. Yearly load = 106 MJ, space to

service-hot-water load ratio = 5,

C::1 ILl

I.O

~ 0.8

~, o.s

o.4

_~0.2

I, 0£

: I I I 1 [ • I w I I I

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_

~ _

/ f " ~ X AREA " "/~.,~ N,~ \soOm= -

,OOm'. ~ 2 0 0 m 2

. ~ ACTUAL D A T A - ISOTROPIC - - - - ACTUAL D A T A - ANISOTROPIC

I i I I I I a I I I 1 ,

- I00 -.60 -20 20 60 I00 140

C O L L E C T O R O R I E N T A T I O N , ~ (DEGREES)

Fig. 7 Effect of collector orientation on the fraction of yearly load supplied by the solar system. Yearly load -- 10 6 MJ, space to

service-hot-water load ratio = 5.

255

I I i I I I i I I I I

EDMONTON 53 ° 30' N COLLECTOR SLOPE 5:5.5 =

- , , 7 " _ . - - - . . . Z •

- , 7 .,..?" _

_ . t ~ ''~ -"~,%.\ 400m z _

- / ' SYMMETRIC- ISCTRO~ 2 0 0 m 2 -

_ ~ - - ASYMMETRIC-ANI$OTROPIC

I m I I I I 1 I I | I

-too -so -20 zo 60 Joo ¢40 COLLECTOR ORIENTATION,~ (DEGREES)

Fig. 8. Effect of collector orientation on the fraction of yearly load supplied by the solar system. Yearly load = 10 6 MJ, space to


i w w I I I v I v t'" 1 r I0]- EDMONTON 53" 30 'N

~ " LCOLLECTOR SLOPE 90" ~ r

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- I00 -60 -20 20 60 I00 140

C O L L E C T O R O R I E N T A T I O N , (~(DEGREES) Fig. 9. Effect of collector orientation on the fraction of yearly load supplied by the solar system. Yearly load = 10 6 MJ, space to


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~ 200m= " SYMM ETRIC-ISOTROPIC

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256 M. IQBAL

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. / / ' ~ % , . COLLECTOR,*

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~ T R I C - I S O ~ 20ore'"

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140



energy demand (i.e. smaller collector surface), the collector orientation has minimal effect. The effect of orientation becomes more important for solar systems designed to provide a higher fraction of the yearly demand for energy. As far as the effect of the two radiation models is concerned, it appears to vary somewhat with the location and collector area. Within the parameters studied in this paper, the maximum difference is not more than 5 per cent. This is within the range of reliability of climatological data and of the accuracy of the/'-chart method itself.

Figure 6-11 are for space to service hot-water load ratio of 5 and yearly load of 106 MJ. The observations made above apply equally to space to service-hot-water load ratio of 15 and the yearly loads of 10 5 and 107 MJ studied in this report.

The above calculations have been repeated for collector slopes of lat.- 15 ° and lat. + 15 °. The comments made above apply equally to these slopes. Naturally, the influence of collector orientation diminishes as the slope decreases.

Before closing, a remark about Vancouver would not be out of place. Under all parametric limits and irrespec- tive of the two radiation models studied in this report, south-facing collectors always produced the largest fraction of the load supplied by the solar system. This is an interesting result considering that for hour pairs around solar noon, global radiation on horizontal surfaces is higher in the afternoons for this location[19].

Finally, it may be concluded that for liquid-based short-term storage residential solar heating systems, the optimum collector orientation is not critical. However, it assumes greater importance as the fraction increases. The influence of collector orientation also increases as the collector slope increases. The final results obtained by using the symmetric-isotropic and asymmetric- anisotropic radiation models do not differ from each other by more than 5 per cent.

Acknowledgements--Financial support from the National Research Council of Canada is gratefully acknowledged. All computations were carried out by Cecilia Cameron.

NOMENCLATURE A collector area, m 2

FR collector heat removal factor fraction of yearly load suplied by solar energy

H monthly average daily global radiation received on a horizontal surface, MJ m -2 day -1

/qu monthly average daily diffuse radiation received on a horizontal surface, MJ m -2 day -~

/~er monthly average daily global radiation received on an inclined and oriented surface, MJ m 2 day

Ho extraterrestrial monthly average daily insolation received'on a horizontal surface, MJ m -2 day

[ monthly average hourly global radiation received on a horizontal surface over 1 hr, kJm-2hr '

fu monthly average hourly diffuse radiation received on a horizontal surface over I hr, kJm 2hr

[b (I-I~), monthly average hourly beam radiation received on a horizontal surface over 1 hr, kJm 2hr

~ , monthly average hourly global radiation received on an inclined and oriented surface over 1 hr, kJm-2hr t

[a~ monthly average hourly diffuse radiation received on an inclined and oriented surface over 1 hr. kJm 2hr

[bar ( I - l d), monthly average hourly beam radiation received on an inclined and oriented surface over I hr, kJm-2hr '

[a~.~ky monthly average hourly sky-diffuse radiation received on an inclined and oriented surface over l hr, kJm 2hr J

f0 extraterrestrial monthly average hourly radiation received on a horizontal surface, kJm 2 hr J

2 I [so solar constant 4871kJm hr L average monthly load, MJ month '

Ly average yearly load, MJ yr J m air mass

UL m_onthly loss coefficient of a collector, Wm-2°C -~ S H~×number of days in a month; monthly average

global radiation on a collector, MJm-Zmonth /3 collector slope from the horizontal position, degrees 3, collector azimuth angle, degrees (east positive) 8 solar declination, degrees (north positive) 0 angle between the beam radiation and surface normal,

degrees 8z zenith angle, degrees

j ground reflectance (ra) energy-weighted monthly average transmissivity-ab-

sorptivity (za)b transmissivity-absorptivity for beam radiation (ra)a transmissivity-absorptivity for diffuse radiation

(b latitude, degrees (north positive) ~o hour angle, degrees, solar noon being zero, mornings

positive ~os sunrise hour angle for a horizontal surface, degrees

(O~r sunrise hour angle for an inclined and oriented surface, degrees

~oss sunset hour angle for an inclined and oriented surface, degrees

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Documents

The influence of collector azimuth on solar heating of residential buildings and the effect of anisotropic sky-diffuse radiation