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A PROGRAM FOR CALCULATION OF SOLAR ENERGY COLLECTION BY

FIXED AND TRACKING COLLECTORS

John D. Garrison

Physics Department, San Diego State University, San Diego, CA 92182-1233, U.S.A.,

email:[email protected], fax: 619-594-5485, ISES member

Abstract- SOCOL, a realistic and versatile FORTRAN program, has been developed to estimate net solar

energy collected by a solar collector per unit collection area. This program was developed to study the

properties of various solar collectors. It is made useful to a wide spectrum of users by allowing them to

choose any or all of 15 possible solar collector types for calculation and comparison. Additional collectors

can be included without undo labor. Either or both of two selective absorbers can be selected for energy

collection calculations. SOCOL allows input for a third selective absorber. SOCOL is programmed to use

solar radiation and surface meteorological data taken from The National Solar Radiation Data Base

(NSRDB) for 239 stations over the USA. It can be adjusted to read other data sets. It takes 20 seconds on a

Compaq Presario 2700 1.13 GHz computer to calculate net solar energy collection per unit area for one

solar collector design using each of two selective absorbers at 5 fixed absorber temperatures for all the

daylight hours of one year at one location. The program output includes sums of solar energy collection

for each day, month and year along with averages and distributions. Averages and distributions for the

solar radiation and surface meteorological data are also obtained so solar energy collection can be related

to these data. SOCOL can be down-loaded from web site: www.sci.sdsu.edu/SOCOL/.
mailto:[email protected]:[email protected]


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INTRODUCTION

The FORTRAN program SOCOL calculates the net solar thermal energy collected per unit area

by any of a variety of solar thermal collectors and a planar PV collector for solar electricity for a particular

site and year. It allows comparison of different collectors. It is useful for estimating energy collection by a

particular collector at a particular location for various fixed operating temperatures and orientations of the

collector, or comparing energy collection at different locations.

The net amount of solar thermal energy collected per unit area by a collector is the amount of

energy absorbed by the absorbing surface minus the energy lost by the absorbing surface to the

environment per unit area. The thermal conduction losses by supports for the absorber can be made small

and are neglected. Energy collection and energy losses by a complete energy system are not considered

here.

Many methods already exist for analysis and design of a complete solar energy system. They are

very useful and well tested. These include the simpler f-chart method (Klein, et al, 1977; Beckman, et

al,1977), the Utilizability method (Whillier, 1953; Liu and Jordan, 1963; Klein, 1978; Collares-Pereira

and Rabl, 1979), and the more thorough and involved, but quite flexible, mathematical simulation methods,

such as TRNSYS (Klein and Beckman, 1976; Klein, et al, 1990; Duffie and Beckman, 1991), for example.

This work is a long overdue continuation and much improved version of an earlier study

(Garrison, et al, 1978). Rabl has done an excellent, somewhat similar study, which is discussed further

below (Rabl,1981). Rabls work has been used by Gordon and Rabl (1982) for an analysis of process heat

plants without storage. Brunold, et al (1994), compare energy collection by two evacuated collectors and

one air flat plate collector with glass capillary transparent insulation.

SOCOL contains parts of a program SOLRAD, used by (Gueymard and Garrison, 1998) for

example, so that solar energy collection can be related to the properties of the solar radiation and surface

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meteorological data. SOCOL goes one step beyond the work of Marion and Wilcox (1994), who use solar

radiation data from the National Solar Radiation Data Base (NSRDB, 1992; NSRDB, 1995) to estimate the

direct and diffuse solar radiation incident on flat plate, concentrating and tracking collectors with varying

orientations and locations. Examples of calculations by SOCOL have been discussed earlier (Garrison,

2000,2002).

1. THE FORTRAN PROGRAM SOCOL

2.1 The data

When SOCOL is started it requests: The station; year of the data; tiltcand azimuthal angle c

of the collector array; angle limits on the sky and collector view horizons; range of numbers of the types of

collectors to be calculated; surface albedo; choice of output sent to the output file; a reduced radiation loss

(low loss ) number; and todays date. Two absorbers are used as standards for calculation of solar energy

collection. One is more suitable for low temperature operation of a collector. The other is more suitable for

higher temperature operation of the collector. If energy collection by a collector using another absorber is

desired then the additional input required for this absorber is: the normal absorptance; 5 hemispherical

emittance values for five absorber operating temperatures; and a weighting factor (Discussed in Subsection

2.3 below). Input for the Planar PV array is discussed below.

The program then reads the solar radiation and surface meteorological data for one year from a file.

The input solar radiation and surface meteorological data currently used are the National Solar Radiation

Data Base for 239 US stations available from the National Climatic Data Center, NOAA, U.S. Department

of Commerce, Washington, D.C. Solar radiation and surface meteorological data for Canadian stations

obtained from Atmospheric Environment Service, Downsview, Ontario, Canada have also been used

(Garrison,2000). SOCOL contains information concerning: the selective absorbers used as standards in the

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program; loss properties and angular response of 15 solar collectors; station data; corrections for deviation

of the orbital motion of the earth from circular motion; and data needed to estimate the distribution of

diffuse radiation over the sky (Perez, et al, 1993).

2.2 Collector designs

Fig. 1 shows simplified transverse cross sections of eight fixed collector designs and their

identifying numbers whose energy collection properties have been included in this program. One single

glazed air flat plate collector (Number 1, with the absorbing surface in air) and seven evacuated collectors

(Numbers 3,5-9,12, with the absorber surfaces in vacuum) are shown. The vacuum envelope for the

evacuated collectors is a glass tube. Solar energy collection is by a plane parallel array of identical collector

tubes, with the plane of the collection area for each tube in the plane of the array. SOCOL calculates

energy collection for these eight types of collectors and seven others not shown. These 15 collectors are

discussed below. The collector concentration C, shown with each collector cross section in Fig. 1, is taken

to be the ratio of normal incidence energy collection area to the absorber surface area. The individual

collectors will now be discussed.

[1,2]Air Flat Plate - In the top upper left of Fig. 1 is shown a simplified partial cross section of

a single glazed air flat plate collector (Number1). A double glazed air flat plate collector (Number 2),

whose energy collection is also calculated, is not shown. These two collectors are discussed in (Duffie and

Beckman,1991, Chap. 6) and (Rabl, 1985, Chap. 1).

[3] Vacuum Tubular (dewar) - Just below the single glazed air flat plate collector in Fig. 1 is

shown a simplified transverse cross section of a fixed evacuated glass tubular (dewar) collector. Tubes of

this type have been discussed by (Beekley and Mather,1975; Schmidt, et al, 1990). Nippon Electric Glass

in Japan and others have used larger diameter tubes of this type for their ICS collector. For this study, the

inner absorber tube is taken to have a diameter which is 92% of the diameter of the outer glass tube. When

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tube axes are oriented in approximately a polar axis direction, they act much like a tracking collector, since

the collecting area viewed from any direction perpendicular to the tube axis does not change, except for

shielding by neighboring tubes. Because of this feature, this collector collects more solar energy per unit

collection area at low operating temperatures than any other collectorconsidered here. Its energy collection

per unit absorber area is the lowest of any of the collectors considered here, since its concentration is only

C = 1/ =0.32. Thus, its energy loss by radiation per unit collection area is large relative to the other

evacuated collectors with higher concentration. This loss can be reduced by the order of 20% by the use of

a silver mirror on the inner surface of the outer glass tube on the lower non-collecting portion of the tube,

and by the use of a very low emissive coating on the corresponding outer surface of the inner tube. A low

emittance, thermally floating shield can be placed between the inner and outer tubes in this region to reduce

further this regions loss by about a factor of two.

[4] Vacuum U-Trough - The simplified cross section of this collector tube has the absorber

surface consist of a semicircular trough in the lower half of the outer glass tube with absorber on both

inside and outside surfaces. Its semicircular cross section is identical to the lower half of the dewar

collector [Number 3]. The energy collection by this collector is intermediate between that of the dewar

collector and the vacuum cusp collector [Number 5] discussed next. The loss of this collector can also be

reduced by the use of a silver mirror on the inner surface of the glass vacuum envelope tube and by the use

of a very low emissive coating on the corresponding outer surface of lower part of the semicircular trough.

A low emittance, thermally floating shield can be placed between the inner trough and outer glass tube in

this region to reduce further this regions loss by about a factor of two.

[5] Vacuum Cusp The simplified cross section of this collector tube is shown just below the

vacuum tubular collector cross section. The surface of the cusp is coated with selective absorber. For this

study, the cusp is assumed to have a width which is 92% of the diameter of the outer vacuum envelope. The

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cusps in an array of these tubes act as a trap for solar radiation, since the reflected part of rays incident on

the absorber surface are often again incident on the absorber and mostly absorbed. The properties of this

collector place it intermediate between the vacuum U-trough collector (Number 4) and horizontal fin

collector (Number 6) in collection and loss properties. The radiation loss by this collector can be reduced

by the order of 30% by silvering the inner surface of the lower half of the glass tube and placing a very low

emissive coating on the bottom of the cusp. Placing a thermally floating low emittance fin just below the

cusp bottom will reduce the bottom loss further by a factor of about two. With this reduction, this collector

can collect more energy per unit collection area than any of the other fixed collectors discussed here at an

operating temperature near 200 C, and more than all other collectors except the dewar and U-trough

collectors with loss reduction at lower temperatures.

[6] Vacuum Horizontal Fin - A simplified transverse cross section of an evacuated, horizontal

fin collector tube is shown just below the vacuum cusp collector in Fig. 1. Collectors of this type are shown

in (Duffie and Beckman,1991, Chap. 6; Rabl, 1985, Chap 1). The internal fin flat plate is coated with a

selective absorber. For this study, the internal fin is assumed to have a width which is 92% of the diameter

of the outer vacuum envelope. The concentration is taken to be 0.49, reduced from 0.50 by the effect of an

energy collection tube thermally in contact with the internal fin (not shown). Commercial production of

this type of collector tube has been by Philips in the Netherlands (Bloem, et al, 1982); Fournelle Energie

Technologies, Canada; Thermomax Technologies, England; Corning of France; Philco Italiana of Italy and

Nippon Electric Glass of Japan, and others. The energy loss by this collector can be reduced by the order of

40% by coating the inner surface of the lower half of the glass tube with silver and by placing a very low

emissive coating on the lower surface of the fin. Placing a thermally floating shield just below the bottom

of the fin will reduce further the bottom loss by about a factor of two. With this loss reduction this collector

can collect more energy than any other of the fixed collectors near 300 C.

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energy collection per unit absorber area of all the fixed collectors discussed here. It has the lowest heat loss

per unit collection area of any of the fixed collectors considered here. Representative references for this

type of collector are: (Snail, et al 1984; Garrison and Fischer-Cripps,1997) and references found therein.

Energy collection by this type of collector tube with acceptance half-angles of 60 o(Number 10)and 45o

(Number 11)is also included in SOCOL

. [13 -14] Parabolic Tracking Evacuated parabolic tracking collectors are not shown in Fig. 1.

SOCOL can calculate energy collection by a single axis parabolic tracking collector (Number13). This

tracking collector is modeled to be similar to the Luz Corporation SEGS arrays LS-2 and LS-3 (Cohen, et al,

1993) who quote a concentration of C=71 for the LS-2 design. This concentration is the ratio of parabolic

mirror width to absorber tube diameter, rather than circumference (Gordon, 2001). Here, C = 71/ =

22.6. The LS-3 has a normal incidence optical efficiency of 0.80, about the same as the vacuum tubular

collector used here with no neighboring tubes. SOCOL can calculate energy collection by a two axis

parabolic tracking collector (Number 14). This is assumed to have a concentration of 500 and a normal

incidence optical efficiency of 0.80.

. [15] Planar PV This is the most common form of solar electric collector, not shown in Fig. 1.

It consists of a plane array of solar cells. The input for this collector consists of the normal efficiency o of

this collector at 20 C, a number for the variation of the relative efficiency /o with incident angle, and a

number for a linear (assumed) variation of efficiency with temperature relative to 20 C (in percent change

per degree Celsius). The variation of relative efficiency with incident angle is expected to have

approximately the same form as the variation of relative absorptance of the selective absorbers of the

thermal collectors and can be specified in the same manner (discussed in Section 2.3 and shown in Fig. 2).

_______________

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If one wishes to design a best collector for a given temperature, one might wish to try

other designs besides the 15 discussed above. For example, the U-trough collector does not need to be

semicircular in cross section, but can be an arc of a circle of larger radius of curvature, placing the design

intermediate between the U-trough and the horizontal fin of infinite radius of curvature. The U-trough or

arc can also be inverted into the upper half of the vacuum envelope tube. Also a V trough can be tried.

Such trials are time consuming since they require ray tracing to determine the angular response of each

design.

__________________

The air flat plate collectors (Numbers 1,2) have a rectangular energy collection area. The absorbing

surface and its bottom insulation are contained in a sealed rectangular box. Both orthogonal transverse

dimensions of the absorber surface are assumed to be largecompared to the height of the upper part of the

side walls of the sealed box which are above the absorber surface, so edge effects will be small.

There exist a number of air flat plate solar collectors with modifications to the basic flat plate design.

See for example, (Oliva, et al, 2000) and (Goetzberger, et al, 1991). Oliva, et al describe an air flat plate

solar collector with a honeycomb-type transparent insulation cover. Goetzberger, et al describe a bifacial

collector with concentration and absorber surface insulation. Energy collection by collectors of this type

can be calculated using SOCOL by including their angular response and loss characteristics in the program.

The evacuated collector tubes are assumed to be long relative to the width across the tube in the

transverse direction so that end effects are small. The tubes in an array are assumed to have a spacing that

is 20% of the transverse tube width. Knowing this spacing permits calculation of the effect of scattering

and attenuation by neighboring tubes on the energy collection of a tube. The effect of the spacing on solar

energy collection is small, of the order of 1%. Exceptions are: The vacuum tubular (dewar) collector

(Number 3), which collects about 15 to 20% more energy when the tubes of an array have a wide

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separation and the tubes are oriented parallel to the polar axis. The other exceptions are the U-trough, cusp

and vertical fin collectors (Number 4,5,7) which also collect somewhat more energy when widely

separated and with the polar axis orientation.

2.3 The absorber surface

The selective absorber literature has been searched rather thoroughly in an attempt to find all absorbers

with measurements of the variation of absorptance with the angle of incidence on the absorber. Although

the number of selective absorbers discussed in the literature is of the order of 1000 or more, only 25

measurements of the absorptance as a function of angle of incidence have been found. Two of these 25

selective absorbers have been selected for use in these studies: The black chrome on Watts nickel absorber

of Pettit and Sowell (1976) with normal incidence absorptance of = 0.95 and the highly selective

cermet absorber of Zhang and Mills (1992), sample R517CuB, with= 0.92. The mathematical form of

the variation of/ with incident angle used to fit the data here is

/ = 1- exp[- c(90 A)d], (1)

whereAis the angle of incidence on the absorber surface in degrees. The adjustable parameters c and d

are varied to yield least square fits to the measured values of absorptance for each absorber. In fitting the

measured values, it is important that the unmeasured value:/ = 0 at A= 90o is included. Fig. 2

shows the variation of the Pettit-Sowell and Zhang-Mills absorbers with angle of incidence. Smooth

selective absorbers with a high selectivity ratio /( is the hemispherical emittance) apparently have

a variation of/ with incidence angle close to that of the Zhang-Mills absorber. See (Reed, 1977).

Energy collection for another absorber requires as input for SOCOL the normal absorptance of the

new absorber; and the position of the curve for / for the new absorber relative to those for the Pettit-

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Sowell and Zhang-Mills curves in Fig.2. In specifying this position, the position of the Pettit-Sowell

absorber curve is taken to be 1.0 and the position of the Zhang-Mills absorber curve 0.0 for linear

interpolation or extrapolation. The Planar PV is treated in the same manner with , replaced by

, o.

2.4 Window transmission and reflection

The window glass for all of these collector designs is assumed to be soda lime glass. The optical

properties of soda lime glass are presented in detail by (Rubin, 1985). For this study, the transmission of

soda lime glass as a function of incident angle has been approximated by

= 2.782 cosG(1-1.011 cosG+0.342 cos2 G),

(2)

where Gis the angle of incidence on the glass surface. Attenuation and bending of radiation in the glass

is small, and has been neglected: reflection= 1 -.

2.5The angular response

The collector angular response is defined equal to the optical efficiency times the cosine of the angle of

incidence of the solar radiation on the collection area. This replaces the incidence angle modifierused in

most work. The angle of incidence on the collector is defined in this study in terms of two angles:X , the

angle the suns rays make with the direction of the axes of the collector tubesunit vector in each array,

and X, the angle the projection of the direction of the incident solar radiation onto the plane transverse

to the collector axis direction makes with the unit vector normal to the array area n. Angles Xand X

are indicated in Fig.3. The cosine of the angle of incidence on the collector area is the product: cos X

sinX. The optical efficiencyat anglesX and Xis determined analytically and/or by ray tracing

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of a group of equally spaced rays incident upon the collection area at angles X and X. Eqs. (1) and

(2) are used. The product of the radiation energy intensity incident with anglesX and X times the

angular response for these two angles is equal to the amount of incident radiation energy intensity which is

collected per unit collection area per unit time. Because of the longitudinal symmetry along the collector

axis direction of all the collector designs, it is sufficient to do analytic calculation or ray tracing only in the

transverse plane whereX= 90o.The collectors have longitudinal symmetry and left-right symmetry of the

transverse cross section of the collectors (other than the horizontal half-fin collector). These symmetries

make the angular response values obtained for anglesX

and X

between 0o

and 90

o

determine the

angular response at other values of Xand X. In SOCOL, the angular response of the horizontal half-fin

collector is the average of the angular response of this collector with the half-fin on the left and on the right

side of the tube. An array is assumed to be made up of an equal number of left and right tubes.

Fig. 4 shows the angular response as a function ofX and Xfor the vertical fin collector of

Fig. 1 using the Pettit-Sowell absorber. Angular responses of other collectors are shown in (Garrison,

2000). The angular response of the collector designs is somewhat greater for collectors using the Pettit-

Sowell absorber, because of the larger value ofoand also the slower drop-off of/ with increasing

angle of incidence. The gain in solar energy collection by this increase in angular response using the Pettit

and Sowell absorber is largely cancelled at the lower collector operating temperatures by the greater losses

associated with the much larger emittance of this absorber. At higher operating temperatures, solar energy

collection is much larger using the Zhang-Mills absorber.

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In SOCOL, the angular response for each collector is represented by a 19x19 element bivariate

histogram of angular response values for equally spaced intervals from 0-90o in both X and X.

SOCOL does a table look-up operation for the angular response using values it calculates forXand X.

2.6 Collector Losses

In SOCOL, energy loss is calculated for five different values of the absorber operating

temperature: T = 40, 70, 120, 200, and 300 C. These have been assumed constant over the collection time

and area. These temperatures are data in SOCOL and can be changed easily. The loss coefficient of the top

surface of the absorber in the air flat plate collectors is obtained by the method of Klein (1975) as given in

(Duffie and Beckman, 1991), Eq. 6.4.9. The heat loss from the lower side of the absorber is determined by

a loss coefficient taken to be hp = 0.6 W/m2- C (about 5 cm of polyurethane foam).

The evacuated collector designs lose thermal energy mainly by radiation from the absorber

surface. A first approximation is to assume that the glass window is at ambient temperature. Going one step

further, this loss is treated as a two step process: Radiation from the absorbing surface to the glass window

and convection and radiation from the window to ambient. The temperature of the window is needed for

this calculation. It is estimated by iteration until the two steps of the process transfer energy at the same

rate. Radiation from the absorbing surface to the glass window is estimated by the equation

q =(T4 TG4)/[(1 -)/A +1/ AFAG + (1 -G)/GAG ] (3)

for a two surface enclosure (Incropera and deWitt, 1990), Eq. 13.23, p. 771. The view factor FAGis set

equal to one for all the collectors treated in SOCOL except the U-trough [Number 4], cusp (Number 5) and

vertical fin (Number 7) where it is set equal to 0.50 (inside), 0.75 (upper part) and 0.72, respectively. The

other symbols in Eq. (3) are:,the Stefan-Boltzmann constant; T, the absorber operating temperature; TG,

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the glass window temperature; A, the absorber area; G, the glass emittance taken to be 0.88; and AG, the

area of the glass window. The absorber hemispherical emittances for the Pettit-Sowell and Zhang-

Mills absorbers are: 0.115, 0.12, 0.14, 0.17, 0.20 and 0.0275, 0.028, 0.030, 0.033, 0.039, respectively, at

the 5 operating temperatures. Eq. (3) takes the following form when the known values are inserted

q =5.67x10-8 ( T4 TG4)/[(C/) + b) (W/m2). (4)

C is the collector concentration. Values of C and b are tabulated as data in SOCOL. The second step of the

heat transfer from window to ambient is calculated by the equation

q = 5.0x10-8 (TG4 TSKY4) + 15 (TG TA) (W/m2) (5)

The first term on the right is an estimation of the radiation loss, while the second term is an estimation of

the convection loss. TSKY is the sky temperature. TA is the ambient temperature. TSKY is calculated using

Berdahl and Martin (1984), if the dew point temperature is in the input surface meteorological data.

Otherwise Swinbank (1963) is used. By symmetry there should be no net radiation transfer between the

neighboring tubes in an array. Generally, the temperature drop from the window glass to ambient

temperature is small relative to the drop from the absorber to the glass. The surface meteorological data on

wind for each hour or day has not been used to vary the coefficient of the convection loss. The

approximation using Eq. 5 calculates this loss in the same manner for all evacuated collectors. Any person

desiring to improve this calculation can modify SOCOL. As a help, there are numerous comments

throughout SOCOL to identify the different calculations.

2.7 Surface albedo

SOCOL calculates the contribution of solar radiation scattered by the ground in front of the

collector to solar energy collection. It assumes that the scattering by the ground is diffuse. Often, this

scattering has a forward component. To account for this effect, the albedo used as input to SOCOL can be

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increased. The contribution from ground scattering is generally quite small. Ground scattering has a larger

effect on diffuse radiation collection.

2.8 Calculation of solar energy collection

The contribution of each part of the sky to the diffuse radiation is determined using the

prescription of Perez, Seals and Michalsky (1993) with sky luminance replaced by sky irradiance. The total

contribution of the diffuse radiation to solar thermal energy collection is obtained by numerical integration,

summing the contributions of 400 elements equally spaced over the sky. To this is added the contribution

of an additional number of elements below the horizontal for ground reflection. For both direct and diffuse

radiation, the thermal energy collected per unit collection area for each sky element for each hour is taken

to be the product of the mean incident radiation energy intensity from the direction of an element of the sky

X and Xthe collector angular response and the time duration. The net total energy collection is given

by

ET = Eb + Ed loss (6)

where Eb, is the direct or beam energy collected, Ed is the diffuse energy collected, loss is the energy loss by

convection and radiation, and ET is the net total energy collected, all per unit collection area. Whenever the

loss exceeds the sum Eb + Ed for any hour, the net total energy collection ET is set equal to zero. The

calculation of the energy collection from diffuse radiation is time consuming. The time to run each hour of

data is greatly reduced by reducing the number of points in the sky from 400 to 100, for example, with some

reduced precision of the calculation.

The equations for the solar time and direction of the sun as a function of time, along with other

needed equations are in the Appendix. The orientation of the collector axes in the plane of the collector

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array is assumed to have only two possible conditions, either horizontal, or lying in the vertical plane

containing the normal to the collector array.

3. TESTS OF THE PROGRAM

SOCOL has been tested in many different ways. For each of a few hours selected at random

during the collection year, all the results of the equations in the energy collection part of the program have

been hand calculated and sometimes visualized with figures, and then compared with the results obtained

by SOCOL. The collection of solar energy for particular hours has been tested for proper behavior. For

example, when the normal to the array is horizontal and the plane of the array is vertical, energy collection

at different azimuthal angles of the array normal are compared to see if the behavior is as expected. Thus,

there should be no direct radiation collection when the normal points north and the hour is in the winter

half of the year. Also, there is less diffuse radiation collection when the normal points north. When the

plane of the collector array is horizontal and the angular response is set equal to the cosine of the zenith

angle (optical efficiency =1), the diffuse energy collection and the direct energy collection for each hour

are the same as the measured diffuse and direct radiation on a horizontal surface.

When the angular response is set equal to the cosine of the incidence angle on the collector array

and the collection area is tilted at the latitude angle and faces south at Albuquerque, NM, USA, the

calculated annual energy collections per unit area for the years 1976-1979 inclusive are: 8641, 8275, 7832,

and 8009 MJ/m2. The mean is 8189 352 (176) MJ/ m2 where the 352 is the standard deviation of a single

year and 176 is the standard deviation of the mean. Marion and Wilcox (1994) give a corresponding value

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of 8400 MJ/m2 and Rabl (1981) gives a corresponding value of 8000 MJ/m2. It is not known what years

Marion and Wilcox, and Rabl have used for their values.

Finally, the solar energy collection of a double glazed air flat plate collector has been calculated

using both the Pettit-Sowell and Zhang-Mills selective absorbers and compared with results that are

obtained using the method of Rabl (1981). The results of the calculation by SOCOL and comparison with

Rabl are presented in Table 1. In the table, T is the absorber operating temperature, T A, is the ambient

temperature (mean for the year) used by Rabl,, is the normal optical efficiency used here in Rabl, and

Q, is the annual energy collection in GJ/m2. The other symbols are as in Rabl. The results by these two

methods are in good agreement.

The difference between the calculated energy collection by one collector and another arises only

from differences in the angular response and differences in heat loss. The heat losses have been checked

carefully by hand calculation. The angular responses have also been checked carefully. The angular

responses of the CPC shaped glass evacuated collector are probably the most prone to error. The first two

of these with half-angles of acceptance of 60oand 45 owere repeated. The average of the angular responses

over the 19x19 bivariate histogram for the two determinations differ by about 1% for both the 60oand 45 o

collectors. All ray tracings for these use a density of 10 rays per collection width of one tube. This ray

density extends across the tube and neighboring tubes in the plane transverse to the tube axis.

4. SAMPLE RESULTS BY SOCOL

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Table 2 shows annual energy collection per unit collection area as a function of absorber

temperature at Albuquerque, New Mexico, USA and Seattle, Washington, USA. This is for nine collector

designs: 1, air flat plate; 3, vacuum tubular; 4, U-trough; 5, cusp; 6, horizontal fin; 8, vertical half-fin; 9,

horizontal half-fin; 12, 35o CPC shaped glass tube; and 13, single axis parabolic tracking. The values in

Table 2 for each collector use the axes orientations: EW, N-S, and polar. The values are for the selective

absorber (Pettit-Sowell or Zhang-Mills) which yields the highest energy collection at each temperature. For

the few cases at lowest temperature where the Pettit-Sowell absorber collects the most energy, the number

is put in italics. The array normal is tilted at the latitude angle for the E-W (and polar) orientation. The low

loss energies in the table are for collectors 3,4,5 and 6 when the lower part of the collectors have low

emissive coatings and thermally floating shields, as discussed earlier. The bordered energy collection

numbers in bold type in Table 2 are the highest values at each temperature. Energy collection by all

collectors is highest for the polar axis orientation, except for the CPC shaped glass collectors. At these

latitudes, the E-W axis orientation collects more energy than the N-S orientation. The evacuated collectors

outperform the air flat plate collectors significantly. Energy collection per unit absorber area is obtained by

multiplying by the concentration. This is of interest since the selective absorber is generally a more

expensive part of the collector. The concentration must be suitably changed for the low loss cases.

Fig. 5 shows the net annual energy collection ET for 35 US stations for the year 1979 ordered by

increasing mean annual clearness index KT for a single glazed air flat plate collector using the Pettit-Sowell

absorber at a temperature of T = 40 C and T = 70 C. ET also varies to a lesser degree with latitude, annual

mean daylight ambient temperature and surface albedo. This accounts largely for the fluctuation in points

in Fig. 5. Also shown is a least square fit to the net energy collection using the relation: ET = 1.282[1-

0.0079(T - Ta)] [(0.95 (Kb+Kd(-0.149+0.92cos(theta L)) 104 - 6(T - Ta)] where Kb is the annual

mean direct beam index, Kd is the annual mean diffuse index, TA is the annual mean daylight ambient

18


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temperature and L is the latitude. The correlation between the fluctuations in the lines connecting the

calculated energy and the RMS fit indicates validity in the choice of the four variables selected (eg. surface

albedo would not be a useful variable).

Table 2 and Fig. 5 are representative of the types of information which can be obtained using

SOCOL. Additional examples may be found in (Garrison, 2000, 2002). SOCOL calculates mean values of

KT , Kd , Kb,cloud amount and opacity, ambient temperature, in addition to ET ,Ed ,Eb, and energy lossfor

each hour, day, month and the entire year.

5. SUMMARY

The FORTRAN program SOCOL is a program of rather general utility which realistically predicts

net hourly solar energy collection for one year or any part thereof at a particular site for which one has

data. This net energy collection can be for any of 15 collector types contained in SOCOL. Any selective

absorber can be used for the absorber surface. The orientation of the collector array can be with the

collector axis horizontal or with the axis lying in a vertical plane containing the array normal. The normal

to the collector array can be tilted at any angle with respect to the vertical and with any azimuthal angle

about vertical. Net solar energy collection for a collector not included in SOCOL can be calculated by

inserting the angular response table and loss charactistics of this collector in SOCOL. The uncertainty of

the calculation of net solar energy collection is believed to be about 5%. This is indicated by comparison

with results of Rabl (1981) and Marion and Wilcox (1994).

ACKNOWLEDGEMENTS- Jeff Gordon has made a number of very helpful suggestions which have

improved this paper. Carl Lampert provided advice concerning selective absorbers and provided an

19


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additional reference for information. The reviewers suggested placing SOCOL on a Web site and the U-

Trough design. Herb Shore provided his time to install the FORTRAN compiler on the Compaq laptop

computer. Jim Varnell, Bill Morris, Denis Poon, and Susan Langsford of the College of Sciences Computer

Group continue to provide the able and friendly help needed in computer operations. Denis Poon provided

assistance in placing SOCOL and supporting material on its web site.

NOMENCLATURE

A absorber area (m2)

AG glass window area (m2)

B angle constant in equation of time

C collector concentration

E time correction (hours)

Eb direct radiation energy collection (KJ/m2) and (MJ/m2)

Ed diffuse radiation energy collection (KJ/m2) and (MJ/m2)

ET net total radiation collection (KJ/m2) and (MJ/m2)

H standard time (hours)

I hourly global radiation (J/m2 - hr)

Id hourly diffuse radiation (J/m2 - hr)

Ib hourly direct normal radiation (J/m2 - hr)

Io hourly normal extraterrestrial radiation (J/m2 - hr)

Ioh hourly extraterrestrial radiation on horizontal surface (W/m2)

KT clearness index

Kd diffuse index

Kb direct (beam)index

T absorber temperature (K)

TA ambient temperature (K)

TD dew point temperature (C)

TG window glass temperature (K)

TSKY sky temperature (K)

b two surface enclosure constant (for loss calculations)

hp air flat plate collector bottom loss coefficient (W/m2-K)

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no number of days since beginning of year

q energy intensity (W/m2)

t solar time, t = 0 at solar noon (hours)

io unit vector in direction of sun

jo unit vector normal to io and ko (= -io x ko )

ko unit vector normal to earths orbital plane

k unit vector parallel to earths axis (north)

i unit vector normal to k in plane ofio and k

j unit vector east at solar noon = k x i

i unit vector normal to earths surface at equator at collector longitude

j unit vector, east at collector longitude

k unit vector parallel to earths axis, equals k

n normal to the plane of the collector array

s south at the latitude and longitude of the collector array

v vertical at collector latitude and longitude

H direction of tube axis when horizontal P direction of tube axis when in plane ofn and v selective absorber absorptance

o selective absorber normal absorptance the angle between the sun direction and the polar axis(See Fig. 1A)

selective absorber hemispherical emittance

G glass window hemispherical emittance,G= 0.88 efficiency at incident angle (optical or PV)

earth rotation angle, =0 at solar noon

C angle that the projection ofnonto the horizontal plane makes with south [east of south is positive]

L longitude, L = 0oat Greenwich, England

LO time zone longitude (multiple of 15o)

o earths orbital angle , o= 0 June 21

R phase correction to ofor circular orbit approximationSee (Goldstein, 1983) Sec. 3.8, pp. 98-102.

S the angle the projection of the direction io of sun onto horizontal planemakes with south

X the angle the projection ofio onto the plane transverse to tube

axis makes with normal to array plane n

reflectance

G ground reflectance, albedo (assumes diffuse reflection)

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Stefan-Boltzmann constant,= 5.67x10-8 (W/m2K4)

window transmission

A incidence angle on selective absorber

G incidence angle on glass window

L latitudeN angle earths axis makes with the normal to the earths orbital plane,N= 23.452o

S angle sun direction makes with south

X angle sun direction makes with tube axis

Z zenith angle

angle of incidence on collector array plane

C angle normal to collector array makes with vertical

REFERENCES

Beekley, D. and Mather, G. (1975) Analysis and experimental tests of high performance tubular solar

collectors. Proceedings Intern. Solar Energy Soc., Los Angeles, Calif., USA.

Beckman, W., Klein, S. and Duffie. J. (1977) Solar heating design by the f-chart method, Wiley-

Interscience, New York.

Berdahl, P. and Martin, M. (1984) Emissivity of clear skies. Solar Energy 32, 663-664.

Bloem, H., de Grijs, J. and de Vaan, R. (1982) An evacuated tubular solar collector incorporating a heat

pipe. Philips Technical Review 40, 181-191.

Brunold, S., Frey, R. and Frei, U. (1994) A comparison of three different collectors for process heat

applications. Optical Materials Technology for Energy Efficiency and Solar Energy conversion XIII,

Wittwer, V., Granqvist, C. and Lampert, C. (eds).Proc. Soc. Photo-optical &Instr. Engineers, Vol. 2255.

Cohen, G., et al (1993) Efficiency testing of SEGS parabolic trough collector. Proc.1993 Amer. Solar

Energy Soc., Washington, D.C., April 25-28, pp. 216-221.

Collares-Pereira, M. and Rabl, A. (1979) Derivation of method for predicting long term average energy

delivery of solar collectors. Solar Energy 23, 223.

22


23/41

Duffie, J. and Beckman, W. (1991) Solar Engineering of Thermal Processes, Second Edition, Wiley-

Interscience, New York.

Duff, W., Duquette, R. Winston, R. and OGallagher, J. (1997) Development, fabrication, and testing of a

new design for the integral compound parabolic evacuated solar collector. Proc. 1997 Amer. Solar Energy

Soc., April, pp. 57-61.

Garrison, J., Craig, G. and Morgan, C. (1978) A comparison of solar thermal energy collection using fixed

and tracking collectors. Proc. 1978 Amer. Solar Energy Soc., Boer, K. and Franta, G. (Eds), Vol. 2.1, pp

919-923, 28-31 August.

Garrison, J. and Fischer-Cripps, A. (1997) Stress in shaped glass evacuated collectors. J. Solar Energy

Engineering 119, 79-84.

Garrison, J. (2000) A comparison of solar energy collection by fixed and tracking collectors, Proc. Int.

Solar Energy Soc. Millenium Solar Forum 2000, Mexico City, Mexico, 17-22 September, pp. 381-386.

Garrison, J. (2002) Program for calculation of solar enery collection by fixed and tracking collectors with

applications, Proc. 2002 Amer. Solar Energy Soc. Conference, Reno, Nevada, USA, 16-19 June.

Goldstein, H. (1981) Classical Mechanics, Second Edition, Addison-Wesley, New York.

Gordon, J. (2001) Private communication.

Groetzberger, A., et al (1991) The bifacial absorber collector: A new highly efficient flat plate collector.

Proc. Int. Solar Energy Soc., Denver, CO, USA, pp. 1212 1217.

Gueymard, C. and Garrison, J. (1998) Critical evaluation of precipitable water and atmospheric turbidity in

Canada using Measured hourly solar irradiance. Solar Energy 62, 291-307.

Gordon, J. and Rabl, A. (1982) Design, analysis and optimization of solar industrial process heat plants

without storage. Solar Energy 28, 519-530.

Incropera, F. and deWitt, D. (1990)Introduction to Heat Transfer, John Wiley and Sons, New York.

23


24/41

Iqbal, M. (1983)An Introduction to Solar Radiation . Academic Press, New York.

Klein, S. and Beckman, W. and Duffie, J. (1977) A design procedure for solar air heating systems. Solar

Energy 19, 509.

Klein, S. and Beckman, W. (1976). TRNSYS-A transient simulation program, ASHRAETrans., 82, 623.

Klein, S. (1978) Calculation of flat plate utilizability. SolarEnergy 21, 393.

Klein, S., et al (1990) TRNSYS users manual, Version13, EES Report 38, Univ. of Wisconsin Engineering

Exp. Station.

Liu, B. and Jordan, R. (1963) A rational procedure for producing the long-term average performance of

flat-plate solar energy collectors. Solar Energy 7, 53.

M. Blanco-Muriel, et al (2001) Computing the solar vector, Solar Energy 70, 431- 441.

Marion, W. and Wilcox, S. (1994) Solar radiation data manual for flat plate and concentrating collectors.

NREL/TP-463-5607, National Renewable Energy Laboratory, Golden, CO.

NSRDB (1992) Users m

anual National Solar Radiation Data Base (1961-1990), Vol. 1. National Renewable Energy Laboratory,

Golden, CO.

NSRDB (1995) Final technical report- National Solar Radiation Data Base (1961-1990), Vol. 2. NREL/TP-

463-5784, National Renewable Energy Laboratory, Golden, CO.

Oliva, A., et al (2000) Craft-Joule Project: Stagnation proof transparently insulated flat plate solar collector

(static). Proc. Int. Solar Energy Soc. Millenium Solar Forum 2000, Mexico City, Mexico, 17-22

September, pp. 167-172.

Perez, R., Seals, R. and Michalsky, J. (1993). All-weather model for sky luminance distribution-

preliminary configuration and validation. Solar Energy, 50, 235-245.

24


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Pettit, R. and Sowell,R. (1976) Solar absorption and emittance properties of several solar coatings. Vacuum

Science and Technology 13, 596-602.

Rabl, A. (1981) Yearly average performance of the principal solar collector types, Solar Energy 27, 215-

233.

Rabl, A. (1985) Active Solar Collectors and Their Applications, Oxford University Press, New York.

Reed, K. (1977) Dependence of the solar absorptance of selective absorber coatings on the angle of

incidence. Solar Concentrating Collectors, Proceedings ERDA Conference on Concentrating Collectors,

Georgia Institute of Technology, Atlanta, GA, September 26 28, pp. 5-59 to 5 61.

Rubin, M. (1985) Optical properties of soda lime glass. Solar Energy Materials 12, 275 - 288.

Schmidt, R., Collins, R. and Pailthorpe, B. (1990). Heat transport in dewar-type evacuated tubular

collectors. Solar Energy, Vol. 45, 291-300.

Snail, K., O'Gallagher, J. and Winston, R. (1984) Stationary evacuated collector with integrated

concentrator. Solar Energy 33, 441 - 449.

Swinbank, W. (1963) Long-wave radiation from clear skies. Quart. J. Royal Meteorological Soc.89, 339.

Whillier, A. (1953) Solar energy collection and its utilization for house heating. Sc.D. Thesis, Mechanical

Engineering, Massachusetts Inst. of Technology.

Winston, R., Duff, W. and Cavallaro, A. (1997) The integrated compound parabolic concentrator: from

development to demonstration. Proc. 1997 Amer. Solar Energy Soc., April, pp. 41-43.

Winston, R., et al (1998) Initial performance measurements from a low concentration version of an

integrated compound parabolic concentrator (ICPC). Proc. Amer. Solar Energy Soc. , Albuquerque, NM,

USA, June 14 - 17, pp. 369 - 373.

Zhang, Q. and Mills, D. (1992) High solar performance selective surface using bi-sublayer cermet film

structures. Solar Energy Materials and Solar Cells 27, 273-290.

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APPENDIX

SUN POSITION AND SOLAR ENERGY COLLECTION EQUATIONS

A1. INPUT DATA FROM NSRDB:

Each datum has symbol, name, units and FORTRAN program array name (in italics):

loh, extraterrestrial radiation on horizontal surface (KJ/m2-hr) NETRH; Io, hourly direct normal

extraterrestrial radiation (KJ/m2-hr) NETR; In , hourly direct normal radiation (KJ/m2-hr) NBRAD; Id ,

hourly diffuse radiation (KJ/m2-hr) NDRAD; cloud amount (in fraction of one) CLOUD; cloud opacity

amount (in fraction of one) OPAC; TA, ambient temperature (K) ATEMP; TD, dew point temperature (C)

DTEMP; (Hourly radiation has been converted from Wh/m2; cloud amounts converted from tenths of sky

covered; TA converted from C.)

A2. SOLAR RADIATION INDICES

Clearness index: KT = IG/Ioh,RAD; Diffuse index: Kd = Id/Ioh,DRAD;

Direct index: Kb = Ib/Io,BRAD

A3. EARTHS ORBITAL MOTION

The orbit of the earth is treated as circular with orbital angular correction Rto o,the orbital angle.

The time has correction E calledEquation of Time. The distance from the sun varies over the year. This is

included in the NSRDB input data as a variation ofNETR.

Fig. 1A shows the relation of two rectangular coordinate systems relating the earths orbital

motion to the direction of the sun. Unit vectors of Fig. 1A are: io, sun direction; ko, normal to orbital plane

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and parallel to orbital angular momentum vector;jo = kox io, the direction at right angles to plane ofioand

ko; k, parallel to earths axis and rotational angular momentum;j, east at solar noon; i =j x k, normal to k

in plane of io and k. For a more accurate determination of sun direction which is suitable for high

concentration tracking collectors see (M. Blanco-Muriel, et al, 2001).

Orbital angle: o= 2 (no-172)/365 + R,

where no is number of days since beginning of the year.

Relations: cos =cos osinN; k = cos io+ sin osinNjo + cosNko;j = kxio/ sin

A4. SOLAR TIME AND ROTATION OF EARTH

B = 2 (no 1)/365

Equation of time (Iqbal, 1983), p. 11:

E = 0.0002865 + 0.0071358 cos B 0.12253 sin B 0.055829 cos 2B 0.1562 sin 2B (hours)

Solar time: t = H 12 + ( L - LO)/15 + E (hours) Lis the longitude at the collector site, and LO

is the time zone longitude.

A5. DEVELOPMENT OF ENERGY COLLECTION EQUATIONS

The new unit vectors in Fig. 2A are associated with rectangular coordinates rotating with the

earth: i, unit vector perpendicular to the earth at the equator at the collector longitude; j, east at collector

longitude; k, same as k. Also shown in Fig. 2A are s, south at collector latitude and longitude; v, vertical

at the collector latitude and longitude. Fig. 3A shows the rectangular coordinate system used at the

collector latitude and longitude, with orthogonal unit vectors s,j (east), and v. The normal to the collector

27


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array n and the direction of the sun io are also shown. Two other unit vectors not in the figure are used:

H, direction of collector tube axes when horizontal;P, direction of collector tube axes when in the

plane ofn and v .

Earth rotation angle: = t/12 (radians, < 0 before solar noon) .

Relations: io= cos k + sini; io i = sin ;ioj = 0; io k = cos;i =cos i + sin

j;

j = - sin i + cos j, v = cosLi+ sinLk; s = sinLi - cosLk; v = cosLcos i +

cosLsin j + sinLk; s = sinLcos i + sinLsin j -cos Lk; n = sinccos cs +

sin csin cj + coscv;H = - sin cs + cos cj; P= sincv cosc cos cs

coscsin cj

Cosine of angle of incidence of radiation on array plane:

cos = io n = sin [ sin ccos c sinL cos sin c sin csin +

cosccosLcos ] + cos [ cos csinL - sinccos ccosL]

Cosine of zenith angleZ: cosZ= v io= cosLcos sin+ sinLcos

Cosine of angle sun direction makes with s:

cos S= ios = sin cos sinL cos cosL

Cosine of angle that projection of sun direction onto horizontal plane makes with south:

cos S= cosS/ sinZ

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Cosine of axial angleXwithH: cosXH= sinZ[cos csin S sin ccos S]

Cosine of axial angle XwithP: cosXP= cosZsinc- sinZcosc[cos Scos c+ sin S

sin c]

Cosine of projected angle Xin plane transverse toH: cos X H = cos/sin XH

Cosine of projected angle Xin plane transverse toP: cos XP= cos/sin XP

Hourly direct radiation collection: Eb= KbIo x (angular response) x timeEB

Hourly total radiation collection: ET = Eb + Ed loss (ET > 0)ET

TABLE 1- DOUBLE GLAZED FLAT PLATE COLLECTOR ANNUAL ENERGY COLLECTION

-A COMPARISON OF RABL MODEL WITH SOCOL SIMULATION-

29


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AlbuquerqueIcoll = 8.0 GJ/m2-y, I = 0.60 kW/m2, TA =13 C (Rabl Data)

Zhang-Mills Absorber

Rabl Model ( o = 0.75) SOCOL Simulation (NSRDB data)T U X Q/o Q Q (annual) Q (ave

C W/m2-C kW/m2 GJ/m2 GJ/m2 GJ/m2 GJ/m2 GJ/m2 GJ/m2 GJ/m21976 1977 1978 1979 Averag

13 0.00 0.000 8.00 6.00 6.10 5.88 5.55 5.68 5.8040 2.09 0.075 6.98 5.24 5.32 5.12 4.82 4.94 5.0570 2.32 0.176 5.70 4.28 4.29 4.11 3.87 3.96 4.06120 2.58 0.368 2.80 2.10 2.63 2.52 2.37 2.42 2.49

Pettit-Sowell Absorber

Rabl Model ( o = 0.77) SOCOL Simulation (NSRDB data)

T U X Q/o Q Q (annual) Q (aveC W/m2-C kW/m2 GJ/m2 GJ/m2 GJ/m2 GJ/m2 GJ/m2 GJ/m2 GJ/m2

1976 1977 1978 1979 Averag13 0.00 0.000 8.00 6.16 6.58 6.34 5.98 6.12 6.2640 2.23 0.080 6.91 5.32 5.55 5.34 5.03 5.15 5.2770 2.50 0.190 5.53 4.26 4.41 4.23 3.98 4.07 4.17120 2.85 0.410 3.32 2.56 2.52 2.42 2.27 2.32 2.38

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TABLE 2 ANNUAL SOLAR ENERGY COLLECTION (MJ/M2)

Year = 1979 Albuquerque KT =0.64 Seattle K T = 0.43

COLLECTOR 40 70 120 200 300 40 70 120 200 300

ARRAY Axis

1 AIR FLAT PL 1G E-W 5583 4087 2058 87 0 2961 1953 810 3 0

3 DEWAR Polar 7396 7079 6317 4445 850 4372 4080 3441 2119 193

N-S 6344 6027 5274 3406 447 3871 3576 2918 1615 79E-W 6697 6383 5644 3858 674 3980 3691 3071 1824 153

3 LOW LOSS Polar 7475 7245 6714 5354 2433 4444 4239 3770 2725 939

DEWAR N-S 6429 6192 5664 4304 1580 3942 3736 3257 2197 598

E-W 6837 6546 6026 4720 2021 4050 3848 3389 2394 763

4 U TROUGH Polar 7231 6919 6170 4338 866 4277 3989 3361 2069 214

N-S 6199 5886 5146 3326 454 3778 3487 2842 1568 86

E-W 6802 6492 5762 3992 796 4037 3752 3138 1899 198

4 LOW LOSS Polar 7279 7041 6461 5002 1953 4330 4106 3601 2506 699

U TROUGH N-S 6247 6009 5434 3970 1209 3830 3605 3088 1982 412E-W 6849 6613 6044 4629 1771 4089 3867 3371 2316 632

5 CUSP Polar 7031 6770 6136 4557 1354 4174 3930 3388 2236 432N-S 6060 5798 5171 3585 779 3706 3460 2902 1745 220

E-W 6637 6377 5758 4235 1304 3947 3705 3174 2070 412

5 LOW LOSS Polar 7093 6931 6529 5474 3120 4243 4088 3723 2877 1350CUSP N-S 6121 5960 5556 4507 2218 3775 3620 3248 2382 942

E-W 6725 6537 6140 5120 2909 4015 3862 3501 2682 1249

6 HORIZONTAL Polar 6331 6121 5618 4367 1800 3768 3571 3130 2193 662

FIN N-S 5275 5057 4560 3327 1080 3195 2999 2552 1627 360

E-W 6203 5995 5493 4252 1739 3686 3490 3052 2127 6356 LOW LOSS Polar 6554 6290 6026 5331 3746 3842 3739 3492 2901 1789

HORIZONTAL N-S 5513 5222 4962 4274 2739 3302 3166 2919 2321 1261

FIN E-W 6425 6162 5899 5210 3639 3760 3657 3411 2826 1729

8 VERTICAL Polar 6005 5887 5592 4811 3055 3598 3485 3213 2571 1389HALF FIN N-S 5105 4988 4693 3916 2206 3146 3032 2758 2099 981

E-W 5625 5508 5216 4455 2774 3371 3258 2989 2365 1241

9 HORIZONTAL Polar 6206 5963 5669 4910 3191 3648 3534 3263 2631 1467

HALF FIN N-S 5245 4978 4688 3932 2285 3129 3014 2742 2103 1014

E-W 6091 5829 5537 4780 3088 3569 3456 3186 2559 1415

12 35 DEG CPC Polar 4469 4286 4104 3660 2762 2648 2574 2401 2011 1352

N-S3518

3346 3166 2739 1928 2037 1966 1795 1416 840E-W 5541 5252 5066 4587 3486 3226 3089 2913 2494 1702

13 ONE AXIS Polar 6231 6214 6166 6015 5637 2945 2931 2895 2788 2537

PARABOLIC N-S 5640 5623 5575 5423 5045 2686 2672 2636 2528 2272

TRACK E-W 5016 4998 4946 4787 4403 2354 2340 2303 2197 1951

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FIGURE CAPTIONS

Fig. 1. A schematic view of the transverse cross sections of 8 of the 15 solar collectors used in this

study. The number of each collector is placed just to the left of each transverse cross sectional view. The

collector concentration C is also shown.

Fig. 2. The variation of absorptance over normal absorptance with incidence angle on the

selective absorbers of Pettit and Sowell (1976) and Zhang and Mills (1992).

Fig. 3. A projected view of the circular cross section of evacuated collector glass tube in the plane

transverse to the tube axis. n is the normal to the plane of the collector array.X is the angle a sun ray

makes with tube axis direction . xis the angle a projection of a sun ray in the plane transverse to

makes with respect to n. io is the direction of the sun.

Fig.4. The angular response of the vertical fin collector (Number 7) using the Pettit and Sowell

(1992) selective absorber.

Fig. 5. The variation of net annual solar energy collection by a single glazed air flat plate collector

shown with increasing mean annual clearness index KT using values calculated by SOCOL for 33 stations.

Points are connected by a solid line. The collector is tilted towards the equator at the latitude angle. A least

square fit of a function of the five variables K d, K d, L, T and Ta, to the net annual energy collection is

shown by the points connected by the dashed line.

Fig. 1A. Two rectangular coordinate systems giving the orientation of the earth with respect to the

sun and the earths orbital plane. Unit vector io is the direction to the sun. Unit vector kois the normal to

the earths orbital plane and parallel to the orbital angular momentum. Unit vector jo = kox io. Unit vector

32


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kis parallel to the earths axis and rotational angular momentum. Unit vector i lies in the plane ofk and io

and is perpendicular to k. Unit vectorj = k x i. The angle is the earths orbital angle about the sun and

Nis the fixed angle the earths axis makes with respect to the normal to the orbital plane ko.

Fig. 2A. The relation of the unit vectors i, j and k of the rectangular coordinate system rotating

with the earth to unit vectors i, j and k of Fig. 1A. The unitvectors k and k coincide. i is normal to the

earths surface at the equator at the longitude of the solar collector site. At solar noon at this longitude, the

earths rotational angle is zero and i is parallel to i. The unit vector j is east at the solar collector

longitude. The unit vector v is vertical at the latitude and longitude of the solar collector site. The unit

vector s is horizontal and directed south at the collector latitude and longitude.s and v lie in the plane ofi

and k. v makes an angle with i equal to the latitude, L.

Fig. 3A. The orientation of the direction of the sun io and the normal to the solar collector array n

with respect to the unit vectors s,j and v of Fig. 2A.cis the angle ofn with respect to v. c is the

angle the projection of n on the horizontal plane makes with s. The angle io makes with v isz (zenith

angle). The angle io makes with sis s. The angle the projection ofio onto the horizontal plane makes with

s is s.

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34

C = 1.0

1

C = 0.51

7

C = 0.89

8

C = 0.32

3

C = 0.89

9

C = 0.39

5

C = 1.4

12

C = 0.4

6


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35

ABSORPTANCE RATIO VS INCIDENCE ANGLE

0.0

0.2

0.4

0.6

0.8

1.0

0 15 30 45 60 75 90

G (DEG)

Pettit-Sowell

Zhang-Mills


36/41

36

n

io

x

x

(N ormal to A rray Pla

(Sun D irectio

(Tube Axi


37/41

37

0.0

0.2

0.4

0.6

0.8

1.0

VACUUM VERTICAL FIN

Angular

Response

x (deg)

x (deg)0

2040

60

80

10

30

50

70

90

o = 0.95


38/41

38

1000

3000

5000

7000

0.40 0.50 0.60 0.70

CLEARNESS INDEXT

Series5

Series6

Series7

Series8

T = 40 C

T = 70 C

SINGLE GLAZED FLAT PLATE COLLEC

ANNUAL ENERGY COLLECTION

SOCOL CALCULATI

RMS FI

RMS ERROR = 130 MJ/m2-y


39/41


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40

k,k'(north)

i

i'

j' (east

v

L

s


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v

j' (east

s

n

io

c

css

z

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