a program for calculation of solar energy collection by fixed and tracking collectors

7/29/2019 A Program for Calculation of Solar Energy Collection by Fixed and Tracking Collectors

1/15

Solar Energy Vol. 73, No. 4, pp. 241255, 20022003 Elsevier Science Ltd

Pergamon P I I : S 0 0 3 8 09 2 X ( 02 )0 0 0 6 6 X All rights reserved. Printed in Great Britain0038-092X/02 /$ - see front matter

www.elsevier.com/locate/solener

A PROGRAM FOR CALCULATION OF SOLAR ENERGY COLLECTION BYFIXED AND TRACKING COLLECTORS

,JOHN D. GARRISON

Physics Department, San Diego State University, San Diego, CA 92182-1233, USA

Accepted 9 August 2002

Communicated by BRIAN NORTON

AbstractSOCOL, a realistic and versatile FORTRAN program, has been developed to estimate net solar energycollected by a solar collector per unit collection area. This program was developed to study the properties ofvarious solar collectors. It is made useful to a wide spectrum of users by allowing them to choose any or all of15 possible solar collector types for calculation and comparison. Additional collectors can be included withoutundue 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 surfacemeteorological data taken from The National Solar Radiation Data Base (NSRDB) for 239 stations over theUSA. It can be adjusted to read other data sets. It takes 20 s on a Compaq Presario 2700 1.13 GHz computer tocalculate net solar energy collection per unit area for one solar collector design using each of two selectiveabsorbers at five fixed absorber temperatures for all the daylight hours of 1 year at one location. The programoutput includes sums of solar energy collection for each day, month and year along with averages anddistributions. Averages and distributions for the solar radiation and surface meteorological data are alsoobtained so solar energy collection can be related to these data. SOCOL can be downloaded from the website:www.sci.sdsu.edu/SOCOL/. 2003 Elsevier Science Ltd. All rights reserved.

1. INTRODUCTION simpler f-chart method (Klein et al., 1977; Beck-

man et al., 1977), the Utilizability method (Whil-The FORTRAN program SOCOL calculates the net lier, 1953; Liu and Jordan, 1963; Klein, 1978;

solar thermal energy collected per unit area byCollares-Pereira and Rabl, 1979), and the more

any of a variety of solar thermal collectors and athorough and involved, but quite flexible, mathe-

planar PV collector for solar electricity for amatical simulation methods, such as TRNSYS (Klein

particular site and year. It allows comparison ofand Beckman, 1976; Klein et al., 1990; Duffie

different collectors. It is useful for estimatingand Beckman, 1991), for example.

energy collection by a particular collector at aThis work is a long overdue continuation and

particular location for various fixed operatingmuch improved version of an earlier study (Gar-

temperatures and orientations of the collector, orrison et al., 1978). Rabl has done an excellent,

comparing energy collection at different locations.somewhat similar study, which is discussed fur-

The net amount of solar thermal energy col-ther below (Rabl, 1981). Rabls work has been

lected per unit area by a collector is the amount of used by Gordon and Rabl (1982) for an analysisenergy absorbed by the absorbing surface minus

of process heat plants without storage. Brunold etthe energy lost by the absorbing surface to the

al. (1994) compare energy collection by twoenvironment per unit area. The thermal conduc-

evacuated collectors and one air flat plate collec-tion losses by supports for the absorber can be

tor with glass capillary transparent insulation.made small and are neglected. Energy collection

SOCOL contains parts of a program SOLRAD, usedand energy losses by a complete energy system

by Gueymard and Garrison (1998) for example,are not considered here.

so that solar energy collection can be related toMany methods already exist for analysis and

the properties of the solar radiation and surfacedesign of a complete solar energy system. They

meteorological data. SOCOL goes one step beyondare very useful and well tested. These include the

the work of Marion and Wilcox (1994), who use

solar radiation data from the National SolarRadiation Data Base (NSRDB, 1992; NSRDB,

1995) to estimate the direct and diffuse solarFax: 11-619-594-5485; e-mail: [email protected] member. radiation incident on flat plate, concentrating and

241


2/15

242 J. D. Garrison

tracking collectors with varying orientations and

locations. Examples of calculations by SOCOL have

been discussed earlier (Garrison, 2000, 2002).

2. THE FORTRAN PROGRAM SOCOL

2.1. The data

When SOCOL is started it requests: the station;

year of the data; tilt u and azimuthal angle f ofc cthe collector array; angle limits on the sky and

collector view horizons; range of numbers of the

types of collectors to be calculated; surface al-

bedo; 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 acollector. 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; five hemis-

pherical emittance values for five absorber oper-

ating temperatures; and a weighting factor (dis-

cussed in Section 2.3 below). Input for the planarFig. 1. A schematic view of the transverse cross sections of

PV array is discussed below.eight of the 15 solar collectors used in this study. The number

The program then reads the solar radiation and of each collector is placed just to the left of each transversesurface meteorological data for 1 year from a file. cross sectional view. The collector concentration C is also

shown.The input solar radiation and surface meteorologi-

cal data currently used are the National Solar

Radiation Data Base for 239 US stations available the absorber surfaces in vacuum) are shown. Thefrom the National Climatic Data Center, NOAA, vacuum envelope for the evacuated collectors is aUS Department of Commerce, Washington, DC. glass tube. Solar energy collection is by a planeSolar radiation and surface meteorological data parallel array of identical collector tubes, with thefor Canadian stations obtained from the Atmos- plane of the collection area for each tube in thepheric Environment Service, Downsview, On- plane of the array. SOCOL calculates energy collec-tario, Canada have also been used (Garrison, tion for these eight types of collectors and seven2000). SOCOL contains information concerning: the others not shown. These 15 collectors are dis-selective absorbers used as standards in the pro- cussed below. The collector concentration C,

gram; loss properties and angular response of 15 shown with each collector cross section in Fig. 1,solar collectors; station data; corrections for de- is taken to be the ratio of normal incidence energyviation of the orbital motion of the earth from collection area to the absorber surface area. Thecircular motion; and data needed to estimate the individual collectors will now be discussed.distribution of diffuse radiation over the sky [1,2] Air flat plate in the top upper left of(Perez et al., 1993). Fig. 1 is shown a simplified partial cross

section of a single glazed air flat plate collector2.2. Collector designs (number 1). A double glazed air flat plate

Fig. 1 shows simplified transverse cross sec- collector (number 2), whose energy collection

tions of eight fixed collector designs and their is also calculated, is not shown. These two

identifying numbers whose energy collection collectors are discussed in Duffie and Beckman

properties have been included in this program. (1991, Chapter 6) and Rabl (1985, Chapter 1).One single glazed air flat plate collector (number [3] Vacuum tubular (dewar) just below the

1, with the absorbing surface in air) and seven single glazed air flat plate collector in Fig. 1 is

evacuated collectors (numbers 3, 59, 12, with shown a simplified transverse cross section of


3/15

A program for calculation of solar energy collection by fixed and tracking collectors 243

a fixed evacuated glass tubular (dewar) collec- below the vacuum tubular collector cross

tor. Tubes of this type have been discussed by section. The surface of the cusp is coated with

Beekley and Mather (1975) and Schmidt et al. selective absorber. For this study, the cusp is

(1990). Nippon Electric Glass in Japan and assumed to have a width which is 92% of the

others have used larger diameter tubes of this diameter of the outer vacuum envelope. The

type for their ICS collector. For this study, the cusps in an array of these tubes act as a trap

inner absorber tube is taken to have a diameter for solar radiation, since the reflected part ofwhich is 92% of the diameter of the outer glass rays incident on the absorber surface are often

tube. When tube axes are oriented in approxi- again incident on the absorber and mostly

mately a polar axis direction, they act much absorbed. The properties of this collector place

like a tracking collector, since the collecting it intermediate between the vacuum U-trough

area viewed from any direction perpendicular collector (number 4) and horizontal fin collec-

to the tube axis does not change, except for tor (number 6) in collection and loss prop-

shielding by neighboring tubes. Because of this erties. The radiation loss by this collector can

feature, this collector collects more solar be reduced by the order of 30% by silvering

energy per unit collection area at low operating the inner surface of the lower half of the glass

temperatures than any other collector consid- tube and placing a very low emissive coating

ered here. Its energy collection per unit ab- on the bottom of the cusp. Placing a thermallysorber area is the lowest of any of the collec- floating low emittance fin just below the cusp

tors considered here, since its concentration is bottom will reduce the bottom loss further by a

only C5 1 /p5 0.32. Thus, its energy loss by factor of about two. With this reduction, this

radiation per unit collection area is large collector can collect more energy per unit

relative to the other evacuated collectors with collection area than any of the other fixed

higher concentration. This loss can be reduced collectors discussed here at an operating tem-

by the order of 20% by the use of a silver perature near 2008C, and more than all other

mirror on the inner surface of the outer glass collectors except the dewar and U-trough

tube on the lower non-collecting portion of the collectors with loss reduction at lower tem-

tube, and by the use of a very low emissive peratures.

coating on the corresponding outer surface of

[6] Vacuum horizontal fin a simplifiedthe inner tube. A low emittance, thermally transverse cross section of an evacuated,

floating shield can be placed between the inner horizontal fin collector tube is shown just

and outer tubes in this region to reduce further below the vacuum cusp collector in Fig. 1.

this regions loss by about a factor of two. Collectors of this type are shown in Duffie and

[4] Vacuum U-trough the simplified cross Beckman (1991, Chapter 6) and Rabl (1985,

section of this collector tube has the absorber Chapter 1). The internal fin flat plate is

surface consist of a semicircular trough in the coated with a selective absorber. For this

lower half of the outer glass tube with absorber study, the internal fin is assumed to have a

on both inside and outside surfaces. Its width which is 92% of the diameter of the

semicircular cross section is identical to the outer vacuum envelope. The concentration is

lower half of the dewar collector (number 3). taken to be 0.49, reduced from 0.50 by the

The energy collection by this collector is effect of an energy collection tube thermally inintermediate between that of the dewar collec- contact with the internal fin (not shown).

tor and the vacuum cusp collector (number 5) Commercial production of this type of collec-

discussed next. The loss of this collector can tor tube has been by Philips in the Netherlands

also be reduced by the use of a silver mirror on (Bloem et al., 1982); Fournelle Energie Tech-

the inner surface of the glass vacuum envelope nologies, Canada; Thermomax Technologies,

tube and by the use of a very low emissive UK; Corning of France; Philco Italiana of Italy

coating on the corresponding outer surface of and Nippon Electric Glass of Japan, and

the lower part of the semicircular trough. A others. The energy loss by this collector can be

low emittance, thermally floating shield can be reduced by the order of 40% by coating the

placed between the inner trough and outer inner surface of the lower half of the glass tube

glass tube in this region to reduce further this with silver and by placing a very low emissiveregions loss by about a factor of two. coating on the lower surface of the fin. Placing

[5] Vacuum cusp the simplified cross a thermally floating shield just below the

section of this collector tube is shown just bottom of the fin will reduce further the bottom


4/15

244 J. D. Garrison

loss by about a factor of two. With this loss this type of collector are Snail et al. (1984)

reduction this collector can collect more and Garrison and Fischer-Cripps (1997) and

energy than any other of the fixed collectors references found therein. Energy collection by

near 3008C. this type of collector tube with acceptance

The subsequent collector designs (numbers half-angles of 608 (number 10) and 458 (num-

712) indicated in Fig. 1 and discussed below ber 11) is also included in SOCOL

have a mirror on the inside surface of the [13,14] Parabolic tracking evacuatedlower half of the glass tube to concentrate solar parabolic tracking collectors are not shown in

radiation onto the inner absorber surface. The Fig. 1. SOCOL can calculate energy collection

internal silver mirrors are assumed to have a by a single axis parabolic tracking collector

reflectance r50.95, independent of angle of (number 13). This tracking collector is

incidence of the solar radiation on the mirror. modeled to be similar to the Luz Corporation

They do not lend themselves to further loss SEGS arrays LS-2 and LS-3 (Cohen et al.,

reduction, as can be done for collector num- 1993) who quote a concentration ofC571 for

bers 36. The loss reductions possible with the LS-2 design. This concentration is the ratio

collectors 36, called low loss, are calculated of parabolic mirror width to absorber tube

in SOCOL by input of the number one for the diameter, rather than circumference (Gordon,

number requested by SOCOL. 2001). Here, C5 71 /p522.6. The LS-3 has a [7] Vacuum vertical fin at the top right of normal incidence optical efficiency of 0.80,

Fig. 1 is shown a simplified transverse cross about the same as the vacuum tubular collector

section of an evacuated vertical fin collector. used here with no neighboring tubes. SOCOL can

For NS or polar axis orientation of these calculate energy collection by a two-axis

collector tubes, this collector design can in- parabolic tracking collector (number 14). This

crease energy collection in the early morning is assumed to have a concentration of 500 and

and late afternoon, relative to the evacuated a normal incidence optical efficiency of 0.80.

horizontal fin collector. [15] Planar PV this is the most common

[8] Vertical half fin at the top of Fig. 1 on form of solar electric collector, not shown in

the right, just below the vertical fin collector is Fig. 1. It consists of a plane array of solar

shown a simplified view of the transverse cross cells. The input for this collector consists ofsection of an evacuated vertical half-fin collec- the normal efficiency h of this collector at0tor tube. Tubes of this type are discussed by 208C, a number for the variation of the relative

Winston et al. (1997, 1998) and Duff et al. efficiency h/h with incident angle, and a0(1997) and references found therein. This has number for a linear (assumed) variation of

ideal CPC concentration (Welford and Win- efficiency with temperature relative to 208C (in

ston, 1989) with acceptance half angle of 908 percent change per degree Celsius). The vari-

with C50.89. ation of relative efficiency with incident angle

[9] Horizontal half fin in Fig. 1 on the right, is expected to have approximately the same

just below the cross section of the evacuated form as the variation of relative absorptance of

vertical half-fin collector tube, is a simplified the selective absorbers of the thermal collec-

view of the transverse cross section of an tors and can be specified in the same manner

evacuated horizontal half-fin collector tube. (discussed in Section 2.3 and shown in Fig. 2).CPC tubes of this type are also discussed by If one wishes to design a best collector for a

Winston et al. (1997, 1998) and Duff et al. given temperature, one might wish to try other

(1997) and references found therein. designs besides the 15 discussed above. For

[1012] CPC shaped glass on the right side example, the U-trough collector does not need to

of Fig. 1 below the evacuated horizontal half- be semicircular in cross section, but can be an arc

fin collector is shown a cross section of a fixed of a circle of larger radius of curvature, placing

evacuated CPC shaped glass solar collector the design intermediate between the U-trough and

tube with acceptance half-angle of 358 (number the horizontal fin of infinite radius of curvature.

12). This collector with small acceptance angle The U-trough or arc can also be inverted into the

has the highest energy collection per unit upper half of the vacuum envelope tube. Also a

absorber area of all the fixed collectors dis- V trough can be tried. Such trials are time-cussed here. It has the lowest heat loss per unit consuming since they require ray tracing to

collection area of any of the fixed collectors determine the angular response of each design.

considered here. Representative references for The air flat plate collectors (numbers 1 and 2)


5/15


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).

have a rectangular energy collection area. The and the tubes are oriented parallel to the polar

absorbing surface and its bottom insulation are axis. The other exceptions are the U-trough, cusp

contained in a sealed rectangular box. Both and vertical fin collectors (numbers 4, 5 and 7)

orthogonal transverse dimensions of the absorber which also collect somewhat more energy when

surface are assumed to be large compared to the widely separated and with the polar axis orienta-

height of the upper part of the side walls of the tion.sealed box which are above the absorber surface,

so edge effects will be small. 2.3. The absorber surfaceThere exist a number of air flat plate solar

The selective absorber literature has beencollectors with modifications to the basic flat plate

searched rather thoroughly in an attempt to finddesign. See for example, Oliva et al. (2000) and

all absorbers with measurements of the variationGroetzberger et al. (1991). Oliva et al. describe

of absorptance a with the angle of incidence onan air flat plate solar collector with a honeycomb-

the absorber. Although the number of selectivetype transparent insulation cover. Goetzberger et

absorbers discussed in the literature is of the orderal. describe a bifacial collector with concentration

of 1000 or more, only 25 measurements of theand absorber surface insulation. Energy collection

absorptance as a function of angle of incidenceby collectors of this type can be calculated using

have been found. Two of these 25 selectiveSOCOL by including their angular response and loss absorbers have been selected for use in thesecharacteristics in the program.

studies: the black chrome on Watts nickel ab-The evacuated collector tubes are assumed to

sorber of Pettit and Sowell (1976) with normalbe long relative to the width across the tube in the

incidence absorptance ofa50.95 and the highly0transverse direction so that end effects are small.selective cermet absorber of Zhang and Mills

The tubes in an array are assumed to have a(1992), sample R517CuB, with a50.92. The0spacing that is 20% of the transverse tube width.mathematical form of the variation of a/a with0Knowing this spacing permits calculation of theincident angle used to fit the data here is

effect of scattering and attenuation by neighboringdtubes on the energy collection of a tube. The a/a 512 exp [2c(902u ) ], (1)0 A

effect of the spacing on solar energy collection is

small, of the order of 1%. Exceptions are: the where u is the angle of incidence on the absorberAvacuum tubular (dewar) collector (number 3), surface in degrees. The adjustable parameters c

which collects about 15 to 20% more energy and d are varied to yield least square fits to the

when the tubes of an array have a wide separation measured values of absorptance for each absorber.


6/15

246 J. D. Garrison

In fitting the measured values, it is important that

the unmeasured value: a/a 50 at u 5908 is0 Aincluded. Fig. 2 shows the variation of the Pettit

Sowell and ZhangMills absorbers with angle of

incidence. Smooth selective absorbers with a high

selectivity ratio a / ( is the hemispherical0emittance) apparently have a variation of a/a0with 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 a of0the new absorber; and the position of the curve

for a/a for the new absorber relative to those for0the PettitSowell and ZhangMills curves in Fig.

2. In specifying this position, the position of the

PettitSowell absorber curve is taken to be 1.0Fig. 3. A projected view of the circular cross section ofand the position of the ZhangMills absorber

evacuated collector glass tube in the plane transverse to thecurve 0.0 for linear interpolation or extrapolation. tube axis. n is the normal to the plane of the collector array. uXThe planar PV is treated in the same manner withis the angle a sun ray makes with tube axis direction v. f isX

a, a replaced by h, h . the angle a projection of a sun ray in the plane transverse to v0 0makes with respect to n. i is the direction of the sun.0

2.4. Window transmission and reflection

The window glass for all of these collectorray tracing of a group of equally spaced raysdesigns is assumed to be soda lime glass. Theincident upon the collection area at angles u andoptical properties of soda lime glass are presented Xf . Eqs. (1) and (2) are used. The product of thein detail by Rubin (1985). For this study, the Xradiation energy intensity incident with angles utransmission of soda lime glass as a function of Xand f times the angular response for these twoincident angle has been approximated by X

angles is equal to the amount of incident radiationt52.782 cos u (121.011 cos uG G energy intensity which is collected per unit collec-2 tion area per unit time. Because of the longi-1 0.342 cos u ), (2)G

tudinal symmetry along the collector axis direc-where u is the angle of incidence on the glass tion of all the collector designs, it is sufficient toGsurface. Attenuation and bending of radiation in do analytic calculation or ray tracing only in thethe glass is small, and has been neglected: reflec- transverse plane where u 5 908. The collectorsXtion r512t. have longitudinal symmetry and leftright sym-

metry of the transverse cross section of the2.5. The angular response collectors (other than the horizontal half-fin col-

The collector angular response is defined equal lector). These symmetries make the angular re-

to the optical efficiency times the cosine of the sponse values obtained for angles u and fX Xangle of incidence of the solar radiation on the between 08 and 908 determine the angular re-collection area. This replaces the incidence angle sponse at other values ofu and f . In SOCOL, theX Xmodifier used in most work. The angle of inci- angular response of the horizontal half-fin collec-

dence on the collector is defined in this study in tor is the average of the angular response of this

terms of two angles: u , the angle the suns rays collector with the half-fin on the left and on theXmake with the direction of the axes of the right side of the tube. An array is assumed to be

collector tubes unit vector v in each array, and made up of an equal number of left and rightf , the angle the projection of the direction of the tubes.Xincident solar radiation onto the plane transverse Fig. 4 shows the angular response as a function

to the collector axis direction makes with the unit ofu and f for the vertical fin collector of Fig. 1X Xvector normal to the array area n. Angles u and using the PettitSowell absorber. Angular re-X

f are indicated in Fig. 3. The cosine of the angle sponses of other collectors are shown in GarrisonXof incidence on the collector area is the product: (2000). The angular response of the collector

cos f sin u . The optical efficiency h at angles designs is somewhat greater for collectors usingX Xu and f is determined analytically and/ or by the PettitSowell absorber, because of the largerX X


7/15


Fig. 4. The angular response of the vertical fin collector (number 7) using the Pettit and Sowell (1976) selective absorber.

value ofa and also the slower drop-off of a/a the glass window is at ambient temperature.0 0with increasing angle of incidence. The gain in Going one step further, this loss is treated as a

solar energy collection by this increase in angular two-step process: radiation from the absorbing

response using the Pettit and Sowell absorber is surface to the glass window and convection and

largely cancelled at the lower collector operating radiation from the window to ambient. The tem-

temperatures by the greater losses associated with perature of the window is needed for this calcula-

the much larger emittance of this absorber. At tion. It is estimated by iteration until the two steps

higher operating temperatures, solar energy col- of the process transfer energy at the same rate.

lection is much larger using the ZhangMills Radiation from the absorbing surface to the glassabsorber. window is estimated by the equation

In SOCOL, the angular response for each collec-4 4

q5s(T 2T )/[(12 ) / A11 /AFG AGtor is represented by a 19319 element bivariate

histogram of angular response values for equally 1 (12 ) / A ] (3)G G Gspaced intervals from 0 to 908 in both u and f .X X

for a two-surface enclosure (Incropera and deWitt,SOCOL does a table look-up operation for the1990, Eq. (13.23), p. 771). The view factor F isangular response using values it calculates for u AGXset equal to one for all the collectors treated inand f .XSOCOL except the U-trough (number 4), cusp

2.6. Collector losses (number 5) and vertical fin (number 7) where it is

set equal to 0.50 (inside), 0.75 (upper part) andIn SOCOL, energy loss is calculated for five

0.72, respectively. The other symbols in Eq. (3)different values of the absorber operating tem-are: s, the StefanBoltzmann constant; T, theperature: T540, 70, 120, 200, and 3008C. Theseabsorber operating temperature; T , the glasshave been assumed constant over the collection Gwindow temperature; A, the absorber area; , thetime and area. These temperatures are data in Gglass emittance taken to be 0.88; A , the area ofSOCOL and can be changed easily. The loss coeffi- Gthe glass window. The absorber hemisphericalcient of the top surface of the absorber in the airemittances for the PettitSowell and Zhangflat plate collectors is obtained by the method ofMills absorbers are: 0.115, 0.12, 0.14, 0.17, 0.20Klein as given in Duffie and Beckman (1991, Eq.and 0.0275, 0.028, 0.030, 0.033, 0.039, respec-(6.4.9)). The heat loss from the lower side of thetively, at the five operating temperatures. Eq. (3)absorber is determined by a loss coefficient taken

2 takes the following form when the known valuesto be h 50.6 W/m C (about 5 cm of poly-p

are insertedurethane foam).The evacuated collector designs lose thermal

28 4 4 2q5 5.67310 (T 2T )/[(C/ )1 b)] (W/m ).Genergy mainly by radiation from the absorber

surface. A first approximation is to assume that (4)


8/15

248 J. D. Garrison

C is the collector concentration.Values of C and b sky element for each hour is taken to be the

are tabulated as data in SOCOL. The second step of product of the mean incident radiation energy

the heat transfer from window to ambient is intensity from the direction of an element of the

calculated by the equation sky u and f the collector angular response andX Xthe time duration. The net total energy collection

28 4 4q55.0310 (T 2T )G SKY is given by

21 15(T 2T ) (W/ m ). (5)G A

E 5E 1E 2 loss (6)T b dThe first term on the right is an estimation of the

radiation loss, while the second term is an estima- where E is the direct or beam energy collected,btion of the convection loss. T is the skySKY E is the diffuse energy collected, loss is thedtemperature. T is the ambient temperature. TA SKY energy loss by convection and radiation, and E isTis calculated using Berdahl and Martin (1984), if the net total energy collected, all per unit collec-the dew point temperature is in the input surface tion area. Whenever the loss exceeds the summeteorological data. Otherwise Swinbank (1963) E 1E for any hour, the net total energy collec-b dis used. By symmetry there should be no net tion E is set equal to zero. The calculation of theTradiation transfer between the neighboring tubes energy collection from diffuse radiation is time-

in an array. Generally, the temperature drop from consuming. The time to run each hour of data isthe window glass to ambient temperature is small greatly reduced by reducing the number of pointsrelative to the drop from the absorber to the glass. in the sky from 400 to 100, for example, withThe surface meteorological data on wind for each some reduced precision of the calculation.hour or day has not been used to vary the The equations for the solar time and directioncoefficient of the convection loss. The approxi- of the sun as a function of time, along with othermation using Eq. (5) calculates this loss in the needed equations are in Appendix A. The orienta-same manner for all evacuated collectors. Any tion of the collector axes in the plane of theperson desiring to improve this calculation can collector array is assumed to have only twomodify SOCOL. As a help, there are numerous possible conditions, either horizontal, or lying incomments throughout SOCOL to identify the differ- the vertical plane containing the normal to theent calculations.

collector array.2.7. Surface albedo

SOCOL calculates the contribution of solar radia-3. TESTS OF THE PROGRAM

tion scattered by the ground in front of the

collector to solar energy collection. It assumes SOCOL has been tested in many different ways.that the scattering by the ground is diffuse. Often, For each of a few hours selected at random duringthis scattering has a forward component. To the collection year, all the results of the equationsaccount for this effect, the albedo used as input to in the energy collection part of the program haveSOCOL can be increased. The contribution from been hand calculated and sometimes visualizedground scattering is generally quite small. Ground with figures, and then compared with the resultsscattering has a larger effect on diffuse radiation obtained by SOCOL. The collection of solar energy

collection. for particular hours has been tested for properbehavior. For example, when the normal to the

2.8. Calculation of solar energy collection array is horizontal and the plane of the array is

The contribution of each part of the sky to the vertical, energy collection at different azimuthal

diffuse radiation is determined using the prescrip- angles of the array normal are compared to see if

tion of Perez et al. (1993) with sky luminance the behavior is as expected. Thus, there should be

replaced by sky irradiance. The total contribution no direct radiation collection when the normal

of the diffuse radiation to solar thermal energy points north and the hour is in the winter half of

collection is obtained by numerical integration, the year. Also, there is less diffuse radiation

summing the contributions of 400 elements equal- collection when the normal points north. When the

ly spaced over the sky. To this is added the plane of the collector array is horizontal and the

contribution of an additional number of elements angular response is set equal to the cosine of thebelow the horizontal for ground reflection. For zenith angle (optical efficiency h51), the diffuse

both direct and diffuse radiation, the thermal energy collection and the direct energy collection

energy collected per unit collection area for each for each hour are the same as the measured


9/15


diffuse and direct radiation on a horizontal sur- The angular responses of the CPC shaped glass

face. evacuated collector are probably the most prone

When the angular response is set equal to the to error. The first two of these with half-angles of

cosine of the incidence angle on the collector acceptance of 608 and 458 were repeated. The

array and the collection area is tilted at the average of the angular responses over the 19319

latitude angle and faces south at Albuquerque, bivariate histogram for the two determinations

NM, USA, the calculated annual energy collec- differ by about 1% for both the 608 and 458tions per unit area for the years 19761979 collectors. All ray tracings for these use a density

inclusive are: 8641, 8275, 7832, and 8009 MJ/ of 10 rays per collection width of one tube. This2 2

m . The mean is 81896352 (176) MJ/ m where ray density extends across the tube and neigh-

the 352 is the standard deviation of a single year boring tubes in the plane transverse to the tube

and 176 is the standard deviation of the mean. axis.

Marion and Wilcox (1994) give a corresponding2

value of 8400 MJ/ m and Rabl (1981) gives a4. SAMPLE RESULTS BY SOCOL2

corresponding value of 8000 MJ/ m . It is not

known what years Marion and Wilcox, and Rabl Table 2 shows annual energy collection per unit

have used for their values. collection area as a function of absorber tempera-

Finally, the solar energy collection of a double ture at Albuquerque, NM, USA and Seattle, WA,glazed air flat plate collector has been calculated USA. This is for nine collector designs: 1, air flat

using both the PettitSowell and ZhangMills plate; 3, vacuum tubular; 4, U-trough; 5, cusp; 6,

selective absorbers and compared with results that horizontal fin; 8, vertical half-fin; 9, horizontal

are obtained using the method of Rabl (1981). half-fin; 12, 358 CPC shaped glass tube; and 13,

The results of the calculation by SOCOL and single axis parabolic tracking. The values in Table

comparison with Rabl are presented in Table 1. In 2 for each collector use the axes orientations:

the table, T is the absorber operating temperature, EW, NS, and polar. The values are for the

T is the ambient temperature (mean for the year) selective absorber (PettitSowell or ZhangMills)Aused by Rabl, h is the normal optical efficiency which yields the highest energy collection at each0used here in Rabl, and Q is the annual energy temperature. For the few cases at lowest tempera-

2

collection in GJ/ m . The other symbols are as in ture where the PettitSowell absorber collects theRabl. The results by these two methods are in most energy, the number is put in italics. The

good agreement. array normal is tilted at the latitude angle for the

The difference between the calculated energy EW (and polar) orientation. The low loss ener-

collection by one collector and another arises only gies in the table are for collectors 3, 4, 5 and 6

from differences in the angular response and when the lower part of the collectors have low

differences in heat loss. The heat losses have been emissive coatings and thermally floating shields,

checked carefully by hand calculation. The angu- as discussed earlier. The energy collection num-

lar responses have also been checked carefully. bers in bold type in Table 2 are the highest values

Table 1. Double glazed flat plate collector annual energy collection a comparison of Rabl model with SOCOL simulation

Albuquerque T5

138CA

Rabl model SOCOL simulation

2 2I 58.0 GJ/m 2y I50.60 kW/m 1976 1977 1978 1979 Averagecoll

T U X Q/h Q Q02 2 2 2 2

C W/m 2C kW/ m GJ /m GJ /m GJ / m

ZhangMills Absorber, h 5 0.75013 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 5.05

70 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

PettitSowell Absorber, h 5 0.77013 0.00 0.000 8.00 6.16 6.58 6.34 5.98 6.12 6.26

40 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 4.17

120 2.85 0.410 3.32 2.56 2.52 2.42 2.27 2.32 2.38


10/15

250 J. D. Garrison

2Table 2. Annual solar energy collection (MJ /m )

Year51979 Albuquerque K 50.64 Seattle K 50.43T T

Collector T40 70 120 200 300 40 70 120 200 300

array Axis

1 Air flat PL 1G EW 5583 4087 2058 87 0 2961 1953 810 3 03 Dewar Polar 7396 7079 6317 4445 850 4372 4080 3441 2119 193

NS 6344 6027 5274 3406 447 3871 3576 2918 1615 79

EW 6697 6383 5644 3858 674 3980 3691 3071 1824 1533 Low loss Polar 7475 7245 6714 5354 2433 4444 4239 3770 2725 939

Dewar NS 6429 6192 5664 4304 1580 3942 3736 3257 2197 598EW 6837 6546 6026 4720 2021 4050 3848 3389 2394 763

4 U trough Polar 7231 6919 6170 4338 866 4277 3989 3361 2069 214NS 6199 5886 5146 3326 454 3778 3487 2842 1568 86EW 6802 6492 5762 3992 796 4037 3752 3138 1899 198

4 Low loss Polar 7279 7041 6461 5002 1953 4330 4106 3601 2506 699U trough NS 6247 6009 5434 3970 1209 3830 3605 3088 1982 412

EW 6849 6613 6044 4629 1771 4089 3867 3371 2316 6325 Cusp Polar 7031 6770 6136 4557 1354 4174 3930 3388 2236 432

NS 6060 5798 5171 3585 779 3706 3460 2902 1745 220EW 6637 6377 5758 4235 1304 3947 3705 3174 2070 412

5 Low loss Polar 7093 6931 6529 5474 3120 4243 4088 3723 2877 1350cusp NS 6121 5960 5556 4507 2218 3775 3620 3248 2382 942

EW 6725 6537 6140 5120 2909 4015 3862 3501 2682 12496 Horizontal Polar 6331 6121 5618 4367 1800 3768 3571 3130 2193 662

fin NS 5275 5057 4560 3327 1080 3195 2999 2552 1627 360EW 6203 5995 5493 4252 1739 3686 3490 3052 2127 635

6 Low loss Polar 6554 6290 6026 5331 3746 3842 3739 3492 2901 1789horizontal N S 5513 5222 4962 4274 2739 3302 3166 2919 2321 1261fin EW 6425 6162 5899 5210 3639 3760 3657 3411 2826 1729

8 Vertical Polar 6005 5887 5592 4811 3055 3598 3485 3213 2571 1389half fin NS 5105 4988 4693 3916 2206 3146 3032 2758 2099 981

EW 5625 5508 5216 4455 2774 3371 3258 2989 2365 12419 Horizontal Polar 6206 5963 5669 4910 3191 3648 3534 3263 2631 1467

half fin NS 5245 4978 4688 3932 2285 3129 3014 2742 2103 1014EW 6091 5829 5537 4780 3088 3569 3456 3186 2559 1415

12 358 CPC Polar 4469 4286 4104 3660 2762 2648 2574 2401 2011 1352N S 3518 3346 3166 2739 1928 2037 1966 1795 1416 840

EW 5541 5252 5066 4587 3486 3226 3089 2913 2494 170213 One axis Polar 6231 6214 6166 6015 5637 2945 2931 2895 2788 2537

parabolic NS 5640 5623 5575 5423 5045 2686 2672 2636 2528 2272track EW 5016 4998 4946 4787 4403 2354 2340 2303 2197 1951

at each temperature. Energy collection by all 5. Also shown is a least square fit to the net

collectors is highest for the polar axis orientation, energy collection using the relation:

except for the CPC shaped glass collectors. AtE 5 1.282[12 0.0079(T2T )]T Athese latitudes, the EW axis orientation collects

3 [(0.95(K 1K (20.14910.92 cos (u ))more energy than the NS orientation. The b d Levacuated collectors outperform the air flat plate 4

310

26(T

2T )]Acollectors significantly. Energy collection per unit

absorber area is obtained by multiplying by the where K is the annual mean direct beam index,bconcentration. This is of interest since the selec- K is the annual mean diffuse index, T is thed Ative absorber is generally a more expensive part annual mean daylight ambient temperature and uLof the collector. The concentration must be suitab- is the latitude. The correlation between the fluc-

ly changed for the low loss cases. tuations in the lines connecting the calculated

Fig. 5 shows the net annual energy collection energy and the RMS fit indicates validity in theE for 35 US stations for the year 1979 ordered choice of the four variables selected (e.g. surfaceTby increasing mean annual clearness index K for albedo would not be a useful variable).Ta single glazed air flat plate collector using the Table 2 and Fig. 5 are representative of the

PettitSowell absorber at a temperature of T5 types of information which can be obtained using

408C and T5708C. E also varies to a lesser SOCOL. Additional examples may be found inTdegree with latitude, annual mean daylight am- Garrison (2000, 2002). SOCOL calculates mean

bient temperature and surface albedo. This ac- values of K , K , K , cloud amount and opacity,T d bcounts largely for the fluctuation in points in Fig. ambient temperature, in addition to E , E , E ,T d b


11/15


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 K using values calculated by SOCOL for 33 stations. Points are connected by a solid line. The collector isTtilted towards the equator at the latitude angle. A least square fit of a function of the five variables K , K , u , T and T , to the netb d L Aannual energy collection is shown by the points connected by the dashed line.

2A glass window area, mand energy loss for each hour, day, month and the GB angle constant in equation of timeentire year.C collector concentration

E time correction, h2 2

E direct radiation energy collection, kJ /m and MJ/ mb

2 25. SUMMARYE diffuse radiation energy collection, kJ/ m and MJ/ md 2 2E net total radiation collection, kJ /m and MJ/ mTThe FORTRAN program SOCOL is a program ofH standard time, h

rather general utility which realistically predicts 2I hourly global radiation, J /m h

2net hourly solar energy collection for 1 year or I hourly diffuse radiation, J/ m hd

2any part thereof at a particular site for which one I hourly direct normal radiation, J /m hb2

I hourly normal extraterrestrial radiation, J /m hhas data. This net energy collection can be for any 0I hourly extraterrestrial radiation on horizontal surface,

0hof 15 collector types contained in SOCOL. Any 2W/ m

selective absorber can be used for the absorberK clearness index

T

surface. The orientation of the collector array can K diffuse indexd

be with the collector axis horizontal or with the K direct (beam) indexbT absorber temperature, Kaxis lying in a vertical plane containing the arrayT ambient temperature, K

A

normal. The normal to the collector array can be T dew point temperature, 8CDtilted at any angle with respect to the vertical andT window glass temperature, K

G

with any azimuthal angle about vertical. Net solar T sky temperature, KSKY

energy collection for a collector not included in b two surface enclosure constant (for loss calculations)2

h air flat plate collector bottom loss coefficient, W/m KSOCOL can be calculated by inserting the angular pn number of days since beginning of year

0response table and loss characteristics of this 2q energy intensity, W/ m

collector in SOCOL. The uncertainty of the calcula-t solar time, t5 0 at solar noon, h

tion of net solar energy collection is believed to i unit vector in direction of sun0be about 65%. This is indicated by comparison j unit vector normal to i and k (52i 3k )0 0 0 0 0

k unit vector normal to earths orbital planewith results of Rabl (1981) and Marion and 0k unit vector parallel to earths axis (north)Wilcox (1994).i unit vector normal to k in plane of i and k

0

j unit vector east at solar noon5k3i

i9 unit vector normal to earths surface at equator atNOMENCLATURE collector longitude

j9 unit vector, east at collector longitude2

A absorber area, m k9 unit vector parallel to earths axis, equals k


12/15

252 J. D. Garrison

2n normal to the plane of the collector array hourly diffuse radiation (kJ / m h) NDRAD; clouds south at the latitude and longitude of the collector amount (in fraction of one) CLOUD; cloud

arrayopacity amount (in fraction of one) OPAC; T ,Av vertical at collector latitude and longitudeambient temperature (K) ATEMP; T , dew point

v direction of tube axis when horizontal DHv direction of tube axis when in plane of n and v temperature (8C) DTEMP; hourly radiation hasP

2a selective absorber absorptance been converted from W h/ m ; cloud amountsa selective absorber normal absorptance0 converted from tenths of sky covered; T con-Ad sun declination

verted from 8C. selective absorber hemispherical emittance

glass window hemispherical emittance, 50.88G G A.2. SOLAR RADIATION INDICESh efficiency at incident angle u (optical or PV)

f earth rotation angle, f50 at solar noon Clearness index: K 5I/I , RAD; diffuseT 0hf angle that the projection of n onto the horizontalc index: K 5I /I , DRAD; direct index: K 5I /d d 0h b bplane makes with south (east of south is positive)

I , BRAD.0f longitude, f 508 at Greenwich, UKL Lf time zone longitude (multiple of 158)LO A.3. EARTHS ORBITAL MOTIONf earths orbital angle, f50 June 210 0f phase correction to f for circular orbit approxi-R 0 The orbit of the earth is treated as circular with

mation. See Goldstein (1981 Section 3.8, pp. 98 102) orbital angular correction f to f , the orbitalR 0f the angle the projection of the direction i of sun ontos 0angle. The time has correction E called Equationhorizontal plane makes with southof Time. The distance from the sun varies over thef the angle the projection of i onto the plane transverseX 0

to tube axis makes with normal to array plane n year. This is included in the NSRDB input data asr reflectance a variation of NETR.r ground reflectance, albedo (assumes diffuse reflection)G Fig. A.1 shows the relation of two rectangular

28 2s StefanBoltzmann constant, s55.67310 , W/ m

4 coordinate systems relating the earths orbitalK

motion to the direction of the sun. Unit vectors oft window transmissionu incidence angle on selective absorber Fig. A.1 are: i , sun direction; k , normal toA 0 0u incidence angle on glass windowG orbital plane and parallel to orbital angularu latitudeL momentum vector; j 5k 3i , the direction at0 0 0u angle earths axis makes with the normal to theN right angles to plane of i and k ; k, parallel to0 0earths orbital plane, u 523.4528N

u angle sun direction makes with southsu angle sun direction makes with tube axisXu zenith anglezu angle of incidence on collector array plane

u angle normal to collector array makes with verticalc

AcknowledgementsJeff Gordon has made a number of veryhelpful suggestions which have improved this paper. CarlLampert provided advice concerning selective absorbers andprovided an additional reference for information. The review-ers suggested placing SOCOL on a website and the U-troughdesign. Herb Shore provided his time to install the FORTRANcompiler on the Compaq laptop computer. Jim Varnell, Bill

Morris, Denis Poon, and Susan Langsford of the College ofSciences Computer Group continue to provide the able andfriendly help needed in computer operations. Denis Poonprovided assistance in placing SOCOL and supporting materialon its website.

APPENDIX A. SUN POSITION AND SOLARFig. A.1. Two rectangular coordinate systems giving theENERGY COLLECTION EQUATIONSorientation of the earth with respect to the sun and the earths

orbital plane. Unit vector i is the direction to the sun. Unit0A.1. INPUT DATA FROM NSRDB

vector k is the normal to the earths orbital plane and parallel0Each datum has symbol, name, units and to the orbital angular momentum. Unit vector j 5k 3i . Unit0 0 0

vector k is parallel to the earths axis and rotational angularFORTRAN program array name (in italics): I ,0hmomentum. Unit vector i lies in the plane of k and i and is

0extraterrestrial radiation on horizontal surface (kJ/ perpendicular to k. Unit vector j5k3i. The angle f is the2 0m h) NETRH; I , hourly direct normal extrater-0 earths orbital angle about the sun and u is the fixed angle theN2restrial radiation (kJ /m h) NETR; I , hourly earths axis makes with respect to the normal to the orbitaln

2direct normal radiation (kJ/ m h) NBRAD; I , plane k .0d


13/15


earths axis and rotational angular momentum; j,

east at solar noon; i5j3k, normal to k in plane

of i and k. For a more accurate determination of0sun direction which is suitable for high con-

centration tracking collectors see Blanco-Murielet al. (2001).

Orbital angle: f 52p (n 2 172)/3651f0 0 R

where n is number of days since beginning of the0year.

Relations: cos d5 cos f sin u ; k0 N

5 cos d i 1 sin f sin u j0 0 N 0

1 cos u k ;j5k3 i /sin d.N 0 0

A.4. SOLAR TIME AND ROTATION OF

EARTH

Fig. A.2. The relation of the unit vectors i9, j9 and k9 of theB5 2p (n 21)/365. rectangular coordinate system rotating with the earth to unit0vectors i, j and k of Fig. A.1. The unit vectors k and k9

Equation of time (Iqbal, 1983, p. 11): coincide. i9 is normal to the earths surface at the equator atthe longitude of the solar collector site. At solar noon at this

E5 0.00028651 0.0071358 cos Blongitude, the earths rotational angle f is zero and i9 is

20.12253 sin B2 0.055829 cos 2B parallel to i. The unit vector j9 is east at the solar collectorlongitude. The unit vector v is vertical at the latitude and20.1562 sin 2B (h).longitude of the solar collector site. The unit vector s is

horizontal and directed south at the collector latitude andSolar time: t5H2 121 (f 2f )/151E (h)L LO longitude. s and v lie in the plane of i9 and k9. v makes an

angle with i9 equal to the latitude, u .Lf is the longitude at the collector site, and f isL LOthe time zone longitude.

k; s5sin u cos f i1sin u sin f j2cos u k;L L LA.5. DEVELOPMENT OF ENERGYn5sin u cos f s1sin u sin f j91cos u v;c c c c cCOLLECTION EQUATIONSv 52sin f s1cos f j9; v 5sin u v2cos uH c c P c c

The new unit vectors in Fig. A.2 are associated cos f s2cos u sin f j9.c c cwith rectangular coordinates rotating with the

earth: i9, unit vector perpendicular to the earth at

the equator at the collector longitude; j9, east at

collector longitude; k9, same as k. Also shown in

Fig. A.2 are s, south at collector latitude and

longitude; v, vertical at the collector latitude and

longitude. Fig. A.3 shows the rectangular coordi-

nate system used at the collector latitude andlongitude, with orthogonal unit vectors s, j9 (east),

and v. The normal to the collector array n and the

direction of the sun i are also shown. Two other0unit vectors not in the figure are used: v ,Hdirection of collector tube axes when horizontal;

v , direction of collector tube axes when in thePplane of n and v.

Earth rotation angle: f5p t/ 12 (radians,fFig. A.3. The orientation of the direction of the sun i and the

0, 0 before solar noon).normal to the solar collector array n with respect to the unit

vectors s, j9 and v of Fig. A.2. u is the angle of n with respectcRelations: i 5cos dk1sin d i; i ?i5sin d; i ?j50 0 0 to v. f is the angle the projection of n on the horizontal planec0; i ?k5cos d; i95cos f i1sin f j; j952sin f0 makes with s. The angle i makes with v is u (zenith angle).0 z

i1cos fj, v5cos u i91sin u k9; s5sin u i92cos The angle i makes with s is u . The angle the projection of iL L L 0 s 0u k9; v5cos u cos f i1cos u sin f j1sin u onto the horizontal plane makes with s is f .sL L L L


14/15

254 J. D. Garrison

Duff W., Duquette R., Winston R. and OGallagher J. (1997)Cosine of angle of incidence of radiation onDevelopment, fabrication, and testing of a new design for

array plane: the integral compound parabolic evacuated solar collector.In Proceedings of the 1997 American Solar Energy Society,

cos u5 i ?n5 sin d[sinu cos f sin u cos f April, pp. 5761.0 c c LGarrison J., Craig G. and Morgan C. (1978) A comparison of

2 sin u sin f sin fc c solar thermal energy collection using fixed and trackingcollectors. In Proceedings of the 1978 American Solar

1 cos u cos u cos f]c L Energy Society, Boer, K. and Franta, G. (Eds), Vol. 2.1, pp.

919923, 2831 August.1 cos d [cos u sin uc L Garrison J. and Fischer-Cripps A. (1997) Stress in shapedglass evacuated collectors. J. Solar Energy Eng. 119, 792 sin u cos f cos u ].c c L84.

Garrison, J. (2000) A comparison of solar energy collection byCosine of zenith angle u : cos u 5 v ? i 5 cos uz z 0 L fixed and tracking collectors. In Proceedings of the Interna-cos f sin d1 sin u cos d. tional Solar Energy Society Millenium Solar Forum 2000,L

Mexico City, Mexico, 1722 September, pp. 381386.Cosine of angle sun direction makes with s:Garrison, J. (2002) Program for calculation of solar energy

collection by fixed and tracking collectors with applications.cos u 5 i ? s5 sin d cos f sin u 2 cos d cos u .S 0 L LIn Proceedings of the 2002 American Solar Energy SocietyConference, Reno, NV, USA, 1619 June.Cosine of angle that projection of sun direction

Goldstein H. (1981). In 2nd edn, Classical Mechanics, Ad-onto horizontal plane makes with south: dison-Wesley, New York.

Gordon, J. (2001) Private communication.

cos f 5 cos u /sin u .s s z Groetzberger, A. et al. ( 1991) The bifacial absorber collector:a new highly efficient flat plate collector. In Proceedings of

Cosine of axial angle u with v : cos u 5 sin the International Solar Energy Society, Denver, CO, USA,X H XHpp. 12121217.u [cos f sin f 2 sin f cos f ].z c s c s

Gueymard C. and Garrison J. (1998) Critical evaluation ofCosine of axial angle u with v : cos u 5X P XP precipitable water and atmospheric turbidity in Canadacos u sin u 2 sin u cos u [cos f cos f 1 sin f using measured hourly solar irradiance. Solar Energy 62,z c z c s c s

291307.sin f ].cGordon J. and Rabl A. (1982) Design, analysis and optimi-Cosine of projected angle f in plane trans-X zation of solar industrial process heat plants without storage.

verse to v : cos f 5 cos u/ sin u . Solar Energy 28, 519530.H XH XHIncropera F. and deWitt D. (1990). Introduction to HeatCosine of projected angle f in plane trans-X

Transfer, John Wiley, New York.verse to v : cos f 5 cos u/ sin u .P XP XP Iqbal M. (1983). An Introduction to Solar Radiation, Academ-Hourly direct radiation collection: E 5K I 3 ic Press, New York.b b 0

Klein S., Beckman W. and Duffie J. (1977) A design pro-(angular response)3 time EB.cedure for solar air heating systems. Solar Energy 19, 509.Hourly total radiation collection: E 5E 1T b Klein S. and Beckman W. (1976) TRNSYS a transient

E 2 loss (E . 0) ET. simulation program. ASHRAE Trans. 82, 623.d TKlein S. (1978) Calculation of flat plate utilizability. Solar

Energy 21, 393.Klein S. et al. (1990). In TRNSYS users manual, Version 13, EESREFERENCES

Report 38, University of Wisconsin Engineering Ex-Beekley D. and Mather, G. (1975) Analysis and experimental perimental Station.

tests of high performance tubular solar collectors. In Liu B. and Jordan R. (1963) A rational procedure forProceedings International Solar Energy Society, Los producing the long-term average performance of flat-plateAngeles, CA, USA. solar energy collectors. Solar Energy 7, 53.

Beckman W., Klein S. and Duffie J. (1977). Solar Heating Blanco-Muriel M. et al. (2001) Computing the solar vector.Design by the f-chart Method, Wiley-Interscience, New Solar Energy 70, 431441.York. Marion W. and Wilcox S. (1994). Solar Radiation Data

Berdahl P. and Martin M. (1984) Emissivity of clear skies. Manual for Flat Plate and Concentrating Collectors. NREL/Solar Energy 32, 663664. TP-463-5607, National Renewable Energy Laboratory, Gol-

Bloem H., de Grijs J. and de Vaan R. (1982) An evacuated den, CO.tubular solar collector incorporating a heat pipe. Philips NSRDB (1992). In Users Manual National Solar RadiationTech. Rev. 40, 181191. Data Base (1961-1990), Vol. 1, National Renewable Energy

Brunold S., Frey R. and Frei U. (1994) A comparison of three Laboratory, Golden, CO.different collectors for process heat applications. In Optical NSRDB (1995). In Final Technical ReportNational Solar

Materials Technology for Energy Efficiency and Solar Radiation Data Base (19611990), Vol. 2, National Renew-Energy Conversion XIII, Proceedings of the Society of able Energy Laboratory, Golden, CO, NREL/ TP-463-5784.Photo-optical and Instrument Engineers, Vol. 2255, Wittwer Oliva A. et al. (2000) Craft-Joule Project: stagnation proofV., Granqvist C. and Lampert C. (Eds.). transparently insulated flat plate solar collector (static). In

Cohen G. et al. (1993) Efficiency testing of SEGS parabolic Proceedings International Solar Energy Society Milleniumtrough collector. In Proceedings 1993 American Solar Solar Forum 2000, Mexico City, Mexico, 1722 Sep-

Energy Society, Washington, DC, April 2528, pp. 216 tember, pp. 167172.221. Perez R., Seals R. and Michalsky J. (1993) All-weather model

Collares-Pereira M. and Rabl A. (1979) Derivation of method for sky luminance distribution preliminary configurationfor predicting long term average energy delivery of solar and validation. Solar Energy 50, 235245.collectors. Solar Energy 23, 223. Pettit R. and Sowell R. ( 1976) Solar absorption and emittance

Duffie J. and Beckman W. (1991). In 2nd edn, Solar Engineer- properties of several solar coatings. Vac. Sci. Technol. 13,ing of Thermal Processes, Wiley-Interscience, New York. 596602.


15/15


Rabl A. ( 1981) Yearly average performance of the principal Welford W. and Winston R. (1989) High Collection Nonimag-solar collector types. Solar Energy 27, 215233. ing Optics. Academic Press, New York.

Rabl A. (1985). Active Solar Collectors and Their Applica- Whillier A. (1953). Solar Energy Collection and its Utilizationtions, Oxford University Press, New York. for House Heating, Mechanical Engineering, Massachusetts

Reed, K. (1977) Dependence of the solar absorptance of Institute of Technology, Sc.D. thesis.selective absorber coatings on the angle of incidence. In Winston R., Duff W. and Cavallaro, A. (1997) The integratedSolar Concentrating Collectors, Proceedings ERDA Confer- compound parabolic concentrator: from development toence on Concentrating Collectors, Georgia Institute of demonstration. In Proceedings 1997 American Solar Energy

Technology, Atlanta, GA, September 2628, pp. 5-595-61. Society, April, pp. 4143.Rubin M. (1985) Optical properties of soda lime glass. Solar Winston R. et al. ( 1998) Initial performance measurements

Energy Mater. 12, 275 288. from a low concentration version of an integrated compoundSchmidt R., Collins R. and Pailthorpe B. (1990) Heat transport parabolic concentrator (ICPC). In Proceedings of the Amer-

in dewar-type evacuated tubular collectors. Solar Energy ican Solar Energy Society, Albuquerque, NM, USA, June45, 291300. 1417, pp. 369373.

Snail K., OGallagher J. and Winston R. (1984) Stationary Zhang Q. and Mills D. (1992) High solar performanceevacuated collector with integrated concentrator. Solar selective surface using bi-sublayer cermet film structures.

Energy 33, 441449. Solar Energy Mater. Solar Cells 27, 273290.Swinbank W. (1963) Long-wave radiation from clear skies. Q.

J. R. Meteorol. Soc. 89, 339.

a program for calculation of solar energy collection by fixed and tracking collectors

Documents