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J. Renewable Sustainable Energy 1, 043112 (2009); doi:10.1063/1.3207801 (18 pages)
Solar collector basics
5917 Royal Oak St., NE Albuquerque, New Mexico 87111-6236, USA
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This is a guide for solar collector use. Section 2 shows the effective number of sunlit hours per day at the solstices and equinox captured by several solar collector types: stationary flat, sun tracking flat, east-west parabolic and two-trough concentrators and a north-south, sun tracking, two-trough concentrator. Section 3 introduces the sun direction from the circular orbit earth; it is accurate enough for most applications. Section 4 develops atmospheric attenuation of sunlight. Section 5 puts it all together for the calculated results presented in Sec. 2.
© 2009 American Institute of Physics
Article Outline
- INTRODUCTION
- SOLAR COLLECTOR PERFORMANCE
- Stationary flat collectors
- Sun tracking flat collector
- East-west parabolic trough concentrator
- East-west two-trough concentrator
- North-south sun tracking concentrator
- Effect of latitude
- Solar collector comparisons
- THEORY: DIRECTION OF THE SUN
- THEORY: ATMOSPHERIC ATTENUATION
- SOLAR COLLECTOR CALCULATIONS
KEYWORDS and PACS
Keywords
ARTICLE DATA
History
Received 16 April 2009
Accepted 29 July 2009
Published 31 August 2009
Accepted 29 July 2009
Published 31 August 2009
- J. L. Richter, Sol. Energy 56, 191 (1996). [Inspec]
- CRC Handbook of Chemistry and Physics, 69th ed. (CRC, Cleveland, 1989).
- J. Meeus, Astronomical Formulae for Calculators, 4th ed. (Willmann-Bell, Richmond, 1988), Chaps. 3, 18, and 21.
Figures (click on thumbnails to view enlargements)
Collector orientation. The α is the collector azimuth angle from due south and β is the dihedral angle between the collector aperture and horizon planes. The collector direction and south lines are in the horizon plane.
FIG. 1 View Enlargement
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Total sun intensity at three times during the year at latitude 35° for S⋅B = 1 showing air attenuation. For the clear sky, daily sun Ts are 5.35, 7.86, and 9.80 h; those for the hazy sky are 3.33, 5.64, and 7.31 h in the order of winter, equinox, and summer.
FIG. 2 View Enlargement
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Performance of a flat-on-the-ground collector such as a cornfield at latitude ϕ = 35°. For clear sky, the Ts are 2.12, 4.70, and 6.84 h; those for the hazy sky are 1.40, 3.57, and 5.41 h.
FIG. 3 View Enlargement
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Performance of a solar collector on a vertical, south facing wall. The azimuth α = 0°, tilt β = 90°, and latitude ϕ = 35°. The verticals in the winter vacuum curve are sunup and sunset. The low summer curves are due to highly acute sun angle on the collector which then shades the sun. The clear Ts are 4.1, 3.3, and 0.8 h and those for the hazy sky are 2.6, 2.5, and 0.6 h.
FIG. 4 View Enlargement
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Performance of a flat stationary collector with azimuth α = 0° and tilt β = ϕ = 35° latitude. The Ts for the clear atmosphere are 4.1, 5.7, and 5.7 h; those for the hazy atmosphere are 2.6, 4.4, and 4.6 h. Between spring and autumn equinoxes the sun rises/sets behind the collector, for which tdark are about ±6.0 h, when the sun is abreast of it.
FIG. 5 View Enlargement
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Performance of a flat stationary collector with azimuth α = 20°, tilt β = 45°, and latitude ϕ = 35°. The Ts for the clear atmosphere are 4.1, 5.4, and 4.9 h; for hazy air they are 2.7, 4.0, and 3.9 h.
FIG. 6 View Enlargement
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Performance of a sun tracking flat collector. The azimuth angle α = 0° and tilt angle β = ϕ = 35° latitude. The clear Ts are 4.9, 7.9, and 9.0 h; those for hazy sky are 3.1, 5.6, and 6.7 h. The solstice vacuum curves (dashed) are lower than equinox by the factor 0.917, cos 23.5°.
FIG. 7 View Enlargement
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The east-west parabolic concentrator. The dark areas are shadows. The system may have any length.
FIG. 8 View Enlargement
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The east-west parabolic concentrator must move with the season. The view is westward at latitude 35°. The small circle is the HFP.
FIG. 9 View Enlargement
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Performance of east-west trough concentrators at latitude ϕ = 35°. The clear air Ts are 4.6, 5.7, and 6.7 h and the hazy ones are 2.9, 4.4, and 5.3 h.
FIG. 10 View Enlargement
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(a) Parabolic PV trough with concentration ratio of 4. The PV shades about one-fifth of the parabola aperture. (b) Concentration ratio across the PV panels; normal sunshine is 1. The parabola focus is F, the marginal ray is at 1.1F, and the outer edge of the slanted PVs is at 0.85F from the parabola vertex; the PV panels are slanted 60.4°.
FIG. 11 View Enlargement
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Two-trough east-west solar concentrator. The main reflector is a stationary cylinder sector with a derived curve secondary reflector that corrects the “spherical” aberration. The small circle is the HFP. The secondary reflector assembly swivels around the cylinder axis according to the declination angle δ. (a) The secondary reflector is small but the HFP moves with it. (b) has a stationary HFP on the cylinder axis. The views are westward at latitude 35°. The performance curves of Fig. 10 apply.
FIG. 12 View Enlargement
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(a) A PV panel illuminated by an EW cylinder reflector with concentration ratio of 3. The unit in (a) swivels around the cylinder axis according to the season angle δ like those shown in Fig. 12. (b) The PV concentration ratio. The marginal spikes are caused by the circular section caustic. The marginal ray is at 0.5R, and the PV panel is at 0.341R from the cylinder reflector.
FIG. 13 View Enlargement
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North-south two-trough concentrator at two times. (a) shows the first light into the concentrator in the morning. (b) shows the concentrator just as it begins to darken in the afternoon. The view is northward.
FIG. 14 View Enlargement
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North-south, two-trough, sun tracking concentrator. The concentrator is oriented NS and is tilted to the latitude angle. The large reflector and HFP are stationary; the secondary reflector rotates around the cylinder axis at the solar rate. The linear hash marks are shadows, and the cross-hatched area is a PV panel to operate the tracking and other subsystems. The view is northward at about 10 a.m.
FIG. 15 View Enlargement
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Performance of the NS tracking, cylindrical main reflector, two-trough concentrator with the hot fluid pipe on the cylinder axis, see Fig. 14. The concentrator is oriented north-south and tilted to the site latitude angle β = ϕ = 35°. The clear T at winter, equinoxes, and summer are 4.6, 7.1, and 8.0 h; those for the hazy atmosphere are 3.0, 5.3, and 6.3 h.
FIG. 16 View Enlargement
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Performance of north-south, sun tracking, two-trough concentrator with tilt β = 0° and latitude ϕ = 35°. The clear atmosphere sunlight grasps for winter, equinox, and summer are 2.5, 5.5, and 8.1 h; those for the hazy atmosphere are 1.6, 4.2, and 6.4 h.
FIG. 17 View Enlargement
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Flat tracking collector with latitude and tilt angles equal to β = ϕ = 20°. The clear sky Ts are 6.25, 8.21, and 8.38 h, and those for hazy sky are 4.34, 6.10, and 6.29 h; see Fig. 7.
FIG. 18 View Enlargement
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Flat tracking collector with latitude and tilt angles equal to β = ϕ = 50°. The clear sky Ts are 2.82, 7.20, and 9.68 h, and those for hazy sky are 1.27, 4.80, and 7.02 h; see Fig. 7.
FIG. 19 View Enlargement
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Comparisons of several collector concepts.
FIG. 20 View Enlargement
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Comparisons of flat sun trackers at different latitudes.
FIG. 21 View Enlargement
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Comparisons of several stationary flat collectors.
FIG. 22 View Enlargement
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Comparison of NS two-trough sun trackers with different tilt angles.
FIG. 23 View Enlargement
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Construction for calculation of atmospheric attenuation. The R = 6371 km is the earth radius; ξ is the sunray angle from the horizon, and H is an altitude above the earth’s surface.
FIG. 24 View Enlargement
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Equation of time for AD 2009. Due to the earth’s elliptic orbit, this is the time difference between true local noon and the longitude adjusted clock noon. The ordinate is the equation of time and the abscissa is the day of the year. 1 deg arc is 4 min time.
FIG. 25 View Enlargement
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Tables
Table I. Symbols.
Table II. Daily collector performance in hours per day.
