Solar thermal collectors and applications

# Concentrating collectors performance

For concentrating collector both optical and thermal analyses are required.

3.2.1. Optical analysis

The concentration ratio (C) is defined as the ratio of the aperture area to the receiver/absorber area, i. e.

Aa

C = a (30)

Ar

For FPC with no reflectors, C = 1. For concentrators C is always greater than 1. For a single axis tracking collector the maximum possible concentration is given by [1,97]:

1

 (31) C m Table 6

Comparison of energy absorbed for various modes of tracking

Tracking mode Solar energy Percent to full tracking

(kW h/m2)

 E SS WS E SS WS Full tracking 8.43 10.60 5.70 100.0 100.0 100.0 E-W polar 8.43 9.73 5.23 100.0 91.7 91.7 N-S horizontal 6.22 7.85 4.91 73.8 74.0 86.2 E-W horizontal 7.51 10.36 4.47 89.1 97.7 60.9

Note: E: equinoxes, SS: summer solstice, WS: winter solstice. sin(0m)

and for two-axes tracking collector [1,97]

 (32) C m 1

sin2(#m) where 6m is the half acceptance angle. The half acceptance angle denotes coverage of one-half of the angular zone within which radiation is accepted by the concentrator’s receiver. Radiation is accepted over an angle of 26m because radiation incident within this angle reaches the receiver after passing through the aperture. This angle describes the angular field within which radiation can be collected by the receiver without having to track the concentrator.

Eqs. (31) and (32) define the upper limit of concentration that may be obtained for a given collector viewing angle. For a stationary CPC the angle 6m depends on the motion of the sun in the sky. For example, for a CPC having its axis in a N-S direction and tilted from the horizontal such that the plane of the sun’s motion is normal to the aperture, the acceptance angle is related to the range of hours over which sunshine collection is required, e. g. for 6 h of useful sunshine collection 26m = 90° (sun travels 15°/h). In this case Cmax = 1/sin(45°) = 1.41.

For a tracking collector 6m is limited by the size of the sun’s disk, small scale errors and irregularities of the reflector surface and tracking errors. For a perfect collector and tracking system Cmax depends only on the sun’s disk which has a width of 0.53° (320) . Therefore,

For single axis tracking: Cmax = 1/sin(160) = 216

For full tracking: Cmax = 1/sin2(160) = 46 747

It can, therefore, be concluded that the concentration ratio for moving collectors is much higher. However, high accuracy of the tracking mechanism and careful construction of the collector is required with increased concentration ratio as 6m is very small. In practice, due to various errors, much lower values that the above maximum ones are employed.

Another factor that needs to be determined is the incidence angle for the various modes of tracking. This can be about a single axis or about two axes. In the case of single axis mode the motion can be in various ways, i. e. east-west, north-south or parallel to the earth’s axis.

The mode of tracking affects the amount of incident radiation falling on the collector surface in proportion to
the cosine of the incidence angle. The amount of energy falling on a surface of 1 m2 for four modes of tracking for the summer and winter solstices and the equinoxes is shown in Table 6 . The amount of energy shown in Table 6 is obtained by applying a radiation model . This is affected by the incidence angle which is different for each mode.

The performance of the various modes of tracking can be compared to the full tracking mode, which collects the maximum amount of solar radiation, shown as 100% in Table 6. Relations for the estimation of the angle of incidence for the various modes of tracking are given in Table 7.

The optical efficiency is defined as the ratio of the energy absorbed by the receiver to the energy incident on the collector’s aperture. The optical efficiency depends on the optical properties of the materials involved, the geometry of the collector, and the various imperfections arising from the construction of the collector. In equation form :

no = pray[(1 — Af tan(6))cos(6)] (33)

The geometry of the collector dictates the geometric factor Af, which is a measure of the effective reduction of the aperture area due to abnormal incidence effects. For a PTC, its value can be obtained by the following relation :

2 Г W2 #

Af = з Wahp + fWa 1 + - f (34)

The most complex parameter involved in determining the optical efficiency of a PTC is the intercept factor. This is defined as the ratio of the energy intercepted by the receiver to the energy reflected by the focusing device, i. e. parabola . Its value depends on the size of the receiver, the surface angle errors of the parabolic mirror, and solar beam spread.

The errors associated with the parabolic surface are of two types, random and non-random . Random errors are defined as those errors which are truly random in nature and, therefore, can be represented by normal probability distributions. Random errors are identified as apparent changes in the sun’s width, scattering effects caused by random slope errors (i. e. distortion of the parabola due to wind loading) and scattering effects associated with the reflective surface. Non-random errors arise in

Table 7

Relations for the estimation of the angle of incidence (0) for the various modes of tracking Mode of tracking Incidence angle Remarks

Full tracking cos(0) = 1

Collector axis in N—S axis cos(0) = cos(5)

polar E—W tracking

Collector axis in N—S axis cos(0) = psin2(a) + cos2(5)sin2(h) or

horizontal E—W tracking cos(0) = cos(F)cos(h) + cos(5)sin2(h)

Collector axis in E—W axis cos(0) = p 1 — c о s 2 ( 5) s i n 2 (h) or

horizontal N—S tracking cos(0) = psin2(5) + cos2(5)cos2(h)

This depends on the accuracy of the tracking mechanism.

This mode collects the maximum possible sunshine

For this mode the sun is normal to the collector at equinoxes

(5 = 0°) and the cosine effect is maximum at the solstices.

When more than one collector is used, front collectors cast shadows on adjacent ones

The greatest advantage of this arrangement is that very small shadowing effects are encountered when more than one collector is used. These are present in the first and last hours of the day The shadowing effects of this arrangement are minimal. The principal shadowing is caused when the collector is tipped to a maximum degree south (5 = 23.5°) at winter solstice. In this case the sun casts a shadow toward the collector at the north

Notes: 5: declination angle, h: hour angle, F : zenith angle. Relations to determine these angles can be found in many solar energy books

 g =
 1 — cos fr2 sin fr
 Erf^
 ( sin fr(1 + cos f)(1 — 2d* sin f) — pP*(1 + cos f
 p2ps*(1 + cos fr) sin fr(1 + cos f)(1 + 2d* sin f) + pp*(1 + cos f
 p2ps*(1 + cos fr)
 r) )
 df
 (1 + cos f)
 (36)
 where

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