Solar thermal collectors and applications

# Concentrating collectors

Similarly, for concentrating collectors the performance equations (70) and (73) described previously are reason­ably well defined as long as the direct beam of solar irradiation is normal to the collector aperture. However, for off-normal incidence angles, the optical efficiency term (no) is often difficult to be described analytically because it depends on the actual concentrator geometry, concen­trator optics, receiver geometry and receiver optics which may differ significantly. As the incident angle of the beam radiation increases these terms become more complex. Fortunately, the combined effect of these three parameters at different incident angles can be accounted for with

Gt Gt

 ci (Tj - Ta)CGb

 n = Fr KaTna

 (79)

 (80)

 Ka

the incident angle modifier. This is simply a correlation factor to be applied to the efficiency curve and is only a function of the incident angle between the direct solar beam and the outward drawn normal to the aperture plane of the collector. It describes how the optical efficiency of the collector changes as the incident angle changes. With the incident angle modifier Eq. (73) becomes:

c2(Ti - Ta)2
CGb

If the inlet fluid temperature is maintained equal to ambient temperature, the incident angle modifier can be determined from:

n(Tfi = Ta) FR [no Jn

where n(Tfi = Ta) is the measured efficiency at the desired incident angle and for an inlet fluid temperature equal to the ambient temperature. The denominator in Eq. (80) is the test intercept taken from the collector efficiency test with Eq. (73) with [no]n being the normal optical efficiency, i. e. at normal angle of incidence.

As an example the results obtained from such a test (Fig. 21) are denoted by the small squares. By using a curve fitting method (second-order polynomial fit), the curve that best fits the points can be obtained [59]:

Kat = i - 0.00384(0) - 0.000i43(0)2 (8i)

For the 1ST collector, the incidence angle modifier kat of the collector, given by the manufacturer is:

kat = cos(0) + 0.0003178(0) - 0.00003985(0)2 (82)

## Solar thermal collectors and applications

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### Limitations of simulations

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