General difficulty
The thermal performance of concentrating collectors depends strongly on the concentration ratio C. The concentration ratio for collectors having tubular absorbers is calculated by the ratio between
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aperture area and unrolled absorber area. Simplified it can be assumed that the diffuse irradiance available for the collector is reduced by the quotient 1/C. Using this assumption the irradiance Gnet which can be used by the collector can be calculated using equation 1.
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Dividing the useable irradiance Gnet by the hemispherical irradiance G yields the useful fraction N described by equation 2.
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Due to this dependence of the useful irradiance Gnet on the concentration ratio C more diligence has to be taken for the determination of the thermal performance of concentrating collectors compared to flat plate collectors.
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Fig. 2. Fraction of useful irradiance N as a function of the concentration ratio C and the
diffuse fraction D
The European Standard EN 12975-2:2006 [1] allows for two test methods for the determination of the thermal performance: the test method under steady state conditions and the test method under quasi-dynamic conditions.
The more detailed test method under quasi-dynamic conditions differentiates between beam irradiance Gbeam and diffuse irradiance Gdfu. Together with the incidence angle modifier for beam irradiance Kbeam(0) and diffuse irradiance Kdfu it is therefore possible to model the influence of the beam irradiance under different incident angles as well as the dependency of the thermal performance on the diffuse fraction. In addition the implementation of the effective heat capacity ceff in the thermal performance model of the collector (see equation 3) allows the description of the dynamic behaviour of the collector under changing radiation levels. By means of the test method under quasi-dynamic conditions the thermal performance of stationary non-concentrating collectors can be determined as well as for tracking concentrating collectors. The relatively high level of detail of the model permits the use of test sequences with wide variation in the level of irradiance.
The simplified test method under steady state conditions abstains from the differentiation of the beam and diffuse irradiance and the metrological determination of the effective heat capacity (see equation 4). The major drawback of these simplifications is the fact that only data can be used for evaluation that was recorded under very constant (steady state) conditions. An additional uncertainty in the test results is created by the use of an incident angle modifier for the hemispherical irradiance K(0) which itself depends on the diffuse fraction predominant during the measurements. Due to these simplifications the test method under steady state conditions is strictly speaking only suitable for collectors with a thermal performance not depending significantly on the nature of the irradiance (beam or diffuse). Hence the test method is not suitable for concentrating collectors at all.
( d3 Л
Q = A П0GbeamKbeam (в) + n0GdjuKdju - ai (f - 3a ) - «1 (f - 3a - Ceff
Q = A(no GK (в) - a, (V -*a ) - a (V -*a )[10] )
For CPC collectors available on the market today with a concentration ratio of 1 < C < 2 the fraction of useful irradiance is reduced up to 25% depending on the diffuse fraction. In the following the impact of this fact on the test results of CPC collectors is described.
