Prediction of the steam-producing power

This model is based on a total of 210 outdoor stagnation experiments, which were carried out between 2003 and 2007 on three different collector types with a total of eight different connection variations (Fig. 1).

Подпись: ETC1c

Подпись: FPC2a Подпись: FPC2b

ETC1a/b

image088 Подпись: FPC3c

FPC2c

The SPP of a collector array depends on numerous parameters such as collector efficiency, system pressure and the piping of the collectors. During the stagnation process, we assume that the two — phase mixture in the collector array has the temperature of saturated steam $s. The theoretical collector performance during stagnation Pstag at the moment of maximum steam spread is calculated as follows:

Подпись:Pstag = GT, stag -Л0 “ a1 (S. )“ a2 (®. “ )2

with

Pstag Theoretical collector performance during stagnation W/m2

GT, stag Effective irradiance during stagnation W/m2

Ss Boiling point of the heat transfer medium °C

Sa Ambient air temperature °C

p0 Conversion factor of the collector —

a1 Temperature-independent heat loss coefficient W/m2K

a2 Temperature-dependent heat loss coefficient W/m2K2

The boiling point 0S of the common heat transfer medium, which consists of a mixture of 60% water and 40% propylene glycol (40%), can be calculated with the help of the system pressure psys at the moment of maximum steam spread:

3S = 100°C + 35.1K • ln (pSyS) (2)

Подпись: Fig. 2. Correlation of the steam-producing-power (SPP) of the investigated collector arrays versus the theoretical stagnation power Pstag.

This calculation takes into account the influence of the system pressure psys, which has an impact on the stagnation behaviour through a changed boiling point. High-performance evacuated-tube collectors are more efficient during the stagnation process and therefore tend to a higher SPP. Hence, an interdependency of SPP and theoretical collector performance during stagnation Pstag is to be expected. Furthermore, the developed model, which describes the correlation of Pstag and SPP, is only influenced by the draining behaviour of the collector array. Fig. 2 shows the dependency of the measured SPP-levels on the theoretical collector performance during stagnation Pstag for the different collector types and array connections.

2

Theoretical stagnation power Pstag in W/m

Although there sometimes have been measured considerable differences in the SPP-values, Fig. 2 shows a clear trend. As expected, SPP rises with theoretical collector performance during stagnation Pstag. Furthermore, almost all lines of best fit have a positive axis intercept, i. e. a great amount of steam is produced by the collector arrays, although the theoretical collector performance during stagnation is zero. This is particularly clear to be seen with the measurement results from variant FK2a, where SPP levels of 60 W/m2 are recorded although the theoretical collector performance during stagnation is zero. The main reason for this discrepancy is the false model assumption, that the collector temperature during stagnation equals the boiling point 0S of the collector field. In fact, this assumption is often not valid for collectors with unfavourable draining

behaviour, because the relatively large amount of liquid remaining in the collector can significantly reduce the average collector temperature.

From the measurements at the outdoor test arrays at ISFH we can derive three classes of collector arrays with good (A), moderate (B) and bad draining behaviour (C). For these three classes the following correlations with rounded coefficients can be produced:

Class A: SPP = 15% Pstag + 10 W/m2

Class B: SPP = 20% Pstag + 40 W/m2 (3)

Class C: SPP = 25% Pstag + 80 W/m2

The designation of the collector draining behaviour during stagnation process is the basis for the following design process. If we calculate SPP using the model equations (3), a standard deviation between the measurement results and the prediction of 25% may be expected.

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