After explaining the assembly of collectors in the previous sections, this section will describe the calculation of the collector performance and efficiency. This is necessary for the further estimation of the output of the whole collector system.

The collector converts solar irradiance E, which is transmitted through the front glass cover with transmittance t onto the collector surface AC, directly to heat. The power output of the solar collector Qout is reduced by losses due to reflection Qref, convection Qconv and heat radiation Qrad

The convection losses Qconv and heat radiation losses Qrad can be combined as Qrc. The heat radiation losses Qrad of selective absorbers are much lower than the radiation losses of non-selective absorbers as described above. A vacuum between the front cover and the absorber can reduce the convection losses Qconv as described for the evacuated flat-plate and tube collector. The reflection losses Qref can be estimated using the reflectance p from the irradiance passing the glass front cover.

With

Qrc « + (l and and the collector power output becomes:

Using the absorptance a = 1 - p of the absorber, the equation reduces to:

n0 is called the optical efficiency. It describes the collector efficiency without any losses due to convection or heat radiation. This is only the case if the absorber temperature is equal to the ambient temperature.

The thermal losses QRC depend on the collector temperature and the ambient temperature as well as on the coefficients a, respectively, a1 and a2:

Table 3.7 shows the optical efficiencies as well as the loss coefficients a1 and a2 for various collectors. The loss coefficients of evacuated tube collectors are much lower than those of non-evacuated flat-plate collectors, hence their higher efficiency at low ambient temperatures or low irradiances. The loss coefficients are usually estimated from collector tests. Some calculations only use the single loss coefficient a instead of the two loss coefficients a1 and a2. However, in that case it is not possible to eliminate only a2 since that can cause

Name |
Type |
n0 a1 |
in W/(m2 |
K) a2 in W/(m2 K2) AC |
in m2 | |

Paradigma Solar 500 |
Flat-plate |
0.805 |
3.79 |
0.009 |
4.7 | |

Solahart M |
Flat-plate |
0.746 |
4.16 |
0.0084 |
1.815 | |

Solahart OYSTER Ko |
Flat-plate |
0.803 |
2.49 |
0.0230 |
1.703 | |

Sonnenkraft SK 500 |
Flat-plate |
0.800 |
3.02 |
0.0013 |
2.215 | |

Wagner Euro C18 |
Flat-plate |
0.789 |
3.69 |
0.007 |
2.305 | |

Microtherm Sydney | ||||||

SK-6 |
Evacuated |
tube |
0.735 |
0.65 |
0.0021 |
0.984 |

Thermolux 2000-6R |
Evacuated |
tube |
0.801 |
1.13 |
0.008 |
1.05 |

Ritter CPC 12 OEM |
Evacuated |
tube |
0.617 |
1.04 |
0.0013 |
2.01 |

Sunda SEIDO 5-16 |
Evacuated |
tube |
0.736 |
1.78 |
0.0130 |
2.592 |

Source: SPF Institut für Solartechnik, 2002

Source: SPF Institut für Solartechnik, 2002

high errors. The coefficient a must be estimated separately from measurements. The collector reference surface AC must always be given with the collector parameters. It is possible to determine the collector efficiency parameters referring to the absorber area, aperture area or total collector area. The absorber area is used as a reference for the following calculations.

The collector efficiency nC can be calculated using the power output of the solar collector Qout as well as the solar irradiance E, which reaches the collector surfaces A

With *Ji

With *Ji

, the collector efficiency becomes:

Figure 3.14 shows the typical collector efficiencies of a flat-plate collector. The thermal losses increase with rising temperature differences between the collector and ambient air. At low solar irradiances the efficiency decreases faster. For instance, at a solar irradiance of only 200 W/m2 the output of the collector of this example becomes zero at a temperature difference of about 40°C.

The stagnation temperature of the collector can also be found from the figure. The stagnation temperature is the temperature at which the collector power output and the collector efficiency are equal to zero (nC = 0). At an irradiance of 400 W/m2, the stagnation temperature of the collector is about 75°C above the ambient temperature. The stagnation temperature can rise above 200°C at irradiances of 1000 W/m2. Therefore, collector materials must be chosen that can resist these relatively high temperatures over a long period of time.

The calculation of the collector efficiency given above is only valid if there is no wind; convective thermal losses will increase with the wind speed.

Modifications of the loss factors can consider this. The optical efficiency n0 also depends on the angle of incidence and the solar spectrum. For very exact calculations these effects must be also taken into account.

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