Collector thermal efficiency
In reality the heat loss coefficient UL in Eqs (2) and (42) is not constant but is a function of collector inlet and ambient temperatures. Therefore:
FrUl = c1 + c1(Ti - Ta) (68)
Applying Eq. (68) in Eqs. (2) and (42) we have:
qu = AjR[raGt - c1 (T - Ta) - c1(T, - Ta)2] (69)
and for concentrating collectors:
qu = FR[GbnoAa - Arc1(Ti - Ta) - Arc2(Ti - Ta)2] (70)
Therefore for FPC, the efficiency can be written as: (Ti - Ta)2
Usually, the second-order terms are neglected in which case c2 = 0 and k2 = 0 (or third-term in above equations is neglected). Therefore, Eqs. (71) and (73) plot as a straight line on a graph of efficiency versus the heat loss parameter (Ti - Ta)/Gt for the case of FPCs and (Ti - Ta)/Gb for the case of concentrating collectors. The intercept (intersection of the line with the vertical efficiency axis) equals to FRra for the FPCs and FRno for the concentrating ones. The slope of the line, i. e. the efficiency difference divided by the corresponding horizontal scale difference, equals to - FRUL and - FrUl/C, respectively. If experimental data on collector heat delivery at various temperatures and solar conditions are plotted, with efficiency as the vertical axis and AT/G (Gt or Gb is used according to the type of collector) as the horizontal axis, the best straight line through the data points correlates collector performance with solar and temperature conditions. The intersection of the line with the vertical axis is where the temperature of the fluid entering the collector equals the ambient temperature, and collector efficiency is at its maximum. At the intersection of the line with the horizontal axis, collector efficiency is zero. This condition corresponds to such a low radiation level, or to such a high temperature of the fluid into the collector, that heat losses equal solar absorption, and the collector delivers no useful heat. This condition, normally called stagnation, usually occurs when no fluid flows in the collector.
A comparison of the efficiency of various collectors at irradiation levels of 500 and 1000 W/m2 is shown in Fig. 20. Five representative collector types are considered:
• Flat-plate collector.
• Advanced flat-plate collector (AFP). In this collector the risers are ultrasonically welded to the absorbing plate, which is also electroplated with chromium selective coating.
• Stationary CPC orientated with its long axis in the east - west direction.
• Evacuated tube collector.
• Parabolic trough collector with E-W tracking.
As seen in Fig. 20 the higher the irradiation level the better the efficiency and the higher performance collectors like the CPC, ETC and PTC retain high efficiency even at
higher collector inlet temperatures. It should be noted that the radiation levels examined are considered as global radiation for all collector types except the PTC for which the same radiation values are used but considered as beam radiation.
As it can be seen from Fig. 20 the advantage of concentrating collectors is that the heat losses are inversely proportional to the concentration ratio C. This leads to the small slope of the collector performance curve. Thus the efficiency of concentrating collectors remains high at high inlet-water temperatures.
The difference in performance can also be seen from the performance equations. For example, the performance of a good FPC is given by
( AT AT2
n = 0.792 - 6.65 - 0.06 (75)
whereas the performance equation of the IST collector (obtained by the Sandia tests ) as given by the manufacturer is:
4.2. Collector incidence angle modifier