## Collector Thermal Efficiency

The collector performance test is performed under steady-state conditions, with steady radiant energy falling on the collector surface, a steady fluid flow rate, and constant wind speed and ambient temperature. When a constant inlet fluid temperature is supplied to the collector, it is possible to maintain a constant outlet fluid temperature from the collector. In this case, the useful energy gain from the collector is calculated from

From Chapter 3, we have seen that the useful energy collected from a solar collector is given by

Moreover, the thermal efficiency is obtained by dividing Qu by the energy input (AaG)

During testing, the collector is mounted in such a way as to face the sun perpendicularly; as a result, the transmittance-absorptance product for the collector corresponds to that of beam radiation at normal incidence. Therefore, the term (ja)n is used in Eqs. (4.3) and (4.4) to denote that the normal transmittance-absorptance product is used.

Similarly, for concentrating collectors, the following equations from Chapter 3 can be used for the useful energy collected and collector efficiency:

Notice that, in this case, Gt is replaced by GB, since concentrating collectors can utilize only beam radiation (Kalogirou, 2004).

For a collector operating under steady irradiation and fluid flow rate, the factors Fr, (?a)n, and UL are nearly constant. Therefore, Eqs. (4.4) and (4.6) plot as a straight line on a graph of efficiency versus the heat loss parameter (T _ Ta)/Gt for the case of flat-plate collectors and (7] - Ta)/GB for the case of concentrating collectors (see Figure 4.3). The intercept (intersection of the line with the vertical efficiency axis) equals FR(Ta)n for the flat-plate collectors and FRn0 for the concentrating ones. The slope of the line, i.e., the efficiency difference divided by the corresponding horizontal scale difference, equals -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 the 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

Flat-plate collector

Concentrating collector

Intercept = FR (xa)n

Flat-plate collector

Intercept = FR (xa)n

Intercept = FRn

Concentrating collector

Intercept = FRn

Slope

FrUL/C

Slope

FrUL/C

FiGURE 4.3 Typical collector performance curves.

AT/Gr 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 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. This maximum temperature (for a flat-plate collector) is given by

As can be seen from Figure 4.3, the slope of the concentrating collectors is much smaller than the one for the flat-plate. This is because the thermal losses are inversely proportional to the concentration ratio, C. This is the greatest advantage of the concentrating collectors, i.e., the efficiency of concentrating collectors remains high at high inlet temperature; this is why this type of collector is suitable for high-temperature applications.

A comparison of the efficiency of various collectors at irradiance levels of 500 W/m2 and 1000 W/m2 is shown in Figure 4.4 (Kalogirou, 2004). Five representative collector types are considered:

• Advanced flat-plate collector (AFP). In this collector, the risers are ultra-sonically welded to the absorbing plate, which is also electroplated with chromium selective coating.

• Stationary compound parabolic collector (CPC) oriented with its long axis in the east-west direction.

• Evacuated tube collector (ETC).

• Parabolic trough collector (PTC) with E-W tracking.

As seen in Figure 4.4, the higher the irradiation level, the better is the efficiency, and the higher-performance collectors, such as the CPC, ETC, and n n

Temperature difference [T-Ta] (°C)

-♦— FPC-1000 —■— AFP-1000 —▲— CPC-1000 —•— ETC-1000 PTC-1000 — FPC-500 —B— AFP-500 —A— CPC-500 —Ö— ETC-500 —PTC-500

Temperature difference [T-Ta] (°C)

-♦— FPC-1000 —■— AFP-1000 —▲— CPC-1000 —•— ETC-1000 PTC-1000 — FPC-500 —B— AFP-500 —A— CPC-500 —Ö— ETC-500 —PTC-500

FiGURE 4.4 Comparison of the efficiency of various collectors at two irradiation levels: 500 and 1000 W/m2.

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.

In reality, the heat loss coefficient, UL, in Eqs. (4.3)-(4.6) is not constant but is a function of the collector inlet and ambient temperatures. Therefore,

Applying Eq. (4.8) in Eqs. (4.3) and (4.5), we have the following. For flat-plate collectors.

Qu = AaFR[(ToO„Gf - c1(Ti - Ta) - c^T - Ta)2] (4.9)

and for concentrating collectors.

Qu = Fr[Gbn0Aa - Arc1(Ti - Ta) - \c2(T - Ta)2] (4.10)

Therefore, for flat-plate collectors, the efficiency can be written as

(T - T ) (T - T )2 n = Fr (Ta) - ci( a ) - c2( ' - a ) (4.11)

Gt Gt and if we denote c0 = FR(Ta) and x = (T _ Ta)/Gt, then n = c0 - c1 x - c2Gtx2 (4.12)

And, for concentrating collectors, the efficiency can be written as n = fr n

and if we denote ko = FRno, k1 = c1/C, k2 = c2/C, and y = (T - Ta)/GB, then n = ko - kiy - k2Gb^y

The difference in performance between flat-plate and concentrating collectors can also be seen from the performance equations. For example, the performance of a good flat-plate collector is given by:

0.792 - 6.65 |
AT |
- 0.06 |
'At 2 ' | ||||||||||

Gt |
whereas the performance equation of the 1ST (Industrial Solar Technologies) parabolic trough collector is
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