Operating data for several years were acquired from a small array of commercial XCPCs installed in Chicago in the late 1980s. These data provided the first direct measurement (O’Gallagher, Win­ston, and Dallas, 2004) of the optical acceptance characteristics of a representative stationary CPC with a design acceptance half-angle of ±35° and a geometric concentration ratio of C = 1.33x (Fig­ure 7.4). The observed incidence angle modifying functions in both the transverse and longitudinal planes are summarized and discussed subsequently. Of particular note is the fact that we found that the CPC collector “sees” about 92% of diffuse radiation rather than about 75%, which is predicted by models in which the diffuse component is assumed to be isotropic. The collector array functioned well for more than 18 years before it was removed after it became shaded by a new multistory build­ing constructed adjacent and just to the west.

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FIGURE 7.2: The 3x collector orientation (53° with respect to the vertical at the latitude of 37°) and measured acceptance angle (18°) are designed to collect solar energy for 6 months of the year around the winter solstice. If thermal energy was required all year, the collector would be repositioned for a summer orientation (21° with respect to the vertical).

These performance data provide direct measurements of several optical characteristics of CPCs that are critical to the accurate modeling of long-term performance projections for these collectors. These characteristics are (1) the transverse and longitudinal IAMs and (2) the “loss-of – diffuse” parameter.

The troughs of this early commercial CPC collector (based on the original Argonne National Laboratory design) have a geometric concentration ratio C = 1.33x (aperture width-to-absorber circumference), and the design acceptance angle (angular cutoff) is ±35°. The array of four panels, each with 12 horizontal (east-west aligned) troughs, was installed as recommended facing directly south and with the normal to the aperture plane tilted with respect to the zenith at the latitude angle for Chicago (42°). This optical design and its deployment are representative of those adopted for most stationary CPC designs so that the measured angular and diffuse acceptance properties can be used to characterize the performance of virtually all such stationary CPCs (O’Gallagher and Winston, 1983).


FIGURE 7.3: The all-day performance curve for the full Breadsprings array near the winter solstice showing available hemispherical insolation, average collector array temperature, and array efficiency as functions of time. The fluctuations in temperature and efficiency near midday show the effects of load variations correlated with lunchtime activities. The all-day efficiency (8:30 to 16:30 h) is 39%.

The all-day performance, which helps separate the angular properties of the concentrator ge­ometry from other effects, as measured on a very clear day near the summer solstice, is shown in Figure 7.5. At any given time, the sun’s rays are incident on the collector aperture at an angle 0I with respect to the aperture normal, which lies in the north-south (meridian) plane tilted at the latitude angle with respect to the zenith. It is conventional to characterize the angular response by resolving this incident direction further into the components 0T and 0L, projected respectively onto the transverse and longitudinal planes containing the aperture normal. CPCs achieve stationary concentration in a trough geometry when tilted at the latitude angle and deployed with the longitudinal axis along the


FIGURE 7.4: Data from this four-panel array of commercial evacuated tube XCPCs should be very representative of most stationary CPCs. The design acceptance angle is ±35°, and the geometric con­centration is 1.33x.

east-west direction so that the transverse angular acceptance is centered on the latitude angle. Thus, the sun at equinox will move along a path that lies in the center of the “wedge” of acceptance (0T = 0°) throughout the day. On the other hand, at solstice, the sun will be at 0T = ±23° (+23 in summer and -23 in winter) at noon and at larger angles throughout the rest of the day. The design acceptance of 0c = ±35° is chosen to allow full collection for a minimum of 7 hours a day at solstice. The data in Figure 7.5 show a peak efficiency at noon near the expected value for ho with a gradual falloff on ei­ther side of noon and a relatively sharp cutoff around ±3% hours (210 minutes) with respect to noon. Note that the turn-on in the morning is slightly rounder than the turn-off in the afternoon, although the sharp transition is still evident. This is due to a small amount of shading from the main wing of the building, which is to the east of the collector array. If both the longitudinal and transverse IAMs were equal to unity (and there was no shading) , the efficiency would rise sharply to its peak value as the sun entered the transverse acceptance before noon and then remain constant until 3% hours after noon. Deviations from this idealized all-day response provide a direct measure of the IAMs.

The data in Figure 7.6 show the measured optical efficiency of this commercial CPC ar­ray as a function of the transverse incidence angle, 0T, near the summer solstice when the sun


■300 -270 -240-210 -180 -150-120 -90 -60 -30 0 30 60 90 120 150 180 210 240 270 300

Time I minutes]

FIGURE 7.5: The all-day performance includes effects due to the angular acceptance of the CPC as well as the longitudinal and transverse IAMs.

moves through the angular cutoff at +35° twice a day. Once inside the design acceptance angle, the efficiency gradually approaches its peak value around noon as the transverse angle never gets much below 0T = +23°. These data clearly show the rounding of the ideal cutoff response due to mirror slope errors and partial throughput outside the acceptance angle due to truncation (Collares-Pereira, O’Gallagher, and Rabl, 1978).

One of the main advantages of CPC collectors relative to other concentrating collectors is their ability to collect a significant fraction of the diffuse radiation. If the diffuse component of inso­lation is isotropic, as is assumed in the simplest insolation models, it can be shown that the fraction of the diffuse that will be “seen” by a collector of geometric concentration C is 1/C and the loss-of – diffuse factor will be (1 – 1/C). From this, it follows that the factor Г in Eq. (3.4) is given by

Г = [1 – f (1 – 1/C)] (7.1)

where f is the fraction of the total insolation due to diffuse radiation. Rewriting Eq. (3.4) and rear­ranging, we can express the dependence of the CPC optical efficiency on the diffuse fraction as




Tranverse Angle Theta

FIGURE 7.6: The ideal acceptance angle for a stationary CPC is compared with actual data near the solstice as the transverse incidence angle 0T passes through the design cutoff toward its noontime value of just less than 23°. The rounding near 35° is expected due to random slope errors of the order 3°-5° and does not affect the long-term performance.

h0( f) = h0,0 – h0,0 Lf (7.2)

where hoo is hjG and the loss-of-diffuse factor is L = (C – 1)/C.

It is well known that the diffuse component is not isotropic, being somewhat more intense at angles closer to the sun’s direction, suggesting that a CPC might see more of the diffuse than pre­dicted by simple models. A more sophisticated radiation model due to Perez (see Perez, Scott, and Stewart, 1983; Perez, Stewart, Arbogast, Seals, and Scott, 1986) gives some analytic support to this conjecture; however, until now, no experimental evidence for this behavior has been presented.

In an effort to explore this further, during 1991 and 1992, we conducted a set of measurements of the optical efficiency as a function of the diffuse fraction for a wide range of insolation conditions. In each case, the diffuse fraction was measured directly by shading a precision spectral pyroheli – ometer with a circular disk held so that it subtended a cone of half-angle 5.7° around the sun. The assumption of isotropic diffuse would lead to the prediction that with C = 1.33, the loss of diffuse should be (0.33)/1.33 = 0.25 and the CPC should collect about 75% of the diffuse insolation. With

hoo @ 0.60, we should expect the slope of a fit to the optical efficiency as a function of diffuse fraction to be -0.15. Instead, the slope of the best-fit line is 0.053, or only about one-third of that predicted. To reiterate, these preliminary measurements indicated that, instead of “losing” 25% of the diffuse radiation, the CPC “loses” only about 8%, and we conclude that these collectors are “seeing” about 92% of the diffuse, substantially more than the 75% usually assumed in long-term performance pro­jections for CPC collectors.

Updated: August 16, 2015 — 10:43 am