Solar energy collection and storage - Solar Energy Sciences and Engineering Applications - page 127

where ε is the angular size of the suns disc, n is the refractive index of the last mate-
rial insolation traversed for the refractive index of air C max,2 D is approximately 216.
For a three-dimensional concentrator, the equivalent upper limit is:

n 2
sin 2 ( ε/ 2)

C max,3 D = (4.3.3)

C max,3 D in typically 46000 for concentrators operating in the refractive index of air. To
maintain high concentration high concentration ratio two-dimensional concentrators
need accurate solar tracking systems as concentration decreases sharply at off-normal
insolation incidence. As they have much larger maximum concentration ratios three-
dimensional systems need less-precise tracking accuracy to yield acceptable optical
performance.
Both the earth's diurnal rotation about its axis and annual rotation about the
sun mean that a tracking solar energy collector must move continually in two axis to
maintain the direct insolation component precisely at normal incidence to the aperture
plane (Rabl, 1985). Two-axis solar tracking is essential to achieve concentration ratios
from 100-1000. Such concentrators can elevate fluids to temperatures at which it is
usually possible to generate electricity using steam turbines or Stirling cycles or to
provide high grade thermal energy for industrial processes. Single axis trackers are
usually oriented either horizontal east-west, or inclined north-south achieving normal
incidence once a day or twice a year respectively.
Stationary concentrating systems with a concentration ratio in the range from
1 to 3 can be integrated into buildings as they obviate the need for moving parts,
complex mounting and associated mechanical systems. Most systems are based
on two-dimensional non-imaging compound parabolic concentrators (CPCs). Build-
ing integration of high temperature solar thermal applications is attractive as a
means of lowering installation cost. The initial investment cost will be reduced
if lower cost reflector materials replaced more extensive use of evacuated tube
collectors.
The two dimensional CPC is termed an ideal concentrator, with a concentration
ratio of 1 / sin θ max , since all the light incident at angles less than the angle of acceptance
will arrive at the absorber. As can be seen in Figure 4.3.1, the CPC is deep in comparison
with the width of the absorber. The arrangement is both impractical and costly in
the practical fabrication of a concentrator (Tripanagnostopoulos et al., 2002; 2004a;
2004b). Increasing the concentration ratio reduces the angle of acceptance resulting in
a considerably deeper trough.
Truncating the height of a CPC does not diminish the aperture significantly, if
a third of the length of a low concentration ratio CPC trough were truncated it
would only reduce the aperture area by about 3%. Thus in most practical solar energy
collectors that employ CPCs, they are truncated significantly.
As the maximum concentration ratio is n /sin θ max it is possible to increase the con-
centration ratio by replacing the air in the trough with a dielectric medium. When a

dielectric medium with a refractive index greater than √ 2 is used, total internal reflec-
tion will ensue at each reflection. A dielectric-medium concentrator without reflectors
can thus be constructed, that will have no reflection losses. This will be of lower cost
if eliminating the cost of the reflector is not offset by the cost of the dielectric material.