Building integrated concentrating solar systems - Solar Energy Sciences and Engineering Applications - page 559

Aperture

Parabola A

Axis
of
parabola

Parabola B

Absorber
Focus of
parabola A

Focus of
parabola B

P Q

2a

Figure 17.2.2 Schematic diagram of a compound parabolic concentrator.

of two different parabolic reflectors that can reflect both direct and a fraction of the
diffuse incident radiation at the entrance aperture onto the absorber, in addition to
the direct solar radiation absorbed directly by the absorber. The axis of the parabola
makes an angle

−θ a with the collector mid-plane and its focus at P (or Q), as
shown in Figure 17.2.2 (Rabl, 1976b). The slope of the end point of the parabola is
parallel to the collector mid-plane. A CPC reflector shape can be designed in different
ways according to the absorber shape. A basic form for a flat one-sided absorber is
shown in Figure 17.2.2.

θ a or

The equation of a CPC with a flat absorber
For the coordinates in Figure 17.2.3, by rotation of the axis and translation of the
origin, in terms of the diameter (2a) and the acceptance angle (

θ

max ), the equation for

a meridian section CPC reflector is (Welford, 1978) is:

y sin θ max ) 2 sin θ max ) 2 r ( r cos θ max + + 2 a (1 + − 2 a cos θ max (2 + sin θ max ) z

a 2 (1 − + sin θ max )(3 + sin θ max ) = 0 (17.2.3)

In polar coordinates, the complete parametric equation becomes (Welford, 1978)

− −

2 f sin( θ θ max ) 2 f cos( θ θ max )

= −

a / ;

=

r z

− −

1 cos θ 1 cos θ

(17.2.4)

where

a / (1

f = + sin θ max )