Page 252 - Design of Solar Thermal Power Plants

4.2 PRINCIPLES FOR CONCENTRATION FIELD LAYOUT 235

solar beam over time on the heliostat mirror surface to select the incident
angle range [q min , q max ], introduce the three design parameters s ¼ f s /L,
t ¼ f t /L, and h ¼ H s /H t (H s and H t are the width and height of the mirror
surface respectively), and derive the optimization expression that pro-
vides the appropriate h, R t , and R s , namely:
h ¼ H s =H t ¼ðcos q min þ cos q max Þ=2; R t ¼ 2f t ¼ 2L=h; R s ¼ 2f s ¼ 2hL
In this case, on a focal plane with the slant distance of L, the focal plane
light spot corresponding to q ¼ q min and q ¼ q max is circular with the
equivalent radius. At this time, the designed incident angle of the toroidal
surface is:
cos q 0 ¼ðcos q min þ cos q max Þ=2 (4.4)
On a more regular basis, the toroidal surface is a special cylindrical
surface. As shown in Fig. 4.9, the toroidal surface is created by the conic
section (generatrix) from the yez plane revolving around the axis that is
parallel to the y-axis; the y-z plane serves as the tangential plane of the
toroidal surface, and the cross section of the toroidal surface with the yez
plane is the tangential curve. Tangential curve expression of the toroidal
surface is:

Cy 2
z ¼ gðyÞ¼ p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (4.5)
2 2
1 þ 1 ð1 þ KÞC y

FIGURE 4.8 Astigmatic-corrected target-aligned heliostat conceived by R. Zaibel et al. in
1995.