Thermal flux at the glass lake

Thermal flux on a glass lake solar thermal store.

Assuming an average annual rated power of 51 W_e per m² of mirror area, peak thermal flux will be about 4 x 51 x 0.71 / 0.4  = 357 W_th per m² land area. Concentrating this flux on a circle having diameter equal to the optics height, H, would give a land-area concentration factor of 28 x 28 = 784, producing a thermal flux of 784 x 0.357 suns = 280 suns. To discharge the lake at 250 suns requires a charging flux of 500 suns, and, since one third of the incident flux is diverted to power generation, a total flux on the lake of 750 suns. That implies a lake with a diameter of 0.61H .

To have the same 250-sun flux at the water wall of the boiler and at the surface of the discharging lake requires the two areas to be equal, and thus the height of the water wall must be one-quarter the diameter of the lake (see diagram below.)

For the area of a cylinder's wall to equal the area of one of its end caps, the height of the wall must be one-quarter the cylinder's diameter.

For an approximately 1 GWe target design, with R_f = 2660 m, and H = 190 m, the lake diameter will be 0.61 x 190 m = 116 m, and the height of the boiler's water wall will be 116 m /4 = 29 m. To accommodate 2.5 times the thermal flux that was modeled in the previous post's thermal simulations requires a lake 2.5 times as deep, and, to keep the same maximum temperature, 2.5² = 6.25 times the optical absorption length. However, that would give a 25m-deep lake with a absorption length of 63 m—so something's got to give.