Fresnelx Calculates intensity and colour distribution of solar radiation falling on up to three surfaces. Run "fresnelx x" to see available commands.
Fresnelx uses the ASTM G-173-03 Direct Normal solar spectrum, the cauchy equation for acrylic to calculate the refractive index at a particular wavelength, the half-angle of the sun as seen on the surface of earth. For each groove on the fresnel lens, it calculates where each of the 2002 rays (280nm to 4000nm) will fall on the absorber (or if it misses entirely). It divides the absorber into a specified number concentric slices so that the energy falling on each slice is equal. It calculates the outer radius and the spectral content of each slice. If two absorbers are specified, then light that misses the first absorber are calculated for the second absorber. If three absorbers is specified, then the center of the second absorber is hollowed to allows the remaining light to fall on the third absorber. The pictures are rendered with povray.
wx - The width of the square fresnel lens in mm (default value 395 mm).
gx - The number of grooves (default value 395)
lx - The Focal length in mm at 589.2 nm (default value 330 mm)
sx - The total number of concentric slices (default value 36)
1x - The concentration level for the first absorber. This determines the absorber distance from the lens (focallength * (1 - 1/sqrt(x))
2x - The concentration level for the second absorber. This determines the absorber distance from the lens (focallength * (1 - 1/sqrt(x))
3x - The concentration level for the third absorber. This determines the absorber distance from the lens (focallength * (1 - 1/sqrt(x))
rx - If this option is not specified, then the first absorber is divided into 36 equal energy slices. If r19 is specified, then the first absorber have slices 1 to 18 and the second absorber have slices 19 to 36.
Rx - Use with rx to specify the third absorber. e.g r13 R25 will cause the first absorber to have slices 1 to 13, the third absorber to have slices 13 to 24 and the second absorber to have slices 25 to 36.
ex - Percentage of available energy to be collected by all absorbers.
Sx - Sun half angle in degree, change to different value if not on earth surface or different distance from sun.
Mx - Calculates the concentration levels for each absorber so that the maximum local concentration level at any slice does not exceed x. There may be no solution if x is too low or too high.
cs:x - Calculates the concentration level for the absorber, by constraining the outer radius of slice s to x mm. There may be no convergence to a solution if x is too small.
1. Fresnelx 11000
Show the calculations for 1000x concentration for a single surface at the front focus. Divide the surface into 36 equal energy slices. The default width is 395mm, focal length of 330mm and number of grooves is 395.
2. Fresnelx M2500 r19
Show the intensity and colour distribution for two surfaces. The first surface have 18 slices and the second surface have 18 slices. The maximum intensity for any slice is limited to 2500x.
3. Fresnelx r19 c18:6 c36:14
Constraint the radius of the first surface to 6mm and the radius of the second surface to 14mm
4. Fresnelx 21000 r0
Show the calculations for 1000x concentration for a single surface at the back focus.
5. Fresnelx w6000 g6000 l5000 r13 R25 M1250
Show the calculations for three surfaces for a fresnel lens of width 6m. The maximum intensity for any slice is limited to 1250x
887.65W/m2 refractive index at 589.2nm(1.492) m(20), eff(99.700%) SunHalfAngle(0.26657o) Total input energy 31955 Watts Acrylic Fresnel Lens Width 6000mm x 0.406mm, Area 36.00m2, Focal Length 5000mm (f/0.833), 6000 grooves Slice Radius Power Tot Tot Ix Ax Area UV Blue Green Red NIR IR 390 492 622 760 1110 4000 mm W W % cm2 % % % % % % 0 31955.32 31955 100.0 1.0 1 360000.00 5.6 13.0 19.6 18.2 27.5 16.0 Cell 1 Concentration Level 255.588x, distance from lens 4687.248mm, 0.9374f, nominal radius 211.742mm 1 25.544 885.01 885 2.8 486.4 17562 20.50 35.4 13.6 14.8 11.8 15.9 8.5 2 30.106 885.01 1770 5.5 1250.0 12642 7.98 21.3 16.5 18.1 14.4 19.4 10.4 3 34.710 884.99 2655 8.3 1063.5 9511 9.37 21.1 16.5 18.1 14.4 19.5 10.5 4 39.415 885.02 3540 11.1 910.0 7376 10.96 19.9 16.7 18.3 14.6 19.8 10.6 5 44.211 885.06 4425 13.8 791.4 5863 12.60 18.9 16.9 18.5 14.8 20.1 10.8 6 49.085 885.04 5310 16.6 697.9 4756 14.29 18.0 17.2 18.7 14.9 20.3 10.9 7 54.062 885.02 6195 19.4 618.2 3921 16.13 16.7 17.6 19.0 15.2 20.5 11.1 8 59.097 884.99 7080 22.2 557.1 3281 17.90 16.1 17.9 19.0 15.2 20.6 11.1 9 64.268 885.01 7965 24.9 497.5 2774 20.04 13.9 18.8 19.4 15.5 21.0 11.3 10 69.553 885.00 8850 27.7 448.7 2369 22.22 11.7 20.1 19.7 15.7 21.3 11.5 11 75.016 885.00 9735 30.5 401.9 2036 24.81 7.8 22.3 20.2 16.1 21.9 11.8 12 80.572 884.99 10620 33.2 367.1 1765 27.16 2.6 26.9 20.4 16.2 22.0 11.9
Cell 3 Concentration Level 169.667x, distance from lens 5383.858mm, 1.0768f, nominal radius 259.883mm 13 21.562 885.00 11505 36.0 682.6 1647 14.61 0.0 0.0 0.0 0.0 35.8 64.2 14 28.111 885.01 12390 38.8 975.7 1574 10.22 0.0 0.0 0.0 5.2 44.1 50.7 15 33.057 885.00 13275 41.5 1049.0 1511 9.50 0.0 0.0 0.0 12.2 35.5 52.3 16 37.117 885.05 14160 44.3 1113.8 1456 8.95 0.0 0.0 0.2 14.1 32.7 53.0 17 40.393 885.01 15045 47.1 1250.1 1411 7.98 0.0 0.0 1.7 12.1 29.4 56.8 18 43.797 885.01 15930 49.9 1107.4 1363 9.00 0.0 0.0 3.5 12.8 34.0 49.7 19 47.246 885.02 16815 52.6 1010.7 1314 9.86 0.0 0.0 5.1 13.1 38.8 43.0 20 50.590 885.01 17700 55.4 969.9 1266 10.28 0.0 0.0 6.0 12.9 43.0 38.1 21 54.757 885.04 18585 58.2 722.9 1207 13.79 0.0 0.0 2.1 15.7 70.5 11.7 22 59.487 885.04 19470 60.9 587.4 1142 16.97 0.0 0.0 0.0 8.3 91.7 0.0 23 67.424 885.01 20355 63.7 315.0 1038 31.65 0.0 0.0 0.0 0.2 99.8 0.0 24 88.710 884.99 21240 66.5 95.5 798 104.41 0.0 0.0 0.0 0.9 99.1 0.0
Cell 2 Concentration Level 314.523x, distance from lens 5281.931mm, 1.0564f, nominal radius 190.875mm, Center hole radius 30.799mm 25 34.677 884.99 22125 69.2 1250.0 732 7.98 0.0 0.0 11.9 29.4 50.6 8.1 26 38.975 884.99 23010 72.0 1002.5 717 9.95 0.0 0.0 15.7 39.4 38.1 6.8 27 43.968 885.00 23895 74.8 766.3 699 13.01 0.0 0.0 20.9 66.3 7.4 5.3 28 49.576 885.03 24780 77.5 605.1 677 16.48 0.0 0.3 26.2 68.6 0.0 4.9 29 56.049 885.00 25665 80.3 464.1 651 21.48 0.0 2.5 31.5 63.6 0.0 2.4 30 63.616 884.99 26550 83.1 350.5 619 28.44 0.0 5.7 38.4 55.2 0.0 0.7 31 72.750 885.01 27435 85.9 254.8 580 39.13 0.0 9.8 49.9 40.1 0.0 0.1 32 84.044 885.00 28320 88.6 179.2 532 55.63 0.0 15.1 75.7 9.2 0.0 0.0 33 98.609 884.99 29205 91.4 119.3 474 83.58 0.0 22.3 77.7 0.0 0.0 0.0 34 118.686 885.00 30090 94.2 72.7 401 137.05 0.0 33.6 66.4 0.0 0.0 0.0 35 150.466 884.99 30975 96.9 37.1 309 268.72 0.0 55.6 44.4 0.0 0.0 0.0 36 235.576 884.99 31860 99.7 9.7 164 1032.20 0.0 95.0 5.0 0.0 0.0 0.0 37 678.458 94.61 31955 100.0 0.1 24 12717.48 6.7 93.3 0.0 0.0 0.0 0.0
Last updated: 20 January 2008