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.
Command line options:
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.
Fresnelx examples
1. Fresnelx 11000
Show the calculations for average 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
777.37W/m2 refractive index at 589.2nm(1.492) m(20), eff(99.990%)
SunHalfAngle(0.26657o)
Total input energy 27985 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 QEff Ix Ax Area UV BlueGreen Red NIR IR
390 492 622 760 1110 4000
mm W W % % cm2 % % % % % %
Cell 1 Concentration Level 329.3x, distance from lens 4724.5mm, 0.94f,
radius 186.5mm
0 26.2 777.3 777 3 50 464 464 22 14 19 20 16 21 9
1 30.7 777.3 1555 6 51 1250 677 8 9 20 22 17 22 10
2 35.1 777.3 2332 8 51 1082 773 9 10 20 21 17 22 10
3 39.6 777.3 3109 11 50 963 813 10 12 20 21 16 22 10
4 43.9 777.4 3887 14 50 873 825 11 13 20 20 16 21 9
5 48.3 777.3 4664 17 50 789 819 13 13 20 20 16 21 9
6 52.7 777.3 5441 19 50 710 801 14 12 21 20 16 21 9
7 57.3 777.3 6219 22 50 633 775 16 8 23 21 16 22 10
8 62.0 777.3 6996 25 51 574 746 17 5 26 21 16 22 10
9 66.7 777.3 7773 28 51 517 715 19 0 29 21 17 22 10
10 71.7 777.3 8551 31 51 467 682 21 0 28 22 17 23 10
11 76.8 777.3 9328 33 52 420 648 24 0 26 22 18 24 10
Cell 3 Concentration Level 170.4x, distance from lens 5383.0mm, 1.08f,
radius 259.3mm
12 22.8 777.3 10105 36 36 613 645 16 0 0 0 0 41 59
13 29.4 777.3 10883 39 43 929 660 11 0 0 0 5 48 47
14 34.4 777.3 11660 42 42 980 674 10 0 0 0 13 41 47
15 38.5 777.3 12437 44 40 1064 690 9 0 0 0 15 37 48
16 41.7 777.3 13214 47 35 1250 709 8 0 0 1 13 32 54
17 45.4 777.3 13992 50 46 999 720 10 0 0 3 15 41 41
18 48.4 777.3 14769 53 43 1111 734 9 0 0 4 13 39 44
19 52.0 777.3 15546 56 57 893 741 11 0 0 6 15 53 26
20 55.9 777.3 16324 58 80 760 742 13 0 0 1 15 80 3
21 60.6 777.3 17101 61 84 575 732 17 0 0 0 8 92 0
22 68.4 777.3 17878 64 81 316 692 32 0 0 0 0 100 0
23 89.3 777.3 18656 67 76 96 551 104 0 0 0 2 98 0
Cell 2 Concentration Level 315.5x, distance from lens 5281.5mm, 1.06f,
radius 190.6mm, Center hole radius 31.4mm
24 35.2 777.3 19433 69 63 1250 525 8 0 0 11 32 50 7
25 39.5 777.4 20210 72 61 998 534 10 0 0 15 44 36 5
26 44.4 777.3 20988 75 60 771 540 13 0 0 20 72 4 4
27 49.9 777.3 21765 78 58 610 543 16 0 0 26 71 0 3
28 56.3 777.3 22542 81 57 469 540 21 0 1 33 65 0 1
29 63.7 777.3 23320 83 56 359 531 28 0 3 40 56 0 0
30 72.6 777.3 24097 86 54 263 514 38 0 7 52 41 0 0
31 83.5 777.3 24874 89 51 187 487 54 0 12 78 10 0 0
32 97.5 777.3 25651 92 49 126 448 79 0 19 81 0 0 0
33 116.7 777.3 26429 94 47 77 393 129 0 30 70 0 0 0
34 147.2 777.3 27206 97 44 39 313 253 0 50 50 0 0 0
35 259.7 777.3 27983 100 41 7 141 1437 0 93 7 0 0 0
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Last updated: Sun, 24 Jan 2021 22:05:59 GMT |