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 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

Animation (works only in IE) of tracking error of 0 to 0.5 degrees with above parameters


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Last updated: 20 January 2008