Secondary reflectors for solar collectors and methods of making the same

1. A method for defining a profile of a secondary reflector configured to receive a light from a field of primary reflectors and direct the light to an absorber tube, the method comprising:

defining an aperture width for the secondary reflector;

a first step of defining a vertical position of an edge surface point of the profile, relative to a horizontal axis, x, on which the plurality of primary reflectors is located;

a second step of calculating a reflected beam spread distribution at the edge surface point resulting from the primary reflectors;

a third step of calculating a principal incidence of an incoming light relative to the edge surface point;

a fourth step of calculating a subsequent surface point of the profile based on the principal incidence; and

repeating the second step, the third step, and the fourth step, in series, until the profile is defined as a plurality of surface points across the width of the aperture, wherein:

defining the secondary reflector aperture comprises:

calculating a primary reflector acceptance angle for an outer-most primary reflector, n, by β n pr =4·σ total ; and

calculating the required aperture width by a 2nd ≅l n ·sin(β n pr ), wherein:

the primary reflector acceptance angle receives at least 95% of the light reflected by the outer-most primary reflector n, assuming the light reflected by the outer-most primary reflector, n, has a Gaussian distribution,

σ total is the total estimated or measured optical error RMS,

a 2nd is the required aperture width, and

l n is the distance between the outer-most primary reflector and the secondary reflector;

the principal incidence is defined as an angle at which a maximum amount of power provided by the light from the primary reflectors is delivered to the absorber tube,

the repeating is completed n times where n>2,

the profile of the secondary reflector minimizes reflective losses to the absorber tube by accounting for the reflected beam spread, and

the secondary reflector is manufactured to have a shape approximating the profile.

2. The method of claim 1 , further comprising, after the profile is defined:

comparing a width of the profile to the width of the aperture, wherein:

if the width of profile does not cover the entire width of the aperture, repeating the first step, the second step, the third step, and the fourth step, in series, until the width of the profile covers the entire width of the aperture.

3. The method of claim 2 , further comprising, after the comparing, optimizing the vertical position of the secondary reflector relative to the primary reflector.

4. The method of claim 1 , wherein the third step comprises:

defining an absorber tube acceptance window, a ab , as a portion of a width of the field of primary reflectors;

iteratively calculating a power intensity, P(x), as a function of position, x, on the horizontal axis by P(x)=g (σ total , β pr (x) where g is a Gaussian intensity distribution function;

identifying a position on the horizontal axis corresponding to a maximum of an integrated area of P(x) across a ab ; and

defining the principal incidence from a straight line between the position and to the edge surface point or a subsequent surface point.

5. The method of claim 1 , wherein the fourth step comprises:

determining a surface tangent vector and a pre-defined step distance, wherein:

the surface tangent is defined as a line perpendicular to a vector bisecting the principal incidence at the current surface point on the profile and a vector connecting the current surface point and a center of the absorber tube, and

the pre-defined step distance determines the next surface point along the surface tangent at the current surface point.

6. The method of claim 1 , further comprising, after the third step:

calculating a dependent variable for the edge surface point, wherein:

the dependent variable comprises at least one of a target reflection direction, a surface normal, a surface tangent, or a step distance, and

the dependent variable, in addition to the principal incidence, is used to calculate the subsequent edge surface point.

7. The method of claim 6 , wherein the target reflection direction is calculated by connecting the edge surface point to the center of the absorber tube.

8. The method of claim 7 , wherein the surface normal is calculated by bisecting the principal incidence and the target reflection direction.

9. The method of claim 6 , wherein the step distance is calculated as the distance between neighboring points as the aperture width divided by n.

10. The method of claim 1 , further comprising, before defining the aperture width:

defining geometry and optics for the field of primary reflectors, wherein:

the geometry and optics provide a metric for defining of the aperture width.

11. The method of claim 1 , wherein the vertical position of a starting edge point of the surface profile is equal to a height of the center of the absorber tube relative to the horizontal axis.

12. The method of claim 1 , wherein 10≤n≤1,000.