In reality, the reflector itself is a three-dimensional shape, i.e., a parabolic cylinder with a finite length (l). The above-described geometrical concepts apply to the cross-section of a parabolic reflector. If you are interested in more explanation of how these formulas were derived, please refer to Duffie and Beckman, 2013 book (Section 7.9) If there are any flaws in the mirror surface or trueness of the angle, additional spreading of the image may occur. Note that these are the minimal theoretical dimensions of the reflected image that would be produced by the ideal parabolic mirror that is perfectly aligned. The formulas include a as a chosen aperture of the reflector (width of the trough), and ( ϕ ) as a measure of parabolic curvature. The equations presented here can be used to estimate the size of the reflected light image on the receiver for different shapes of parabolic reflectors. The diameter of the cylindrical receiver (D), which would intercept the entire reflected image can be theoretically calculated using aperture width ( a), and rim angle ( ϕ ) as follows (Duffie and Beckman, 2013): ![]() Being reflected at a point on the parabolic surface, the beam hits the focal plane, where it produces an image of a certain dimension, centered around the focal point. Since the sun is not really a point source, solar beam incident on the reflector is represented as a cone with an angular width 0.53 o (so the half-angle between the cone axis and its side is 0.267 o). Consider Figure 2.10, which illustrates this idea. This type of collectors relies on sun tracking to ensure that the beam radiation is directed parallel to the parabolic axis.Ī parabolic mirror produces an image of the sun on the surface of the receiver, so the receiver size needs to be matched to the image size. Parabolic trough is one of the most widely implemented technologies for sunlight concentration at the utility scale. Parabolic trough (Figure 2.9) is a typical example of an imaging concentrator that utilizes the geometric relationships discussed above.
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