**A RADIATION CONCENTRATOR INCORPORATING COMPOUND CONFOCAL UNEVEN PARABOLIC PRIMARY REFLECTOR, TAILORED SECONDARY REFLECTOR AND TAILORED RECEIVER**

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**G02B21/00***;*

**F21V7/00***;*

**G02B5/00**

**G02B19/00**US20100232176A1 | 2010-09-16 |

I Claim: 1 - A radiation concentrator comprising of: a primary reflector, for which the cross section is given by a pair of uneven parabolas arranged on either side of the axis of the system, said uneven parabolas having a common focus on the axis of the system, said uneven parabolas being rotated in opposite directions relative to the axis of the system through rotational angles defined by the angles between the axes of said uneven parabolas and the axis of the system; a receiver placed at the common focus of said uneven parabolas, in such a way that it directly absorbs a part of the radiation reflected from all points on the primary reflector; and a secondary reflector, for which the cross section is given by a pair of concave curves, arranged on either side of the axis of the system, facing the diagonally opposite uneven parabola of the primary reflector. 2 - A radiation concentrator as said in claim 1, wherein the rotational angle of said uneven parabolas is 1/4 3 - A radiation concentrator as said in claim 2, wherein the said uneven parabolas extends inwards, towards the axis of the system, through an inner rim angle that is equal to the rotational angle. 4 - A radiation concentrator as said in claim 3, wherein the upper and lower edges of the receiver's cross section lie on the axis of the system, at the point of intersection with the upper ray and middle ray, from the outer edge of the primary reflector. 5 - A radiation concentrator as said in claim 4, wherein the horizontal edges of the receiver's cross section lie on the trajectory of the upper rays from the apexes of said uneven parabolas of the primary reflector on either side of the axis of the system. 6 - A radiation concentrator as said in claim 5, wherein the curve that forms the receiver's cross section extends from the upper and lower edges, along line segments tangent to the caustics, formed by the upper rays and the middle rays from the primary reflector, till the point of tangency and continued along said caustics till the horizontal edges. - A radiation concentrator as said in claim 6, wherein the lower end of both curves that forms the cross section of secondary reflector is at the intersection of the upper ray, from outer edge of said uneven parabola of the primary reflector on same side of the axis of the system as the curve of the secondary reflector, with the lower ray, from outer edge of said uneven parabola of the primary reflector on the other side of the axis of the system. - A radiation concentrator as said in claim 7, wherein the upper section of both curves that forms the cross section of secondary reflector are trajectories orthogonal to the middle rays, from said uneven parabolas of the primary reflector on the either side of the axis. - A radiation concentrator as said in claim 8, wherein the lower sections of both curves that form the cross section of secondary reflector are circular arcs, for which the center of curvature is at the lower edge of the receiver. |

Field of Invention This invention relates to radiation concentrators that employ parabolic reflectors which may be used as solar collectors, to collect solar energy in the form of thermal energy which may be converted to electric energy as its receiver attains high temperature. The radiation concentrators may be a dish type (3D) concentrator or a trough type (2D) concentrator.

Prior Art The efficiency of a solar collector depends upon the concentration achieved by it. The efficiency increases, as the concentration achieved increases. The ideal concentration (theoretically achievable maximum) for a 3-D concentrator is l/sin 0 and for a 2-D concentrator it is l/sin0; where Θ is half the angle subtended by the radiation source (2Θ).

The solar collectors according to the prior art include imaging concentrators like parabolic reflectors and non-imaging concentrators like compound parabolic concentrators (CPC), compound elliptical concentrators (CEC) etc. The non-imaging concentrator, CPC gives ideal concentration when employed as a trough type (2-D) concentrator. But for concentrating radiation from very far away sources like the sun, the CPC will have to be impractically tall; and hence cannot be use as an ideal solar collector. Imaging concentrators, such as parabolic reflectors are much more compact but they cannot achieve high concentrations that non-imaging concentrators can deliver.

For an imaging concentrator employing parabolic reflector, the receiver may be a flat receiver or an Omni-directional receiver (a conventional Omni-directional receiver has a circular cross section). For a trough type solar collector with a flat receiver, the maximum concentration achieved is 50% of the ideal concentration; when the rim-angle of the parabolic reflector is 45°. For a trough type solar collector with an Omni-directional receiver, the maximum concentration achieved is about 32% of the ideal concentration; when the rim-angle of the parabolic reflector is 90°. One way to increase the concentration of a parabolic reflector with a flat receiver, according to the prior art, is to combine the parabolic reflector with a non imaging concentrator, like CPC or CEC, as primary and secondary reflectors / concentrators respectively. CPC is a special case of CEC and CEC is more suitable to be used as secondary concentrator. The combination of parabolic primary with CEC secondary reflector gives a maximum concentration, for 2Θ =0.52°, of approximately 96% of the ideal concentration, for rim angle approximately 9°. A parabolic reflector of rim angle approximately 9° has its focus at a very large distance which makes it an impractical design. A more practical design of the combination of parabolic primary with CEC secondary reflector has a parabolic reflector of rim angle approximately 45° and 40° which gives an approximate combined concentration of 70% and 75%. A parabolic reflector of rim angle approximately 45° and 40° will have its focus, and thereby the receiver, away from the aperture; which makes the design difficult to track the sun.

In the combination of parabolic primary with non imaging concentrator secondary, the surface of the secondary reflectors has to touch the receiver, it causes the loss of heat from the receiver; also much heat is radiated from the other side of the flat receiver tube or plate.

Reflectors which are made of glass will not be able to withstand the thermal shock and breaks.

There are some designs with insulators between receiver and the secondary reflectors and around the flat tubular receivers. This makes the shape of the secondary reflector imperfect and prevents the incoming radiation from reaching the receiver surface. And as no insulator is a perfect insulator some heat will still be lost by conduction. Also heating on one side can cause the receiver to bend.

For a parabolic reflector with an Omni-directional receiver, one way to increase the concentration according to the prior art, is to reshape the receiver to better fit all the edge rays reflected by the parabolic reflector. This receiver captures all the rays reflected off the parabolic reflector and is smaller than what a conventional circular receiver would need to be to do the same. Yet the concentration achieved is much lower than the ideal concentration.

The combination of parabolic primary with secondary concentrators having multiple entry apertures is another way to increase the concentration of a parabolic reflector with an Omni-directional receiver. In this combination, the primary and secondary concentrators are divided into sections. Each section of the secondary concentrator collects light from corresponding section of the primary concentrator. This kind of device has been proposed with a large number of divisions for primary and secondary concentrators. Though this kind of device can have the primary reflectors of rim angle up to 90°, the secondary concentrator becomes complex and difficult to manufacture. The secondary reflectors have to touch the receiver surface which makes it impossible to use a secondary reflector having the perfect shape for this device. Also the light rays passing through the secondary undergo multiple reflections and thereby reducing the energy of the light beam.

There are combinations of parabolic reflector primary with various Tailored Edge Ray Concentrator secondary reflectors with an Omni-directional receiver, according to the prior art. This method enables us to design simple secondary optics that attains high concentrations at large primary rim angles. For example, for a rim angle of 90°, an acceptance angle (2Θ) of 0.007 rad (0.4°) and a concentration of 70% of the ideal maximum. The shading of the primary by the secondary is about 2%. All the light reflected by the primary reaches the secondary. However, in this method also, the secondary reflectors have to touch the receiver surface and the light rays undergo multiple reflections by the secondary reflector.

Objects of the invention

An object of the invention is to device a system of radiation concentrator, incorporating parabolic primary reflectors that give good concentration ratio, for small acceptance angle, at rim-angles near 90°; so that the receiver of the system is very close to the aperture. Another object of the invention is to design a system of radiation concentrator, which achieves high concentration of radiation; with minimum energy loss due to multiple reflections. Yet another object of the invention is to design a system of radiation concentrator, where at least some of the radiation from the source, is absorbed directly by the receiver, without any reflection, at least half of the radiation reflected from the primary reflector is absorbed by the receiver and re-reflect the rest of the radiation, reflected from the primary reflector, to the receiver by a secondary reflector with a single reflection. Yet another object of the invention is to design a system of radiation concentrator, which incorporates a secondary reflector that is not in contact with the receiver and is simple and easy to manufacture. Yet another object of the invention is to design a system of radiation concentrator, which incorporates a receiver that has a minimum surface area and absorbs all the radiation that enters the aperture; excluding those blocked by the secondary reflector. Summary of the invention

The invention incorporates a primary reflector consisting of two uneven confocal parabolic reflectors on either side of the axial plane of the system; where axes of both the uneven parabolic reflectors are directed to the centers of diagonally opposite halves of the radiation source. As the uneven parabolic reflectors focus the radiation from their diagonally opposite half of the source to their common focus, a receiver placed at the common focus absorbs a half of these rays directly. The receiver in this invention is shaped to fit in the envelope, formed by the upper edge rays and the middle rays (the middle rays are those rays which pass through the angular bisectors of the angles formed between the upper and lower edge rays reflected from the primary reflector) from both halves of the radiation source. Such a receiver has a surface area much smaller than the surface area of the re-shaped receivers in the systems according the prior art and absorbs the upper half of radiation reflected from all points of the primary reflector. The secondary reflector employed in this invention has an upper and a lower surface. Upper surface is shaped along the normals to the reflected middle rays from both the uneven parabolic reflectors and the lower surface is shaped along circular arcs with their centers at the lower edge of the receiver. Such a secondary reflector reflects the lower half of radiation reflected from all points of the primary reflector to the receiver. Also, this reflector is easy to manufacture and does not touch the surface of the receiver. It is also possible to construct a primary-secondary combination of this type where the rim angles of the primary parabolic reflectors are near 90°. In such a construction, the receiver will be very close to the aperture. Also the secondary reflector has a gap directly above the receiver which allows some radiation to fall on the receiver directly. As this design of radiation concentration system gives good concentration for small acceptance angle and as being an uncomplicated design, it can be easily implemented in a trough or dish type solar collector system. Brief description of drawings

An exemplary embodiment of the present invention is illustrated by way of example in the accompanying drawings in which like reference numbers indicate the same or similar elements and in which:

Figure 1 is a diagrammatic representation of the cross section of an exemplary embodiment of the present invention; for a distant source that subtends an angle 5°; Figure 2 is a diagrammatic representation of the cross section of the primary reflector of the exemplary embodiment illustrating its geometry;

Figure 3 is a diagrammatic representation of the cross section of the primary reflector of the exemplary embodiment illustrating the trajectory of light reflected from it;

Figure 4 is a diagrammatic illustration explaining the method of construction of an approximation of the left caustic curve formed by the upper rays and the middle rays;

Figure 5 is a diagrammatic representation of the cross section of the receiver of the exemplary embodiment illustrating its geometry;

Figure 6 is a diagrammatic representation of the cross section of the exemplary embodiment illustrating the position of lower edges and different sections of the secondary reflector;

Figure 7 is a diagrammatic representation of the cross section of the exemplary embodiment illustrating the geometry of the lower section of the secondary reflector;

Figure 8 is a diagrammatic representation of the cross section of the exemplary embodiment illustrating the trajectory of light reflected from the lower section of the secondary reflector; Figure 9 is a diagrammatic representation of the cross section of the exemplary embodiment illustrating the orthogonal trajectories through which the cross section of the upper section of the secondary reflector is constructed;

Figure 10 is a diagrammatic illustration explaining the method of construction of an approximation of the left orthogonal trajectory;

Figure 11 is a diagrammatic representation of the cross section of the exemplary embodiment illustrating the position of the upper edge of the secondary reflectors;

Figure 12 is a diagrammatic representation of the cross section of the exemplary embodiment illustrating the trajectory of light reflected from the upper section of the secondary reflector;

Figure 13 is a graph showing the effective concentration, for different embodiments of the invention as a trough type solar collector, having different outer rim angles.

Figure 14 is a graph showing the percentage of concentration relative to the ideal concentration, for different embodiments of the invention as a trough type solar collector, having different outer rim angles. Detailed description of an exemplary embodiment of the invention

An exemplary embodiment of the invention, a trough type radiation concentrator, suitable for a radiation source which subtends an angle of 5°, is described in the following part. The geometry of the radiation concentrator and the trajectory of light, after being reflected by the concentrator, is explained with the help of its cross sectional view. Please refer to figure- 1; the trough type radiation concentrator includes a primary reflector (1), a two part secondary reflector (2) and a receiver (3).

As shown in figure-1 and figure-2; the cross section of the primary reflector (1) consists of two uneven parabolas, the left uneven parabola (5a) and the right uneven parabola (5b), having the same focal length and focal point (4) arranged on either side of the axis of the system (103). While describing the cross sectional view of the primary reflector and the trajectory of light, the left side of the primary reflector will be further referred to as the left uneven parabola (5a) and the right side of the primary reflector will be further referred to as the right uneven parabola (5b) in this document. The uneven parabolas, the left uneven parabola (5a) and the right uneven parabola

(5b), are rotated in opposite directions, keeping the common focus (4) as the center. The rotational angle (157) of the uneven parabolas are defined by the angle formed between the axis (101a) of the left uneven parabola (5a) or the axis (101b) of the right uneven parabola (5b) and the axis of the system (103); which is l/4th the angle subtended by the radiation source. The axis (101a) of the left uneven parabola (5a) and the axis (101b) of the right uneven parabola (5b) pass through the midpoints of the diagonally opposite halves of the radiation source; when the axis of the system (103) is aligned towards the center of the source. In such an arrangement the left uneven parabola (5a) focuses on the right half of the radiation source and similarly the right uneven parabola (5b) focuses on the left half of the radiation source.

The left uneven parabola (5a) extends from its apex (6a) towards the axis of the system (103) and the right uneven parabola (5b) extends from its apex (6b) towards the axis of the system (103); and are joined together to form the vertex of the primary reflector (7). The angle formed between the axis of the system (103) and the axis (101a) of the left uneven parabola (5a) and similarly, the angle formed between the axis of the system (103) and the axis (101b) of the right uneven parabola (5b) are termed as the inner rim angles. The inner rim angles are denoted by -Θ/2; where the angle subtended by the radiation source is denoted as 2Θ. The angle formed between the axis (101a) and the parabolic radius (104), from the left edge (8a), of the left uneven parabola (5a) and similarly, the angle formed between the axis (101b) and the parabolic radius (105), from the right edge (8b), of the right uneven parabola (5b), are termed as the outer rim angles. The outer rim angles can have any value less than 90- 2Θ degrees, which is denoted by

Any point on the left uneven parabola (5a) and the right uneven parabola (5b) corresponds to some value for the parameter ψ; which is the angle between the parabolic radius from the point and the axis of the uneven parabola. And the parameter ψ varies from 1|/ , the outer rim angle, to -Θ/2, the inner rim angle, of both the left uneven parabola (5a) and the right uneven parabola (5b).

Figure 3 shows the trajectory of the reflected light, on the cross sectional view of the primary reflector, from the points on the left uneven parabola and the right uneven parabola, corresponding to the values of the parameter ψ = , ψ _{3 }, ψ _{2 }, ψι and -Θ/2. Further in this document, we name the points on the left uneven parabola and the right uneven parabola, by the parameter value to which the point corresponds.

The edge rays from the right side of the source, upon being reflected from points on the left uneven parabola and the edge rays from the left side of the source, upon being reflected from points on the right uneven parabola, passes through points on the axis of the system (103), above the focus (4); and are termed as the upper rays. As shown in figure 3; the upper rays from the left uneven parabola include the upper ray (au) from the point \|/ _{R } (8a), the upper ray (hu) from the point ψ _{3 } (15), the upper ray (gu) from the point ψ _{2 } (14) and the upper ray (fu) from the point ψι (13). Similarly, the upper rays from right uneven parabola include the upper ray (bu) from the point \|/ _{R } (8b), the upper ray (cu) from the point ψ _{3 } (10), the upper ray (du) from the point ψ _{2 } (11), the upper ray (eu) from the point ψι (12).

The rays from the center of the radiation source, upon being reflected from all points on the primary reflector, passes through points on the axis of the system (103), below the focus (4); and are termed as the middle rays. As shown in figure 3, the middle rays from the left uneven parabola include the middle ray (am) from the point (8a), the middle ray (hm) from the point ψ _{3 } (15), the middle ray (gm) from the point ψ _{2 } (14) and the middle ray (fm) from the point ψ _{1 } (13). Similarly, the middle rays from the right uneven parabola include the middle ray (bm) from the point \|/R (8b), the middle ray (cm) from the point ψ _{3 } (10), the middle ray (dm) from the point ψ _{2 } (11), the middle ray (em) from the point ψι (12). All the upper rays and the middle rays forms an angle +Θ/2 or -Θ/2 with the parabolic radius from the points of their reflection.

The edge rays from the left side of the source, upon being reflected from points on the left uneven parabola and the edge rays from the right side of the source, upon being reflected from points on the right uneven parabola, forms an angle Θ with the parabolic radius from the points of their reflection and passes through points, on the axis of the system (103), below the focus (4), and are termed as the lower rays. As shown in figure 3, the lower rays from the left uneven parabola include the lower ray (al) from the point \|½ (8a), the lower ray (hi) from the point ψ _{3 } (15), the lower ray (gl) from the point ψ _{2 } (14) and the lower ray (fl) from the point ψι (13). Similarly, the lower rays from of the right uneven parabola include the lower ray (bl) from the point \|/R (8b), the lower ray (cl) from the point ψ _{3 } (10), the lower ray (dl) from the point ψ _{2 } (11) and the lower ray (el) from the point ψι (12).

The edge rays from the right side of the source, upon being reflected from points between the apex of the left uneven parabola and the axis of the system (103) and similarly, the edge rays from the left side of the source, upon being reflected from points, between the apex of the right uneven parabola and the axis of the system (103) do not pass through points on the axis of the system (103); but are still termed as the upper rays in conformity with the nomenclature of the other upper rays. In the same way, the edge rays from the left side and from the center of the source, upon being reflected from the point -Θ/2 (7) on the left uneven parabola and the edge rays from the right side and the center of the source, upon being reflected from the point -Θ/2 (7) on the right uneven parabola, also do not pass through points on the axis of the system (103); but are still termed as the lower rays and the middle rays respectively; in conformity with the nomenclature of the other lower rays and the middle rays. As shown in figure-3, such rays include the upper ray (nu), the middle ray (nm) and the lower ray (nla) from the point -Θ/2 (7) of the left uneven parabola and the upper ray (nm), the middle ray (nu) and the lower ray (nib) from the point -Θ/2 (7) of the right uneven parabola. The upper ray (nu) and the middle ray (nm) reflected by the left uneven parabola is same as the middle ray (nu) and the upper ray (nm) reflected by the right uneven parabola, at the vertex of the primary reflector(7).

As shown in figure-3, the entire upper rays from the right uneven parabola and the entire middle rays from the left uneven parabola traces out a right caustic curve (124a) engulfing the focus (4) from the right side. Similarly, the entire middle rays from the right uneven parabola and the entire upper rays from the left uneven parabola traces out a left caustic curve (124b) engulfing the focus (4) from the left side.

A method of constructing the right caustic curve (124a) and the left caustic curve (124b) is its approximation by line segments, tangent to the right caustic curve (124a) and the left caustic curve (124b). These tangential line segments are along the entire middle and upper rays from the primary reflector. Every adjacent tangential line segment on the right caustic curve (124a) is along the middle rays from the adjacent points on the left uneven parabola and along the upper rays from the adjacent points on the right uneven parabola. Every adjacent tangential line segment on the left caustic curve (124b) is along the middle rays from the adjacent points on the right uneven parabola and along the upper rays from the adjacent points on the left uneven parabola.

The position of the points of reflection on the right uneven parabola and on the left uneven parabola, relative to the focus and to the axis of the system, can be determined from the parametric equation of parabola rotated through an angle Θ/2. The parabolic radius from any point on the right or left uneven parabola, corresponding to a particular value for the parameter ψ, forms an angle ψ + Θ/2 with the axis of the system. The trajectory of the upper rays, the middle rays and the lower rays relative to the focus and the axis of the system, can be determined from the position of the points of reflection and the angle formed by them with the corresponding parabolic radius.

Please refer to figure-4, which explains the method of approximating the left caustic curve by nine line segments. The first line segment (140) is along the middle ray (bm) from 1|/R, the second line segment (141) is along the middle ray (cm) from ψ _{3 }, the third line segment (142) is along the middle ray (dm) from ψ _{2 }, and the fourth line segment (143) is along the middle ray (em) from ψι; where the points represented by the parameter ψ are points on the right uneven parabola. The fifth line segment (144) is along the upper ray (nu) from -Θ/2, the sixth line segment (145) is along the upper ray (fu) from ψι , the seventh line segment (146) is along the upper ray (gu) from ψ _{2 } , the eighth line segment (147) is along the upper ray (hu) from ψ _{3 } and the ninth line segment (148) is along the upper ray (au) from 1|/R; where the points represented by the parameter ψ are points on the left uneven parabola.

The first end point (149) and the second end point (150), of the second tangential line segment (141) are the points where the middle ray (cm) intersects with the middle ray (bm) from \|/R and the middle ray (dm) ψ _{2 } on the right uneven parabola respectively. Similarly, the end points of any tangential line segment that is a part of the left caustic curve (124b), are the points of intersection of the ray containing the tangential line segment either with the middle ray or the upper ray, whichever is applicable, from the adjacent points on the primary reflector. The right caustic curve can also be approximated in a similar way. By choosing a closer adjacent point of reflection, more accurate caustic curves can be constructed, as a larger number of smaller line segments tangent to the curves are obtained.

Please refer to figure-5; the lower edge (30) of the receiver's cross section is at the intersection of the axis of the system (103) with the middle ray (am) from the point \|/R of the left uneven parabola. The upper edge (29) of the receiver's cross section is at the intersection of the axis of the system (103) with the upper ray (au) from the point \|/R of the left uneven parabola. The upper left section (31) of the receiver's cross section is constructed along the tangent to the left caustic curve (124b) from the upper edge (29) to the point of tangency; which is termed as upper left tangent point (35). The upper right section (32) of the receiver's cross section is constructed along the tangent to the right caustic curve (124a) from the upper edge (29) to the point of tangency; which is termed as upper right tangent point (36). The lower left section (33) of the receiver's cross section is constructed along the tangent to the left caustic curve (124b) from the lower edge (30) to the point of tangency; which is termed as lower left tangent point (37). The lower right section (34) of the receiver's cross section is constructed along the tangent to the right caustic curve (124a) from the lower edge (30) to the point of tangency; which is termed as lower right tangent point (38). The middle left section (39) of the receiver's cross section is along the left caustic curve (124b), form upper left tangent point (35) to the lower left tangent point (37). The middle right section (40) of the receiver's cross section is along the right caustic curve (124a), form the upper right tangent point (36) to the lower right tangent point (38). The left most point (41) of the receiver's cross section is along the upper ray (lu) from the apex of the left uneven parabola and the right most point (42) of the receiver's cross section is along the upper ray (mu) from the apex of the right uneven parabola. The width of the receiver's cross section is the distance between the apex of the left uneven parabola and the apex of the right uneven parabola.

Please refer to figure-6; the lower right edge (24a) of the secondary reflector's (2) cross section is at the point of intersection, between the lower ray (al) from \|/R (8a) of the left uneven parabola and the upper ray (bu) from the 1|/ (8b) of the right uneven parabola. Similarly the lower left edge (24b) of the secondary reflector's cross section is at the point of intersection, between the lower ray (bl) from the \|/R (8b) of the right uneven parabola and the upper ray (au) from the 1|/R (8a) of the left uneven parabola. The lower left edge (24b) and the lower right edge (24a) of the secondary reflector's cross section defines the aperture of the secondary reflector. A secondary reflector with such an aperture accepts all the rays reflected from the primary reflector (1), with the lowest possible shading of the primary reflector (1). The point of incidence (25a) on the right side of the secondary reflector's cross section by the middle ray (am) from VJTR (8a) of the left uneven parabola, is termed as the right transition point (25a) of the secondary reflector's cross section. Similarly the point of incidence (25b) on the left side of the secondary reflector's cross section by the middle ray (bm) from \|/ _{R } (8b) of the right uneven parabola, is termed as the left transition point (25b) of the secondary reflector. The secondary reflector's cross section is divided into lower right section (23 a) and lower left section (23b) below the transition points (23 a and 23b), and upper right section (22a) and upper left section (22b) above the transition points (23 a and 23b). The upper right section (22a) and upper left section (22b) of the secondary reflector joins smoothly with the lower right section (23 a) and lower left section (23b) of the secondary reflector at the transition points.

Please refer to figure-7, the lower right section (23a) and lower left section (23b) of the secondary reflector's cross section are circular arcs with common center of curvature at the lower edge (30) of the receiver's (3) cross section. The radius of curvature (118 or 119) of the lower right section (23a) and the radius of curvature (120 or 121) of the lower left section (23b) of the secondary reflector has a length equal to the distance between the lower edge (30) of the receiver's (3) cross section and the lower right edge (24a) or the lower left edge (24b) of the secondary reflector's cross section.

Please refer to figure-8; all the rays between the middle ray (am) and the lower ray (al) from the point i|/ _{R } (8a) on the left uneven parabola is incident on the lower right section (23a) of the secondary reflector's cross section. As we move through the adjacent points on the primary reflector (1), towards its vertex (7), lesser and lesser rays reflected from the left uneven parabola is incident on the lower right section (23a) of the secondary reflector's cross section. And only the lower ray (il) form the point ψ _{4 } (16) on the left uneven parabola is incident on the lower right section (23a) of the secondary reflector's cross section. The lower ray (al) from the point \|/R (8a) on the left uneven parabola is reflected to the upper edge (29) of the receiver's (3) cross section. The middle ray (am) from the point \|/R (8a) of the uneven parabola, being parallel to the surface normal (119) of the secondary reflector's cross section at the right transition point (25a), is reflected along the same path as the incident ray; which is tangent to the receiver's (3) cross section. It is implied that the rays between the middle ray (am) and the lower ray (al) from the point \|/R (8a) on the left uneven parabola are also reflected to points on the receiver (3). The lower ray (il) form the point ψ _{4 } (16) on the left uneven parabola that reaches the right transition point (25a) of the secondary reflector's cross section is also reflected to another point on the receiver's (3) cross section, below its upper edge (29). And it can be concluded that all the rays that reaches the lower right section (23 a) and the lower left section (23b) of the secondary reflector's cross section is reflected to the receiver's (3) cross section.

Please refer to figure-9; the trajectory on the right side (122a), starting from the right transition point (23a), orthogonal to the extrapolated middle rays (am, hm, gm, fm and nm) from the left uneven parabola and the trajectory on the left side (122b), starting from the left transition point (23b), orthogonal to the extrapolated middle rays (am, bm, cm, dm and nu) from the right uneven parabola, are the curves that coincide with the upper right section and the upper left section of the cross section of the secondary reflector respectively. As the entire middle rays from the left uneven parabola are tangents to the right caustic curve (124a) and the entire middle rays from the right uneven parabola are tangents to the left caustic curve (124b), the family of trajectories orthogonal to the extrapolated middle rays on the right and left side are involutes obtained from the right caustic curve (124a) and the left caustic curve (124b), by attaching an imaginary taut string to the caustic curves and tracing their free ends as they are wound onto the caustic curves.

An approximation of the family orthogonal trajectories, including the orthogonal trajectory on the right (122a) and the orthogonal trajectory on the left (122b), may be constructed by the continuum of line segments joining the free ends of an entire set extrapolated middle rays. The term free end of the extrapolated line segment is used in analogy with the free end of the imaginary taut string that traces the involutes.

Please refer to figure- 10, which explains the method of constructing an approximation of the left orthogonal trajectory. In this example also we make use of the same exemplary approximation of the left caustic curve used in the previous section. Please refer to figure-4 also. The first extrapolated line segment (130), which is the extrapolated part of the middle ray (bm) from the point \|/ _{R } of the right uneven parabola, starts at the point of its intersection (149) with the middle ray (cm) from the next point, ψ _{3 } on the right uneven parabola. The free end (25b) of the first extrapolated line segment (130) is at the left transition point (25b) of the secondary reflector's cross section. The second extrapolated line segment (131), which is the extrapolated part of the middle ray (cm) from the point ψι on the right uneven parabola, starts at the point of its intersection (150) with the middle ray (dm) from the next point, ψ _{2 } on the right uneven parabola. The length of the second extrapolated line segment (131) is obtained by subtracting the length the second tangential line segment (141), that forms the left caustic curve, from the length of the previous extrapolated line segment, i.e. the first extrapolated line segment (130). Similarly the length of every extrapolated line segment, which is the extrapolated part of a middle ray, is obtained by subtracting the length of the tangential line segment along the same middle ray that makes up the approximate caustic curve, from the length of the previous extrapolated line segment. As the starting point (150), the direction and the length of the second extrapolated line segment (131) can be determined, the free end (135) of the second extrapolated line segment (131) can be located relative to the focus and the axis of the system. Similarly, the free end (136) of the third extrapolated line segment (132), the free end (137) of the fourth extrapolated line segment (133) and the free end (138) of the fifth extrapolated line segment (134) can be located. An approximation of the left orthogonal trajectory is formed by the continuum of line segments, which are referred to as the orthogonal line segments. The first orthogonal line segment (126) joins the free end (25b) of the first extrapolated line segment (130) and the free end (135) of the second extrapolated line segment (131), the second orthogonal line segment (127) joins the free end (135) of the second extrapolated line segment (131) and the free end (136) of the third extrapolated line segment (132), the third orthogonal line segment (128) ) joins the free end (136) of the third extrapolated line segment (132) and the free end (137) of the fourth extrapolated line segment (133),and the fourth orthogonal line segment (129) joins the free end (137) of the fourth extrapolated line segment (133) and the free end (138) of the fifth extrapolated line segment (134). The right orthogonal trajectory may also be constructed in a similar way.

By choosing a closer adjacent point of reflection more accurate orthogonal trajectories can be constructed, as a larger number of smaller orthogonal line segments joining a larger number of free ends of the extrapolated middle rays are obtained. The direction and trajectory of the middle rays from adjacent points on the primary reflector (1) varies in a smooth manner on either side of its vertex (7). As shown in figure- 11, there are two middle rays (nu and nm) from the vertex (7). The orthogonal trajectories that make up the cross section of the secondary reflector (2) terminate at the upper right edge (26a) and the upper left edge (26a) of the secondary reflector (2). And hence, the secondary reflector (2) has an opening between the upper right edge (26a) and the upper left edge (26a), directly above the receiver (3), through which some light from the source reaches the receiver (3) directly.

Please refer to figure- 12, the normal to the upper right section (22a) of the secondary reflector's cross section at the point (28) where the lower ray (jl) from the point ψ5 (17) of the left uneven parabola (5a) is incident, is parallel to the middle ray (fm) form the point ψ _{1 } (13) from the uneven parabola (5a). And similarly the normal to the upper right section (22a) of the secondary reflector's cross section at the point (27) where the lower ray (kl) from the point ψ _{6 } (18) of the left uneven parabola (5a) is incident, is parallel to the middle ray (gm) form the point ψ _{2 } (14) from the uneven parabola (5a). The lower ray (jl) from the point ψ5 (17) and the lower ray (kl) from the point ψ _{6 } (18), from the left uneven parabola (5a) are reflected on to the receiver (3). All the middle rays from the left uneven parabola (5a), being parallel to the surface normals to the upper right section (22a) of the secondary reflector's cross section are reflected back along the same trajectory, which is tangent to the right caustic (124a) and are incident on the receiver (3). And it can be concluded that all the rays from the middle ray through the lower ray, from all points on the primary reflector (1) that reaches the upper right section (22a) and the upper left section (22b) of the secondary reflector's (2) cross section, are reflected to the receiver (3).

Best Method

Different embodiments of the invention, for a particular radiation source subtending an angle 2Θ, having primary reflector of different outer rim angle values, have the secondary reflectors and the receivers of different relative sizes. Once the cross section of the concentrator according to this invention is constructed, for a particular outer rim angle and for a particular source, the concentrator can be easily made as a trough type concentrator or a dish type concentrator. These different embodiments also have different concentration ratios and there exists at least one embodiment, for both trough type and dish type, which has the maximum concentration for each radiation source that subtends a different angle, 2Θ.

The embodiment of the invention, as a trough type solar collector, has a very small cross section for the secondary reflector and the receiver tube relative to the primary reflector, owing to the fact that the angle subtended by the Sun (2Θ) is approximately 0.52°. The ratio of reduced surface area of the aperture, due to the shading of the primary reflector by the secondary reflector, to the surface area of the receiver is termed as the effective concentration ratio. The effective concentration ratio for different embodiments of the invention as trough type solar collector having different outer rim angles has been calculated numerically and is shown in figure- 13 as a graph. The percentage of concentration relative to the ideal concentration, for different embodiments of the invention as a trough type solar collector, having different outer rim angles is shown in figure- 14. The optimum effective concentration ratio for the trough type solar collector is achieved when the outer rim angle is approximately 85° and the achieved effective concentration ratio is approximately 183, which is 80.16% of the ideal concentration. List of reference symbols

1 Primary Reflector

Secondary Reflector

Receiver

Focus

a Left uneven parabola

b Right uneven parabola

a Apex of the left uneven parabola

b Apex of the right uneven parabola

Vertex of the primary reflector / A point on the left or right uneven parabola

corresponding to the value for the parameter ψ = -Θ/2

a A point on the left uneven parabola corresponding to the value for the parameter ψ = ψ _{ρ } b A point on the right uneven parabola corresponding to the value for the parameter ψ = ψ„

10 A point on the right uneven parabola corresponding to the value for the parameter ψ = ψ _{3 }

11 A point on the right uneven parabola corresponding to the value for the parameter ψ = ψ _{2 }

12 A point on the right uneven parabola corresponding to the value for the parameter ψ = ψι

13 A point on the left uneven parabola corresponding to the value for the parameter ψ = ψι

14 A point on the left uneven parabola corresponding to the value for the parameter ψ = ψ _{2 }

15 A point on the left uneven parabola corresponding to the value for the parameter ψ = ψ _{3 }

16 A point on the left uneven parabola corresponding to the value for the parameter ψ = ψ _{4 }

17 A point on the left uneven parabola corresponding to the value for the parameter ψ = ψ _{5 }

18 A point on the left uneven parabola corresponding to the value for the parameter ψ = ψ _{6 } 2a Upper right section of secondary reflector

2b Upper left section of secondary reflector

3a Lower right section of secondary reflector

3b Lower left section of secondary reflector

4a Lower right edge of secondary reflector

4b Lower left edge of secondary reflector

5a Right transition point of secondary reflector

5b Left transition point of secondary reflector / free end of the first extrapolated line

segment

6a Upper right edge of secondary reflector

6b Upper left edge of secondary reflector A point on the upper right section of secondary reflector

A point on the upper right section of secondary reflector

Upper edge of the receiver

Lower edge of the receiver

Upper left section of the receiver

Upper right section of the receiver

Lower left section of the receiver

Lower right section of the receiver

Upper left tangent point on the receiver

Upper right tangent point on the receiver

Lower left tangent point on the receiver

Lower right tangent point on the receiver

Left middle section of the receiver

Right middle section of the receiver

Left most point of the receiver

Right most point of the receiver

a Axis of left uneven parabola

b Axis of right uneven parabola

Axis of the system

Parabolic radius of the left uneven parabola towards the point on its left edge Parabolic radius of the right uneven parabola towards the point on its right edge A radial line of the lower right section of the secondary reflector

A radial line of the lower right section of the secondary reflector

A radial line of the lower left section of the secondary reflector

A radial line of the lower left section of the secondary reflector

a Right orthogonal trajectory

b Left orthogonal trajectory

a Right caustic curve

b Left caustic curve

First orthogonal line segment of the exemplary left orthogonal trajectory Second orthogonal line segment of the exemplary left orthogonal trajectory Third orthogonal line segment of the exemplary left orthogonal trajectory Fourth orthogonal line segment of the exemplary left orthogonal trajectory 130 First extrapolated line segment

131 Second extrapolated line segment

132 Third extrapolated line segment

133 Fourth extrapolated line segment

134 Fifth extrapolated line segment

135 Free end of the second extrapolated line segment

136 Free end of the third extrapolated line segment

137 Free end of the fourth extrapolated line segment

138 Free end of the fifth extrapolated line segment

140 First line segment of the exemplary left caustic curve

141 Second line segment of the exemplary left caustic curve

142 Third line segment of the exemplary left caustic curve

143 Fourth line segment of the exemplary left caustic curve

144 Fifth line segment of the exemplary left caustic curve

145 Sixth line segment of the exemplary left caustic curve

146 Seventh line segment of the exemplary left caustic curve

147 Eighth line segment of the exemplary left caustic curve

148 Ninth line segment of the exemplary left caustic curve

149 First end point of the second line segment of the exemplary left caustic curve

150 Second end point of the second line segment of the exemplary left caustic curve 157 Rotational angle of the uneven parabolas nu The trajectory of the upper ray from a point on the left uneven parabola corresponding to the value for the parameter ψ = -Θ/2 / The trajectory of the middle ray from a point on the right uneven parabola corresponding to the value for the parameter ψ = -Θ/2 nm The trajectory of the middle ray from a point on the left uneven parabola corresponding to the value for the parameter ψ = -Θ/2 / The trajectory of the upper ray from a point on the right uneven parabola corresponding to the value for the parameter ψ = -Θ/2 nla The trajectory of lower ray from the point on the left uneven parabola corresponding to the value for the parameter ψ = -Θ/2

nib The trajectory of lower ray from the point on the right uneven parabola corresponding to the value for the parameter ψ = -Θ/2 The trajectory of light reflected from every other point of the primary reflector is referenced by a two letter symbol. The first letter of the two letter symbol represents the following:

a The trajectory of light from a point on the left uneven parabola corresponding to the value for the parameter ψ = ψ _{κ }

b The trajectory of light from a point on the right uneven parabola corresponding to the value for the parameter ψ = ψ _{κ }

c The trajectory of light from a point on the right uneven parabola corresponding to the value for the parameter ψ = ψ _{3 }

d The trajectory of light from a point on the right uneven parabola corresponding to the value for the parameter ψ = ψ _{2 }

e The trajectory of light from a point on the right uneven parabola corresponding to the value for the parameter ψ = ψΐ

f The trajectory of light from a point on the left uneven parabola corresponding to the value for the parameter ψ = ψι

g The trajectory of light from a point on the left uneven parabola corresponding to the value for the parameter ψ = ψ _{2 }

h The trajectory of light from a point on the left uneven parabola corresponding to the value for the parameter ψ = ψ _{3 }

i The trajectory of light from a point on the left uneven parabola corresponding to the value for the parameter ψ = ψ _{4 }

j The trajectory of light from a point on the left uneven parabola corresponding to the value for the parameter ψ = ψ _{5 }

k The trajectory of light from a point on the left uneven parabola corresponding to the value for the parameter ψ = ψ _{6 }

1 The trajectory of light from the apex of the left uneven parabola

m The trajectory of light from the apex of the right uneven parabola

The second letter of the two letter symbol represents the following:

u Upper ray of the light

m Middle ray of the light

1 Lower ray of the light

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