SOLAR DEFLECTION DEVICE

Abstract

Solar deflection device (1) comprising at least the following components: a hollow funnel (2), comprising a funnel wall (2a) that comprises a reflective surface (2b) on an inside of the funnel (2) for reflecting electromagnetic radiation, an inlet aperture (3) of said funnel (2), wherein the inlet aperture (3) extends within an inlet plane (3a), an exit aperture (4) of said funnel (2), wherein the exit aperture (4) extends within an exit plane (4a) and wherein the area (4b) enclosed by the exit aperture (4) has a different size than the area (3b) enclosed by the inlet aperture (3), a curved line that (5) extends from the center (3c) of the inlet aperture (3) to the center (4c) of the exit aperture (4), wherein for each plane (6a) that intersects said curved line (5) perpendicularly, the reflective surface (2b) of the funnel wall (2a) has a cross-section (6) within said plane (6a), wherein said cross-section (6) encloses an area (6b) and is centered around the curved line (5), a deflection angle (7) that is enclosed between said plane (6a) and the inlet plane (3a).

Claims

1. Solar deflection device (1) comprising at least the following components: a hollow funnel (2), comprising a funnel wall (2a) that comprises a reflective surface (2b) on an inside of the funnel (2) for reflecting electromagnetic radiation, an inlet aperture (3) of said funnel (2), wherein the inlet aperture (3) extends within an inlet plane (3a), an exit aperture (4) of said funnel (2), wherein the exit aperture (4) extends within an exit plane (4a) and wherein the area (4b) enclosed by the exit aperture (4) has a different size than the area (3b) enclosed by the inlet aperture (3), a curved line that (5) extends from the center (3c) of the inlet aperture (3) to the center (4c) of the exit aperture (4), wherein for each plane (6a) that intersects said curved line (5) perpendicularly, the reflective surface (2b) of the funnel wall (2a) has a cross-section (6) within said plane (6a), wherein said cross-section (6) encloses an area (6b) and is centered around the curved line (5), a deflection angle (7) that is enclosed between said plane (6a) and the inlet plane (3a).

2. Solar deflection device according to claim 1, wherein the area (3b, 4b, 6b) enclosed by the inlet aperture (3), the exit aperture (4) and/or the cross-section (6) has an oval, particularly a circular shape or elliptical shape.

3. Solar deflection device according to claim 1, wherein at essentially each point of the curved line (5), the curved line (5) has a curvature that is larger than zero.

4. Solar deflection device according to claim 1, wherein said curved line (5) is an arc line, particularly a circular arc line with a radius (R.sub.c), or a non-parabolic line.

5. Solar deflection device according to claim 1, wherein the aperture area (3b) of the inlet aperture (3) is larger than the aperture area (4b) of the exit aperture (4).

6. Solar deflection device according to claim 1, wherein the size of the enclosed area (6b) of the cross-section (6), particularly the diameter (6d) of the cross-section (6) is a continuous function (S) of said deflection angle (7).

7. Solar deflection device according to claim 6, wherein the function (S) is continuously differentiable at least once, particularly twice, more particularly three times.

8. Solar deflection device according to claim 6, wherein the function (S) is a monotonic function, particularly a strictly monotonic function.

9. Solar deflection device according to claim 6, wherein the function (S) is an interpolating function, including the diameter (3d) of the inlet aperture (3) and the diameter (4d) of the exit aperture (4) as interpolation points.

10. Solar deflection device according to claim 6, wherein the function (S) comprises a spline, particularly a linear, a quadratic or a cubic, particularly a natural cubic spline.

11. Solar deflection device according to claim 9, wherein the function (S) comprises or is a piecewise particularly natural cubic spline connecting a plurality of interpolation points, wherein particularly the size of the enclosed area (3b), particularly the diameter (3d), of the inlet aperture (3) and the size of the enclosed area (4b), particularly the diameter (4d) of the exit aperture (4) are two of the plurality of interpolation points and wherein particularly a third interpolation point corresponds to the size of the enclosed area (6b), particularly to the diameter (6d) of the cross-section (6).

12. Solar deflection device according to claim 1, wherein the solar deflection device comprises a nominal half acceptance angle (9) between 30 and 60, preferably 45.

13. Solar deflection device according to claim 1, wherein the inlet aperture (3) and the exit aperture (4) enclose a deflection angle (7) between 30 and 60, preferably 45.

14. Solar deflection device according to claim 1, wherein the inlet plane (3a) and the exit plane (4a) are perpendicular to the curved line (5).

Description

[0048] Further features and advantages of the invention shall be described by means of a detailed description of embodiments with reference to the Figures and examples. It is specifically shown in:

[0049] FIG. 1 a schematic cross-section of a solar deflection device according to the invention;

[0050] FIG. 2 a cross-section through the solar deflection device;

[0051] FIG. 3 a three-dimensional view of a solar deflection device according to the invention;

[0052] FIG. 4 a cross-section through a solar deflection device whose width is described by an interpolation function comprising three knots;

[0053] FIG. 5 a cross-section through a solar deflection device whose width is described by an interpolation function;

[0054] FIG. 6 a cross-section through a toroidal angle rotator;

[0055] FIG. 7 a cross-section through a light pipe;

[0056] FIG. 8 a cross-section through a multi-compound solar deflection device;

[0057] FIG. 9 a cross-section through eccentric flow line concentrator;

[0058] FIG. 10 a cross-section through an EAR concentrator and a multi-compound EAR concentrator;

[0059] FIG. 11 a diagram of the acceptance efficiency versus the eccentricity of the solar deflection device;

[0060] FIG. 12 a diagram of the average number of reflections versus the eccentricity of the solar deflection device;

[0061] FIG. 13 a diagram of the optical efficiency versus the eccentricity of the solar deflection device;

[0062] FIG. 14 a diagram of the optical efficiency versus the eccentricity of the solar deflection device;

[0063] FIG. 15 a setup of the ray-tracing simulation; and

[0064] FIG. 16 a three-dimensional grid-rendering of the solar deflection device.

[0065] FIG. 1 to FIG. 3 and FIG. 16 show one embodiments of the solar deflection device 1 according to the invention. The solar deflection device 1 comprises an inlet aperture 3 comprised in an inlet plane 3a, wherein the inlet aperture 3 is centered around an optical axis A of a solar concentrator and is furthermore arranged at the focal plane F of the solar concentrator. The solar deflection device 1 further comprises a funnel 2 comprising a reflective funnel surface 2b on an inside of the funnel 2. The funnel 2 is tapered and leads to an exit aperture 4 comprised in an exit plane 4a that encloses a deflection angle 7 with the inlet plane 3a. The inlet and exit aperture 3, 4 are particularly circular and comprise an inlet diameter 3d and an exit diameter 4d respectively. The lateral shift between the centers 3c, 4c of the inlet and exit aperture 3, 4, is called the center-to-center eccentricity e.sub.c. In this example the diameter 4d of the exit aperture 4 is 50 mm, wherein the deflection angle 7 between the inlet plane 3a and the exit plane 4a is 45. The nominal half acceptance angel 9 is the largest angle under which incident rays of radiation are still guided through the solar deflection device 1, wherein said half acceptance angle 9 is measured from a surface-normal of e.g. the inlet aperture 3 (in FIG. 1 the surface normal is corresponding to the optical axis A). It is assumed that incident rays enclosing a smaller angle are transmitted by the solar deflection device 1. In most examples the nominal half acceptance angle 9 is considered to be 45. Such a nominal half acceptance angle 9 gives rise to a so-called geometric concentration of C=1/sin.sup.2().

[0066] Wherein C is the geometric concentration and is the nominal half acceptance angle 9.

[0067] In the following some figures of merit will be introduced that are typically used to describe a solar concentrator and/or solar deflection device 1.

[0068] Geometric Concentration:

[0069] The geometric concentration C is the ratio of the inlet aperture area 3b to the exit aperture area 4b. For circular inlet and exit apertures 3, 4 the geometric concentration C is equal to the ratio of the square of the inlet aperture diameter 3d to the exit aperture diameter 4d.

C=A.sub.i/A.sub.o=(D.sub.i/D.sub.o).sup.2(Eq. 1)

with
D.sub.i denoting the inlet aperture diameter 3d,
D.sub.o denoting the exit aperture diameter 4d,
A.sub.i denoting the inlet aperture area 3b, and
A.sub.o denoting the exit aperture area 4b.

[0070] While the geometric concentration C can in principle have any value (D.sub.o may be made arbitrarily small), there is a theoretical upper limit of C above which some of the radiation within the half acceptance angle must be rejected by the solar deflection device 1. This limit is set by conservation of tendue and is equal in three dimensions to:

C=1/sin.sup.2()(Eq. 2)

[0071] Usually this is taken as the limit for C, since a higher geometric concentration C will necessarily lead to losses in acceptance efficiency. For the given problem with =45, the maximum geometric concentration C equals 2. Unless otherwise stated, the following designs considered here are constructed with C=2.

[0072] Optical Efficiency

[0073] The optical efficiency .sub.optical is the fraction of radiant power entering the inlet aperture 3 of the solar deflection device 1, which reaches the exit aperture 4 accounting for all loss mechanisms (rejection and absorption):

.sub.optical=Q.sub.o/Q.sub.i(Eq. 3)

with Q.sub.i being the power of the radiation incident on the inlet aperture within the nominal half acceptance angel, and Q.sub.o being the power at the exit aperture.

[0074] Acceptance Efficiency

[0075] The acceptance efficiency .sub.acc is the optical efficiency .sub.optical considering losses only by ray rejection, i.e. for a solar deflection device 1 with perfect mirrors (reflectivity of 1). It is a function only of the geometry of the solar deflection device 1 and the distribution of incident radiation at the inlet aperture 3.

.sub.acc=.sub.optical(=1)(Eq. 4)

[0076] A solar deflection device 1, particularly a solar radiation concentrator is called ideal, if it has no rejection, i.e. an acceptance efficiency of 1, for all rays within the nominal half acceptance angle 9 (also referred to as ).

[0077] Average Number of Reflections

[0078] The average number of reflections n is a figure of merit for assessing the degree to which electromagnetic radiation is absorbed by mirror surfaces of finite reflectivity.

[0079] Following the work of Rabl [2] an approximation for the optical efficiency .sub.optical of an optical system with finite reflectivity is:

.sub.optical().sub.acc.Math.(Eq. 5)

[0080] The average number of reflections n can therefore be obtained from:

[00001]$\begin{array}{cc}n\frac{\log \left({}_{\mathrm{optical}}\left(\right)/{}_{\mathrm{acc}}\right)}{\log \left(\right)}& \left(\mathrm{Eq}..Math.6\right)\end{array}$

Eq. (5) can subsequently be used to estimate the optical efficiency .sub.optical for a different reflectivity , provided the reflectivity is high and reasonably close to the value used in the Eq. (6) to evaluate n.

[0081] Expected Efficiency

[0082] An estimate of the attainable efficiency of a redirecting and concentrating solar deflection device can be estimated by considering typical values of the acceptance efficiency .sub.acc and the average number of reflections n. Assuming an acceptance efficiency .sub.acc of 90% and on average one reflection to redirect the ray plus one reflection to concentrate yields:

.sub.optical()=0.9.sup.2(Eq. 7)

[0083] Assuming a mirror reflectivity of 95% yields .sub.optical equals 81%. This is regarded as a reasonable value to aim for with the solar deflection device 1 according to the invention.

[0084] Design Strategyfrom Two Dimensions to Three Dimensions

[0085] In general, solar deflection devices profiles are designed in two dimensions. Most three dimensional designs considered have circular inlet and exit apertures. Where axial symmetry is possible three dimensional profiles are obtained by revolving 2D axes about the optic axis. Where not, three dimensional profiles are obtained by lofting circular inlet and exit apertures using the two dimensional profile as guide curves.

[0086] Examples of Various Designs of Solar Deflection Devices [0087] a) The toroidal angle rotator (TAR) was investigated by Collares-Pereira and Mendes [1] for redirecting concentrated radiation who showed that such a device has no rejection. Unfortunately, for incident radiation having an angular aperture smaller than 90, the angular aperture is not conserved by the toroid, even in the meridian section. The extreme ray striking the inner circle with an angle .sub.i,max is dilated to a maximum angle of .sub.o,max when the exit aperture cuts the ray exactly out of phase. At this point the outlet angle is dilated to:

[00002]$\cos \left({}_{o,\max }\right)=\frac{r}{R}.Math.\cos \left({}_{i,\max }\right),$

wherein R is the outer radius of the torus and r is the inner radius of the torus. [0088] b) Chaves and Collares-Pereira developed an angle rotator that is capable of redirecting radiation through any rotation angle while preserving angular aperture (in the meridian section) [3]. The angle rotator consists of three flat mirrors and one elliptic mirror (EAR, see FIG. 10 left side; taken from [4]). Since the elliptic angle rotator preserves angular aperture, it may be used before or after a concentrating optic without loss of ideality (in the meridian section). [0089] c) The Compound Parabolic Concentrator (CPC) is an ideal concentrator in two dimensions for an infinite source of half-angular aperture .sub.acc. In revolved three-dimensional geometry, it falls short of ideality due to partial rejection of non-meridian (skew) rays. [0090] d) A light pipe (LP) is a simple extruded section which can be used to guide radiation. In the meridian section it preserves angular aperture and may therefore be used before and after a solar concentrator, see FIG. 7. [0091] e) The CPC-TAR-LP consists of a CPC with the inlet placed at the focal plane. A torus is placed at the exit of the CPC to redirect radiation from the exit of the CPC. A light-pipe is used to gain further eccentricity. The inner radius of the torus is chosen as zero, since in general a higher eccentricity with a fewer number of reflections can be achieved when combining a small inner radius torus with a light-pipe than when using a large inner radius torus alone. The length of the light-pipe placed at the end of the torus is chosen to achieved a center-to-center eccentricity of 60 mm, see FIG. 8 left side. [0092] f) Due to the high number of reflections in the CPC-TAR-LP, the TAR-CPC was investigated. The TAR-CPC configuration can achieve a higher eccentricity with fewer reflections that the CPC-TAR-LP configuration since rotation is performed before the CPC such that the CPC length contributes to the eccentricity. It is expected that the TAR-CPC will suffer from a low acceptance efficiency due to dilation of the angular aperture by the torus, see FIG. 8 right side. [0093] g) The EAR-CPC has the advantages of the TAR-CPC but with the EAR preserving angular aperture thus hypothetically leading to a higher acceptance efficiency. Drawbacks are difficulties in manufacturability, reduced design flexibility as the EAR design is fixed by the angular aperture and rotation angle as opposed to the TAR where the inner radius can be chosen independent of the rotation angle, see FIG. 10 right side. [0094] h) Any two mirrors placed along lines of flow of a Lambertian radiator constitute an ideal concentrator in two dimensions. Considering the lines of flow of an inverted V-wedge receiver as in FIG. 9 reveals some interesting concentrator profiles. The lines of flow are confocal parabolas with focus at the tip of the wedge. By placing mirrors along any two flowlines, an ideal eccentric concentrator with exit aperture rotated by an angle 90.sub.c with an arbitrarily large eccentricity can be obtained. The main drawback of these designs is a high average number of reflections due to the high length to aperture (slenderness) ratio. To partially overcome this, the so-called Eccentric FlowLine Concentrator (EFLC) can be truncated on the inlet side with little loss of concentration and eccentricity. FIG. 9 shows a schematic drawing of an EFLC constructed from the lines of flow 200 from an inverted V-wedge receiver. Placing mirrors 201 along any two lines of flow constitute an ideal concentrator in two dimensions. The inlet side of the EFLC can be truncated to shorten the concentrator and reduce the average number of reflections without significant loss of concentration and eccentricity

[0095] Tailored Toroid Concentrator (TTC)

[0096] FIG. 1 to FIG. 3 and FIG. 16 show a solar deflection device 1 according to the invention that in the following is referred to as tailored toroid concentrator (TTC).

[0097] Such a TTC concentrates and redirects electromagnetic radiation and might be used for directing concentrated electromagnetic radiation particularly from a single stationary source particularly to a plurality of apertures of a multiple-cavity receiver, for example an array of cavities, each with an individual aperture.

[0098] The TTC is a tailored concentrator based on a torus with geometry modified to achieve ideal concentration at maximum optical efficiency. The TTC particularly comprises all or some of the following features: [0099] electromagnetic radiation is collected by a circular inlet aperture 3 of radius within a nominal half acceptance angle 9 (), and redirected to a circular exit aperture 4 with a radius r.sub.o or with a diameter 4d that is smaller than the radius r.sub.i or diameter 3d of the inlet aperture 3 respectively, [0100] the exit aperture 4 is tilted by a rotation angle of , wherein said rotation angle corresponds to the largest deflection angle 7, and wherein the exit aperture 4 is furthermore laterally displaced by an eccentricity e.sub.c, with respect to the inlet aperture 3, [0101] the eccentricity e.sub.c and rotation angle may be chosen to achieve the required separation and inclination of the plurality of cavity apertures, [0102] the geometric concentration C=A.sub.i/A.sub.o is set equal to the theoretical limit of 1/sin.sup.2() imposed by the three-dimensional conservation of tendue, [0103] the TTC features low average number of reflections n, compared to composite devices comprised of existing optical components, thus minimizing power loses due to finite reflectivity of mirror surfaces, [0104] the optical efficiency .sub.optical through the TTC may approach that of conventional non-imaging concentrators which only concentrate and do not redirect radiation, [0105] the geometry of the TTC is defined by a curved line 5 that is particularly a circular arc centerline in the two-dimensional cross-section through the plane of symmetry of the TTC (as shown in FIG. 2), [0106] the geometric concentration C can be reduced from the theoretical limit by slightly increasing the exit aperture diameter 4d, leading to an increase in optical efficiency .sub.optical, [0107] the three dimensional geometry is formed by a series of circular cross-sections 6 cut at a deflection angle 7 () with respect to the inlet aperture 3, [0108] the normal of each circular cross-section 6 is tangent to the centerline 5 at the point of intersection, [0109] the diameter 6d or radius (r()) of each circular cross-section 6 is defined by a function S, particularly a taper function S, with r=S(), where S is particularly an interpolant of linear, quadratic, or cubic form, [0110] the mirror profiles may be tailored by changing the taper function S to maximize optical efficiency .sub.optical, [0111] the inner R.sub.i and outer radii R.sub.o of the solar deflection device 1 are chosen to meet the required eccentricity e.sub.c and rotation angle (see e.g. FIG. 5).

Example of an Embodiment of a TTC

[0112] The construction of such a tailored toroidal concentrator particularly begins in the x-z plane with a curved line 5, particularly a circular arc centerline covering a rotation angle and radius R.sub.c centered at the origin as shown in FIG. 2. The inlet aperture 3 extends along the inlet plane 3a along the x-y-axis. The circular inlet aperture 4 with a radius r.sub.i that is smaller than the radius of the circular arc centerline R.sub.c, is centered at the start of said curved line 5 (defining a deflection angle of =0), laying in the x-y plane. The center-to-center eccentricity e.sub.c of the TTC is given by e.sub.c=R.sub.c(1cos()). Each deflection angle 7 in the range between 0 defines a cross-section 6 that is comprised in a plane 6a that intersects the inlet plane 3a enclosing said deflection angle 7 and that is perpendicular to said curved line 5 at the point of intersection with the curved line 5. The circular exit aperture 4 with a radius r.sub.o that is smaller than the radius of the inlet aperture r.sub.i, r.sub.o<r.sub.i<r.sub.c, is centered at the end (=) of the curved line 5 through a plane whose normal is tangent to the end of the curved line 5. The exit aperture radius r.sub.o is nominally chosen as r.sub.i=r.sub.o sin(), corresponding to the theoretical limit of geometric concentration C for partially collimated incident radiation of nominal half acceptance angle . Selecting a slightly larger exit aperture radius r.sub.o may be beneficial in improving optical efficiency .sub.optical, with a slight reduction from the theoretical maximum geometric concentration C.

[0113] The reflective surface 2b of the TTC is defined by a series of circular cross-sections 6 from the inlet to exit aperture 3 on planes 6a whose normals n are tangent to the curved line 5 at the intersection point where the respective plane 6a intersects the curved line, as shown in FIG. 3. The taper of the solar deflection device 1 is the function S describing the radius r of each circular cross section 6 as a function of the deflection angle 7 (also referred to as ). The complete parametric equations of the surface in three dimensions, for an origin placed at the center of the curved line 5, with x-z as the symmetry plane of the TTC, are:

r=S()

x=(r cos()+R.sub.c)cos()

y=(r cos()+R.sub.c)sin()

z=r sin()

for 0, and 0<2. The resulting shape is a surface from the circular inlet aperture 3 to the circular exit aperture 4 through the circular cross-sections 6 of radius r=S().

[0114] Various taper functions S are possible, but generally interpolating functions are used. Depending on the number of interpolation points (also termed knots) used in addition to the endpoints (=0, r.sub.i) and (=, r.sub.o), different interpolation functions (also termed interpolants) may be used. The simplest interpolant is (with zero additional knots) the linear interpolant r()=r.sub.i(r.sub.ir.sub.o)/. An additional interpolation point may be defined at the waist of the device at a deflection angle .sub.w (given a nominal value of ) and radius r.sub.w. It is then possible to define a piecewise linear spline, a parabola (quadratic), or piecewise cubic spline through the three knots. For .sub.w=, a value of r.sub.w=(r.sub.i+r.sub.o) produces a linear interpolant for a spline of any degree. The waist control point can be tailored to maximize the optical transfer efficiency of the TTC. Additional knots provide additional degrees of freedom to tailor the TTC.

[0115] Due to its high degree of smoothness, the cubic spline is a preferred interpolant for the taper function S. For one additional interpolation point at the waist, a natural cubic spline S() may be fitted through knots I(0, r.sub.i), W(.sub.w, r.sub.w) and O(.sub.o, r.sub.o). The 3-point spline has two segments: the first segment ranges from the inlet to the waist, and second segment ranges from the waist to the exit, with second derivatives set to zero at the two ends (natural spline), and first and second derivatives matched at W.

[0116] The interpolant for the j.sup.th segment has the form:

S.sub.j()=a.sub.j+b.sub.jt.sub.j+c.sub.jt.sub.j.sup.2+d.sub.jt.sub.j.sup.3

where t.sub.j=t.sub.1=/.sub.w for the first segment, and t.sub.j=t.sub.2=(.sub.w)/(.sub.w) for the second segment. The coefficients of the interpolant are:

a.sub.1=r.sub.i

a.sub.2=r.sub.w

b.sub.1=0.25(5r.sub.i+6r.sub.wr.sub.o)

b.sub.2=0.5(r.sub.i+r.sub.o)

c.sub.1=0

c.sub.2=0.75(r.sub.i2r.sub.w+r.sub.o)

d.sub.1=0.25(r.sub.i2r.sub.w+r.sub.o)

d.sub.2=0.25(r.sub.i+2r.sub.wr.sub.o)

[0117] One way to design such a TTC is to choose the inlet (and/or exit) aperture for maximum concentration C=1/sin.sup.2(), and subsequently tailor the waist radius r.sub.w at half the rotation angle to yield the highest optical efficiency .sub.optical.

[0118] The particularly highest optical efficiency .sub.optical can be estimated for example by a computer simulation.

[0119] Results of Estimating a TTC Shape with Computer Simulations

[0120] Ray-tracing simulations were performed in LightTools 7.1.0 using solid model geometries built in SolidWorks 2011. The radiation source was modelled as a Lambertian disk of radius 2.5 m at a distance of 2.5 m from the focal plane (i.e. subtending a rim angle of 45). A low number of rays (25 000) were traced for each simulation to facilitate the investigation of many designs. The estimated error on the power reaching the exit plane was below 1% for all simulations (see FIG. 15)

[0121] The results are compared to other solar deflection devices.

[0122] The acceptance efficiency of a 45 three dimensional Compound parabolic concentrator (CPC) is used as a reference. As mentioned above, the CPC is an ideal concentrator in two dimensions for an infinite source of half-angular aperture .sub.acc. In revolved three-dimensional geometry, it falls short of ideality due to partial rejection of non-meridian (skew) rays.

[0123] In FIG. 11 it is shown that the EFLCs 101 (represented by the diamond-shaped markers) have the highest acceptance efficiency .sub.acc due to their ideal two dimensional construction. For large eccentricity e.sub.c (i.e. very slender designs), the EFLC 101 actually surpasses the three-dimensional CPC 102 (represented by the square-shaped marker at 0 degree 0 in terms of acceptance efficiency. The CPC-TAR-LP design 103 (represented by the circular shaped marker) also has a very high acceptance efficiency .sub.acc which should essentially be equivalent to that of the CPC 102 alone since both the TAR and the LP are ideal in three dimensions. The TTC 100 shown (represented the square-shaped marker at 60 e.sub.c) has an optimized waist width and performs better than expected considering that it is not constructed from an ideal two-dimensional geometry. The EAR-CPC 104 performs reasonably well but is the lowest of the high-performance designs due to slight dilation of angular aperture through the EAR in 3D. The TAR-CPC 105 performs poorly due to significant dilation of angular aperture by the TAR. Furthermore the results of an EAR-CPC 106 and an EFLC 107 design each with a geometric concentration C of 1.8 are shown.

[0124] In FIG. 12 it is shown that the long slender designs, particularly the EFLC 101 and the CPC-TAR-LP 103 have a very high average number of reflections n for high eccentricities e.sub.0. The EAR-CPC 104 and TTC 100 designs have a comparable average number of reflections n. The TAR-CPC 105 has the lowest average number of reflections n owing to its extremely compact design.

[0125] The combined effect of the acceptance efficiency .sub.acc and the average number of reflections n is shown in FIG. 13 and FIG. 14. The EFLC 101 is a promising design for low eccentricities e.sub.c but is impractical for high eccentricities e.sub.c due to an increased average number of reflections n. The EAR-CPC 104 is a potential candidate for medium eccentricities e.sub.c, but is long for a given aperture diameter. The TTC 100 is particularly the best design for high eccentricities e.sub.c. Furthermore the results of an EAR-CPC 106 and an EFLC 107 design each with a geometric concentration C of 1.8 are shown.

Example of a Specific Design of a TTC

[0126] Inlet aperture diameter, D.sub.i=40 mm; [0127] Outlet aperture diameter, D.sub.o=30 mm; [0128] Eccentricity e.sub.c=50 mm; [0129] Normalized eccentricity, e.sub.c/D.sub.i=1.25; [0130] Geometric concentration, C=(D.sub.i/D.sub.o).sup.2=16/91.78; [0131] Maximal acceptance angle, .sub.max=sin.sup.1(C.sup.0.5)=48.6; [0132] Nominal half acceptance angle, =45; [0133] tendue loss, sin.sup.2 .sub.i/sin.sup.2 .sub.max=0.94; [0134] Outlet inclination, =45

[0135] Source Specification

[0136] Simulations were performed with a Lambertian disk source approximating the geometry of a solar simulator. [0137] Focal length, f=1 m; [0138] Source diameter, D.sub.max=2.25 m; [0139] Maximum rim angle, .sub.max=tan.sup.1(D.sub.max/2f)=48.4; [0140] Nominal rim angle, .sub.norm=45; [0141] Source diameter at nominal rim angle, D.sub.nom=2 m; [0142] Aim area diameter, D.sub.i=40 mm

[0143] Geometry Specification

[0144] Three different geometric constructions with an increasing number of degrees-of-freedom were investigated. In all cases, the three dimensional geometry was obtained by lofting from the circular inlet aperture to the circular outlet aperture along the specified guide curves.

[0145] Baseline

[0146] The baseline design consists of a circular centerline 5 with a radius R.sub.c which governs the position of the inlet and outlet aperture 3, 4. The cross-section through the reflective surface are represented by two curved lines (i.e. the guide profiles), particularly a circular arc. The design has no degrees of freedom to be used as optimization parameters.

[0147] Spline 1

[0148] The Spline 1 design utilizes the height H and eccentricity e.sub.c to position the inlet and outlet apertures 3, 4. The two guide profiles 300, 301that are the cross-sectional lines of the funnel 2 representing the funnel wall 2aare natural cubic splines passing through the inlet and outlet aperture 3, 4 edges wherein the guide profile's 300, 301 shape is controlled by a knot 302 placed between a beginning and an end of the respective guide profile, particularly at the waist of the solar deflection device 1. There are three degrees of freedom which may be used as optimization parameters. The optimization parameters are particularly given by the radius R.sub.w from one of the guide profiles 300, the radius r.sub.w of the funnel 2 at a particular deflection angle and the height H of the funnel 2 as shown in FIG. 4.

[0149] Spline 2

[0150] The Spline 2 design is similar to the Spline 1 design, but the placement of the knots is not restricted to be collinear with the origin. The two guide profiles 300, 301 on the inside and outside of the solar deflection device 1 may be chosen independently. There are five degrees of freedom which may be used as optimization parameters. The optimization parameters are particularly given by [0151] the radius of the line in the x-z plane from the origin to the interior knot of the inner guide profile R.sub.i, [0152] the same but for the outer guide profile R.sub.o, [0153] a first deflection angle .sub.i of the line in the x-z plane from the origin to the interior knot of the inner guide profile 300, [0154] a second deflection angle .sub.o of the line in the x-z plane from the origin to the outer knot of the outer guide profile 301, and [0155] the height H of the solar deflection device 1 device as shown in FIG. 5.

[0156] Optimization was performed to maximize optical efficiency for a reflectivity of 95% at the nominal acceptance angle using 10.sup.5 rays. The alternate engine in LightTools was used with an exit criterion of less than a 10-5% improvement on the objective function. However, it is likely that the noise floor of the MC simulation provides a less strict exit criterion.

[0157] After the optimization, the resulting designs were traced with 10.sup.6 rays. The results for an incident radiant power of Q.sub.i=100 W, are shown below. The values of the output power Q.sub.o are equal to the percent optical efficiency of the design.

TABLE-US-00001 = 1 = 0.95 = 0.9 <n> Q.sub.o Q.sub.rej Q.sub.abs Q.sub.o Q.sub.rej Q.sub.abs Q.sub.o Q.sub.rej Q.sub.abs Baseline 3.57 99.16 0.93 0.00 83.04 0.26 16.70 69.85 0.08 30.07 Baseline* 3.79 99.16 0.93 0.00 82.12 0.26 17.62 68.42 0.08 31.50 Spline 1 3.05 98.42 1.58 0.00 84.91 0.69 14.40 73.27 0.32 26.42 Spline 2 2.82 98.78 1.22 0.00 95.94 0.71 13.35 74.71. 0.41 24.88 *with a 5 mm light pipe at the exit of the concentrator

[0158] The design parameters for the optimized designs are given below:

TABLE-US-00002 Spline 1 Spline 2 R.sub.w 125.42 R.sub.i 123.43 r.sub.w 39.77 R.sub.o 157.31 H 98.40 T.sub.i 20.20 T.sub.o 40.14 H 97.39

REFERENCES

[0159] [1] M. Collares-Pereira, et al., (1985). Redirecting concentrated radiation, Proceedings of SPIE, 2538, pp. 131-135. [0160] [2] A. Rabl, (1977). Radiation transfer through specular passagesa simple approximation, International Journal of Heat and Mass Transfer, 20, pp. 323-330. [0161] [3] J. Chaves and M. Collares-Pereira, (2002). Ideal concentrators with gaps, Applied Optics, 41, pp. 1267-1276. [0162] [4] J. Chaves, Introduction to nonimaging optics: CRC Press, 2008.

REFERENCE LIST

[0163] 1 solar deflection device [0164] 2 funnel [0165] 2a funnel wall [0166] 2b reflective surface [0167] 3 inlet aperture [0168] 3a inlet plane [0169] 3b inlet area [0170] 3c center of inlet area [0171] 3d diameter of inlet aperture [0172] 4 exit aperture [0173] 4a exit plane [0174] 4b exit area [0175] 4c center of exit area [0176] 4d diameter of exit aperture [0177] 5 curved line [0178] 6 cross-section [0179] 6a plane of cross-section [0180] 6b are of cross-section [0181] 6d diameter of cross-section [0182] 7 deflection angle [0183] 9 nominal half acceptance angle [0184] 100 TTC/Tailored Toroidal Concentrator design [0185] 101 EFLC design [0186] 102 CPC/Compound Parabolic Concentrator design [0187] 103 CPC-TAR-LP design [0188] 104 EAR-CPC design [0189] 105 TAR-CPC design [0190] 106 EAR-CPC design for C=1.8 [0191] 107 EFLC design for C=1.8 [0192] 200 lines of flow [0193] 201 mirrors [0194] 300 guide profile [0195] 301 guide profile [0196] 302 knot [0197] A optical axis [0198] D.sub.i diameter of inlet aperture [0199] D.sub.o diameter of exit aperture [0200] r.sub.i radius of inlet aperture [0201] r.sub.o radius of exit aperture [0202] H height of solar deflection device [0203] r.sub.w waist radius [0204] e.sub.c eccentricity [0205] F focal plane [0206] S function [0207] maximum deflection angle