SOLAR THERMAL CONCENTRATOR APPARATUS, SYSTEM, AND METHOD

Abstract

An apparatus is disclosed including: a trough shaped reflector extending along a longitudinal axis and including at least one reflective surface having a shape which substantially corresponds to an edge ray involute of the absorber.

Claims

1. An apparatus comprising: an elongated tubular absorber extending along a longitudinal axis and disposed adjacent to a reflector, wherein a cross-sectional shape of said elongated tubular absorber is a polygon with three or more sides when said cross-sectional shape is obtained transverse to the longitudinal axis; a heat transfer fluid adapted to flow within the elongated tubular absorber to extract heat from the elongated tubular absorber; and said reflector extending along the longitudinal axis of said elongated tubular absorber for concentrating light onto said elongated tubular absorber.

2. The apparatus of claim 1, wherein said reflector is a trough shaped reflector.

3. The apparatus of claim 2, wherein said elongated tubular absorber is disposed at a bottom of said trough shaped reflector.

4. The apparatus of claim 2, wherein said reflector comprises at least one reflective surface.

5. The apparatus of claim 1, wherein said elongated tubular absorber comprises a tubular inside part adapted to accommodate said flow of said heat transfer fluid.

6. The apparatus of claim 1, wherein the cross-sectional shape of said elongated tubular absorber is a square.

7. The apparatus of claim 1, wherein the polygon is a regular polygon.

8. The apparatus of claim 1, wherein the polygon is an irregular polygon.

9. An apparatus, comprising: an elongated tubular absorber extending along a longitudinal axis and disposed adjacent to a reflector, wherein a cross-sectional shape of said elongated tubular absorber, transverse to the longitudinal axis, is a regular polygon with three or more sides, and wherein said elongated tubular absorber is adapted to accommodate flow of a heat transfer fluid; and said reflector extending along the longitudinal axis of said elongated tubular absorber; and said reflector for reflecting incident light onto said elongated tubular absorber.

10. An apparatus, comprising: an elongated tubular absorber extending along a longitudinal axis and disposed adjacent to a reflector, wherein a cross-sectional shape of said elongated tubular absorber, transverse to the longitudinal axis, is an irregular polygon with three or more sides, and wherein said elongated tubular absorber is adapted to accommodate flow of a heat transfer fluid; and said reflector extending along the longitudinal axis of said elongated tubular absorber; and said reflector for reflecting incident light onto said elongated tubular absorber.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0053] The accompanying drawings are not intended to be drawn to scale. In the drawings, each identical or nearly identical component that is illustrated in various figures is represented by a like numeral. For purposes of clarity, not every component may be labeled in every drawing. In the drawings:

[0054] FIG. 1 is an illustration of the solar geometry.

[0055] FIG. 2 is an illustration of a system for converting solar light into another form of energy.

[0056] FIG. 3A is a side view of a concentrator assembly.

[0057] FIG. 3B is a perspective view of a concentrator assembly.

[0058] FIG. 4A is a top view of a concentrator assembly.

[0059] FIG. 4B is a side view of a concentrator assembly.

[0060] FIG. 4C is a cross section of an absorber used in the concentrator assembly of FIGS. 4A-4B.

[0061] FIG. 5A is a top view of a concentrator assembly.

[0062] FIG. 5B is a side view of a concentrator assembly.

[0063] FIG. 5C is a cross section taken transverse the longitudinal axis of an absorber used in the concentrator assembly of FIGS. 5A-5B.

[0064] FIG. 5D is a cross section taken through the longitudinal axis of an absorber used in the concentrator assembly of FIGS. 5A-5B.

[0065] FIG. 6A is a top view of a concentrator assembly.

[0066] FIG. 6B is a side view of a concentrator assembly.

[0067] FIG. 6C is a cross section taken transverse the longitudinal axis of an absorber used in the concentrator assembly of FIGS. 6A-6B.

[0068] FIG. 6D is a cross section taken through the longitudinal axis of an absorber used in the concentrator assembly of FIGS. 6A-6B.

[0069] FIG. 6E is a perspective view of an absorber used in the concentrator assembly of FIGS. 6A-6B.

[0070] FIG. 7A is an illustration of a cross-section of a concentrator assembly of a first embodiment.

[0071] FIG. 7B is an illustration of a cross-section of a concentrator assembly of a second embodiment.

[0072] FIGS. 8A-8E are ray traces of the concentrator assembly of FIG. 7 for rays incident at a variety of angles ranging from 35 degrees to +35 degrees.

[0073] FIGS. 9A-9B are illustrations of exemplary reflective surfaces for a concentrator assembly.

[0074] FIGS. 10A-10B show plots of collector efficiency versus inlet temperature under a variety of conditions.

[0075] FIGS. 11A-11B show plots of collector efficiency versus inlet temperature under a variety of conditions.

[0076] FIG. 11C shows a plot of collector efficiency versus inlet temperature under a variety of conditions for several types of collectors.

[0077] FIG. 12 is a plot of relative efficiency versus angle of incidence of solar light for an exemplary concentrator assembly.

[0078] FIG. 13 is an illustration of a concentrator design method.

[0079] FIGS. 14A and 14B illustrate the use of virtual absorbers in a concentrator design method.

[0080] FIGS. 15A and 15B illustrate a concentrator assembly featuring an absorber/concentrator gap, and a design method therefore.

[0081] FIG. 16 is a plot of the ratio of virtual absorber area to absorber area vs. gap loss for a concentrator assembly featuring an absorber/concentrator gap.

[0082] FIGS. 17A-20 show several embodiments of an optimal design concentration schematic.

DETAILED DESCRIPTION OF THE INVENTION

[0083] From a thermodynamic viewpoint, the solar geometry may be described in direction cosines, which are the momenta of the light rays. Referring to FIG. 1, the sun over the year occupies a band 101 inside a unit radius circle 102 which is sin 23.5 deg. This band is nearly Vi the area of the circle, from which follows, e.g. as described in detail U.S. Pat. No. 6,467,916 to Roland Winston (incorporated herein by reference in its entirety), that the maximum theoretical concentration for a trough shaped concentrating reflector using no seasonal adjustments is very close to 2.

[0084] In some embodiments, this limit may be increased. In cases where the target (absorber) is immersed in a refractive material having an index of refraction (n), this limit is multiplied by n squared because the momentum of a light ray is actually the index of refractiondirection cosine. For example, for n1.5 (typical of glass or PMMA) and restricting the absorber irradiance to 60 deg., the maximum concentration becomes 3. In some embodiments featuring a low concentration design which can be switched seasonally between 2 positions each year (summer and winter) the limits are multiplied by 2 (4-6 concentration). For example, embodiments described herein may feature a concentration of about 4 or more.

[0085] FIG. 2 shows a system 200 for converting solar light into another form of energy, e.g., heat. A concentrator assembly 201 receives light from the sun. One or more concentrators concentrate the incident solar light onto one or more absorbers, which convert the light to heat. This heat is transferred from the concentrator assembly 201, e.g., using a circulating heat transfer fluid to a heat exchanger 202. The heat exchanger 202 outputs the heat received from the concentrator assembly 201. The output heat may be used for any suitable purpose including, e.g., providing building heating, generation of electricity, generation of mechanical power, etc.

[0086] FIGS. 3 A and 3B illustrate exemplary embodiments of the concentrator assembly 201. The concentrator assembly 201 includes one or more optical concentrators 203. Three concentrators 203 are shown in FIG. 3A, five are shown in FIG. 3B, and any other number may be used in other embodiments. Each concentrator 203 concentrates incident solar light onto a corresponding absorber 204. The absorber 204 absorbs concentrated solar light and transforms it to heat.

[0087] As shown, the concentrators 203 and absorbers 204 are arranged in a linear array. However, any suitable arrangement may be used. The concentrators 203 are trough shaped reflectors having an open top end and tapering to a trough bottom. The inner surface of the trough is reflective, e.g., with a reflectivity to solar light of e.g., 80% or more, 90% or more, 95% or more, etc. In some embodiments, the reflective surface may include a reflective coating, e.g., of the types available from Alanod Solar GmbH of Ennepetal, Germany and ReflecTech, Inc. of Arvada, Colo.

[0088] The absorbers 204 are elongated tubular (e.g., cylindrical) elements positioned at or near the bottom of the trough shaped reflectors. As shown, each of the concentrators 203 is symmetric about an optical plane (indicated with a dashed line in FIG. 3A). In one embodiment, the concentrator 203 may include a U shape. In another embodiment, the concentrator 203 may include any shape known in the art so as to concentrate an optical amount of energy to a predetermined location. In some embodiments, a heat transfer working fluid (e.g., water, oil, an organic fluid, or any other suitable fluid known in the art) flows through the absorbers 204 (e.g., in a series arrangement, in a parallel arrangement, etc.). Heat from the absorbers 204 is transferred to the fluid, which flows out of the concentrator assembly 201 to the heat exchanger 202. The energy preferably is captured and used for a predetermined purpose.

[0089] As shown, the concentrators 203 and corresponding absorbers 204 are arranged in a linear array. In some embodiments, the concentrators may be arranged with a center to center spacing of 1.0 m or less, 0.5 m or less, 0.25 m or less, 0.1 m or less, e.g., in the range of 100-400 mm. In some embodiments, the absorbers 204 may have an outer diameter of 100 mm or less, 75 mm or less, 50 mm or less, e.g., in the range of 40-60 mm.

[0090] As described greater detail below, in some embodiments, concentrators 203 concentrate substantially all solar light incident at angles to the optic plane less than an acceptance angle to the absorber 204. In some embodiments, the concentrator 203 concentrates light incident at angles less than the acceptance angle with an efficiency at the thermodynamic limit. In some embodiments, the concentrator 203 concentrates light incident at angles less than the acceptance angle with a geometric concentration ratio of C of 1.0 or more, 1.1 or more, 1.25 or more, 1.5 or more, 1.75 or more, 1.85 or more, 1.9 or more, 2 or more, etc. In some embodiments this concentration is provided over the year without tracking.

[0091] FIGS. 4A-4C illustrate an exemplary embodiment of the collector assembly 201 featuring absorbers 204 having a counter flow arrangement. As shown, absorbers 204 are cylindrical members having an outer transparent evacuated enclosure 401 (e.g., a glass tube). Located within the enclosure is a tubular absorber fin 403 (e.g., an extruded aluminum or copper pipe) which absorbs solar light incident through the enclosure 401 and transforms the light to heat. The absorber fin 401 may include a selective surface 405 which exhibits a high absorptivity to solar light and a low emissivity (thereby limiting radiative heat loss). For example, in some embodiments, the selective surface 405 may exhibit an absorptivity of 0.75 or more, 0.9 or more, 0.95 or more, 0.99 or more etc. (e.g., in the range of 0.9 to 0.99). For example, in some embodiments, the selective surface 405 may exhibit an emissivity of 0.25 or less, 0.10 or less, 0.05 or less, 0.025 or less etc. (e.g., in the range of 0.04 to 0.05). In some embodiments, the selective surface exhibits these absorptivity and emissivity properties at temperature of 100 C or greater, 150 C or greater, 175 C or greater, or 200 C or greater (e.g., in the range of 150-200 C). In some embodiments, the selective surface comprises an aluminum nitride coating, e.g., sputtered on to the outer (vacuum facing) surface of absorber fin 401. In other embodiments, any other suitable surface or coating known in the art may be used.

[0092] Absorber fin 403 is disposed about an inner tube 407 (e.g., an extruded aluminum or copper pipe). Heat transfer working fluid flows in to the inner tube 407 to the end of the tube. The fluid returns from the end of the tube through an annular space between the inner tube 407 and the absorber fin 403 (i.e., in a counter-flow arrangement). As the fluid passes through the absorber 204, the fluid absorbs heat from the absorber fin 403 and carries the heat away from the absorber 204. That is, the fluid enters the absorber at a first temperature, is heated during its passage, and is output at a second temperature higher than the first temperature.

[0093] In some embodiments, absorber fin 403 may be made of glass (or other non-metallic material) and coated with a selective surface 405. In some such embodiments, the absorber fin 403 and the enclosure 401 may be joined using only glass on glass seals, or may be constructed as an integral unit. Similarly, inner tube 407 may be made of glass (or other non-metallic material) allowing for the reduction or elimination of glass on metal seals and/or allowing absorber 204 to be formed as an integral or substantially integral unit. In one embodiment, the reflective material may comprise a reflective paint, or a mirrored surface.

[0094] Concentrator assembly 201 includes a plumbing system 409 which facilitates the flow of heat transfer fluid through the absorbers 204. A pump 411 pumps fluid along an input plumbing line 412 and into the absorbers 204. For example, pump 411 may pump the fluid with a mass flow rate of 40 g/s or more, 50 g/s or more, 60 g/s or more, 70 g/s or more, 80 g/s or more, e.g., in the range of 40-45 g/s. As described above, the fluid is heated during counter flow action. An output plumbing line 413 carries the heated fluid away from concentrator assembly 201, e.g., to heat exchanger 202. The pump 411 may be powered by various means and in one embodiment from the collected heat.

[0095] FIGS. 5A-5D illustrate an exemplary embodiment of the collector assembly 201 featuring absorbers 204 having an alternative counter flow arrangement. As shown, absorbers 204 are cylindrical members having an outer transparent evacuated enclosure 401 (e.g., a glass tube). Located within the enclosure is a tubular absorber fin 403 (e.g., an extruded aluminum or copper pipe) which absorbs solar light incident through the enclosure 401 and transforms the light to heat. The absorber fin 403 may include a selective surface 405 which exhibits a high absorptivity to solar light and a low emissivity (thereby limiting radiative heat loss). For example, in some embodiments, the selective surface 405 may exhibit an absorptivity of 0.75 or more, 0.9 or more, 0.95 or more, 0.99 or more etc. (e.g., in the range of 0.9 to 0.99). For example, in some embodiments, the selective surface 405 may exhibit an emissivity of 0.25 or less, 0.10 or less, 0.05 or less, 0.025 or less etc. (e.g., in the range of 0.04 to 0.05). In some embodiments, the selective surface exhibits these absorptivity and emissivity properties at temperature of 100 C or greater, 150 C or greater, 175 C or greater, or 200 C or greater (e.g., in the range of 150-200 C). In some embodiments, the selective surface comprises an aluminum nitride coating, e.g., sputtered on to the outer (vacuum facing) surface of absorber fin 401. In other embodiments, any other suitable surface or coating known in the art may be used.

[0096] In contrast to the example shown in FIGS. 4A-4C, in the absorber of the current example absorber fin 403 is not disposed about an inner tube 407. Instead, a counter flow heat exchange pipe 501 runs along and is in thermal contact with the inner surface of the absorber fin 403. The heat exchange pipe 501 includes an outer tube 502 closed at one end and disposed about an inner tube 503. Heat transfer working fluid flows into the inner tube 503 to the end of the pipe 501. The heat transfer fluid returns through the annular space between the inner tube 503 and the outer tube 502. As the fluid passes through the absorber 204, the fluid absorbs heat from the absorber fin 403 and carries the heat away from the absorber 204. That is, the fluid enters the absorber at a first temperature, is heated during its passage, and is output at a second temperature higher than the first temperature. If the direction of flow is reversed, the heat exchange is still useful. Because of the high vacuum, the lowest resistance path for the heat is through the fluid.

[0097] Heat exchange pipe 501 may be, e.g., welded or otherwise joined to absorber fin 403. In some embodiments, one or more portions of heat pipe 501 and one or more potions of absorber fin 403 are formed as an integral unit. In another embodiment, the pipe 501 may be connected by a mechanical fastener.

[0098] Concentrator assembly 201 includes a plumbing system 409 which facilitates the flow of heat transfer fluid through the absorbers 204. A pump 411 pumps fluid along an input plumbing line 412 and into the absorbers 204. For example, pump 411 may pump the fluid with a mass flow rate of 40 g/s or more, 50 g/s or more, 60 g/s or more, 70 g/s or more, 80 g/s or more, e.g., in the range of 40-45 g/s. As described above, the fluid is heated during counter flow action in heat pipe 501. An output plumbing line 413 carries the heated fluid away from concentrator assembly 201, e.g., to heat exchanger 202.

[0099] FIGS. 6A-6E illustrate an exemplary embodiment of collector assembly 201 featuring absorbers 204 having a so called U-tube flow arrangement. As shown, absorbers 204 are cylindrical members having an outer transparent evacuated enclosure 401 (e.g., a glass tube). Located within the enclosure is a tubular absorber fin 403 (e.g., an extruded aluminum or copper pipe) which absorbs solar light incident through the enclosure 401 and transforms the light to heat. The absorber fin 401 may include a selective surface 405 which exhibits a high absorptivity to solar light and a low emissivity (thereby limiting radiative heat loss). For example, in some embodiments, the selective surface 405 may exhibit an absorptivity of 0.75 or more, 0.9 or more, 0.95 or more, 0.99 or more etc. (e.g., in the range of 0.9 to 0.99). For example, in some embodiments, the selective surface 405 may exhibit an emissivity of 0.25 or less, 0.10 or less, 0.05 or less, 0.025 or less etc. (e.g., in the range of 0.04 to 0.05). In some embodiments, the selective surface exhibits these absorptivity and emissivity properties at temperature of 100 C or greater, 150 C or greater, 175 C or greater, or 200 C or greater (e.g., in the range of 150-200 C). In some embodiments, the selective surface comprises an aluminum nitride coating, e.g., sputtered on to the outer (vacuum facing) surface of absorber fin 401. In other embodiments, any other suitable surface or coating known in the art may be used.

[0100] In contrast to the example shown in FIGS. 4A-4C and FIGS. 5A-4C, in the absorber of the current example absorber fin 403 is not disposed about an inner tube 407 and does not include a counter-flow heat exchange pipe 501. Instead, a U-shaped tube 601 runs along and is in thermal contact with the inner surface of the absorber fin 403. Heat transfer working fluid flows into the U-shaped tube 601 through an input at a proximal end of the absorber 204. The fluid flows down an input portion of the tube to a distal end of absorber 204. The end of the U-shaped tube 601 includes a curve portion which directs the fluid back through an output portion of the tube to an output located at the proximal end of the absorber 204.

[0101] As the fluid passes through the absorber 204, the fluid absorbs heat from the absorber fin 403 and carries the heat away from the absorber 204. That is, the fluid enters the absorber at a first temperature, is heated during its passage, and is output at a second temperature higher than the first temperature. Note that the input portion and output portion of the U-shaped tube 601 are spaced apart from each other. Preferably, the spacing is optimized. Advantageously, the arrangement reduces or eliminates heat flow from the warmer fluid exiting the tube to the cooler fluid entering the tube. Accordingly, the efficiency of the heat exchange between the absorber 204 and the heat exchange working fluid is increased, e.g., in comparison to flow configurations featuring a counter-flow type arrangement.

[0102] U-shaped tube 601 may be, e.g., welded or otherwise joined to absorber fin 403. In some embodiments, one or more portions of U-shaped tube 601 and one or more portions absorber fin 403 are formed as an integral unit, e.g., an integral unit of extruded metal (e.g., aluminum or copper).

[0103] Concentrator assembly 201 includes a plumbing system 409 which facilitates the flow of heat transfer fluid through the absorbers 204. A pump 411 pumps fluid along an input plumbing line 412 and into the absorbers 204. For example, pump 411 may pump the fluid with a mass flow rate of 40 g/s or more, 50 g/s or more, 60 g/s or more, 70 g/s or more, 80 g/s or more, e.g., in the range of 40-45 g/s. As described above, the fluid is heated during passage through the U-shaped tube 601. An output plumbing line 413 carries the heated fluid away from concentrator assembly 201, e.g., to heat exchanger 202.

[0104] Although the embodiments shown above feature a direct flow plumbing configuration, it is to be understood that other plumbing configurations known in the art may be used. For example, in some plumbing configurations, pump 411 is omitted, and the flow of the heat transfer working fluid is driven, e.g., by gravity or thermal convection.

[0105] FIG. 7A illustrates a cross-section of a concentrator assembly 201 of a first embodiment. The concentrator assembly 201 illustrated in FIG. 7A shows a cross section of a trough shaped reflective surface 701 of concentrator 203 designed for the absorber fin of FIG. 4. FIG. 7B illustrates a cross-section of a concentrator assembly 201 of a second embodiment. The concentrator assembly 201 illustrated in FIG. 7B shows a cross section of a trough shaped reflective surface 701 of concentrator 203 may be designed for the absorber fin of FIGS. 5 and 6. The reflective surface 701 illustrated in FIGS. 7A and 7B extends in and out of the plane of the page along a longitudinal axis. Cylindrical absorber 204 is located at the bottom of the trough and also extends along the direction of the longitudinal axis. The top of the trough forms an input aperture. The reflective surface is shaped such that substantially all light rays incident on the input aperture at angles less than an acceptance angle are directed to a surface of absorber 204 (e.g., the surface of a cylindrical absorber fin 403 of absorber 204). FIGS. 8A-8E are ray traces of the reflector surface 701 of FIG. 7A, which illustrate the concentration of light at angles less than an acceptance angle of 34 degrees. The ray traces of the reflector surface 701 of a different shape, for example the reflector surface illustrated in FIG. 7B, would be very similar.

[0106] The acceptance angle can be designed according to the desired concentration factor, the concentrated flux profile and the orientation of the absorber tubes (East-West or North-South, horizontal or tilted, etc.). In one embodiment, the tilt may be determined based on a location of system. Orienting the absorber tubes North-South (N-S) requires larger acceptance angles to ensure sufficient illumination throughout the day, which reduces the concentration factor. Therefore, an East-West (E-W) orientation is generally advantageous. However, a N-S oriented reflector (with the larger acceptance angle) does accept more diffuse solar irradiation and so too has some positive performance attributes. Additionally, reflectors with larger acceptance angles will generally require less reflector area, which provides an economic advantage. FIGS. 9A and 9B show exemplary shapes for the reflective surface 701. In FIG. 9A the surface 701 has been optimized for use with a concentrator 204 oriented in the N-S direction and has an acceptance angle of 60 degrees. In FIG. 9B the surface 701 has been optimized for use with a concentrator 204 oriented in the E-W direction, with an acceptance angle of 34 degrees.

[0107] FIGS. 10A-10B illustrate plots of collector efficiency versus heat exchange fluid intake temperature for concentrator assemblies 201 in various configurations. The collector efficiency is defined as the ratio of the useful power extracted from the collector divided by the product of the collected irradiance and the effective aperture area of the collector (defined as the length of the active area of the absorber tube 204, which is the area covered by the selective coating 405, times the width of the reflector). Various collector efficiencies may change depending on one or more parameters and the plot forms no limitations to the present disclosure.

[0108] Plots are shown for concentrator assemblies with absorbers 204 in the U-Tube (e.g., as shown in FIGS. 6A-6E), X-Tube (the X-tube has similar heat exchange properties to the counter flow tube), and counter flow (CF) (e.g., as shown in FIGS. 5A-5D) configurations. In each case, the concentrator assemblies are in the E-W arrangement. The type of reflective surface used is indicated (i.e. 92% reflectivity material available from Alanod or 94% reflectivity material available from ReflecTech). In each case the ambient temperature is 25 C, and the incident solar irradiance is G=1000 W/m.sup.2. FIG. 10A shows efficiencies based on direct normal incidence (DNI). FIG. 10B shows efficiencies based on effective irradiance (i.e., the direct irradiance plus the diffuse irradiance divided by the concentration ratio of the concentrator assembly).

[0109] Referring to FIGS. 10A and 10B, at an inlet temperature of 200 C, the U-Tube configuration (with ReflecTech and Alanod reflective surfaces) provides the highest collector efficiency of about 45% or more. At an inlet temperature of 200 C, the X-Tube and CF configurations provide similar collector efficiency in comparison to each other, but inferior efficiency compared to the U-Tube configuration. However, for inlet temperatures in the range of 40 C to 140 C, the X-Tube configuration provides the best performance of any configuration.

[0110] FIGS. 11A and 11B are plots of collector efficiency versus heat exchange fluid intake temperature for concentrator assemblies 201 in various configurations. The collector efficiency is defined as the ratio of the useful power extracted from the collector divided by the product of the collected irradiance and the effective aperture area of the collector (defined as the length of the active area of the absorber tube 204, which is the area covered by the selective coating 405, times the width of the reflector).

[0111] Plots are shown for concentrator assemblies with absorbers 204 in the U-Tube (e.g., as shown in FIGS. 6A-6E) configuration for both E-W and N-S arrangement. The type of reflective surface used is indicated (i.e. 92% reflectivity material available from Alanod or 94% reflectivity material available from ReflecTech). In each case the ambient temperature is 25 C, and the incident solar irradiance is G=1000 W/m.sup.2. FIG. 11A shows efficiencies based on direct normal incidence (DNI). FIG. 11B shows efficiencies based on effective irradiance (i.e., the direct irradiance plus the diffuse irradiance divided by the concentration ratio of the concentrator assembly).

[0112] Referring to FIGS. 11A and 11B, at an inlet temperature of 200 C, the U-Tube configuration (with ReflecTech and Alanod reflective surfaces) with E-W arrangement provides the highest collector efficiency of about 45% or more. At 200 C, the N-S arrangement provides inferior efficiency compared to E-W. However, for inlet temperatures in the range of 40 C to 140 C, the N-S arrangement provides better performance than the E-W arrangement.

[0113] FIG. 11C shows plots of collector efficiency versus operating temperature (mean temperature above ambient) for concentrator assemblies 201 in comparison to collector efficiencies of other types of collectors known in the art. The collector efficiency is defined as the ratio of the useful power extracted from the collector divided by the product of the collected DNI irradiance and the effective aperture area of the collector. In each case the ambient temperature is 25 C, and the incident solar irradiance is G=800 W/m.sup.2. The concentration ratio for each collector type is indicated.

[0114] Plots are shown for concentrator assemblies with absorbers 204 in the U-Tube (e.g., as shown in FIGS. 6A-6E) configuration for both E-W and N-S arrangement. Plots are also shown for three non-tracking collectors: a flat plate solar collector, an Apricus evacuated heat pipe collector, and a Winston/Bergquam collector featuring an evacuated tube having an internally located non-imaging (compound parabolic concentrator) collector. Plots are also shown for two tracking collectors: a Chromasun linear Fresnel mirror collector and a Sopogy parabolic trough collector.

[0115] Referring to FIG. 11C, note that at temperatures near 200 C, the U-Tube E-W concentrator outperforms all other collectors (tracking or non-tracking). Further at temperatures in the range of 100-200 C, the U-Tube E-W and U-Tube N-S concentrators perform much better than the non-tracking flat plate and Apricus collectors, and comparable to or better than the remaining collectors.

[0116] FIG. 12 shows a plot of the relative efficiency of a collector featuring an E-W oriented absorber in the U-tube configuration as a function of the angle of incident solar radiation. Note that the relative efficiency is substantially constant at about 100% over angles less than the 35 degree acceptance angle of the concentrator 203 designed for E-W.

[0117] In the examples described above, it is advantageous if the reflective surface 701 of the concentrators 203 has a shape which ensures that all or substantially all (e.g., in the absence of losses such as those due to imperfect reflectivity) light rays incident on the concentrator 203 at angles less than an acceptance angle are concentrated to an absorber. This condition provides for efficient use of the absorber 204, which, in many applications is a costly component, e.g., with a cost that increases with size.

[0118] In some embodiments, the shape of the reflective surface 701 may be determined by considering the active surface of absorber 204 (e.g., selective surface 405) to be a light emitting surface and requiring that the reflective surface 701 be shaped such that no light rays emanating from the surface of absorber 204 return to the absorber 204. In the terminology of radiation transfer, the view factor from absorber back to itself is zero. It follows from energy conservation that light starting from the emitting surface will (after zero, one or more reflections) invariably reach the sky. The shape factor is one. Note, that in this discussion, it is understood that material losses, like imperfect reflectivity are not included. In one embodiment, the radiation shape factor from the desired phase space of the sky is also at maximum, the shape factor from desired phase space of sky to light emitting surface is also one. In special cases, both shape factors can be one, giving a class of non-imaging optical concentrators described. However, in most cases this is not practical and a compromise solution is sought. The following describes methods for ensuring the shape factor from the absorber is one, which is frequently the option. The following also describes techniques for obtaining improved or optimal designs which take into account practical considerations for real absorbers, e.g., concentrator/absorber gaps. For example, the shape may comprise involutes of a circle arc. For example, the shape may also comprise parabolic shape for the concentrator.

[0119] For example, FIG. 13 illustrates a method of designing a concentrator 203 for a cylindrical absorber 204 in which the shape factor from the absorber is one. Here, the active surface of the absorber is taken to be the outer surface of the cylinder. The reflective surface 701 of the concentrator 203 includes two symmetrically disposed edge ray involutes 1301 of the cylinder.

[0120] As used herein, an edge ray involute of an absorber is a curve determined using the following procedure. A taught string is considered to be wrapped around the absorber 204. While maintaining the string taught and holding its length constant, an end 1305 of the string is unwrapped until the string is tangent to the surface of the absorber 204. The path of the end of the string defines a first portion 1302 of the edge ray involute 1301. At this point, the edge ray involute is equivalent to the standard involute familiar from differential geometry (see, e.g., http://mathworld.wolfram.com/Invinvolute.html).

[0121] Next, the string is extended to include a segment 1304 extending from the end of the unwrapped segment 1306 to an end 1307 which normally intersects (i.e. intersects at right angles to) a line 1303. The line 1303 extends from an edge point of the entrance aperture 1310 of the concentrator 203 at an angle corresponding to the acceptance angle of the concentrator 203. The line 1303 corresponds to the wave front of an edge ray of the concentrator 203 (i.e., the ray incident with the maximum acceptance angle of the concentrator).

[0122] The extended string has the form of a taught string which extends around a push pin placed at the end of the unwrapped segment 1302 to the line 1303. The end 1307 of the string is allowed to slide (frictionlessly) along line 1303 while maintaining the normal orientation of segment 1304 to the line 1303. Thus, as the end 1307 slides with the string kept taught, the position of the push pin is adjusted to maintain the normal orientation of segment 1304 to line 1303. The path of push pin continues to trace out the remaining portion 1308 of the edge ray involute.

[0123] As the slope of the involute defined by the movement of push pin increases towards infinity, the process is stopped, and one half of the reflective surface 701 of concentrator 203 has been defined. The remainder of the surface may be obtained by reflection in the optic plane of the concentrator 203. Alternatively, the process may be ended before the slope approaches infinity to produce a truncated design (e.g., in cases where material costs, weight, or other considerations preclude full extension of the reflective surface).

[0124] Not wishing to be bound by theory, using the framework of the Hottel string method familiar from thermodynamics (see, e.g., Hoyt C. Hottel, Radiant-Heat Transmission 1954, Chapter 4 in William H. McAdams (ed.), Heat Transmission, 3rd ed. McGraw-Hill), which is herein incorporated by reference in its entirety, it can be shown that the above described string-based design method will result in a concentrator design which operates at the thermodynamic limit. As will be apparent to one skilled in the art, the method may be easily adapted to absorbers having other cross sectional shapes, including square shapes, round shapes, irregular shapes, etc. Further, the design method may be used, in some cases, for example flat absorbers to obtain three dimensional concentrators by rotation of the two dimensional solution about the optic axis.

[0125] The design method described above may be implemented as software on a computer. The output of the design method software may be, e.g., a data file, an image, a print out, etc. The output of the design method software may control one or more automated fabrication tools to fabricate a concentrator. The designs may be evaluated and/or optimized using optical design tools, e.g., including ray tracing applications and other optical design applications know in the art.

[0126] The string method described above will necessarily result in a design where the active surface of the absorber 204 is in contact with the reflective surface 701 of the concentrator 203 at one or more points. In practice, it may be impossible to meet this condition. For example, as described above, the active surface of an absorber 204 may be a selective surface 405 located within an evacuated enclosure 401. The presence of the enclosure 401 requires a gap between the selective surface 405 and the reflective surface 701 of the concentrator 203. Such a gap will result in a design which does not operate at the thermodynamic limit (i.e., the shape factor from the active surface of the absorber 204 may be less than one or some light incident on the concentrator may miss the absorber).

[0127] The following presents techniques for providing advantageous concentrator designs which take into account an absorber/concentrator gap. Consider a linear (2-D) non-imaging concentrator. In the absence of dielectric materials (no refraction) the angular acceptance is an ellipse in direction cosines with semi axes sin(.sub.0) and 1. For the current model, this phase space ellipse is considered uniformly populated in a Lambertian sense. Then the maximum flux concentration C.sub.o is 1/sin(.sub.0) and the maximum irradiance on the absorber is I.sub.0/sin(.sub.0) (all material losses, etc are neglected). I.sub.0 is the irradiance on the aperture.

[0128] As noted above, idealized designs have no geometrical losses, the reflectors touch the absorber, one simply chooses CC.sub.0 (or less, e.g., to save material via truncation) and the design is determined. But in a practical design, the reflector cannot touch the absorber (resulting in a gap) and C is not necessarily C.sub.0, it can be smaller or larger. The following describes a method of making design choices which result in an advantageous concentrator design even in the presence of a concentrator/absorber gap.

[0129] Solar collector performance can be modeled as:

Q.sub.out=.sub.0Q.sub.inQ.sub.loss

[0130] where .sub.0 is the optical efficiency, Q.sub.in is the insolation (I) multiplied by the aperture area (A) and Q.sub.loss is a function of T (absorber temperature), T.sub.A (ambient temperature) and perhaps some other factors. For evacuated receivers, Q.sub.loss is to an excellent approximation A.sub.abs (T.sup.4T.sub.A.sup.4) where A.sub.abs is the absorber area, c is the emissivity and =5.6710.sup.8 in MKS units. Then the operating efficiency

=Q.sub.out/Q.sub.in=.sub.0Q.sub.loss/Q.sub.in=.sub.0[A.sub.abs/A]f(T,T.sub.A)/I

[0131] Since A/A.sub.abs=C, the [0132] geometrical [0133] concentration

=.sub.0[1/C]f(T,T.sub.A)/I.

[0134] Accordingly, the design procedure involves maximizing by appropriately selecting .sub.0 and C. Several approaches are available for accommodating a gap between absorber and reflector. Referring to FIG. 14A, one approach is to surround the physical absorber 204 by a virtual absorber 1401 which contacts the reflective surface 701 of the concentrator 203. The virtual absorber 1401 has virtual absorber area A.sub.abs. Then .sub.0 rescales as

.sub.0=(A.sub.abs/A.sub.abs).sub.0 [0135] as follows from reciprocity and the view factor from A.sub.abs to A.sub.abs=1. Designing for

A.sub.abs/A=

sin()=1/C.sub.0 while A.sub.abs/A=1/C gives

=.sub.0[1/C]f(T,T.sub.A)/I=

(A.sub.abs/A.sub.abs)(A.sub.abs/A)f(T,TA)/I=

(C).sub.0(A.sub.abs/A.sub.abs)(A.sub.abs/A)f(T,T.sub.A)/I=

(A.sub.abs/A.sub.abs)(A.sub.abs/A.sub.abs)(1/C)f(T,T.sub.A)/I=

(A.sub.abs/A.sub.abs)[.sub.0(sin()f(T,T.sub.A)/I].

[0136] Note C has been replaced by 1/sin (0). Note that, in practice there is usually some truncation to save reflector material, so C may be less.

[0137] Accordingly, a reflector design may be optimized by making A.sub.abs/A.sub.abs approach 1, e.g., as shown in FIG. 14B. Once this optimum virtual absorber shape has been determined, the shape of the concentrator may be obtained, e.g., using the string method described above with the virtual absorber 1401 in place of the actual absorber 204.

[0138] Note that

Q.sub.out=A=(CA.sub.abs)[.sub.0(sin()f(T,T.sub.A)/I]=

[A.sub.abs/sin()][.sub.0(sin()f(T,T.sub.A)/I]

is independent of A.sub.abs. That is, the absorber has the maximum irradiance allowed by thermodynamics (second law). For additional background on the use of virtual absorbers in concentrator design, see R. Winston, Ideal Flux Concentrators with Reflector Gaps, Applied Optics 17, 1668 (1978), which is incorporated by reference in its entirety.

[0139] Another approach to dealing with a concentrator/absorber gap is to immerse the absorber in a cavity. See, e.g., R. Winston, Cavity Enhancement by Controlled Directional Scattering, Appl. Opt. 19, 195 (1980), which is incorporated by reference in its entirety.

[0140] In this case .sub.0 is essentially unchanged, but C is significantly reduced. This gives =.sub.0[1/C]f(T, T.sub.A)/I and there is the possibility of trading off .sub.0 against C. In other words, one can only partially immerse the absorber in the cavity, thereby incurring some loss, but restore some of the lost C in the concentrator design. This tradeoff is temperature dependent; and typically it is more advantageous to increase C when the temperature is high.

[0141] The cavity design may take a variety of forms, e.g., single or multiple V-shaped grooves or W-shaped grooves. There is a natural upper bound for the groove design in a cylindrical absorber, where the gap distance between the absorber and the concentrator is equal to the radius of the absorber. In the trade-off between concentration and gap loss, the engineering optimum is neither extreme but rather some intermediate choice between a fully cavity immersed absorber, and no cavity at all (i.e., a design based on the virtual absorber technique described above). As shown in FIG. 16, in typical embodiments the concentration increases linearly with gap size, but the gap loss only increases quadratically, thereby favoring partial immersion. Note the gap loss calculated by our thermodynamic (string) method is the average over the acceptance angle. The loss at a particular angle may vary and is typically greatest at zero angle, and substantially zero near the angle of acceptance.

[0142] For example, referring to FIG. 15A, trough shaped concentrator 203 features a V-shaped cavity portion 1501 running along the bottom of the trough and providing partial immersion of the cylindrical absorber 204. The shape of the remaining portion 1502 of the trough is determined, e.g., using the virtual absorber and string method described above. As shown, the design is characterized by a virtual to physical absorber ratio of A.sub.abs/A.sub.abs=0.92 and a gap loss of 0.01.

[0143] Appendix 1 includes an exemplary algorithm script written in the well known Scilab scientific computing environment (available at http://www.scilab.org) for designing a concentrator of the type described above. As will be understood by those skilled in the art, this particular exemplary algorithm may be modified or extended based on particular design requirements.

[0144] In other embodiments, other suitable values for A.sub.abs/A.sub.abs and gap loss may be chosen. In general, once these values are selected, one is still left with the choice of cavity parameters, e.g., choosing the coordinates of the V-shaped cavity aperture and the opening half angle of the V. In some embodiments, a large opening angle (i.e. a shallow V) is favorable to minimize material used.

[0145] The following describes an exemplary method for determining the cavity parameters. Referring to FIG. 15B, a cylindrical absorber 204 of radius r is centered at the origin. One locates the center (O.sub.x, O.sub.y) of the image 1504 of the cylindrical absorber which would be formed if the reflective V-shaped cavity is extended as shown (indicated with a dotted line), so that the top of the image circle is even with or slightly above the aperture of the cavity. Based on this requirement, the end points of the cavity aperture may be determined. For example, a Scilab script shown in Appendix 1 may be used to determine the position of the end points in an exemplary embodiment. Here, the end points are at coordinates x=+/0.48, y=1.25. The final step in determining the cavity parameters is to determine y.sub.min. The opening half angle of the V-shaped cavity and y.sub.min are related by tan ()=x/(yy.sub.mm). Further, it can be shown that O.sub.y=2 y.sub.min sin.sup.2.

[0146] Based on these relations, one can calculate a table of possible values of y.sub.min, , O.sub.y, (yO.sub.y) and compare with r to find a reasonable solution. Table 1 below is an exemplary table of values for the design shown in FIGS. 15A-15B. In this case, with r=1.05, one sees that y.sub.min=1.52 is a reasonable choice.

TABLE-US-00001 TABLE 1 y.sub.min O.sub.y (y-O.sub.y) 1.6 53.7 2.08 0.83 1.54 58.8 2.25 1.10 1.53 59.6 2.28 1.03 1.52 60.5 2.30 1.05 1.50 62.3 2.35 1.30 1.40 72.6 2.55 1.30
Although the specific examples described above have dealt with concentrating radiation to an absorber to generate heat, it is to be understood that in various embodiments the absorber may be a transducer which converts solar light to another form of energy. For example, the absorber may include photovoltaic material which generates electricity in response to incident light. In some embodiments, the absorber may transform incident light into multiple different forms of energy, e.g., electricity and heat. For example, U.S. Provisional Patent Ser. No. 61/378,301, filed Aug. 30, 2010, the entire contents of which are incorporated herein by reference, describes absorbers which include PV material and selective thermal absorbers.

[0147] In contrast to conventional optical design, the solar concentrators of this disclosure are designed from the principles of thermodynamics, and in particular the second law. TdS=dE+PdV is arguably the most important equation in Science. If we were asked to predict what currently accepted principle would be valid 1,000 years from now, the Second Law of thermodynamics would be a good bet. From this we can derive entropic forces: F=T grad S, The Stefan-Boltzmann radiation law (const. T.sup.4), Information theory (Shannon, Gabor), Accelerated expansion of the Universe, and even Gravity. We can illustrate the Failure of conventional optics by a thought experiment; small bodies A, B at foci of an ellipse as shown in FIG. 17A. A portion of the ellipse is replaced by a sphere centered at A.

[0148] It appears that FAB<<FBA where FAB is the probability of radiation starting at A reaching Betc so A would heat up at the expense of B cooling down, but that violates the second law.

[0149] To understand these things it is best to start with the theory of furnaces. We start with a three wall furnace shown in FIG. 17B. Fij are probabilities of radiation from wall i reaching wall j. As there are 6 unknown Fij, six equations are needed. Three come from energy conservation, and 3 from the second law. The results follow readily from inspection.

F12=(A1+A2A3)/(2A1)

F13=(A1+A3A2)/(2A1)

F23=(A2+A3A1)/(2A2)

[0150] where A1, A2, A3 are the three sides shown in FIG. 17B.

[0151] FIG. 17C shows a 4-wall enclosure, which is a configuration of greater interest. The 4-wall enclosure readily reduces to two 3-wall enclosures so that we can apply the above formula.

F14=[(A5+A6)(A2+A3)]/(2A1)

F23=[(A5+A6)(A1+A4)]/(2A2).

[0152] Turning to FIG. 17D, there is shown a schematic view of a radiation source 1700, an aperture 1702 and an absorber 1704 that includes a general convex or flat shape. A number of parameters of the absorber and aperture will be shown and now explained for optimal operation and for manufacturing. The present disclosure includes a convex or flat shape that provides a high probability that the solar radiation will concentrate at a preselected portion to capture as much solar radiation as possible. As can be seen a number of relationships are established between the radiation source, the aperture and the absorber as shown by 1, 2, 3. Suppose the radiation source 1 (example the sun) is maintained at temperature T1. Then the temperature of the absorber 3 will reach T1 if and only if F31=1.

[0153] Proof: q13=T1*.sup.4A1F13=T1*.sup.4A3F31, where qij is the radiation transfer from i to j.

[0154] But q3total=T3*.sup.4A3q13 at steady state.

T3T1(second law).fwdarw.F31=1 if and only if T3=T1.

[0155] The first law of thermodynamics (energy conservation) allows q12=q13 which implies F12=F13 for a maximally efficient concentrator. Define the geometric concentration C=A2/A3. The second law requires A1 F13=A3F31. Then F12=F13 implies A1 F12=A3F31. This implies A3F31 is constant independent of the optical design. C is maximum when A3 is minimum which implies F31 is maximum=1. Again we find that the combination of maximum concentration and maximum efficiency requires F31=1. We can think of this as maximum thermodynamic efficiency. F31=1 also provides an important relation for concentration because A3=A1 F12 but A1 F12=A2F21 by the second law. It follows that Cmax=1/F21 which expresses maximum concentration as the reciprocal of the probability that radiation from the concentrator aperture (A2) regarded as a black body would reach the source A1.

[0156] An important case is the source 1 at (example very far away, like the sun). Suppose we wish to efficiently concentrate energy from a range of sun angles+/, for example, a range of angles sufficient to substantially include the solar angles during the year so that tracking is not needed. Mathematically the measure of far away is set by the dimension of A2 (L2) so that far means d>>L2, where d is the distance between 1 and 2. As d approaches the strings become parallel.

Long StringShort string=S1S2=L2 sin

.

[0157] F21 approaches sin .

[0158] Notice is the maximum angle of radiation incident on A2. Cmax=1/sin .

[0159] As the distance approaches infinity, the sun's rays appear almost parallel to one another. Therefore, as we approach infinity, F21 is equal to sin , where is equal to the angle of the essentially parallel sun's rays at one sun angle with respect to the axis as shown in FIG. 18. Therefore, Cmax=1/sin and note that in this embodiment, the maximum angle on A2 is . For three dimensions,

F21=(S1S2.sup.2/L2.sup.2),

[0160] where L2 is the diameter of A2. As we approach infinity, F21 is equal to sine .sup.2.

[0161] Therefore Cmax=1/sin.sup.2 , another example of the principle that maximum concentration is the reciprocal of the probability that radiation from the concentrator aperture regarded as a black body would reach the source.

[0162] Another way to obtain the sine law is to consider the angular momentum with respect to the axis of symmetry shown in FIG. 20. The optical momentum is P=n(L, M, N), where n is the index of refraction and L, M, N are the direction cosines of the rays and the maximum angular momentum at the entrance A2 of the concentrator is J=(L2/2) sin , and at the exit A3 the maximum value of J is L3/2, where L3 is the diameter of A3. Since J is conserved, the maximum concentration is (L2/L3).sup.2=1/sin.sup.e . For simplicity we have assumed n=1 in this example.

[0163] In another embodiment of the present disclosure, the present invention may be used in a water desalination and purification plant that removes salt from various types of water sources including sea water, brackish water etc. with the objective of providing fresh water for every day consumer use. There are two main types of desalination technologies that are most prevalent today. The most common are various distillation processes that require high temperatures for operation. The second type is reverse osmosis, which requires high pressure to drive pure water through a membrane separation process. Water purification focuses more on the removal of various particulate, organic and inorganic impurities from existing fresh water supplies or when attempting to implement water reclamation projects.

[0164] In another embodiment of the present disclosure, the solar array may include a reflective surface that is a Compound Parabolic Concentrator (CPC). For example, the reflective surface may include a two dimension compact parabolic concentrator that is an ideal concentrator, i.e., it works perfectly for all rays within the acceptance angle q, and rotating the profile about the axis of symmetry gives the 3-D CPC. The 3-D CPC is very close to ideal reflective surface.

[0165] In another embodiment of the present disclosure, the solar array may also include Collimator for a Tubular Light Source. The collimator may include a predetermined shape on each side of the tubular light source to collect the light in a predetermined location as discussed.

[0166] Although the specific examples described above have dealt with concentrating radiation from a relatively large solid angle of incidence onto a relatively small target (e.g. concentrating solar light onto an absorber), it will be understood that they may equally well be applied to broadcasting radiation from a relatively small source to a relatively large solid angle (e.g. collecting light from an LED chip to form a beam or sheet of light). The small source may, for example, include a light emitting diode, an organic light emitting diode, a laser, or a lamp.

[0167] Although a number of exemplary light concentrators have been described, in various embodiments, any other suitable concentrator may be used. For example, in some embodiments, non-imaging concentrators of the type described in Roland Winston et al, Nonimaging Optics, Academic Press (Elsevier, 2005) may be used, including concentrator designed using the edge ray principle as described therein. In various embodiments concentrators may include reflective, refraction, diffractive or other elements. In some embodiments, at least a portion of the concentrator may reflect light by total internal reflection.

[0168] One or more or any part thereof of the techniques described herein can be implemented in computer hardware or software, or a combination of both. The methods can be implemented in computer programs using standard programming techniques following the method and figures described herein. Program code is applied to input data to perform the functions described herein and generate output information. The output information is applied to one or more output devices such as a display monitor. Each program may be implemented in a high level procedural or object oriented programming language to communicate with a computer system. However, the programs can be implemented in assembly or machine language, if desired. In any case, the language can be a compiled or interpreted language. Moreover, the program can run on dedicated integrated circuits preprogrammed for that purpose.

[0169] Each such computer program is preferably stored on a storage medium or device (e.g., ROM or magnetic diskette) readable by a general or special purpose programmable computer, for configuring and operating the computer when the storage media or device is read by the computer to perform the procedures described herein. The computer program can also reside in cache or main memory during program execution. The analysis method can also be implemented as a computer-readable storage medium, configured with a computer program, where the storage medium so configured causes a computer to operate in a specific and predefined manner to perform the functions described herein.

[0170] A number of embodiments of the invention have been described. Nevertheless, it will be understood that various modifications may be made without departing from the spirit and scope of the invention.

[0171] As used herein the term light and related terms (e.g. optical) are to be understood to include electromagnetic radiation both within and outside of the visible spectrum, including, for example, ultraviolet and infrared radiation.

[0172] As will be understood by one skilled in the art, for any and all purposes, particularly in terms of providing a written description, all ranges disclosed herein also encompass any and all possible subranges and combinations of subranges thereof. Any listed range can be easily recognized as sufficiently describing and enabling the same range being broken down into at least equal halves, thirds, quarters, fifths, tenths, etc. As a non-limiting example, each range discussed herein can be readily broken down into a lower third, middle third and upper third, etc. As will also be understood by one skilled in the art all language such as up to, at least, greater than, less than, and the like include the number recited and refer to ranges which can be subsequently broken down into subranges as discussed above.

[0173] Definitions that are contained in text incorporated by reference are excluded to the extent that they contradict definitions in this disclosure. For the purposes of this disclosure and unless otherwise specified, a or an means one or more.

[0174] As used herein, the term comprising is intended to mean that the compositions and methods include the recited elements, but not excluding others. Consisting essentially of when used to define compositions and methods, shall mean excluding other elements of any essential significance to the combination for that intended purpose. Consisting of shall mean excluding more than trace elements of other ingredients and substantial method steps for making or using the concentrators or articles of this invention.

[0175] The construction and arrangements of the solar energy concentrator, as shown in the various exemplary embodiments, are illustrative only. Although only a few embodiments have been described in detail in this disclosure, many modifications are possible (example, variations in sizes, dimensions, structures, shapes and proportions of the various elements, values of parameters, mounting arrangements, use of materials, colors, orientations, etc.) without materially departing from the novel teachings and advantages of the subject matter described herein. Some elements shown as integrally formed may be constructed of multiple parts or elements, the position of elements may be reversed or otherwise varied, and the nature or number of discrete elements or positions may be altered or varied. The order or sequence of any process, logical algorithm, or method steps may be varied or re-sequenced according to alternative embodiments. Other substitutions, modifications, changes and omissions may also be made in the design, operating conditions and arrangement of the various exemplary embodiments without departing from the scope of the present disclosure.

[0176] Having thus described several aspects of at least one embodiment of this invention, it is to be appreciated various alterations, modifications, and improvements will readily occur to those skilled in the art. Such alterations, modifications, and improvements are intended to be part of this disclosure, and are intended to be within the spirit and scope of the invention. Accordingly, the foregoing description and drawings are by way of example only.

TABLE-US-00002 APPENDIX I %Mind the Gap Version 2 N0=1000; N1=100; N2=1000; %Define parameters R=1.05; %10.5mm R1=1.35; % 13.5mm D1=2.7; %27mm theta=(2*pi/360)*(40); %40deg phi=(2*pi/360)* 14; %14deg psi=(pi/2)+theta; scale=1.0; % --------------------------------------------------------------------------------- L1 =scale*pi*R* (1/(sin(theta){circumflex over ()}2)+((cot(theta)){circumflex over ()}2)*(1/(sin(theta))+1){circumflex over ()}2){circumflex over ()}(1/2); inc=(L 1 +3 * R)/N2; L=(5*R*pi/2)+(R*(theta2*phi))+L1; % --------------------------------------------------------------------------------- x0=R*sin(psi)L1 *sin(theta); y0=R*cos(psi)+L1 *cos(theta); % --------------------------------------------------------------------------------- %profile for involution gamma=(psiphi)/N1; sl=(psiphi)*R; xi(1)=R*cos(theta)+s1*sin(theta); yi(1)=R* sin(theta)s1*cos(theta); xl(1)=xi(1); rho(1)=sqrt(xi(1){circumflex over ()}2+yi(1){circumflex over ()}2); n=1; while (rho>=R1); sn=s1 R*((n1)*gamma); xi(n)=R*cos(theta(n1)*gamma)+sn*sin(theta(n1)*gamma); yi(n)=R* sin(theta(n1)*gamma)sn*cos(theta(n1)*gamma); xl(n)=xi(n); rho=sqrt(xi(n){circumflex over ()}2+yi(n){circumflex over ()}2) n=n+1 %vee a=xi(n1); b=yi(n1); end; %Vee c=1.54; %ymin x6(1)=a y6(1)=b x6(2)=0; y6(2)=c; x6(3)=a; y6(3)=b; %--------------------------------------------------------- %profile for one reflection flag=0; i=0; s=(2*cos(theta)/N0)*(L1* sin(theta)R*sin(psi)); %--------------------------------------------------------- for n=1:N0; i=0; flag=0; xn=((n1)*s)/cos(theta)+x0; Lt=L((n1)*s*tan(theta)); % ---------------------------------------------------- while(flag==0) i=i+1; sL=i*inc; xtn=sL*sin(theta)+xn; ytn=y0sL*cos(theta); % ---------------------------------------------------- Rt=(xtn{circumflex over ()}2+ytn{circumflex over ()}2){circumflex over ()}(1/2); beta1=asin(ytn/Rt); beta2=acos(R/Rt); % ---------------------------------------------------- alpha=(3*pi/2)(beta1+beta2); Lt2=sL+(xtn{circumflex over ()}2+ytn{circumflex over ()}2R{circumflex over ()}2){circumflex over ()}(1/2)+R* alpha; if((Lt2>=Lt)&(flag==0)) flag=1; x(n)=xtn; y(n)=ytn; x2(n)=xtn; end; end; end; d=8.5; %85mm xt(1)=x(1); yt(1)=y(1); xtl(1)=xt(1); n=1; while (x(n)<=d/2) xt(n)=x(n); yt(n)=y(n); xtl(n)=x(n); n=n+1; end; %------------------------------------------------------------------------------------ %absorber circle profile for j=1:100; angle=(j1)*2*pi/100; x3(j)=R*cos(angle); y3(j)=R* sin(angle); end; %--------------------------------------------- %Output values plot(xi,yi,x1,yi,xt,yt,xt1,yt,x3,y3,x6,y6); axis equal; grid; title(theta=40deg, phi=14deg, R=1.05cm, R1=1.35cm, ymin=1.54cm,d=8.5cm); c,xi,yi,xt,yt print, ====================================================== %maximizes CPC with gap %r2=r1+gap %Cmax=1/sin(theta); %x=C/Cmax; %y=gap Loss *(C/Cmax); r1=1.05; r2=1.35; z=r2/r1; alf=acos(r1/r2); bet=sqrt(z*z1)alf; fi=asin(r1/r2); psimin=fi; xmin=(psimin+fi+1/tan(fi))/pi; xmax=1+bet/pi; for i=1:10; x(i)=xmin+i *(xmaxxmin)/10; psi=pi *x(i)(fi+1/tan(fi)); y(i)=(fi+1/tan(fi))(psi+cos(psi)/sin(fi)); y(i)=y(i)/pi; end; xmax plot(x,y) axis equal; grid; title(R1=10.5mm,R2=13.5mm,gap=3mm); print,