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Solar fiber-optic mini-dish concentrators: first experimental results and field experience
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Solar Energy Vol. 72, No. 6, pp. 459–472, 2002 2002 Elsevier Science Ltd S 0 0 3 8 – 0 9 2 X ( 0 2 ) 0 0 0 2 5 – 7 All rights reserved. Printed in Great Britain 0038-092X / 02 / $ - see front matter
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SOLAR FIBER-OPTIC MINI-DISH CONCENTRATORS: FIRST EXPERIMENTAL RESULTS AND FIELD EXPERIENCE DANIEL FEUERMANN*, JEFFREY M. GORDON** ,† and MAHMOUD HULEIHIL* *Department of Solar Energy and Environmental Physics, Jacob Blaustein Institute for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus 84990, Israel **The Pearlstone Center for Aeronautical Engineering Studies, Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beersheva 84105, Israel Received 12 March 2002; accepted 19 April 2002 Communicated by JOACHIM LUTHER
Abstract—The experimental realization and field experience of a recently proposed solar fiber-optic mini-dish concentrator are reported. The prototype is 200 mm in diameter. We have repeatably transported concentrated sunlight in a one-millimeter-diameter optical fiber and measured flux levels of 11–12 kilosuns at a remote target (up to 20 m away). The prototype—assembled from off-the-shelf parts and customized items that rely solely upon existing commercial technologies—proved impervious to dust penetration and condensation. For the particular application of solar surgery, dielectric second-stage concentrators were designed and fiber tips were sculpted to boost flux concentration by a factor of 2 to 4, for light extraction into air and tissue, respectively. Our findings strengthen the feasibility of the efficient and complete de-coupling of the collection and remote delivery of highly concentrated solar radiation. 2002 Elsevier Science Ltd. All rights reserved.
physical and engineering concepts into a functional prototype (Feuermann and Gordon, 2001b). Fig. 1 is a schematic of the mini-dish unit. Fig. 2 includes photographs in the field of our first operating prototype (200 mm in diameter, with a focal length of 120 mm), including the remote extraction (delivery) of sunlight at flux levels surpassing 11 kilosuns (i.e., 11 000 suns) from an optical fiber 1.0 mm in diameter, at a distance up to 20 m from the mini-dish collector. The sections that follow provide a detailed component-by-component description of the design, assembly, testing and field measurements. With this itemized accounting, we then proceed to report on the performance and analysis of our outdoor solar experiments on the assembled prototype. This is followed by our observations regarding future generations of improved viable solar fiber-optic mini-dishes.
1. INTRODUCTION
Certain solar applications uniquely require very high photon densities, i.e., high flux concentration. Recent innovations include solar surgery (Feuermann and Gordon, 1998), solar-pumped lasers (Arashi and Kaneda, 1993), the solar-driven synthesis of carbon nanomaterials (Pitts et al., 1993; Flamant et al., 1999) and electricity generation with advanced semiconductor materials (Feuermann and Gordon, 2001a; Reddy et al., 2001). An essential element in the practical realization of these applications is the total separation of the collection and delivery of highly concentrated sunlight, including high efficiencies for collection and optical transport. Toward solving this problem in a pragmatic and modular fashion, the use of solar fiber-optic mini-dishes was proposed (Cariou et al., 1982; Feuermann and Gordon, 1998, 1999, 2001a; Gordon, 2001). This article constitutes a detailed report on the experimental results and field experience in which these miniaturized concentrators were translated from
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2. PROTOTYPE CONCENTRATOR DESIGN
A paraboloidal dish is specified completely by its diameter D and rim half-angle f. The fnumber of the dish, f 5 (focal length) /(diameter) 5 F /D
Author to whom correspondence should be addressed. Tel.: 1972-7-659-6923; fax: 1972-7-659-6921; e-mail: [email protected] 459
is related to f by
(1)
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flux that reaches the focal plane (Baum and Strong, 1958). The focal spot diameter d max that accepts essentially all reflected rays is (Rabl, 1976) Duss1 1 16f 2d 2 d max 5 ]]]] . 8fs16f 2 2 1d
(5)
The corresponding averaged flux concentration is sin 2 (f ) cos 2 (f ) ]]]]] C avg 5 . flux u s2
(6)
For comparison, the thermodynamic limit for flux concentration (in air) is (Rabl, 1976; Welford and Winston, 1989) 1 C max . flux 5 ] u 2s
Fig. 1. Schematic of a solar fiber-optic mini-dish. A small flat mirror below the focal plane redirects solar rays reflected from the dish downward to facilitate practical coupling into an optical fiber. Extreme rays are shown traced into the fiber, which is enclosed in a protective sleeve. Concentrated sunlight is transported in the optical fiber to a remote application— illustrated here as solar surgery (Feuermann and Gordon, 1998)—with the option of a significant boost in power density with a nonimaging secondary concentrator at the distal end (Drawing courtesy of New Scientist (Marks, 1999)).
1 /f 5 4 tan(f / 2).
(2)
The diameter d min of the approximately uniform-flux core region of the focal spot is d min 5 2Dfus
(3)
where us is the effective solar half-angle (a convolution of the actual size of the solar disk with optical errors in the mini-dish contour, tracker accuracy and fiber alignment), which is taken throughout to be sufficiently small that sin(us ) ¯ us . As justified in Section 6, we adopt a realistic value for us of 0.005 radian. The concentration in the core region is the highest local flux a paraboloidal dish generates (Rabl, 1976) 2
sin (f ) core C flux 5 ]] u s2
(4)
and encompasses a fraction cos 4 (f / 2) of the total
(7)
In Section 7, we shall explore how overall flux concentration can be heightened to the thermodynamic limit, at high collection efficiency, with dielectric secondary concentrators sculpted from the distal tips of optical fibers. When designing for maximum flux concentration from the dish, one selects the fiber core diameter d fiber to be d min ; while for maximum efficiency designs d fiber will be closer to d max . Furthermore, achieving a reasonably low number of fibers per collection area demands systems of relatively low f-number. Fiber core diameters can of course be chosen between d min and d max . A comprehensive study of the associated efficiency– concentration tradeoff for paraboloidal concentrators covering a wide range of f-numbers was presented in Feuermann et al. (1999). The optimal compromise between efficiency and concentration is case-specific, with Feuermann et al. (1999) providing the quantitative tools for such determinations. We selected a mini-dish diameter D 5 200 mm, a focal length F 5 120 mm (hence f 5 458), and an optical fiber core diameter d fiber 51.0 mm as a consequence of several considerations. 1. The dish size should be sufficiently small that eventual mass production of the dishes, and modularity, would be feasible. 2. The dish should be small enough to permit affordable production of prototypes by a number of companies. 2 3. The number of optical fibers per m of minidishes should be as small as possible for eventual large-scale viability. Hence high concentration is required, which in turn demands high rim-angle dishes (Eq. (4)).
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Fig. 2. Photographs of our first operational prototype in the field. (a) Photograph of the assembled fiber-optic mini-dish, dual-axis tracker, tracker sensors and scope for determining tracker accuracy (foreground). (b) Front view, with a 20-meter long optical fiber, where the fiber output has approximately 1 / 4 the brightness of the sun. (c) Side view of Fig. 2b. The solar fiber-optic mini-dish is at the far left and the technician holding the distal fiber end is at the far right. (d) Projection of the output from the 20-meter fiber onto a white diffuse screen.
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4. High rim-angle dishes enjoin optical fibers of high numerical aperture (NA). NA5sin(uair ), with 2uair denoting the full angular range of rays incident from air, that nominally is supported by the optical fiber, i.e., for which total internal reflection is respected. Therefore we constrained ourselves to commercially available fibers of high NA and large core diameters. Our aim was to achieve the highest flux concentration at high radiative efficiency for practical configurations. The flux concentration achievable in the mini-dish alone is proportional to (NA)2 . (Equivalently, the number of fibers, per square meter of solar collecting area, is proportional to 1 /(NA)2 .) At us 5 0.005 radian, a dish with the dimensions noted above can be used between the extremes of (a) maximum concentration with d fiber 5 d min 5 1.2 mm; and (b) maximum efficiency with d fiber 5 d max 5 2.0 mm. Realizable flux concentration is also proportional to the fiber’s transmittance, so fiber core materials with near-negligible attenuation integrated over the full solar spectrum are essential (such as pure quartz). Furthermore, the number of (expensive) optical fibers, per square meter of solar collecting area, is proportional to 1 /(d fiber )2 . Therefore we aimed to use commercially available fibers with the highest NA, lowest attenuation, and largest core diameter. 3. PRACTICAL CONCERNS
As we embarked upon the experimental program reported here, our principal practical concerns were:
3.1. Dust penetration and accumulation on the mirror or fiber tip, as well as condensation in the space between the glazing and the mirror These were not expected to pose a major problem, based on the success of related technologies for totally different applications. For example, the reflectors in car headlights (of dimensions comparable to our mini-dish units) remain clean for years in demanding environments. We produced a tight encasement of the mirror, proximate fiber tip and small flat mirror with two O-rings: one between the glazing and the encasement, and the other between the mirror and the encasement. The opening in the center of the parabolic mirror (for insertion of the fiber holder) was sealed by a small flange machined into the sleeve in a metal-to-metal seal. The optical fibers are manufactured with a protective
plastic buffer, and sit snugly inside the fiber holder. Thus there is virtually no dust penetration. Moreover, we did not observe any condensation inside the dish at any time.
3.2. Achieving adequate mirror contour accuracy We did not find commercial off-the-shelf highquality parabolic mirrors for the dimensions required. The only practical fabrication technique for the first handful of prototypes was diamond turning of an aluminum substrate followed by first-surface silver coating and a protective thin layer of silica. Diamond turning can provide a dish contour accuracy of several microns, which translates into a mirror slope error of order 0.0001 radian. Several manufacturers have demonstrated comparable accuracy with plastic (coated) mirrors produced by mold injection (Avimo, 2001; Syntec, 2002; G-S, 2002). Improper diamond turning can result in deleterious diffraction losses that stem from excessive groove width. If the groove size is kept well below the wavelength range of the solar spectrum (which is readily achievable with commercial equipment), then diffraction losses can be rendered negligible.
3.3. Accurate alignment of all elements and positioning of the small flat mirror Alignment of the elements was achieved by producing the machined encasement on an accurate lathe. The positioning of the mirrors and glazing relative to the encasement was checked with a laser in our indoor laboratory. There was a tolerance of 60.1 mm in positioning the fiber tip because the fiber’s core diameter (d fiber 5 1.0 mm) was less than the diameter of the uniform flux core region in the focal plane of the dish (d min 5 1.2 mm). A small frame with adjustment screws that attached to the back of the mini-dish maintained the fiber at its proper position and permitted fine-tuning of fiber tip location in the x, y and z directions to within about 60.05 mm. Element alignment in future mass-produced units should be achievable with common manufacturing methods, such as those used for automatic pencils and plastic lenses. Our design introduces a small flat mirror to re-direct rays reflected from the dish downward, so that a rigidly-positioned optical fiber can point upward and thereby obviate the practical problems associated with the conventional downwardfacing absorber in solar dishes. Furthermore, cleaning the protective glazing would be problematic were the fibers to extend outwards and be
Solar fiber-optic mini-dish concentrators: first experimental results and field experience
required to bend backwards behind the dish. This is particularly important for modules comprising tens to hundreds of mini-dishes. In eventual largevolume production, we recommend that the small mirror be deposited directly on the protective glazing. But for the first prototypes, toward granting maximum operational flexibility, we had the small mirror deposited on a pedestal that extends downward from the glazing.
3.4. Tracking precision We identified several commercially-available small precision dual-axis trackers, of which two certified a tracking accuracy of better than 60.002 radian. Tracker details and test results are reported in Section 6.
3.5. Commercial availability of suitable lowattenuation optical fibers that can withstand high solar flux The attenuation of commercial quartz-core optical fibers, integrated over the solar spectrum, is sufficiently low that flux levels of order 10 kilosuns are easily accommodated (Polymicro, 2001; Feuermann et al., 2002). Whereas the bestsuited optical fibers should have relatively large diameters and high NA, practical problems arose because: (a) fiber stiffness is a strongly increasing function of fiber diameter; and (b) we did not discover commercial fibers with core diameters much above 1.0 mm that are suitable for concentrated sunlight. While fiber manufacturers confirmed that there is no major material or technological factor that militates against high-NA fibers, the highest NA fibers that we found produced commercially have a nominal NA of 0.66, and could be purchased from only one company (Polymicro, 2001). We purchased samples of all the commercially-available so-called high-NA fibers for comparative testing and evaluation. For the highest-NA fibers, the core diameter is 1.0 mm. Some of the fibers with a nominal NA of about 0.4 are available with core diameters up to 2.0 mm. Test results are summarized in Section 5.2. 4. LABORATORY EQUIPMENT
Outdoor measurements on the assembled prototype are of limited value unless the performance of each component is first characterized separately under controlled conditions. Consequently, individual components were tested in the laboratory prior to assembly. These measurements included the mini-dish contour accuracy, mirror
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specular reflectivities of both the small flat mirror and the parabolic dish, transmission of the cover glazing, as well as attenuation and angular transmission of optical fibers and sculpted fiber tips. A source of collimated white light and a He–Ne laser together with a calibrated integrating sphere were used to test optical properties of components in the visible and near infrared. The measurement procedures for the angular transmission and attenuation of optical fibers were documented in Feuermann et al. (2002). Fig. 2a is a photograph of the assembled prototype installed outdoors. The installation comprised: (1) a battery-driven dual-axis solar tracker and stand, (2) a telescope-like device used in determining tracker accuracy (Section 6), (3) accommodation of the full fiber-optic mini-dish assembly, and (4) a pyrometric power meter to measure radiative output at the fiber’s distal end.
5. EVALUATION OF OPTICAL ELEMENTS
5.1. Mini-dish We ordered several diamond-turned parabolic mirrors from two companies (referred to as A and B), and developed in-house procedures for assessing contour accuracy, reflectivity and specularity. Lacking sophisticated profiling equipment, we determined the contour accuracy by comparing the spot size produced in the dish focal plane by a distant (approximately point) light source against the theoretical result. Reflectivity was measured with a laser and integrating sphere. Specularity was ascertained by comparing the observed spread of a laser beam reflected from several points on the mirror to the calculated value for a parabola. Satisfactory accord between our in-house measurements, and those from an independent testing laboratory to which one of the mini-dishes was sent, established confidence in our procedures for the precision required for our solar concentrator. Company A also independently supplied the mirror’s measured spectral reflectivity from a witness piece, which confirmed our measurements (a) with the laser and (b) integrated over the lamp’s (white-light) spectrum. Our measurements revealed that only Company A’s mirrors satisfied our specifications, to wit, a specular reflectivity (integrated over the solar spectrum) of 0.96, with a contour error commensurate with us not exceeding 0.005 radian. Fig. 3 highlights the distinction between the image produced with a surface that does not
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Fig. 3. Illustration of diffraction losses. Photographs of a far-field target irradiated by laser light or white light that has been reflected from mini-dishes A and B. (a) Dish A, laser light. (b) Dish A, white light. (c) Dish B, laser light. (d) Dish B, white light.
appear to suffer from diffractive losses (Company A), and one that does (Company B). The reflected spot should be a single disk of light. With Company B’s dish, optical interference results in a sizable fraction of the reflected light being distributed at distances far beyond the diameter of the central spot.
5.2. Optical fibers The optical characterization of the fibers was reported in Feuermann et al. (2002). In particular, we measured the transmission of the fibers, as a function of incidence angle, for a broad-spectrum collimated light source. We divided optical losses into: (a) Fresnel reflections off the air-quartz interfaces; (b) attenuation in the fiber’s core; and (c) residual losses. The Fresnel reflective losses (around 4%
per air-quartz interface) and attenuation in the core (no more than 1% for fiber lengths of up to 10 m) were predictable from known material properties and the attenuation spectrum provided by the manufacturers. They were confirmed experimentally. Based on manufacturers’ claims, the residual losses were expected to be negligible. However, we discovered significant transmission losses at off-normal incidence that increased dramatically with incidence angle within the fiber’s NA. Sample measurements are plotted in Fig. 4. Integrated over the fiber’s nominal NA, these residual losses reached 20% in some instances. At angles near (but less than) the fiber’s NA, losses could exceed 50%. Transmission losses of this magnitude have also been documented in other laboratories (Irvin and Nakamura, 1991; Liang et al., 1997), al-
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Fig. 4. Measured angular response of commercial low-attenuation optical fibers of nominal NA50.66, intended for high-flux solar applications. L / d5ratio of fiber length to core diameter.
though a satisfactory model to account for the losses and predict how they depend on fiber properties had not been forthcoming. We identified these losses as light leakage from the core to the cladding of the fiber, and developed a theory to model the phenomenon (Feuermann et al., 2002). Fig. 5 is a photograph that highlights this sort of light leakage, with red laser light injected into one of the NA50.66 optical fibers at an angle within the fiber’s nominal NA. With our theoretical model, we can forecast how light leakage depends on: (1) the properties of the fiber cladding, and (2) fiber length. The highest degree of light leakage occurred in the highest-NA (teflon-clad) fibers, which mitigated our reaching the originally predicted maximum power densities. The shortfall is around 20% for fiber lengths of a few meters. Our model can predict the improvements related to the use of superior existing cladding materials that can produce the same NA yet result in negligible leakage.
5.3. Protective glazing and small flat mirror We used BK7 Schott glass windows for good transmissivity, with anti-reflective coatings on
both sides, produced by WZW Ltd (Switzerland). The theoretical prediction for Fresnel reflective losses was 1% at each air–glass interface, plus a 1% absorption loss in the glazing. The small flat mirror was specified to have a specular reflectivity of 97% integrated over the solar spectrum. We measured the transmission of the glazings to be 0.9760.005, and the specular reflectivity of the small flat mirrors to be 0.9660.005. 6. SOLAR TRACKER
We aimed for a tracking accuracy better than 60.18. Attainable flux concentration is proportional to 1 /(us )2 . us comprises the natural size of the solar disk (0.0047 radian) enlarged by contributions from: mirror contour errors, imperfect specularity of the mirrors, diffraction from the mini-dish, tracking inaccuracy, and alignment errors in the mini-dish and fiber placement. The errors are viewed as statistically independent. So the effective (us )2 is the sum of the squares of these individual errors. For example, when a tracker accuracy of 0.058 (0.00087 rad) and a mini-dish contour and diffraction error of around 0.0015 radian are convolved with the finite size of the solar disk (Rabl, 1985), the effective us
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Fig. 5. Photograph to illustrate light leakage from the fiber’s core through its cladding and buffer. Laser light was injected into the fiber at an angle within the fiber’s nominal NA. In this black-and-white reproduction, the fiber appears white where light leakage occurs. In the absence of leakage, the light should only be visible at the entrance and exit of the fiber (and not along its length). The light exiting the fiber is projected onto a small screen.
increases to 0.005 radian. This is the value assumed in the analyses that follow. The agreement reported in Section 9 between experimental measurements of flux concentration and predictions based on us 5 0.005 radian supports this estimate. Standard accurate dual-axis solar trackers are produced for the mechanical loads commonly encountered in large solar dishes and heliostats (each unit being tens to hundreds of m 2 in area). We required only a small tracker that could accommodate at most a few prototypes. Two US companies, Small Power Systems Inc (SPS) and Enhancement Electronics Inc (EEI), claimed they could satisfy our specifications with a robust device for continuous outdoor use. One tracker was purchased from each company. To measure tracker accuracy, we built a tubular pinhole camera, and compared the movement of the sun’s image at the tube’s exit against a reference position. The tube has a high aspect ratio and is internally black (see Fig. 2a). It effectively absorbs all solar radiation outside the solar disk. Tracker accuracy measurements were performed under clear-sky conditions during the central daytime hours, with a sample run for the SPS tracker presented in Fig. 6. The SPS tracker exhibited an average accuracy of 60.058 with essentially continuous tracking motion. The EEI
tracker, however, moved in sharp distinct steps of 0.18. Namely, the tracker remains stationary until a tracking movement is required, and then abruptly advances by 0.18. Given the optical tolerances needed to reach power densities of order 10 W mm 22 , we proceeded with the SPS tracker. 7. SECOND-STAGE CONCENTRATORS
The applications being considered here—especially solar surgery—demand ultra-high flux concentration. The concentration that can be achieved in the paraboloidal mini-dish at reasonably high collection efficiency is less than half the thermodynamic limit (Eqs. (4) and (7)). Realizable concentration from the mini-dish alone is further reduced by the restricted NA in commerciallyavailable off-the-shelf optical fibers of admissibly high transmission over the solar spectrum. Accordingly, from the start, our system designs incorporated second-stage nonimaging concentrators, with the intention of boosting flux concentration to the maximum extent possible. A second-stage concentration enhancement can in principle be performed either at the proximate fiber end in the dish, or in the distal fiber tip at the remote absorber. Introducing a maximum-concentration second stage in the dish necessitates fibers with a NA near 1.0 (Feuermann and Gordon,
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Fig. 6. Absolute value of the measured tracking error of the SPS tracker, and the normal beam irradiation, for a typical clear day (7 May 2001).
1999). Such fibers could in principle be produced, but would suffer from severe fragility and are not commercially available. Accordingly, we designed second-stage concentrators at the remote delivery point. We chose a one-fiber-one-secondary-concentrator strategy with sculpted fiber tips: the ability to generate immense flux concentration from individual units without the need for active cooling. We designed dielectric nonimaging concentrators that are sculpted directly from the distal tips of the optical fibers. Our strategy was to design devices that, barring material imperfections, would produce flux levels approaching the thermodynamic limit. The actual measured performance of the manufactured concentrators would fall short of maximum concentration only due to flaws in the materials and production processes. The thermodynamic limit for the secondary flux concentration boost C max from an optical fiber 2 with numerical aperture NA is (Welford and Winston, 1989)
S D
n C max 5 ] 2 NA
2
(8)
where n denotes the refractive index of the medium into which the light is extracted. This secondary boost augments the maximum concentration produced by the mini-dish (Eq. (4)) to an overall concentration that in principle reaches the thermodynamic limit when light is extracted into a medium of refractive index n (Rabl, 1976)
S D
n max C flux 5 ] us
(Eq. (9) being a generalization of Eq. (7)). For optical fibers with NA50.66, C max 52.3 and 4.1 2 for light extraction into air and water, respectively (n51.33–1.34, which is also approximately that of many biological tissues). Our secondary concentrators are based on edgeray and V-cone designs (Welford and Winston, 1989), for an input NA of 0.66 and an exit NA of 1.00, i.e., an exit half-angle of 908. Concentrator cross-sections are drawn in Fig. 7. In these designs, the concentrator profiles are tailored to
2
(9)
Fig. 7. Cross-sections of our dielectric nonimaging sculpted fiber tip secondary concentrators. Each concentrator is a natural extension of the optical fiber used to transport sunlight concentrated in the mini-dish to a remote target (i.e., the concentrator tip is not cut separately and then attached).
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meridional rays only. Namely, it is a two-dimensional procedure applied to an axisymmetric 3D device. We performed 3D raytrace simulations, and confirmed that skew-ray rejection is at the 1–2% level for all the devices we designed. An exit NA of 1.00 creates a subtle problem for radiation measurement with commercial integrating spheres and power meters which typically are certified for light injection angles up to 6458. The exit-angle constraint posed no problem for the measurements depicted in the preceding sections, which were inherently restricted to NA values within around 0.7. We could not, however, obtain accurate radiative power measurements from the sculpted fiber tips where a substantial fraction of the power emerges beyond 458. Presently we are exploring viable measurement techniques with readily available equipment. Polymicro Inc (Polymicro, 2001) agreed to
attempt to produce the sculpted fiber tips drawn in Fig. 7. Fig. 8 offers photographs of two samples, with and without light transmission (8a and 8b, respectively). Fig. 8b reveals a less-than-perfect shape: light leakage from the sculpted tips due to imperfect manufacturing (mostly, above and beyond contour errors). As even visual inspection confirmed, light leakage remained at such high levels that these second-stage concentrators were deemed unsuitable for the planned solar experiments. Reports from other laboratories indicate that sculpted tips of these dimensions, with the required accuracy and negligible defects, can be produced, at least in-house (Liang et al., 1997). Currently we are investigating alternative routes for the commercial preparation of our sculpted fiber tip secondary concentrators. For a properly produced tip, the expected boost in flux concentration is more than a factor of 2, to around
Fig. 8. Photographs of some sculpted tip secondary concentrators. (a) Without light transmission through the fibers (magnified view, untapered fiber diameter51.00 mm). (b) With laser light transmission through the fiber, to illustrate light leakage that stems from imperfect manufacturing. Note the light leakage at the entrance to the sculpted tip and along its contour.
Solar fiber-optic mini-dish concentrators: first experimental results and field experience
25 kilosuns, for the extraction of sunlight into air, and a factor of 4, to around 45 kilosuns, for the extraction of light into water or tissue. 8. OPERATING PROTOTYPE AND EXPERIMENTAL RESULTS
Photographs of a completed prototype are presented in Fig. 2. We positioned the optical fiber in the mini-dish with a two-pronged strategy. First, we calculated the precise position for the fiber’s proximate tip and, guided by visual inspection, sited the fiber accordingly. Then we exposed the mini-dish assembly to the sun (with dual-axis tracking in operation), and fine-tuned the fiber’s position by simultaneously measuring the radiative output at the fiber’s distal end and adjusting the position of the fiber’s proximate tip. The final position was chosen so as to maximize power output. Experiments were performed at Ben-Gurion University’s Sede Boqer Campus, under clear-sky conditions, and covered periods within 64 h of solar noon for durations of up to several hours on
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clear days distributed throughout the year. The power output at the fiber’s distal end was measured with an Ophir Ltd pyrometer-detector power meter, and the normal solar beam irradiance was measured with an Eppley normalincidence pyrheliometer. There was no measurable degradation of the optical or mechanical elements due to outdoor exposure during our experiments. A future task is establishing whether the dearth of degradation persists with long-term continuous operation. The pyrheliometer has a full acceptance angle of 0.100 radian. Our concentrator, however, is designed for the far smaller angular extent of the solar disk. We had no direct measurement of circumsolar radiation. For solar climates similar to that in Sede Boqer, clear-day circumsolar fractions tend to be in the range of 1–6% (Rabl, 1985; Gueymard, 2001). We conservatively adopted a nominal uniform correction from measured solar beam to collectible radiation of 0.98. Typical measured values are: (1) a remote power delivery of 8 W, (2) at a collectible solar beam irradiance of 900 W m 22 . With a fiber core
Table 1. Representative and repeatable experimental results for our solar fiber-optic mini-dish prototype, for nominal fiber lengths of 1, 7 and 20 m a Component
Protective glazing with anti-reflective coating Paraboloidal mini-dish mirror Small flat secondary mirror Air–quartz interface at the fiber tips (per tip) Light leakage from fiber core to cladding: 1 meter fiber 7 meter fiber 20 meter fiber Attenuation in the fiber core Net prototype throughput with: 1 meter fiber 7 meter fiber 20 meter fiber
Measured optical throughput
Improved optical throughput attainable with existing materials or production techniques
0.97 0.96 0.96
0.97 0.97 0.97
0.96
0.99 0.99
0.87 0.82 0.79 0.99
0.99 0.88
0.71 0.66 0.64
Maximum possible flux concentration in a loss-less system5(NA /us )2 517.4 kilosuns Maximum flux concentration with real materials and improved optical throughput515.3 kilosuns Representative experimental results for: Optical fiber core diameter51.0060.03 mm, fiber nominal NA50.66 Effective solar angular radius (incorporating all optical errors) us 5 0.005 radian Fiber length
Measured power output from distal fiber tip (W)
Measured normal beam irradiance (W m 22 )
Power density attained experimentally (W m 22 )
Corresponding flux concentration (kilosuns)
Predicted flux concentration including losses (kilosuns)
1.1 m 7.2 m 20.0 m
7.8560.3 8.160.3 8.160.3
838620 921620 931620
10.060.6 10.360.6 10.360.6
11.960.8 11.560.8 11.160.8
12.460.8 11.560.8 11.260.8
a We also include detailed accounting of optical performance on a component-by-component basis. The performance of each element individually is based on our indoor laboratory measurements.
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diameter of 1.0 mm, this corresponds to a flux concentration of more than 11 kilosuns. Representative measurements are summarized in Table 1 for three different fiber lengths, along with the predictable optical losses associated solely with material properties. The predicted flux levels are consistent with our measured values, to within the experimental uncertainty. The agreement between the measured outdoor performance of the assembled prototype and the projections would appear to indicate that all key effects have been accounted for. Also included are the potential improvements attainable with existing materials and technologies, i.e., without the need for future advances in optical surfaces or production techniques.
9. OBSERVATIONS AND QUALIFICATIONS
Our mini-dish prototype was purposely slightly oversized in order to accommodate fibers of varying diameter and NA. That means that the NA of the mini-dish (0.707) is larger than that of the optical fiber (0.66), and that both the dish focal length and diameter could have been smaller. A mini-dish with the uniform-flux core region of its focal spot equal to the fiber core diameter, d fiber 5 1.00 mm, would have F 5 100 mm and D 5 151 mm. Alternatively expressed, whereas our actual mini-dish typically intercepted 28 watts of collectible solar beam irradiation (of 900 W m 22 ), a mini-dish exactly matched to the fibers would intercept 16 watts. Given known material properties and our ability to account for all system losses (Table 1), we can assess that the power density produced in the core region of the focal spot of the mini-dish was approximately 15.4 kilosuns. The attainable flux concentration can be noticeably improved exclusively through the use of superior existing materials and technologies, i.e., without the need for future advances in material or production technologies. Hence we have included in Table 1 what we view as tenable projections of the performance of solar fiber-optic mini-dishes of the type we have designed, built and tested. Optical fibers with core diameters up to 2.0 mm are commercially available, but only for noticeably lower NA. The highest nominal NA value, for which we found optical fibers with core diameters of 1.5 and 2.0 mm at admissibly low attenuation over the solar spectrum, was 0.4. These largediameter fibers have enough mechanical flexibility to remain robust in solar concentrator systems.
They might enhance cost-effectiveness by reducing the number of fibers per unit of collection area. Our mini-dishes were diamond turned. This was the only feasible method we identified for producing a handful of precision concentrators. Diamond-turned devices are inherently expensive, and could not be deemed economically feasible for large mini-dish systems. A workable alternative is preparing a die and mold-injecting minidishes in mass production (with subsequent mirror deposition). With a precision die, the price for creating and coating a mini-dish would be dramatically less than the diamond-turning procedure: about several US$ per mirrored mini-dish at very high volume production. But the precision die typically costs of the order of tens of thousands of US$ (G-S, 2002; Syntec, 2002). A future mini-dish system of sufficient extent could benefit from this economy of scale, and could thereby advance the demonstration of economic and technical feasibility. Finally, a recent outgrowth of our experimental program is high-flux photovoltaic power generation with advanced multi-junction semiconductors. The concept was originally delineated in Feuermann and Gordon (2001a), and subsequently commissioned for experimental realization (Reddy et al., 2001).
10. SUMMARY
In the first phase of our solar fiber-optic minidish program, the primary milestones included: 1. The experimental realization of our proposed solar fiber-optic mini-dish, including the design, construction, and testing of an operational prototype. We have demonstrated the collection, concentration and transmission of sunlight to remote targets. Discussions with producers of molds and injection-molded optical elements indicate that the miniaturized units (200 mm in diameter, with a focal length of 120 mm) are well suited to mass production. 2. The measurement of flux concentration exceeding 11 kilosuns at a remote receiver (20 m removed), solely from the fiber-optic mini-dish (primary) concentrator. Flux levels in the encased mini-dish at the proximate fiber tip exceed 15 kilosuns, for a system with a numerical aperture of 0.66. There appear to be no unaccounted-for loss mechanisms, i.e., we can confidently project optical performance from known material properties. It should be feas-
Solar fiber-optic mini-dish concentrators: first experimental results and field experience
ible eventually to attain up to 30% higher flux concentration, based wholly on available materials and existing production technologies. 3. Testing the tracking accuracy of small dualaxis trackers suitable for miniaturized highconcentration units, and establishing a tolerance of 60.058. 4. An experimental study of the measurement of the angular transmission characteristics of optical fibers suitable for high-flux solar uses, including the discovery of deleterious light leakage (Feuermann et al., 2002). A theoretical model that can account for these observations permits distinguishing between inherent limitations versus technological problems for the design and selection of optical fibers for future systems. 5. The design, fabrication and preliminary testing of sculpted optical fiber tips that serve as secondary concentrators intended to markedly increase delivered power density as desired for solar surgery. 6. The absence of noticeable thermal, optical or material degradation in any system component. The second phase of our experimental program will focus on: (a) the construction and testing of large multi-unit modules; (b) measuring long-term continuous outdoor performance toward establishing system robustness; (c) fabricating and demonstrating secondary concentrators relatively free of manufacturing defects, that can actually approach the thermodynamic limit to concentration; and (d) demonstrating solar surgical (biomedical) procedures.
NOMENCLATURE Cflux C max flux C max 2 C core flux C avg flux D d fiber d min d max F f kilosun n NA
flux concentration thermodynamic limit for (overall) flux concentration thermodynamic limit for the flux concentration boost from a secondary concentrator flux concentration in the uniform-flux core region of the focal spot of a paraboloidal dish flux concentration averaged over the full focal spot of a paraboloidal dish paraboloidal dish diameter optical fiber core diameter diameter of the maximum-flux core region in the focal spot of the paraboloidal dish focal spot diameter that encompasses all reflected rays of the paraboloidal dish focal length f-number of paraboloidal dish 10 3 suns (flux concentration) refractive index of the medium into which concentrated sunlight is extracted numerical aperture
f uair us
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rim half-angle of the paraboloidal dish half-angle of acceptance of the optical fiber effective solar angular radius
Acknowledgements—This research was supported by grants from the Israel Ministry of National Infrastructures (Jerusalem) and the Rita Altura Foundation (Los Angeles, CA). We are indebted to Michael Altura for his encouragement and sponsorship. We thank Jonathan Molcho of Ben-Gurion University’s Department of Electrical and Computer Engineering for generously granting the use of facilities and space in his laboratory, as well as his valuable recommendations in the selection of measurement equipment. We are also grateful to David Faiman of Ben-Gurion University’s Blaustein Institute for Desert Research for the use of facilities and technical assistance at the Ben-Gurion National Solar Energy Center.
REFERENCES Arashi H. and Kaneda Y. (1993) Solar-pumped laser and its second harmonic generation. Solar Energy 50, 447–451. Avimo Precision Polymer Optics (2001) 560 West Terrace Dr., San Dimas, CA 91773. Private communication. Baum W. A. and Strong J. D. (1958) Basic optical considerations in the choice of a design for a solar furnace. Solar Energy 2(3–4), 37–45. Cariou J. M., Dugas J. and Martin L. (1982) Transport of solar energy with optical fibers. Solar Energy 29, 397–406. Feuermann D. and Gordon J. M. (1998) Solar surgery: remote fiber-optic irradiation with highly concentrated sunlight in lieu of lasers. Opt. Eng. 37, 2760–2767. Feuermann D., Gordon J. M. and Ries H. (1999) High-flux solar concentration with imaging designs. Solar Energy 65, 83–90. Feuermann D. and Gordon J. M. (1999) Solar fiber-optic mini-dishes: a new approach to the efficient collection of sunlight. Solar Energy 65, 159–170. Feuermann D. and Gordon J. M. (2001a) High-concentration photovoltaic designs based on miniature parabolic dishes. Solar Energy 70, 423–430. Feuermann D. and Gordon J. M. (2001b) Experimental realization of solar fiber-optic mini-dishes. Israel Ministry of National Infrastructures. Final technical report RD-242001, Contract No. 99-1-36 / 99-11-024, November 2001. Feuermann D., Gordon J. M. and Huleihil M. (2002) Light leakage in optical fibers: experimental results, modeling and the consequences for solar concentrators. Solar Energy 72, 195–204. Flamant G., Ferriere A., Laplaze D. and Monty C. (1999) Solar processing of materials: opportunities and new frontiers. Solar Energy 66, 117–132. G-S Plastic Optics (2002) 408 St. Paul St., Rochester, NY. Private communication. Gueymard C. A. (2001) Parameterized transmittance model for direct beam and circumsolar spectral irradiance. Solar Energy 71, 325–346. Gordon J. M. (2001) Solar energy engineering: a mini-revolution in Israel. Refocus March, 34–37. Irvin B. R. and Nakamura T. (1991) Characterization of optical fibers for solar energy transmission. In Proceedings Second ASME-JSES-JSME International Solar Energy Conference, Reno, Nevada, 17–22 March 1991, pp. 359–366. ASME, NY. Liang D., Nunes Y., Fraser-Monteira L., Fraser-Monteira M. L. and Collares-Pereira M. (1997) 200 W solar energy delivery with optical fiber bundles. SPIE Proc. 3139, 217–224. Marks P. (1999) Saved by the light. New Scientist 27 Feb, . Pitts J. R., Hale M. J., Bingham C., Lewandowski A. and King D. E. (1993) Formation of fullerenes in highly concentrated solar flux. J. Phys. Chem. 97, 8701–8702.
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Polymicro Technologies LLC (2001) 18019 N. 25th Ave., Phoenix, AZ. Private communications. Rabl A. (1976) Comparison of solar concentrators. Solar Energy 18, 93–111. Rabl A. (1985). Active Solar Collectors and Their Applications, Oxford University Press, NY. Reddy T. A., Scoles K., Eisenstein B., Feuermann D. and
Gordon J. M. (2001) Modular photovoltaic power systems using solar fiber-optic mini-dish concentrators. US Department of Energy Contract DE-FC36-01GO11000. Syntec Technologies Inc. (2002) 7100 Junction Road, Pavillion, NY. Private communication. Welford W. T. and Winston R. (1989). High Collection Nonimaging Optics, Academic Press, San Diego.
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Solar Energy Vol. 72, No. 6, pp. 459–472, 2002 2002 Elsevier Science Ltd S 0 0 3 8 – 0 9 2 X ( 0 2 ) 0 0 0 2 5 – 7 All rights reserved. Printed in Great Britain 0038-092X / 02 / $ - see front matter
www.elsevier.com / locate / solener
SOLAR FIBER-OPTIC MINI-DISH CONCENTRATORS: FIRST EXPERIMENTAL RESULTS AND FIELD EXPERIENCE DANIEL FEUERMANN*, JEFFREY M. GORDON** ,† and MAHMOUD HULEIHIL* *Department of Solar Energy and Environmental Physics, Jacob Blaustein Institute for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus 84990, Israel **The Pearlstone Center for Aeronautical Engineering Studies, Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beersheva 84105, Israel Received 12 March 2002; accepted 19 April 2002 Communicated by JOACHIM LUTHER
Abstract—The experimental realization and field experience of a recently proposed solar fiber-optic mini-dish concentrator are reported. The prototype is 200 mm in diameter. We have repeatably transported concentrated sunlight in a one-millimeter-diameter optical fiber and measured flux levels of 11–12 kilosuns at a remote target (up to 20 m away). The prototype—assembled from off-the-shelf parts and customized items that rely solely upon existing commercial technologies—proved impervious to dust penetration and condensation. For the particular application of solar surgery, dielectric second-stage concentrators were designed and fiber tips were sculpted to boost flux concentration by a factor of 2 to 4, for light extraction into air and tissue, respectively. Our findings strengthen the feasibility of the efficient and complete de-coupling of the collection and remote delivery of highly concentrated solar radiation. 2002 Elsevier Science Ltd. All rights reserved.
physical and engineering concepts into a functional prototype (Feuermann and Gordon, 2001b). Fig. 1 is a schematic of the mini-dish unit. Fig. 2 includes photographs in the field of our first operating prototype (200 mm in diameter, with a focal length of 120 mm), including the remote extraction (delivery) of sunlight at flux levels surpassing 11 kilosuns (i.e., 11 000 suns) from an optical fiber 1.0 mm in diameter, at a distance up to 20 m from the mini-dish collector. The sections that follow provide a detailed component-by-component description of the design, assembly, testing and field measurements. With this itemized accounting, we then proceed to report on the performance and analysis of our outdoor solar experiments on the assembled prototype. This is followed by our observations regarding future generations of improved viable solar fiber-optic mini-dishes.
1. INTRODUCTION
Certain solar applications uniquely require very high photon densities, i.e., high flux concentration. Recent innovations include solar surgery (Feuermann and Gordon, 1998), solar-pumped lasers (Arashi and Kaneda, 1993), the solar-driven synthesis of carbon nanomaterials (Pitts et al., 1993; Flamant et al., 1999) and electricity generation with advanced semiconductor materials (Feuermann and Gordon, 2001a; Reddy et al., 2001). An essential element in the practical realization of these applications is the total separation of the collection and delivery of highly concentrated sunlight, including high efficiencies for collection and optical transport. Toward solving this problem in a pragmatic and modular fashion, the use of solar fiber-optic mini-dishes was proposed (Cariou et al., 1982; Feuermann and Gordon, 1998, 1999, 2001a; Gordon, 2001). This article constitutes a detailed report on the experimental results and field experience in which these miniaturized concentrators were translated from
†
2. PROTOTYPE CONCENTRATOR DESIGN
A paraboloidal dish is specified completely by its diameter D and rim half-angle f. The fnumber of the dish, f 5 (focal length) /(diameter) 5 F /D
Author to whom correspondence should be addressed. Tel.: 1972-7-659-6923; fax: 1972-7-659-6921; e-mail: [email protected] 459
is related to f by
(1)
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flux that reaches the focal plane (Baum and Strong, 1958). The focal spot diameter d max that accepts essentially all reflected rays is (Rabl, 1976) Duss1 1 16f 2d 2 d max 5 ]]]] . 8fs16f 2 2 1d
(5)
The corresponding averaged flux concentration is sin 2 (f ) cos 2 (f ) ]]]]] C avg 5 . flux u s2
(6)
For comparison, the thermodynamic limit for flux concentration (in air) is (Rabl, 1976; Welford and Winston, 1989) 1 C max . flux 5 ] u 2s
Fig. 1. Schematic of a solar fiber-optic mini-dish. A small flat mirror below the focal plane redirects solar rays reflected from the dish downward to facilitate practical coupling into an optical fiber. Extreme rays are shown traced into the fiber, which is enclosed in a protective sleeve. Concentrated sunlight is transported in the optical fiber to a remote application— illustrated here as solar surgery (Feuermann and Gordon, 1998)—with the option of a significant boost in power density with a nonimaging secondary concentrator at the distal end (Drawing courtesy of New Scientist (Marks, 1999)).
1 /f 5 4 tan(f / 2).
(2)
The diameter d min of the approximately uniform-flux core region of the focal spot is d min 5 2Dfus
(3)
where us is the effective solar half-angle (a convolution of the actual size of the solar disk with optical errors in the mini-dish contour, tracker accuracy and fiber alignment), which is taken throughout to be sufficiently small that sin(us ) ¯ us . As justified in Section 6, we adopt a realistic value for us of 0.005 radian. The concentration in the core region is the highest local flux a paraboloidal dish generates (Rabl, 1976) 2
sin (f ) core C flux 5 ]] u s2
(4)
and encompasses a fraction cos 4 (f / 2) of the total
(7)
In Section 7, we shall explore how overall flux concentration can be heightened to the thermodynamic limit, at high collection efficiency, with dielectric secondary concentrators sculpted from the distal tips of optical fibers. When designing for maximum flux concentration from the dish, one selects the fiber core diameter d fiber to be d min ; while for maximum efficiency designs d fiber will be closer to d max . Furthermore, achieving a reasonably low number of fibers per collection area demands systems of relatively low f-number. Fiber core diameters can of course be chosen between d min and d max . A comprehensive study of the associated efficiency– concentration tradeoff for paraboloidal concentrators covering a wide range of f-numbers was presented in Feuermann et al. (1999). The optimal compromise between efficiency and concentration is case-specific, with Feuermann et al. (1999) providing the quantitative tools for such determinations. We selected a mini-dish diameter D 5 200 mm, a focal length F 5 120 mm (hence f 5 458), and an optical fiber core diameter d fiber 51.0 mm as a consequence of several considerations. 1. The dish size should be sufficiently small that eventual mass production of the dishes, and modularity, would be feasible. 2. The dish should be small enough to permit affordable production of prototypes by a number of companies. 2 3. The number of optical fibers per m of minidishes should be as small as possible for eventual large-scale viability. Hence high concentration is required, which in turn demands high rim-angle dishes (Eq. (4)).
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Fig. 2. Photographs of our first operational prototype in the field. (a) Photograph of the assembled fiber-optic mini-dish, dual-axis tracker, tracker sensors and scope for determining tracker accuracy (foreground). (b) Front view, with a 20-meter long optical fiber, where the fiber output has approximately 1 / 4 the brightness of the sun. (c) Side view of Fig. 2b. The solar fiber-optic mini-dish is at the far left and the technician holding the distal fiber end is at the far right. (d) Projection of the output from the 20-meter fiber onto a white diffuse screen.
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4. High rim-angle dishes enjoin optical fibers of high numerical aperture (NA). NA5sin(uair ), with 2uair denoting the full angular range of rays incident from air, that nominally is supported by the optical fiber, i.e., for which total internal reflection is respected. Therefore we constrained ourselves to commercially available fibers of high NA and large core diameters. Our aim was to achieve the highest flux concentration at high radiative efficiency for practical configurations. The flux concentration achievable in the mini-dish alone is proportional to (NA)2 . (Equivalently, the number of fibers, per square meter of solar collecting area, is proportional to 1 /(NA)2 .) At us 5 0.005 radian, a dish with the dimensions noted above can be used between the extremes of (a) maximum concentration with d fiber 5 d min 5 1.2 mm; and (b) maximum efficiency with d fiber 5 d max 5 2.0 mm. Realizable flux concentration is also proportional to the fiber’s transmittance, so fiber core materials with near-negligible attenuation integrated over the full solar spectrum are essential (such as pure quartz). Furthermore, the number of (expensive) optical fibers, per square meter of solar collecting area, is proportional to 1 /(d fiber )2 . Therefore we aimed to use commercially available fibers with the highest NA, lowest attenuation, and largest core diameter. 3. PRACTICAL CONCERNS
As we embarked upon the experimental program reported here, our principal practical concerns were:
3.1. Dust penetration and accumulation on the mirror or fiber tip, as well as condensation in the space between the glazing and the mirror These were not expected to pose a major problem, based on the success of related technologies for totally different applications. For example, the reflectors in car headlights (of dimensions comparable to our mini-dish units) remain clean for years in demanding environments. We produced a tight encasement of the mirror, proximate fiber tip and small flat mirror with two O-rings: one between the glazing and the encasement, and the other between the mirror and the encasement. The opening in the center of the parabolic mirror (for insertion of the fiber holder) was sealed by a small flange machined into the sleeve in a metal-to-metal seal. The optical fibers are manufactured with a protective
plastic buffer, and sit snugly inside the fiber holder. Thus there is virtually no dust penetration. Moreover, we did not observe any condensation inside the dish at any time.
3.2. Achieving adequate mirror contour accuracy We did not find commercial off-the-shelf highquality parabolic mirrors for the dimensions required. The only practical fabrication technique for the first handful of prototypes was diamond turning of an aluminum substrate followed by first-surface silver coating and a protective thin layer of silica. Diamond turning can provide a dish contour accuracy of several microns, which translates into a mirror slope error of order 0.0001 radian. Several manufacturers have demonstrated comparable accuracy with plastic (coated) mirrors produced by mold injection (Avimo, 2001; Syntec, 2002; G-S, 2002). Improper diamond turning can result in deleterious diffraction losses that stem from excessive groove width. If the groove size is kept well below the wavelength range of the solar spectrum (which is readily achievable with commercial equipment), then diffraction losses can be rendered negligible.
3.3. Accurate alignment of all elements and positioning of the small flat mirror Alignment of the elements was achieved by producing the machined encasement on an accurate lathe. The positioning of the mirrors and glazing relative to the encasement was checked with a laser in our indoor laboratory. There was a tolerance of 60.1 mm in positioning the fiber tip because the fiber’s core diameter (d fiber 5 1.0 mm) was less than the diameter of the uniform flux core region in the focal plane of the dish (d min 5 1.2 mm). A small frame with adjustment screws that attached to the back of the mini-dish maintained the fiber at its proper position and permitted fine-tuning of fiber tip location in the x, y and z directions to within about 60.05 mm. Element alignment in future mass-produced units should be achievable with common manufacturing methods, such as those used for automatic pencils and plastic lenses. Our design introduces a small flat mirror to re-direct rays reflected from the dish downward, so that a rigidly-positioned optical fiber can point upward and thereby obviate the practical problems associated with the conventional downwardfacing absorber in solar dishes. Furthermore, cleaning the protective glazing would be problematic were the fibers to extend outwards and be
Solar fiber-optic mini-dish concentrators: first experimental results and field experience
required to bend backwards behind the dish. This is particularly important for modules comprising tens to hundreds of mini-dishes. In eventual largevolume production, we recommend that the small mirror be deposited directly on the protective glazing. But for the first prototypes, toward granting maximum operational flexibility, we had the small mirror deposited on a pedestal that extends downward from the glazing.
3.4. Tracking precision We identified several commercially-available small precision dual-axis trackers, of which two certified a tracking accuracy of better than 60.002 radian. Tracker details and test results are reported in Section 6.
3.5. Commercial availability of suitable lowattenuation optical fibers that can withstand high solar flux The attenuation of commercial quartz-core optical fibers, integrated over the solar spectrum, is sufficiently low that flux levels of order 10 kilosuns are easily accommodated (Polymicro, 2001; Feuermann et al., 2002). Whereas the bestsuited optical fibers should have relatively large diameters and high NA, practical problems arose because: (a) fiber stiffness is a strongly increasing function of fiber diameter; and (b) we did not discover commercial fibers with core diameters much above 1.0 mm that are suitable for concentrated sunlight. While fiber manufacturers confirmed that there is no major material or technological factor that militates against high-NA fibers, the highest NA fibers that we found produced commercially have a nominal NA of 0.66, and could be purchased from only one company (Polymicro, 2001). We purchased samples of all the commercially-available so-called high-NA fibers for comparative testing and evaluation. For the highest-NA fibers, the core diameter is 1.0 mm. Some of the fibers with a nominal NA of about 0.4 are available with core diameters up to 2.0 mm. Test results are summarized in Section 5.2. 4. LABORATORY EQUIPMENT
Outdoor measurements on the assembled prototype are of limited value unless the performance of each component is first characterized separately under controlled conditions. Consequently, individual components were tested in the laboratory prior to assembly. These measurements included the mini-dish contour accuracy, mirror
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specular reflectivities of both the small flat mirror and the parabolic dish, transmission of the cover glazing, as well as attenuation and angular transmission of optical fibers and sculpted fiber tips. A source of collimated white light and a He–Ne laser together with a calibrated integrating sphere were used to test optical properties of components in the visible and near infrared. The measurement procedures for the angular transmission and attenuation of optical fibers were documented in Feuermann et al. (2002). Fig. 2a is a photograph of the assembled prototype installed outdoors. The installation comprised: (1) a battery-driven dual-axis solar tracker and stand, (2) a telescope-like device used in determining tracker accuracy (Section 6), (3) accommodation of the full fiber-optic mini-dish assembly, and (4) a pyrometric power meter to measure radiative output at the fiber’s distal end.
5. EVALUATION OF OPTICAL ELEMENTS
5.1. Mini-dish We ordered several diamond-turned parabolic mirrors from two companies (referred to as A and B), and developed in-house procedures for assessing contour accuracy, reflectivity and specularity. Lacking sophisticated profiling equipment, we determined the contour accuracy by comparing the spot size produced in the dish focal plane by a distant (approximately point) light source against the theoretical result. Reflectivity was measured with a laser and integrating sphere. Specularity was ascertained by comparing the observed spread of a laser beam reflected from several points on the mirror to the calculated value for a parabola. Satisfactory accord between our in-house measurements, and those from an independent testing laboratory to which one of the mini-dishes was sent, established confidence in our procedures for the precision required for our solar concentrator. Company A also independently supplied the mirror’s measured spectral reflectivity from a witness piece, which confirmed our measurements (a) with the laser and (b) integrated over the lamp’s (white-light) spectrum. Our measurements revealed that only Company A’s mirrors satisfied our specifications, to wit, a specular reflectivity (integrated over the solar spectrum) of 0.96, with a contour error commensurate with us not exceeding 0.005 radian. Fig. 3 highlights the distinction between the image produced with a surface that does not
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Fig. 3. Illustration of diffraction losses. Photographs of a far-field target irradiated by laser light or white light that has been reflected from mini-dishes A and B. (a) Dish A, laser light. (b) Dish A, white light. (c) Dish B, laser light. (d) Dish B, white light.
appear to suffer from diffractive losses (Company A), and one that does (Company B). The reflected spot should be a single disk of light. With Company B’s dish, optical interference results in a sizable fraction of the reflected light being distributed at distances far beyond the diameter of the central spot.
5.2. Optical fibers The optical characterization of the fibers was reported in Feuermann et al. (2002). In particular, we measured the transmission of the fibers, as a function of incidence angle, for a broad-spectrum collimated light source. We divided optical losses into: (a) Fresnel reflections off the air-quartz interfaces; (b) attenuation in the fiber’s core; and (c) residual losses. The Fresnel reflective losses (around 4%
per air-quartz interface) and attenuation in the core (no more than 1% for fiber lengths of up to 10 m) were predictable from known material properties and the attenuation spectrum provided by the manufacturers. They were confirmed experimentally. Based on manufacturers’ claims, the residual losses were expected to be negligible. However, we discovered significant transmission losses at off-normal incidence that increased dramatically with incidence angle within the fiber’s NA. Sample measurements are plotted in Fig. 4. Integrated over the fiber’s nominal NA, these residual losses reached 20% in some instances. At angles near (but less than) the fiber’s NA, losses could exceed 50%. Transmission losses of this magnitude have also been documented in other laboratories (Irvin and Nakamura, 1991; Liang et al., 1997), al-
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Fig. 4. Measured angular response of commercial low-attenuation optical fibers of nominal NA50.66, intended for high-flux solar applications. L / d5ratio of fiber length to core diameter.
though a satisfactory model to account for the losses and predict how they depend on fiber properties had not been forthcoming. We identified these losses as light leakage from the core to the cladding of the fiber, and developed a theory to model the phenomenon (Feuermann et al., 2002). Fig. 5 is a photograph that highlights this sort of light leakage, with red laser light injected into one of the NA50.66 optical fibers at an angle within the fiber’s nominal NA. With our theoretical model, we can forecast how light leakage depends on: (1) the properties of the fiber cladding, and (2) fiber length. The highest degree of light leakage occurred in the highest-NA (teflon-clad) fibers, which mitigated our reaching the originally predicted maximum power densities. The shortfall is around 20% for fiber lengths of a few meters. Our model can predict the improvements related to the use of superior existing cladding materials that can produce the same NA yet result in negligible leakage.
5.3. Protective glazing and small flat mirror We used BK7 Schott glass windows for good transmissivity, with anti-reflective coatings on
both sides, produced by WZW Ltd (Switzerland). The theoretical prediction for Fresnel reflective losses was 1% at each air–glass interface, plus a 1% absorption loss in the glazing. The small flat mirror was specified to have a specular reflectivity of 97% integrated over the solar spectrum. We measured the transmission of the glazings to be 0.9760.005, and the specular reflectivity of the small flat mirrors to be 0.9660.005. 6. SOLAR TRACKER
We aimed for a tracking accuracy better than 60.18. Attainable flux concentration is proportional to 1 /(us )2 . us comprises the natural size of the solar disk (0.0047 radian) enlarged by contributions from: mirror contour errors, imperfect specularity of the mirrors, diffraction from the mini-dish, tracking inaccuracy, and alignment errors in the mini-dish and fiber placement. The errors are viewed as statistically independent. So the effective (us )2 is the sum of the squares of these individual errors. For example, when a tracker accuracy of 0.058 (0.00087 rad) and a mini-dish contour and diffraction error of around 0.0015 radian are convolved with the finite size of the solar disk (Rabl, 1985), the effective us
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Fig. 5. Photograph to illustrate light leakage from the fiber’s core through its cladding and buffer. Laser light was injected into the fiber at an angle within the fiber’s nominal NA. In this black-and-white reproduction, the fiber appears white where light leakage occurs. In the absence of leakage, the light should only be visible at the entrance and exit of the fiber (and not along its length). The light exiting the fiber is projected onto a small screen.
increases to 0.005 radian. This is the value assumed in the analyses that follow. The agreement reported in Section 9 between experimental measurements of flux concentration and predictions based on us 5 0.005 radian supports this estimate. Standard accurate dual-axis solar trackers are produced for the mechanical loads commonly encountered in large solar dishes and heliostats (each unit being tens to hundreds of m 2 in area). We required only a small tracker that could accommodate at most a few prototypes. Two US companies, Small Power Systems Inc (SPS) and Enhancement Electronics Inc (EEI), claimed they could satisfy our specifications with a robust device for continuous outdoor use. One tracker was purchased from each company. To measure tracker accuracy, we built a tubular pinhole camera, and compared the movement of the sun’s image at the tube’s exit against a reference position. The tube has a high aspect ratio and is internally black (see Fig. 2a). It effectively absorbs all solar radiation outside the solar disk. Tracker accuracy measurements were performed under clear-sky conditions during the central daytime hours, with a sample run for the SPS tracker presented in Fig. 6. The SPS tracker exhibited an average accuracy of 60.058 with essentially continuous tracking motion. The EEI
tracker, however, moved in sharp distinct steps of 0.18. Namely, the tracker remains stationary until a tracking movement is required, and then abruptly advances by 0.18. Given the optical tolerances needed to reach power densities of order 10 W mm 22 , we proceeded with the SPS tracker. 7. SECOND-STAGE CONCENTRATORS
The applications being considered here—especially solar surgery—demand ultra-high flux concentration. The concentration that can be achieved in the paraboloidal mini-dish at reasonably high collection efficiency is less than half the thermodynamic limit (Eqs. (4) and (7)). Realizable concentration from the mini-dish alone is further reduced by the restricted NA in commerciallyavailable off-the-shelf optical fibers of admissibly high transmission over the solar spectrum. Accordingly, from the start, our system designs incorporated second-stage nonimaging concentrators, with the intention of boosting flux concentration to the maximum extent possible. A second-stage concentration enhancement can in principle be performed either at the proximate fiber end in the dish, or in the distal fiber tip at the remote absorber. Introducing a maximum-concentration second stage in the dish necessitates fibers with a NA near 1.0 (Feuermann and Gordon,
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Fig. 6. Absolute value of the measured tracking error of the SPS tracker, and the normal beam irradiation, for a typical clear day (7 May 2001).
1999). Such fibers could in principle be produced, but would suffer from severe fragility and are not commercially available. Accordingly, we designed second-stage concentrators at the remote delivery point. We chose a one-fiber-one-secondary-concentrator strategy with sculpted fiber tips: the ability to generate immense flux concentration from individual units without the need for active cooling. We designed dielectric nonimaging concentrators that are sculpted directly from the distal tips of the optical fibers. Our strategy was to design devices that, barring material imperfections, would produce flux levels approaching the thermodynamic limit. The actual measured performance of the manufactured concentrators would fall short of maximum concentration only due to flaws in the materials and production processes. The thermodynamic limit for the secondary flux concentration boost C max from an optical fiber 2 with numerical aperture NA is (Welford and Winston, 1989)
S D
n C max 5 ] 2 NA
2
(8)
where n denotes the refractive index of the medium into which the light is extracted. This secondary boost augments the maximum concentration produced by the mini-dish (Eq. (4)) to an overall concentration that in principle reaches the thermodynamic limit when light is extracted into a medium of refractive index n (Rabl, 1976)
S D
n max C flux 5 ] us
(Eq. (9) being a generalization of Eq. (7)). For optical fibers with NA50.66, C max 52.3 and 4.1 2 for light extraction into air and water, respectively (n51.33–1.34, which is also approximately that of many biological tissues). Our secondary concentrators are based on edgeray and V-cone designs (Welford and Winston, 1989), for an input NA of 0.66 and an exit NA of 1.00, i.e., an exit half-angle of 908. Concentrator cross-sections are drawn in Fig. 7. In these designs, the concentrator profiles are tailored to
2
(9)
Fig. 7. Cross-sections of our dielectric nonimaging sculpted fiber tip secondary concentrators. Each concentrator is a natural extension of the optical fiber used to transport sunlight concentrated in the mini-dish to a remote target (i.e., the concentrator tip is not cut separately and then attached).
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meridional rays only. Namely, it is a two-dimensional procedure applied to an axisymmetric 3D device. We performed 3D raytrace simulations, and confirmed that skew-ray rejection is at the 1–2% level for all the devices we designed. An exit NA of 1.00 creates a subtle problem for radiation measurement with commercial integrating spheres and power meters which typically are certified for light injection angles up to 6458. The exit-angle constraint posed no problem for the measurements depicted in the preceding sections, which were inherently restricted to NA values within around 0.7. We could not, however, obtain accurate radiative power measurements from the sculpted fiber tips where a substantial fraction of the power emerges beyond 458. Presently we are exploring viable measurement techniques with readily available equipment. Polymicro Inc (Polymicro, 2001) agreed to
attempt to produce the sculpted fiber tips drawn in Fig. 7. Fig. 8 offers photographs of two samples, with and without light transmission (8a and 8b, respectively). Fig. 8b reveals a less-than-perfect shape: light leakage from the sculpted tips due to imperfect manufacturing (mostly, above and beyond contour errors). As even visual inspection confirmed, light leakage remained at such high levels that these second-stage concentrators were deemed unsuitable for the planned solar experiments. Reports from other laboratories indicate that sculpted tips of these dimensions, with the required accuracy and negligible defects, can be produced, at least in-house (Liang et al., 1997). Currently we are investigating alternative routes for the commercial preparation of our sculpted fiber tip secondary concentrators. For a properly produced tip, the expected boost in flux concentration is more than a factor of 2, to around
Fig. 8. Photographs of some sculpted tip secondary concentrators. (a) Without light transmission through the fibers (magnified view, untapered fiber diameter51.00 mm). (b) With laser light transmission through the fiber, to illustrate light leakage that stems from imperfect manufacturing. Note the light leakage at the entrance to the sculpted tip and along its contour.
Solar fiber-optic mini-dish concentrators: first experimental results and field experience
25 kilosuns, for the extraction of sunlight into air, and a factor of 4, to around 45 kilosuns, for the extraction of light into water or tissue. 8. OPERATING PROTOTYPE AND EXPERIMENTAL RESULTS
Photographs of a completed prototype are presented in Fig. 2. We positioned the optical fiber in the mini-dish with a two-pronged strategy. First, we calculated the precise position for the fiber’s proximate tip and, guided by visual inspection, sited the fiber accordingly. Then we exposed the mini-dish assembly to the sun (with dual-axis tracking in operation), and fine-tuned the fiber’s position by simultaneously measuring the radiative output at the fiber’s distal end and adjusting the position of the fiber’s proximate tip. The final position was chosen so as to maximize power output. Experiments were performed at Ben-Gurion University’s Sede Boqer Campus, under clear-sky conditions, and covered periods within 64 h of solar noon for durations of up to several hours on
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clear days distributed throughout the year. The power output at the fiber’s distal end was measured with an Ophir Ltd pyrometer-detector power meter, and the normal solar beam irradiance was measured with an Eppley normalincidence pyrheliometer. There was no measurable degradation of the optical or mechanical elements due to outdoor exposure during our experiments. A future task is establishing whether the dearth of degradation persists with long-term continuous operation. The pyrheliometer has a full acceptance angle of 0.100 radian. Our concentrator, however, is designed for the far smaller angular extent of the solar disk. We had no direct measurement of circumsolar radiation. For solar climates similar to that in Sede Boqer, clear-day circumsolar fractions tend to be in the range of 1–6% (Rabl, 1985; Gueymard, 2001). We conservatively adopted a nominal uniform correction from measured solar beam to collectible radiation of 0.98. Typical measured values are: (1) a remote power delivery of 8 W, (2) at a collectible solar beam irradiance of 900 W m 22 . With a fiber core
Table 1. Representative and repeatable experimental results for our solar fiber-optic mini-dish prototype, for nominal fiber lengths of 1, 7 and 20 m a Component
Protective glazing with anti-reflective coating Paraboloidal mini-dish mirror Small flat secondary mirror Air–quartz interface at the fiber tips (per tip) Light leakage from fiber core to cladding: 1 meter fiber 7 meter fiber 20 meter fiber Attenuation in the fiber core Net prototype throughput with: 1 meter fiber 7 meter fiber 20 meter fiber
Measured optical throughput
Improved optical throughput attainable with existing materials or production techniques
0.97 0.96 0.96
0.97 0.97 0.97
0.96
0.99 0.99
0.87 0.82 0.79 0.99
0.99 0.88
0.71 0.66 0.64
Maximum possible flux concentration in a loss-less system5(NA /us )2 517.4 kilosuns Maximum flux concentration with real materials and improved optical throughput515.3 kilosuns Representative experimental results for: Optical fiber core diameter51.0060.03 mm, fiber nominal NA50.66 Effective solar angular radius (incorporating all optical errors) us 5 0.005 radian Fiber length
Measured power output from distal fiber tip (W)
Measured normal beam irradiance (W m 22 )
Power density attained experimentally (W m 22 )
Corresponding flux concentration (kilosuns)
Predicted flux concentration including losses (kilosuns)
1.1 m 7.2 m 20.0 m
7.8560.3 8.160.3 8.160.3
838620 921620 931620
10.060.6 10.360.6 10.360.6
11.960.8 11.560.8 11.160.8
12.460.8 11.560.8 11.260.8
a We also include detailed accounting of optical performance on a component-by-component basis. The performance of each element individually is based on our indoor laboratory measurements.
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diameter of 1.0 mm, this corresponds to a flux concentration of more than 11 kilosuns. Representative measurements are summarized in Table 1 for three different fiber lengths, along with the predictable optical losses associated solely with material properties. The predicted flux levels are consistent with our measured values, to within the experimental uncertainty. The agreement between the measured outdoor performance of the assembled prototype and the projections would appear to indicate that all key effects have been accounted for. Also included are the potential improvements attainable with existing materials and technologies, i.e., without the need for future advances in optical surfaces or production techniques.
9. OBSERVATIONS AND QUALIFICATIONS
Our mini-dish prototype was purposely slightly oversized in order to accommodate fibers of varying diameter and NA. That means that the NA of the mini-dish (0.707) is larger than that of the optical fiber (0.66), and that both the dish focal length and diameter could have been smaller. A mini-dish with the uniform-flux core region of its focal spot equal to the fiber core diameter, d fiber 5 1.00 mm, would have F 5 100 mm and D 5 151 mm. Alternatively expressed, whereas our actual mini-dish typically intercepted 28 watts of collectible solar beam irradiation (of 900 W m 22 ), a mini-dish exactly matched to the fibers would intercept 16 watts. Given known material properties and our ability to account for all system losses (Table 1), we can assess that the power density produced in the core region of the focal spot of the mini-dish was approximately 15.4 kilosuns. The attainable flux concentration can be noticeably improved exclusively through the use of superior existing materials and technologies, i.e., without the need for future advances in material or production technologies. Hence we have included in Table 1 what we view as tenable projections of the performance of solar fiber-optic mini-dishes of the type we have designed, built and tested. Optical fibers with core diameters up to 2.0 mm are commercially available, but only for noticeably lower NA. The highest nominal NA value, for which we found optical fibers with core diameters of 1.5 and 2.0 mm at admissibly low attenuation over the solar spectrum, was 0.4. These largediameter fibers have enough mechanical flexibility to remain robust in solar concentrator systems.
They might enhance cost-effectiveness by reducing the number of fibers per unit of collection area. Our mini-dishes were diamond turned. This was the only feasible method we identified for producing a handful of precision concentrators. Diamond-turned devices are inherently expensive, and could not be deemed economically feasible for large mini-dish systems. A workable alternative is preparing a die and mold-injecting minidishes in mass production (with subsequent mirror deposition). With a precision die, the price for creating and coating a mini-dish would be dramatically less than the diamond-turning procedure: about several US$ per mirrored mini-dish at very high volume production. But the precision die typically costs of the order of tens of thousands of US$ (G-S, 2002; Syntec, 2002). A future mini-dish system of sufficient extent could benefit from this economy of scale, and could thereby advance the demonstration of economic and technical feasibility. Finally, a recent outgrowth of our experimental program is high-flux photovoltaic power generation with advanced multi-junction semiconductors. The concept was originally delineated in Feuermann and Gordon (2001a), and subsequently commissioned for experimental realization (Reddy et al., 2001).
10. SUMMARY
In the first phase of our solar fiber-optic minidish program, the primary milestones included: 1. The experimental realization of our proposed solar fiber-optic mini-dish, including the design, construction, and testing of an operational prototype. We have demonstrated the collection, concentration and transmission of sunlight to remote targets. Discussions with producers of molds and injection-molded optical elements indicate that the miniaturized units (200 mm in diameter, with a focal length of 120 mm) are well suited to mass production. 2. The measurement of flux concentration exceeding 11 kilosuns at a remote receiver (20 m removed), solely from the fiber-optic mini-dish (primary) concentrator. Flux levels in the encased mini-dish at the proximate fiber tip exceed 15 kilosuns, for a system with a numerical aperture of 0.66. There appear to be no unaccounted-for loss mechanisms, i.e., we can confidently project optical performance from known material properties. It should be feas-
Solar fiber-optic mini-dish concentrators: first experimental results and field experience
ible eventually to attain up to 30% higher flux concentration, based wholly on available materials and existing production technologies. 3. Testing the tracking accuracy of small dualaxis trackers suitable for miniaturized highconcentration units, and establishing a tolerance of 60.058. 4. An experimental study of the measurement of the angular transmission characteristics of optical fibers suitable for high-flux solar uses, including the discovery of deleterious light leakage (Feuermann et al., 2002). A theoretical model that can account for these observations permits distinguishing between inherent limitations versus technological problems for the design and selection of optical fibers for future systems. 5. The design, fabrication and preliminary testing of sculpted optical fiber tips that serve as secondary concentrators intended to markedly increase delivered power density as desired for solar surgery. 6. The absence of noticeable thermal, optical or material degradation in any system component. The second phase of our experimental program will focus on: (a) the construction and testing of large multi-unit modules; (b) measuring long-term continuous outdoor performance toward establishing system robustness; (c) fabricating and demonstrating secondary concentrators relatively free of manufacturing defects, that can actually approach the thermodynamic limit to concentration; and (d) demonstrating solar surgical (biomedical) procedures.
NOMENCLATURE Cflux C max flux C max 2 C core flux C avg flux D d fiber d min d max F f kilosun n NA
flux concentration thermodynamic limit for (overall) flux concentration thermodynamic limit for the flux concentration boost from a secondary concentrator flux concentration in the uniform-flux core region of the focal spot of a paraboloidal dish flux concentration averaged over the full focal spot of a paraboloidal dish paraboloidal dish diameter optical fiber core diameter diameter of the maximum-flux core region in the focal spot of the paraboloidal dish focal spot diameter that encompasses all reflected rays of the paraboloidal dish focal length f-number of paraboloidal dish 10 3 suns (flux concentration) refractive index of the medium into which concentrated sunlight is extracted numerical aperture
f uair us
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rim half-angle of the paraboloidal dish half-angle of acceptance of the optical fiber effective solar angular radius
Acknowledgements—This research was supported by grants from the Israel Ministry of National Infrastructures (Jerusalem) and the Rita Altura Foundation (Los Angeles, CA). We are indebted to Michael Altura for his encouragement and sponsorship. We thank Jonathan Molcho of Ben-Gurion University’s Department of Electrical and Computer Engineering for generously granting the use of facilities and space in his laboratory, as well as his valuable recommendations in the selection of measurement equipment. We are also grateful to David Faiman of Ben-Gurion University’s Blaustein Institute for Desert Research for the use of facilities and technical assistance at the Ben-Gurion National Solar Energy Center.
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