Roland Winston Schools of Engineering &Natural Sciences The University of California, Merced

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1 Nonimaging Optics Applications in Solar Generation Contemporary Energy Issues EE 290N UC Berkeley March 2, 2009 Roland Winston Schools of Engineering &Natural Sciences The University of California, Merced KAON 2005 International Workshop, Northwestern University, June 13-17

2 Limits to Concentration from max sun ~ 0.5 we measure sun ~ 6000 (5670 ) Then from T 4 - solar surface flux~ 58.6 W/mm 2 The solar constant ~ 1.35 mw/mm 2 The second law of thermodynamics C max ~ 44,000 Coincidentally, C max = 1/sin 2

3 1/sin 2 θ Law of Maximum Concentration The irradiance, of sunlight, I, falls off as 1/r 2 so that at the orbit of earth, I 2 is 1/sin 2 θ xi 1, the irradiance emitted at the sun s surface. The 2 nd Law of Thermodynamics forbids concentrating I 2 to levels greater than I 1, since this would correspond to a brightness temperature greater than that of the sun. In a medium of refractive index n, one is allowed an additional factor of n 2 so that the equation can be generalized for an absorber immersed in a refractive medium as Nonimaging Optics 3

4 During a seminar at the Raman Institute (Bangalore) in 2000, Prof. V. Radhakrishnan asked me: How does geometrical optics know the second law of thermodynamics?

5 First and Second Law of Thermodynamics NIO is the theory of maximal efficiency radiative transfer It is axiomatic and algorithmic based As such, the subject depends much more on thermodynamics than on optics `

7 Chandra

8 B 3 P B 3 Q B 1 B 2 B 1 B 2 B 4 Q (a) (b) P Radiative transfer between walls in an enclosure

9 Strings 3-walls F12 = (A1 + A2 A3)/(2A1) 1 3 F13 = (A1 + A3 A2)/(2A1) F23 = (A2 + A3 A1)/(2A2) 2 qij = AiFij Fii = 0 F12 + F13 = 1 F21 + F23 = 1 F31 + F32 = 1 Ai Fij = Aj Fji 3 Eqs 3 Eqs

10 Strings 4-walls F12 + F13 + F14 = 1 F21 + F23 + F24 = 1 F14 = [(A5 + A6) (A2 + A3)]/(2A1) F23 = [(A5 + A6) (A1 + A4)]/(2A2)

11 Limit to Concentration F23 = [(A5 + A6) (A1 + A4)]/(2A2) = sin( as A3 goes to infinity This rotates for symmetric systems To sin 2 ( )

12 the string method slider 2D concentrator with acceptance (half) angle string absorbing surface

13 the string method

14 the string method

15 the string method

16 the string method

17 the string method stop here, because slope becomes infinite

18 the string method

19 Nonimaging Optics Fundamentals Edge-ray wave front C The Edge-Ray Principle A A Β'Α ΑC B' A B A BB' AC Β' Β Β Α' AA' sin AA' BB' / sin Compound Parabolic Concentrator (CPC) (tilted parabola sections) B B

20 Nonimaging Optics Fundamentals Edge-ray wave front C The Edge-Ray Principle A A 2D étendue = A A sin AA' BB' sin concentration limit in 2D! / B B 2D étendue = B B sin( /2) = B B

21 2D cylindrical optics: nonimaging optics basics: the string example: collimator for a tubular light source 2 R/sin slider method étendue conserved ideal design! tubular light source R kind of involute of the circle 21

22 Analogy of Fluid Dynamics and Optics fluid dynamics optics phase space (twice the dimensions of ordinary space ) general etendue positions momenta incompressible fluid positions directions of light rays multiplied by the index of refraction of the medium volume in phase space is conserved Nonimaging Optics 22

23 Imaging in Phase Space Example: points on a line. An imaging system is required to map those points on another line, called the image, without scrambling the points. In phase space Each point becomes a vertical line and the system is required to faithfully map line onto line. Nonimaging Optics 23

24 Edge-ray Principle Consider only the boundary or edge of all the rays. All we require is that the boundary is transported from the source to the target. The interior rays will come along. They cannot leak out because were they to cross the boundary they would first become the boundary, and it is the boundary that is being transported. Nonimaging Optics 24

25 Edge-ray Principle It is very much like transporting a container of an incompressible fluid, say water. The volume of container of rays is unchanged in the process. conservation of phase space volume. The fact that elements inside the container mix or the container itself is deformed is of no consequence. Nonimaging Optics 25

26 Edge-ray Principle To carry the analogy a bit further, suppose one were faced with the task of transporting a vessel (the volume in phase-space) filled with alphabet blocks spelling out a message. Then one would have to take care not to shake the container and thereby scramble the blocks. But if one merely needs to transport the blocks without regard to the message, the task is much easier. Nonimaging Optics 26

27 Nonimaging Optics 27

28 BRIGHTER THAN THE SUN an experiment on the roof of the U of C HEP Building Roof top Physics

29 Ultra High Flux Experiment

34 Availability of Solar Flux over a range Suns Conc.= 1-4 Fixed Heating&Cooling, PV Conc.= Conc.= ,000 1 axis tracking and seasonal 2 axis tracking (dish&tower) Power generation, Heating&Cooling, Low CPV Power generation High CPV Conc.= 20, ,000 2 axis tracking Solar Furnace, Materials, Lasers, Space Propulsion, Experiments

35 Can a Stationary Solar Concentrator Exist? C parabolic trough <= 1/ sin30 0 << 1! (NO) C nature = 1/sin30 0 = 2! (Yes) A factor 2 is significant for thermal conversion permitting T = C For PV conversion, C is boosted by index of refraction (say, n=1.5) C=3-4 for fixed concentrators For tracking concentrators C can be 100,000!

36 Flat plate collectors are limited to temperatures below 100 C 80% 70% Compound Parabolic Concentrator Efficiency 60% 50% 40% 30% 20% 10% 0% Flat plate collector Temperature above ambient [ C] (for 1,000 W/m 2 )

38 Engine 26 Fire House in Chicago

39 UC Merced 250C Thermal Test Loop

40 Coriolis Force Flow Meter

41 XCPC Solar Thermal Collector at UC Merced Solar Testing Facility

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51 70.00% 65.00% Efficiency vs Temperature U-Tube 60.00% 55.00% 50.00% 45.00% 40.00% 80g/s NS 100g/s NS 120g/s NS 140g/s NS 80g/s EW 100g/s EW 120g/s 35.00% 30.00% Temperature [C]

52 60.00% 50.00% 40.00% 30.00% Efficiency (PSolRad) 20.00% 10.00% 0.00% Azimuth Angle

54 PALO ALTO WATER SolFocus Array

55 3D Rendering of Our New Design PMMA cover Secondary mirror Solar cell on heat spreader Primary mirror Heat sink

56 Features of Our New Design Light impinging on the primary mirror is not focused onto the cell, but onto the secondary mirror This results in a uniform cell illumination with an average concentration of 500 suns Secondary mirror Light radially distributed along cell Focal ring on secondary mirror Primary mirror

57 Dimensions (in mm)

58 Theoretical limit (n=1.5; 60 exit angle) Theoretical limit (n=1; 60 exit angle) Dielectric TIR Aplanat (circular) XR (circular) Two aplanatic (air filled) mirrors + prism Two aplanatic (glass filled) mirrors Fresnel lens without secondary AR... Aspectratio (depth/aperture diameter) 3 2 AR=0.3 AR=0.3 AR=0.6 1 AR=0.3 0 AR= ,000 1,200 1,400 58

59 With Apologies to Benny Goodman It don t mean a thing If it doesn t have Sin =n/ C

60 California State Mining Mineral Museum

artifacts, rare specimens of crystalline gold, well as mineral specimens from

61 The Client Fricot Nugget Needs & Wants Redesigned fixture lighting Redesigned spot lighting No heat No UV Museum contains over 13,000 objects including mining artifacts, rare specimens of crystalline gold, well as mineral specimens from California and around the world. Historical relevance form CA s birth as gold country

62 Day Lighting System How it works

63 Sunlight enters primary mirror

64 Light is reflected to secondary mirror Reflects back down to glass filter Light then propagates to Large Core Plastic Optic Fiber (LCPOF)

65 Direct Sunlight Light Out Concentrated 500X Light Tube

66 Refurbishing the Lighting Lab

67 Construction Team Stair s

68 Testing and Data 1 meter diameter circle 5 rings

69 Data Analysis Light Output Being Measured = 446 Lumens Light from 60 Watt light bulb = 870 Lumens

70 Data Analysis First Quadrant Lux Gradient:

71 Data Analysis Contour plots of the Lux gradients from one tube: 1 Lux = 1 Lumen/m 2

72 Design Issues Problem: Light Discoloration Solution: Theatrical Lighting Film

73 Design Issues Problem: Tracker Stepping Solution: Take readings at the instant of brightest light

74 Future Goals Next Semester Complete More Testing Ready tracker for installation at CSMMM Construct Replica Display Box Overall Goals Developing a ballast system for hybrid lighting Lighting the existing museum Developing plans for lighting the new museum

75 What s Ahead? Can we evade the Etendue limit of Concentration? YES, by down-shifting the solar spectrum. R. L Garwin (1960), Eli Yablonvitch (1980) and others Nonimaging Optics 75

76 Recall, B=dP/dAdLdM so P/A = [BdLdM] another useful relation, B= (1/ P/Mode Now, [dldm] = sin 2 so the best we can do with optics is to boost P/A by 1/sin 2 But if we down-shift the solar spectrum B can be boosted by exp[h( which is >>>>>1! Nonimaging Optics 76

77 Thank you

An Evacuated PV/Thermal Hybrid Collector with the Tube/XCPC design

An Evacuated PV/Thermal Hybrid Collector with the Tube/XCPC design Lun Jiang Chuanjin Lan Yong Sin Kim Yanbao Ma Roland Winston University of California, Merced 4200 N.Lake Rd, Merced CA 95348 ljiang2@ucmerced.edu