University of Nevada, Reno

University of Nevada, Reno

Infrared Non-Imaging Device for a Full-Spectrum Solar Energy System

A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering

By Daniel J. Dye Dr. Byard D. Wood, Thesis Advisor May 2003

© Daniel James Dye (2003)

We recommend that the thesis prepared under our supervision by DANIEL JAMES DYE entitled Infrared Non-Imaging Device for a Full-Spectrum Solar Energy System be accepted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE

Byard Wood, Ph.D., Advisor Jeff Muhs, M.S., Committee Member Ronald Phaneuf, Ph.D., At-Large Member Marsha H. Read, Ph.D., Associate Dean, Graduate School

May, 2003

i ABSTRACT

A full-spectrum solar collector/receiver system is being designed by a research team lead by Oak Ridge National Laboratory and the University of Nevada, Reno. This solar energy system is unique in that it utilizes the majority of the solar spectrum by splitting the visible light and the infrared (IR) energy for two different end uses.

This research is concerned with the optics that will provide uniform irradiance of the IR energy on the thermophotovoltaic (TPV) array. The benchmark full-spectrum collector/receiver and prototype TPV array have been built, so the work performed here is to match the two systems together. A non-imaging (NI) system for the IR flux incident on the TPV array mounted behind the secondary mirror is designed. Several different cross-sectional shapes, as well as reflective and refractive tubes are investigated. It is shown that a rectangular-shaped, hollow, internal-reflecting tube is the best choice for the benchmark system.

ii ACKNOWLEDGEMENTS I wish to express my gratitude to my advisor, Dr. Byard Wood, for his guidance, encouragement, and support in this research project. I would also like to thank him for giving me the opportunity to work with him on this project. I would like to thank Dr. Ronald Phaneuf and Jeff Muhs for serving on my thesis committee. I would especially like to thank my wife, Nichole Dye, and my parents, Steve and Carol Paulsen, for their tremendous support, encouragement, and enthusiasm in this portion and in all of my education. Thanks are due to my fellow students in the Energy Systems Laboratory that are working on this project. Their support and team work has made this an enjoyable project to work on. There are several team members on this project, including Oak Ridge National Laboratory, J.X. Crystals, and 3M, that have assisted me and given me insight into this project, and I would like to express my gratitude to them as well. Thanks are also due to Mike Lemich, the Mechanical Engineering department’s machinist, for his assistance in building the non-imaging test device and structure for the tracking system. This project was funded in part by: Cooperative Agreement, DE-FC26-01NT41164 National Energy Technology Laboratory, United States Department of Energy

iii TABLE OF CONTENTS

ABSTRACT ACKNOWLEDGEMENTS LIST OF TABLES LIST OF FIGURES CHAPTER 1 2

3

4

5

References Appendix A B C

INTRODUCTION LITERATURE REVIEW 2.0 Introduction 2.1 Thermophotovoltaic Cells 2.2 Non-Imaging Optics 2.3 Conclusions MODELING 3.0 Introduction 3.1 Benchmark System Model 3.2 TracePro Modeling 3.3 Post Processing ANALYSIS OF THE NON-IMAGING DEVICE FOR THE FULL-SPECTRUM SOLAR ENERGY SYSTEM 4.0 Introduction 4.1 Focal Point Length-to-Diameter Ratio Effects on NonImaging Devices 4.2 Geometric Configuration of the First Generation Non-Imaging Device 4.3 Refractive and Reflective Tubes for the Benchmark System Non-Imaging Device CONCLUSIONS 5.0 Introduction 5.1 Square Refractive and Reflective Tubes for Non-Imaging Devices 5.2 Non-Imaging Device for the Full-Spectrum Solar Energy System 5.3 Non-Imaging Device Testing

Page i ii iv v 1 9 9 10 11 14 15 15 16 21 32 34 34 35 57 70 74 74 74 76 78 84

ASTM E891-82 Direct Normal Irradiance Table SMARTS v. 2.9.1 Input TracePro Sample Flux Report

86 89 90

iv LIST OF TABLES TABLE 2.1 2.2 4.1 4.2 4.3 4.4 4.5 4.6

Summary Performance of the GaSb Cell TPV Array Performance Results Coefficients used in Equation 4.1 Non-Imaging Device Results Rectangular, Silhouette, Octagonal, and Cylindrical Tube Results TPV Array Configuration Options Comparison Between HIR and TIR Tubes for the 100 Cell TPV Array Comparison Between HIR and TIR Tubes for the 96 Cell TPV Array

Page 10 11 38 54 68 71 73 73

v LIST OF FIGURES FIGURE 1.1 1.2 1.3 1.4 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 3.14 3.15 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 4.14

Full-spectrum solar energy system with hybrid lighting Benchmark full-spectrum collector/receiver Photobioreactor concept using concentrated day-lighting Secondary mirror assembly and fiber optic cable array Primary parabolic mirror Secondary mirror assembly Full-spectrum collector/receiver assembly Primary parabolic mirror spectral response Secondary mirror spectral response Air Mass 1.5 direct normal irradiance spectrum reflected off the primary mirror Air Mass 1.5 direct normal irradiance spectrum transmitted through the secondary mirror Insert object menus in TracePro Apply properties menu Raytrace options menu Grid raytrace menu Flux variation versus ray flux from the source Example 2-D incident flux map Sample Scheme code 3-D flux map from MathCAD Solar concentrating system used in analysis Silica index of refraction for 0.7 < λ < 1.8 µm Incident angles at focal point (β), slope (α), focal length (f), diameter (D), radius (r), and outer radius (R) Average focal point incident angle versus f/D ratio of the parabolic mirror Refracted ray when n1 < n2. β is the incident angle and γ is the refracted angle Average exit aperture incident angle for HIR and TIR tubes Histograms of entrance and exit aperture angular distribution Rays at entrance region of HIR and TIR tubes Reflectivity and transmissivity versus incident angle Minimum cell flux on the target PV array versus NI tube length/width ratio Minimum-to-average flux ratio versus NI tube length-to-width ratio Average flux versus NI tube length for f/D = 0.5 Length-to-width ratio versus f/D ratio at the peak minimum flux point Modified Cassegrain full-spectrum collector/receiver with NI device

Page 2 3 4 5 17 17 18 19 19 20 20 22 23 25 26 27 29 31 33 36 38 40 41 42 43 44 45 46 48 51 53 55 57

vi FIGURE 4.15 4.16 4.17 4.18 4.19 4.20 4.21 4.22 4.23 4.24 4.25 5.1 5.2 5.3 5.4 5.5

Raytrace figures show path of solar irradiance through optics Non-imaging geometries investigated 100 cell GaSb TPV array 100 cell GaSb TPV array side view AM 1.0 direct normal solar irradiation curve Flux distributions at different lengths of the rectangular NI device Comparison of the four configurations investigated over the length of the NI device Comparison of the three non-cylindrical geometries Minimum-to-average flux ratio versus NI tube length Minimum flux versus NI tube length 100 cell and proposed 96 cell TPV arrays NI device test setup 46.5 in. parabolic spun aluminum mirror from D.H. Satellite Mirror with ReflecTech coating Spectral reflectivity of ReflecTech coating Tracking system

Page 58 59 60 61 62 63 64 65 66 67 72 79 80 81 81 83

1

CHAPTER 1 INTRODUCTION

A research team has been formed to develop a full-spectrum solar energy system that can provide both day-lighting and electricity generation [1]. This team, lead by the University of Nevada, Reno (UNR) and Oak Ridge National Laboratory (ORNL), is comprised of several universities, national laboratories, and industry partners. UNR has held a leadership role in the project, as well as performed research on the various technical challenges the project has faced. These challenges will be described briefly and the relevance of the research to the full-spectrum solar energy system will be shown in the subsequent chapters.

A full-spectrum solar energy system has the potential to greatly increase the efficiency of solar energy systems [2, 3]. Until now, the dominant solar energy systems have collected energy for thermal uses, electricity generation, or day-lighting. These systems generally utilize one portion of the solar spectrum and waste the rest. For example, standard silicon photovoltaic (PV) cells are only responsive up to 1.15 µm, which is only a portion of the full solar spectrum, and combined with reflection and other losses the maximum theoretical efficiency is only 23% [4, 5]. If a system can utilize the majority of the spectrum, such as the visible portion for day-lighting and the infrared (IR) portion for electrical or thermal uses, then it has significant advantages and potential over current solar energy systems.

2 Figure 1.1 shows the concept of a full-spectrum system with hybrid lighting luminaires in an interior room.

Figure 1.1: Full-spectrum solar energy system with hybrid lighting. Adapted from [1]

A benchmark solar collector/receiver system for a full-spectrum solar energy system is being designed and built by the research team lead by UNR and ORNL to demonstrate the technical feasibility of this type of system. This solar energy system is unique in that it utilizes the majority of the solar spectrum by splitting the IR energy and visible light for two different end uses. The visible light will be used for day-lighting and the IR energy for electrical power generation. For day-lighting purposes, it is often necessary to remove the IR energy before the light enters the room to avoid excessive heating loads.

3 Also, in transmitting day-light through fiber optic cables or light guides, it is necessary to remove the IR energy before transmission so it will not destroy the cables. While the majority of the energy delivered from the collector/receiver will be in the visible spectrum, capturing and using the available IR energy as opposed to simply separating and wasting it can represent an increase in overall system efficiency.

The benchmark collector/receiver is a modified Cassegrain system that uses a large parabolic mirror and a secondary mirror comprised of multiple planar segments, as shown in Figure 1.2. The secondary mirror’s segments have a spectrally selective cold mirror coating that lets IR energy pass through while reflecting the visible light.

Figure 1.2: Benchmark full-spectrum collector/receiver. Adapted from [1]

4 The benchmark collector/receiver system built at ORNL has demonstrated effective collection and transfer of the visible portion of the solar spectrum, but no work has been done on the IR portion. The visible portion of the solar spectrum is separated from the IR at the secondary mirror and concentrated at the entrance of multiple fiber optic cables on an array. Transmittance of the day-light is currently through 3M’s large core plastic optical fibers [6]. These optical fibers will be connected to hybrid luminaires for daylighting or photobioreactors for CO2 mitigation. Figure 1.1 shows the concept for interior day-lighting, while Figure 1.3 shows the concept for a photobioreactor.

Figure 1.3: Photobioreactor concept using concentrated day-lighting. Adapted from [7]

5 It is important that the IR energy be separated from the light entering the fiber optic cables or the lifespan of the cables will be extremely short. If even a portion of the IR energy is directed into the cables, excessive heat fluxes will occur and the fibers will burn. The IR spectrum is, therefore, passed through the secondary optics of the collector, as well as absorbed by filters or quartz rods at the fiber entrance. Pictures of the prototype secondary mirror are shown in Figure 1.4.

Figure 1.4: Secondary mirror assembly and fiber optic cable array. Adapted from [1, 8]

6 The majority of the IR energy that passes through the secondary mirror is concentrated at the focal point of the primary mirror. Instead of wasting this energy by dissipating it behind the secondary mirror, special PV cells can easily be used to convert it into electricity. In order to don the title “Full-Spectrum Solar Energy System,” the IR portion of solar irradiance, representing approximately 58% of Air Mass 1.5 direct normal irradiance, must be utilized. The simplest use of this IR energy is for PV cells tailored to this spectrum. Gallium antimonide (GaSb) thermophotovoltaic (TPV) cells, developed by JX Crystals [9], are responsive to the spectrum 0.7 µm < λ < 1.8 µm which represents 90% of the IR irradiance, or 53% of the total solar irradiance of Air Mass 1.5. TPV cells, such as GaSb, are more tailored to the IR spectrum, where standard PV cells are more tailored to the visible spectrum. Compared with standard silicon cells, which can only capture the spectrum out to approximately 1.15 µm, the GaSb cells represent a much better utilization of the IR energy.

The research presented here is concerned with the optics that will provide uniform irradiance of the IR energy on the TPV array. JX Crystals has produced a TPV array to be used with a 2.5 m2 parabolic primary mirror [10], but this array is not optimized for use in the small 1 m2 benchmark system. This array will work with the benchmark system, but due to the size and shape of the array it will not demonstrate the true potential power generation of the integrated PV in the benchmark full-spectrum system. Despite this fact, a non-imaging (NI) device will be designed to couple this array with the benchmark system.

7 The work performed here is to develop optical components to combine the existing benchmark collector/receiver and TPV systems for optimal performance. Several configurations were investigated to see which cross-sectional geometry would provide the maximum transfer efficiency and lowest flux variation. The transmission of a solid total internal reflecting (TIR) tube and a hollow internal reflecting (HIR) tube were also compared to determine which system would produce the best results for the benchmark collector and TPV array. These systems were chosen because they were the most widely suggested and analyzed types of NI devices in the literature. The optimum transmission efficiency of this system will be presented and recommendations for a better matched TPV array for the benchmark system will be made.

The effect that the focal length-to-diameter (f/D) ratio has on the required length of a NI device is also investigated in this research. The benchmark system has a relatively short f/D ratio, which causes high reflection losses at the entrance of the TIR tube or on the inside reflecting walls of the HIR tube. In the future, longer f/D ratios of the primary mirror could be used, which would decrease reflection losses if a refractive NI device is used, as well as possibly decrease the entrance angles into the fiber optic cables. This could have negative effects on the overall alignment and tracking requirements of the system, so system optimization modeling will be required. The results of the raytrace analysis will be presented and conclusions will be made about the optimum tube length of the NI device versus the f/D ratio.

8 The optical representation of the full-spectrum collector/receiver and the design iterations of the NI device were performed with TracePro versions 2.4 to 3.0. An accurate solid model was built based on shop drawings and manufacturer specifications that allowed for the quick implementation and testing of different component designs. The visible optics of this model compared well with experimental data, so it was used extensively in the modeling of the IR optics. More details on modeling are presented in Chapter 3 and the results of the modeling will be presented in Chapter 4.

9

CHAPTER TWO LITERATURE REVIEW

2.0 Introduction

Several papers were reviewed to obtain a background on the operation and performance of thermophotovoltaics (TPV) and solar collectors. Specifically, high concentration dishes and the required secondary optics were investigated to obtain an idea of how the optics work and how well they should perform.

JX Crystals has produced a TPV array to be used with a 2.5 m2 parabolic primary mirror. This array will be used with the 1 m2 benchmark system, but it is not optimized for this system and will therefore not demonstrate the full potential of the integrated photovoltaics (PV). However, there are a couple of papers describing the performance of gallium antimonide (GaSb) TPV cells and how these cells perform in an array.

For the non-imaging (NI) device investigation, a few papers were looked at that discussed NI optics for square-shaped target planes. One paper was reviewed that supported the conclusions of the raytracing analysis and lead to the comparison of the hollow internal reflecting (HIR) and total internal reflecting (TIR) systems. Papers were found that dealt with both types of systems, and the collection efficiency of these systems are comparable.

10 2.1 Thermophotovoltaic Cells

The GaSb cells chosen for use with the full-spectrum collector/receiver have been tested both individually under varying solar concentrations and as an array under flash-test conditions. The results of these tests will be presented here.

During individual cell testing, Table 2.1 was produced summarizing the performance of the GaSb cells [9]. The tests were performed with a single GaSb cell placed at the focal point of a 20 in. parabolic concentrator and a cold mirror in front of the TPV cell to reflect the visible spectrum and transmit the infrared (IR) spectrum to the cell. The cold mirror used in these tests is comparable to the one used on the benchmark system.

Table 2.1: Summary Performance of the GaSb Cell. Adapted from [9] (a) Solar IR Power to IR Flux Density Cell Temp Max Power Cell 2 Cell [W] [C] [W] Efficiency [W/cm ] Concentration(b) Vmax [V] Imax [A] 4.92 3.936 97 0.346 0.98 0.399 6.89 6.4 5.12 125 18 0.377 1.683 0.634 9.91 8.28 6.624 162 18 0.38 2.413 0.917 11.07 10.84 8.672 213 20 0.387 3.898 1.507 13.9 11.04 8.832 217 0.392 3.55 1.392 12.61 17.85 14.28 351 27 0.38 7.252 2.756 15.4 19.14 15.312 376 30 0.373 7.81 2.916 15.24 24.01 19.208 472 34 0.363 9.72 3.528 14.7 (a): Based on the cell aperture 10mm x 12.5mm 2 (b): Based on the 1-sun AM1.5 (global) flux that passes through the cold mirror = 0.040725W/cm .

The highest efficiency reached during testing was 15.4%, which the author claims matches the theoretical efficiency of 16%. With an anti-reflective coating, this efficiency should reach 18%.

11 The array to be used with the full-spectrum solar energy system was then designed and built by JX Crystals for a conceptual 2.5 m2 parabolic concentrator [10]. NI optics would be required to uniformly distribute the high intensity IR flux evenly across the array surface and a 5 W fan and heat sink would be required on the back of the TPV array to cool the cells for better performance. The array is built by mounting the individual cells in a shingle fashion on a thin dielectric layer on a metal substrate. The cells are then soldered together into rows and the rows are wired in series to complete the circuit. The 180 cm2 array is expected to produce 175 W from the 2.5 m2 concentrator. The results from the array tests are presented in Table 2.2 [10]. The irradiance, flash-test source spectrum, and cell temperatures were not provided.

Table 2.2: TPV Array Performance Results. Adapted from [10]

Isc Voc Imax Vmax Pmax

= = = = =

5.70 A 47.72 V 5.13 A 34.52 V 177.16 W

2.2 Non-Imaging Optics

In order for the designed TPV array or any PV array to work efficiently in a solar concentrating system, some type of NI optics must be employed to uniformly distribute the flux over the array surface to ensure that all cells receive equal flux. Most of the

12 work done with NI optics has been for small concentrators such as parabolic mirrors and Fresnel lenses with individual PV cells as their target. Several of these small concentrating PV systems would then need to be connected to form a large array with usable power generation. This would require that each of the individual concentrators be aligned with the NI device (if the system has one) and PV cell, and that each of the concentrators track the sun with equal precision. A simpler system would be a large concentrating mirror or lens with a NI device and array of PV cells. In this system, there is only one optical system to align instead of several individual systems. Both systems would require two-axis tracking.

A square, refractive NI device has been proposed for use with parabolic concentrators [11]. The research considered several options, and results indicated that for a concentrator with a focal point to diameter (f/D) ratio of 0.6, a square shaped solid tube of fused silica would produce the desired flux uniformity of ± 5% and better than 90% transfer of the collected full-spectrum irradiance. It is noted that there will be losses at the entrance of the refractive tube, but nearly all of the light that enters the tube will reach the exit aperture due to total internal reflection.

In one work performed on designing 1000-sun solar concentrator systems based on miniature parabolic dishes [12], overall optical efficiencies were predicted to be 8% with anti-reflective coatings or about 75% without anti-reflective coatings. With gallium arsenide (GaAs) PV cell efficiencies around 22-28%, the overall system efficiency of 20% is realistic. This is a system comprised of a 10 cm parabolic mirror, planar

13 secondary mirror, and a refractive square-shaped tube transmitting the solar irradiance to the single PV cell which is placed on a heat sink to passively manage the cell temperature. An array of these miniature dishes would be placed behind a glazing on a rack and they would simultaneously track the sun. In order for this to work well, each individual optical system would have to be aligned to the array.

In a paper describing kaleidoscope-based secondary optics for large area paraboloidal dishes [13], the authors point out that there are three objectives that need to be fulfilled: maximum collection efficiency, uniform irradiance on the absorber, and desired solar flux concentration. Given a paraboloidal mirror and a prescribed maximum flux level for the absorber, it is possible to design the secondary optics to reach but not exceed the maximum flux allowed. If the absorber can be sized to any area desirable, then the concentration ratio on the absorber can easily be tailored. The authors show that with an HIR NI tube, or kaleidoscope, with a reflectivity of 90%, very good results can be obtained. They show that with a hexagonal-shaped kaleidoscope, in front of a 400 m2 dish with a hexagonal aperture, the minimum to maximum flux ratio can be 0.94, while the transmission losses are only about 7.5% for the 90% reflective mirrors. This high flux transmission is due to the fact that not all rays are reflected off the walls before striking the absorber.

14 2.3 Conclusions

There are several papers which give ideas on how to design NI devices and how the design should perform. However, due to the specific geometry of the prototype TPV array that will be used, none of these papers provide a design that could readily be used with the benchmark system. The process of trying several different options and performing a detailed spectral raytrace analysis will have to be performed.

15

CHAPTER 3 MODELING

3.0 Introduction

The majority of the modeling performed for this research was done with TracePro version 3.0 [14]. Post-processing of data was performed primarily with Microsoft Excel version 2002, with MathCAD version 2001 performing calculations of incident angles, refracted angles, concentration, etc. Occasionally, AutoCAD version 2002 was used for modeling the system before importing it into TracePro, but for the most part the threedimensional system models were built directly in TracePro. The system models of the benchmark collector/receiver are shown below, exactly as they were modeled in TracePro. Also, the methods used to build models, define raytrace sources such as solar irradiance, and analyze the data or export it for post-processing are shown. Equations used in Excel for processing the data to obtain incident angles and flux variations are also presented.

16

3.1 Benchmark System Model

3.1.0 Introduction

The benchmark collector/receiver system, exactly as built at Oak Ridge National Laboratory (ORNL), was modeled in TracePro. The main components of the system will be presented. AutoCAD drawings of the system, obtained from ORNL, were used to produce the solid models of the system. Surface properties of the primary and secondary mirrors were obtained from the manufacturer and used in the model. The visible optics of the model were analyzed and predicted to be approximately 79% efficient. This compares well to the experimental data that shows an efficiency of 80%.

3.1.1 Benchmark System Components

The benchmark collector as built is comprised of four main components: the primary mirror, the secondary mirror, the fiber optic cable array, and the supporting structure. Figure 3.1 shows the primary parabolic mirror with dimensions and Figure 3.2 shows the secondary mirror with dimensions. In Figure 3.3, the eight-fiber array is shown surrounding the secondary mirror’s supporting shaft and located in the shadow of the secondary mirror. The top flange holding the fibers in the array is where the additional infrared (IR) filters or quartz glass rods, used for thermal management, are mounted.

17

Figure 3.1: Primary parabolic mirror

Figure 3.2: Secondary mirror assembly

18

Figure 3.3: Full-spectrum collector/receiver assembly

The 46.5 in. parabolic mirror is a glass molded mirror with an enhanced aluminum surface. This coating is highly reflective from the visible spectrum through the IR. The spectral reflectivity of the mirror is shown in Figure 3.4. The spectral transmissivity of the secondary mirror is shown in Figure 3.5. The secondary mirror transmissivity has not been documented beyond 0.9 µm, but based on private communication [15], it is approximately 95% transmissive beyond 0.8 µm and is modeled as such. Given Air Mass (AM) 1.5 direct normal (DN) irradiance as a source, Figures 3.6 and 3.7 show the amount of solar irradiance that is reflected off of the primary mirror, and then transmitted through the secondary mirror. AM 1.5 is the ratio of the length of atmosphere that beam radiation passes through to the length that it would pass through at the equator at noon at sea level. AM 1.5 is a commonly used approximation for the United States.

19

Primary Mirror Reflectivity

% Reflectivity

100 90 80 70 60 0.5

1.0

1.5

2.0

2.5

Wavelength [µm] Figure 3.4: Primary parabolic mirror spectral response

Secondary Mirror Transmissivity

% Transmissivity

100 80 60 40 20 0 0.3

0.4

0.5

0.6

0.7

0.8

Wavelength [µm] Figure 3.5: Secondary mirror spectral response

0.9

20

AM 1.5 D.N. Irradiance 800

Reflected off Primary Mirror

2

Irradiance [W/m *micron]

1000

600 400 200 0 0.3

0.8

1.3

1.8

2.3

Wavelength [micron]

Figure 3.6: Air Mass 1.5 direct normal irradiance spectrum reflected off the primary mirror

AM 1.5 D.N. Irradiance 800

Transmitted Through Secondary Mirror

2

Irradiance [W/m *micron]

1000

600 400 200 0 0.3

0.8

1.3

1.8

Wavelength [micron]

Figure 3.7: Air Mass 1.5 direct normal irradiance spectrum transmitted through the secondary mirror

2.3

21 3.2 TracePro Modeling

3.2.0 Introduction

TracePro is a raytracing program used heavily in this project to geometrically and spectrally test optical designs. Lens, filter, and reflector systems are set up using the built-in solid modeling capabilities of TracePro or by importing designs from other CAD packages. Ray sources are defined by the user, which allows for the use of spectral irradiance data of lamps, solar irradiation, or other light sources that are known. Material and surface absorption, reflection, and transmission properties can be applied to accurately model an optical system. The process is outlined below and described to aid others in using this powerful tool for their optical design.

3.2.1 Solid Modeling within TracePro

Solid modeling within TracePro is relatively easy and intuitive compared to other solid modeling programs. If designs have already been built in other three-dimensional CAD programs, then it is possible to import them, but building models within TracePro allows the program to run more efficiently.

Dialogue boxes for inserting a solid object or a reflector are shown in Figure 3.8. These allow the user to simply pick the type of object, enter the dimensions, location, and

22 orientation, and then insert the object. Once this is done, the material and surface properties may be defined, as shown in Figure 3.9.

Figure 3.8: Insert object menus in TracePro

Inserting lenses is similar to reflectors or other objects, in that the dimensions and specifications of the lens must be known. Once the lens is entered, the material properties of the lens must be defined. TracePro has an extensive built-in database of glass and plastic materials, as well as spectral properties for many types of surfaces, but special materials and surfaces may be defined by the user. ASCII files may be set up that contain information about the absorption, reflection, transmission, angular dependence, and other properties of the material or surface.

23 Applying properties is accomplished by picking the object, or a particular surface, and choosing the Apply Properties dialogue box from the Define menu. There are several tabs available, as shown in Figure 3.9, but the Material and Surface tabs are the most commonly used. Surface sources can also be defined easily at this point, although solar irradiation modeling is more easily done with a grid source, which will be defined later.

Figure 3.9: Apply properties menu

24 3.2.2 Modeling Solar Irradiation or Other Light Sources

Solar irradiation modeling in TracePro is more difficult than with the built-in surface source models, but can be very accurate if properly set up. A solar irradiation curve, such as AM 1.5, or other light source curve, must be selected and a table of the flux values versus wavelength must be obtained. Data for AM 1.5 is presented in Appendix A and can be obtained from either ASTM standard E 891-82 [16], SMARTS Code version 2.9 [17], or other sources. In Appendix A, the first column is the wavelength λ in µm, the second column is delta λ in µm, the third column is the direct irradiance, E, in W/m2*µm, the fourth column is the integrated irradiance in the range from 0.3 µm < λ < λi, and the fifth column is the ratio of the flux at that wavelength compared to the maximum flux in the AM 1.5 spectrum. The irradiance is integrated using a modified trapezoidal integration technique. Appendix B lists the SMARTS input code.

3.2.2a Wavelengths and Weights

The individual wavelengths are entered through the Raytrace Options (Analysis: Raytrace Options: Wavelengths) menu box, as shown in Fig. 3.10. A corresponding weight of each wavelength is entered as well. The weight is based on the ratio of the wavelength flux to the maximum flux of a wavelength in that spectrum. For example, if λ1 = 0.48 µm has the highest flux of the particular spectrum being modeled with a value of 1078.4 W/m2*µm, and λ2 has a flux of 539.2 W/m2*µm, then the weight of 0.48 µm is 1.0 and the weight of λ2 is 0.5. The weights or ratios are given in Appendix A.

25

Figure 3.10: Raytrace options menu

3.2.2b Grid Ray Source

Once the individual wavelengths and corresponding weights are entered, the size of the grid source, which is the type of ray source used to model solar irradiance, must be specified. This is done through the Analysis: Grid Raytrace: Grid Setup menu, as shown in Figure 3.11. The grid boundary should be defined to be slightly larger than the dimensions of the system being analyzed. The grid pattern used for true Monte Carlo raytracing is a random grid, as opposed to a square or circular pattern, so a high number of rays must be traced in order to reduce the number of holes and clusters from the source.

26

Figure 3.11: Grid raytrace menu

3.2.2c Number of Rays per Wavelength

The number of rays per wavelength is defined by the user. Once a model of the optical system is setup, the user must determine the ray flux, or number of rays per unit area, that is required to produce a uniform grid source. Since the purest form of Monte Carlo raytracing is obtained from using a random ray source, the number of rays per square meter can be on the order of 10 to 20 million.

27 The number of rays traced from the source is chosen based on the minimum number of rays that produce a reasonably uniform source flux. Tracing too many rays from the source causes extreme run times with TracePro and was therefore avoided. A sample collector/receiver system was placed in front of the random source and the number of rays traced was increased until the flux variation across the array surface was minimized for a specific length of non-imaging (NI) tube. This was also compared to simply putting the array of cells directly in front of the flux source. Figure 3.12 shows the flux variation across the array inside the NI device and directly in front of the ray source versus the number of rays traced. Up to 45 million rays per square meter were traced in the analysis, and it was determined that about 10-15 million rays per square meter was sufficient for a good trade-off between accuracy and required computation time. For the majority of the results presented in this research, approximately 12.5 million rays per square meter were traced. Variation From Random Flux Source 95 85 Array Inside Non-Imaging Tube

Flux Variation [%]

75

Array Directly In Front of Flux Source

65 55 45 35 25 15 5 0

5

10

15

20

25

Million Rays per Square Meter

Figure 3.12: Flux variation versus ray flux from the source

30

28 3.2.2d Peak Flux

The peak flux of a ray is actually the power in Watts that a single ray of the highest intensity wavelength will start with from the source. All of the other wavelengths will start each ray with power equal to its weight multiplied by the peak flux. The peak flux is calculated based on the area of the source, number of rays per wavelength, weights of the individual wavelengths, and total flux from the source.

Peak Flux =

Total Flux(W / m 2 ) * Source Area(m 2 ) Number of Rays per Wavelength * Sum of the Weights

Equation 3.1

Once the origin and direction of a source are defined, the ray source is ready for analysis. At this point, it is a good idea to test the source. A disc of known area, such as 0.25 m2, can be placed in front of the source and the incident energy flux and ray flux can be determined after the rays are traced. Due to round-off errors, small alterations to the peak flux value may be required in order to get an accurate energy flux compared to the known value of the light source.

3.2.3 Analysis Options in TracePro

Several types of analyses can be performed within TracePro. These include, but are not limited to: flux levels, flux distribution, spectral data, ray histories, number of incident rays, absorption, reflection, and transmission losses. The simplest analysis option in

29 TracePro is to investigate the quantity and distribution of flux incident on a surface. After the raytrace is performed, a surface of an object can be picked and an irradiance map can be plotted as shown in Figure 3.13. This map also contains information about the number of incident rays and the total irradiance. A cross-plot of the 2-D flux distribution can also be shown on the surface.

Figure 3.13: Example 2-D incident flux map

There are two types of raytracing modes: Analysis and Simulation. In analysis mode, TracePro saves all of the ray data during the simulation for the generation of flux maps and ray history tables when the model has finished running. In simulation mode, much less ray data is saved, which saves system memory and allows a lot more rays to be

30 traced from the source. During tests of the optimum number of rays to be traced from the source, the computer would hang or freeze frequently when over 10 million rays were traced in analysis mode, but when in simulation mode up to 50 million rays were traced without noticeable problems. For most of the tests performed here, the raytraces were performed in simulation mode, except when figures were needed or when setting up the optical system and ray source. The flux totals on the surfaces of objects, such as a photovoltaic (PV) array, can be obtained from simulation mode.

3.2.4 Scheme Programming in TracePro

In TracePro, there is a Macro window where the designer can use the Scheme programming language [18] for editing systems and running multiple analyses. Most of the results in this research were obtained by running Scheme codes through TracePro. This code is used to analyze a sequence of prepared TracePro files and save the flux data to text files. This way, the user can set up a batch of files on the computer, turn on the program, and wait for all of the flux results to be output into text files for post-processing. The code can be written in a text file and called up through the Macro window.

An example of the code required to perform a grid raytrace in simulation mode is shown in Figure 3.14. This code was used multiple times to run 2500 or more TracePro files. The three files listed in the code shown in Figure 3.14, “f0.7 Silica 0, f0.7 Silica 05, and f0.7 Silica 10,” are examples of three different files the Scheme code had TracePro open, run, and output data. The target array was moved, starting from the focal point, down the

31 NI tube in small increments until the desired results were obtained. When finished, all of the text files with the flux data were imported into Excel and the post-processing analysis of the flux variation and flux totals was performed.

(define rootPath "c:/RepetitiveRaytrace/") (define fileList (list ;; this is a list of *.oml files without the file extension "f0.7 Silica 0" "f0.7 Silica 05" "f0.7 Silica 10" )) (define RepetitiveRaytrace (lambda ( ) (define filename "" ) (for-each (lambda (a) (file:close-all) (file:open (string-append rootPath a ".oml" ) ) (raytrace:set-simulation-prompt-off) (raytrace:grid ) (set! filename (string-append rootPath a "_Flux.txt" ) ) (reports:surface-flux-save filename "total" ) (print filename) ) fileList ) (file:close-all) (print (string->symbol "Repetitive Raytraces complete") ) )) (display "(RepetitiveRaytrace)" ) (newline) Figure 3.14: Sample Scheme code

32 3.3 Post-Processing

3.3.0 Excel

The majority of the post-processing was simply computing averages, totals, and variations of incident flux across an array of cells. It involved importing the text files generated by TracePro into Excel and selecting the surfaces of interest and the desired results, which are usually either number of incident rays, quantity of incident energy, or quantity of absorbed energy. From here, figures were made that showed how the flux variation, average, total, etc. across an array surface changes with the length of the NI device.

Sometimes it is necessary to determine the incident angles of all rays incident on a surface so that the average and range can be computed. Equations are developed in the next chapter for the focal plane of a parabola and for the array plane inside a refractive or reflective NI device. However, incident ray tables for a surface can be generated within TracePro that give the history of the ray as well as the x, y, and z position of each incident ray on the surface, the x, y, and z vector components of the ray, and the x, y, and z normals of the surface the ray strikes. From this data, the incident angle of the array on the surface can be computed, as shown in Equation 3.2.

θ i = 180 deg − a cos( x vector ⋅ x norm + y vector ⋅ y norm + z vector ⋅ z norm )

Equation 3.2

33 Calculating the average incident angle at the focal point of the parabola with data exported from TracePro into Excel produces results that are within 0.05% of the results obtained from the analytical models.

3.3.1 MathCAD

MathCAD was used for computing the average incident angle equations of the parabola developed in the next chapter, as well as several other tasks. MathCAD has a nice threedimensional plot feature that is very useful for producing high quality figures of the incident flux levels on a surface. The flux levels at several points on a grid on a surface, with the resolution user defined, can be exported to a text file, imported into Excel, and then imported into MathCAD. This can be used as an analytical tool that provides visual insight of the physical phenomena. A three-dimensional plot of the flux profile on a surface near the focal point of a parabolic mirror is shown in Figure 3.15.

Figure 3.15: 3-D flux map from MathCAD

34

CHAPTER 4 ANALYSIS OF NON-IMAGING DEVICES FOR THE FULLSPECTRUM SOLAR ENERGY SYSTEM

4.0 Introduction

In this chapter, a study on the general effects of primary mirror focal point length-todiameter (f/D) ratio for both refractive and reflective systems and the development of the non-imaging (NI) device for the full-spectrum collector/receiver is presented. In the first section, the general equations of a parabola and refraction are shown, then equations for the average incident angle on a plane at the focal point of the parabola and after the rays have entered the solid glass refractive tube are developed. Raytracing results are presented that compare the effectiveness of refractive and reflective NI devices for several different primary mirror configurations. In the second section, the analysis of the geometric configurations of the first generation NI device is shown and the results of raytracing presented. The optimum cross-sectional geometry of the NI tube is discussed and recommendations are made. In the final section, a comparison between a refractive total internal reflecting (TIR) and hollow internal reflecting (HIR) tube used as the NI device for the benchmark collector/receiver is shown. Also, a better matched thermophotovoltaic (TPV) array configuration is proposed and the efficiencies of the first generation and proposed second generation systems are predicted.

35 4.1 Focal Point Length-to-Diameter Ratio Effects on Non-Imaging Devices

4.1.0 Introduction

A NI device with a square or rectangular cross-section, used as the secondary optics with a primary parabolic concentrator, can provide near-uniform irradiance on a planar target, such as an array of photovoltaic (PV) cells [11,19]. Without the NI device, the concentrated irradiance at the focal plane of a parabolic collector, Fresnel lens, or other solar concentrator is too non-uniform for the efficient operation of a PV array. Both TIR tubes, such as a solid block of fused silica, and HIR tubes, which are hollow tubes with reflective inner walls, have been considered in this investigation. HIR tubes have reflection losses as the rays propagate down the tube, but there is no entrance loss if the tube cross-sectional area is larger than the focal point diameter of the concentrator. TIR tubes have less reflection losses inside the tube, but there are reflection losses at the entrance aperture that depend on the incident angle of the irradiance. When designing a NI device for a PV array or any other planar target that requires uniform irradiance, it is necessary to investigate the transmission losses of the TIR and HIR tubes to decide which is best for the given collector geometry.

This section is part of the project to develop a NI device for this full-spectrum solar energy system. As mentioned before, the NI device will be responsible for transmitting the infrared (IR) portion of the solar spectrum to a Gallium Antimonide (GaSb) TPV

36 array. This study was performed to see how different primary concentrators would affect the design of the NI tube, in case later system iterations use different primary mirrors.

For the analysis performed in this section, the chosen collector is a one-meter diameter parabolic mirror, shown in Figure 4.1, with a concentration ratio of approximately 300 which is close to the maximum efficiency concentration of the GaSb cells. The f/D ratio is the key geometrical relationship of the parabola and the focal lengths in this analysis ranged from 0.3m to 1.1m.

Target Plane

Non-Imaging Device

Parabolic Mirror

Figure 4.1: Solar concentrating system used in analysis

37 4.1.1 Analysis

4.1.1a Modeling

The raytrace analysis was performed with TracePro version 3.0, as described in Chapter 3. The solid model of the system shown in Figure 4.1 was built within TracePro. The spectral properties of the surfaces were defined, a light source was configured, and the incident irradiance on the cells of the target PV array was analyzed. The target PV array was placed near the focal point in the NI tube, and then moved down the NI tube incrementally until the flux approached a minimum variation. Batches of these files were set up and a Scheme macro was written that ran TracePro through all of the files and saved the results in text files for post-processing.

4.1.1b Total Internal Reflecting Tube

In the raytrace analysis of the TIR systems, a solid block of silica was used as the NI tube. The near IR spectrum of Air Mass (AM) 1.5, from 0.7 < λ < 1.8 µm, was used as the irradiance source, which gives approximately 395 W/m2 irradiance. This spectrum was chosen because the GaSb TPV array to be used in the full-spectrum solar energy system is responsive to it [10]. TracePro computes the spectrally dependent index of refraction of the silica which has an average for this spectrum of 1.448. Equation 4.1 [20] shows the angular-dependent index of refraction equation used in TracePro. This is an extended Schott interpolation formula. Table 4.1 [21] gives the constants used in

38 Equation 4.1. Figure 4.2 shows the index of refraction versus the wavelength as well as the average index of refraction in the range 0.7 < λ < 1.8 µm.

a a a a a N 2 (λ ) = a1λ8 + a 2 λ 6 + a 3 λ 4 + a 4 λ 2 + a 5 + 6 + 7 + 8 + 9 + 10 2 4 6 8 λ λ λ λ λ10

Equation 4.1

Table 4.1: Coefficients used in Equation 4.1 Index Coefficient a1 a2 a3 a4 a5 a6 a7 a8 a9 a10

Value -1.0879094e-007 1.178263e-006 -0.00010566342 -0.0091597438 2.1041789 0.0087151759 0.00010559999 -9.5081909e-007 1.2538273e-007 -1.9052371e-009

1.456 1.454 Silica Index of Refraction Index of Refraction

1.452 Average Index of Refraction 1.45 1.448 1.446 1.444 1.442 1.44 0.7

0.9

1.1 1.3 Wavelength [micron]

1.5

1.7

Figure 4.2: Silica index of refraction for 0.7 < λ < 1.8 µm

39 4.1.1c Hollow Internal Reflecting Tube

In the raytrace analysis of the HIR tubes, an average surface reflectivity of 97% was assumed for the inner walls. The reflectivity is of course spectrally dependent, but only an average value is available so it was necessary to trace only a single wavelength. The TracePro default value of λ = 0.5461 µm was used. A total of 12.5 million rays per square meter were traced from the source for each iteration, with a source flux of one W/ray. The total flux from the source was then normalized to 395 W/m2 available in the IR spectrum so that the transmission efficiencies of the two systems could be compared.

4.1.2 Equations of a Parabola

The equation relating the height y of the parabola surface, based on the distance r from the central axis is y (r ) =

r2 4f

Equation 4.2

where f is the focal point length of the mirror shown in Figure 4.3. The slope of the parabola at a point r is given by slope(r ) =

r 2f

Equation 4.3

and the angle of the slope α is given in Equation 4.4.  r 2f

α (r ) = a tan

  

Equation 4.4

40

Ray

Focal Point β

α

Mirror β

f

r

α

R D

Figure 4.3: Incident angles at focal point (β), slope (α), focal length (f), diameter (D), radius (r), and outer radius (R)

The angle β of an incident ray on the target plane at the focal point, as measured positive from the downward-axis of the parabola, is twice the slope angle. This is shown in Equation 4.5. 

 r 2f

β (r ) = 2 a tan 

   = 2α  

Equation 4.5

When a light source is directed normal to the axis of the mirror, so that all of the reflected rays are concentrated at the focal point, the average incident angle at the focal point is

β =

R

 r 

0



∫ 4 ⋅ a tan 2 ⋅ f  ⋅ π ⋅ r ⋅ dr π ⋅R



2

Equation 4.6

where R is the outside radius of the parabolic mirror. A graph showing how the average incident angle reduces with increasing f/D ratio is shown in Figure 4.4.

41

Average Incident Angle at Focal Point 70

Incident Angle [deg]

60 50 40 30 20 10 0 0.3

0.5

0.7

0.9

1.1

1.3

1.5

f/D Ratio

Figure 4.4: Average focal point incident angle versus f/D ratio of the parabolic mirror

An advantage to the TIR system over the HIR system is that upon entering the tube, the photons will straighten due to refraction. If an index matching fluid is used between the TIR tube exit and the PV array, the Fresnel losses and incident angles between the silica tube exit aperture and PV array surface can be kept to a minimum. From Snell’s law shown in Equation 4.7 we can calculate the incident angle on the target plane, γ, of a ray that has entered the solid silica tube with angle β. This is shown in Figure 4.5.

n 2 sin γ = n1 sin β

Equation 4.7

42

γ

n2 n1

β Figure 4.5: Refracted ray when n1 < n2. β is the incident angle and γ is the refracted angle

Equations 4.6 and 4.7 can be rearranged to give equation 4.8, the average incident angle, γ’, after the rays have entered the silica tube. Figure 4.6 shows a comparison of the average incident angle versus f/D ratio of a HIR tube and a TIR tube.

γ′=

R

 n air

0

 np

∫ a sin

  r ⋅ sin  2 ⋅ a tan  2⋅ f 

π ⋅ R2

     ⋅ 2 ⋅ π ⋅ r ⋅ dr    

Equation 4.8

43

Average Incident Angle versus f/D Ratio 60

HIR Tubes TIR Tubes

Incident Angle [deg]

50 40 30 20 10 0 0.3

0.4

0.5

0.6

0.7 f/D Ratio

0.8

0.9

1

1.1

Figure 4.6: Average exit aperture incident angle for HIR and TIR tubes

Histograms of the angular distribution at the focal point and inside the silica tube of the five different systems investigated are shown in Figure 4.7. At the focal point for the f/D = 0.3 system, the average incident angle, given by Equation 4.6, is approximately 57 degrees from the normal. After the rays have entered the silica refractive tube, the average incident angle is reduced to 34 degrees from the normal. The f/D = 0.3 system has the greatest difference in the distribution between the focal point and refracted rays, as can be seen in Figure 4.7. Figures representing the reflected and refracted rays are shown in Figure 4.8.

44 f/D = 0.3 Silica Tube Angular Distribution

f/D = 0.3 Focal Point Angular Distribution

Frequency Cumulative %

1000

Frequency

800 600

5000

90%

4500

80%

4000

70%

3500

70%

60%

3000

60%

2500

50%

2000

40%

30%

1500

30%

20%

1000

20%

10%

500

10%

50% 40%

400 200 0 8

3.5

7 10.5 14 17.5 21 24.5 28 31.5 35 38.5 42 Incident Angle

Figure 4.7a

Figure 4.7b

f/D = 0.5 Focal Point Angular Distribution

f/D = 0.5 Silica Tube Angular Distribution

1400

3000

100% 90%

Frequency Cumulative %

1000

70%

800

60% 50%

600

40%

400

30%

90% 80% 70%

2000

20%

200

100% Frequency Cumulative %

2500

80% Frequency

1200

60% 1500

50% 40%

1000

30% 20%

500

10%

10%

0

0

0% 0

5

10

15

20

25

30

35

40

45

14

17.5

21 24.5

28

Figure 4.7d

f/D = 0.7 Focal Point Angular Distribution

f/D = 0.7 Silica Tube Angular Distribution

90% Frequency Cumulative %

500

50%

400

40%

300

30%

200

20%

100

10%

0

0% 6

9

12 15 18 21 24 27 30 33 36 39 Incident Angle

Figure 4.7e

100% 90%

Frequency Cumulative %

1200

70% 60%

31.5

1400

80%

600

3

10.5

Figure 4.7c

100%

0

7

Incident Angle

900 700

3.5

Incident Angle

1000 800

0% 0

50

Frequency

Frequency

80%

0% 0

15.5 23 30.5 38 45.5 53 60.5 68 75.5 Incident Angle

Frequency

90%

Frequency Cumulative %

0

0% 0.5

100%

100%

Frequency

1200

80%

1000

70%

800

60% 50%

600

40%

400

30% 20%

200

10%

0

0% 0

3

6

9

12

15

Incident Angle

Figure 4.7f

18

21

24

45 f/D = 0.9 Focal Point Angular Distribution

f/D = 0.7 Silica Tube Angular Distribution

1200 Frequency Cumulative %

1000

1600

80%

1400

600

50% 40%

400

Frequency

60%

30%

200 0 3

6

9

12

15

18

21

24

27

90% 80% 70% 60%

1000

50%

800

40%

600

30%

20%

400

20%

10%

200

10%

0

0% 0

100% Frequency Cumulative %

1200

0% 0

30

2

4

6

8

10

12

14

16

Incident Angle

Incident Angle

Figure 4.7g

Figure 4.7h

f/D = 1.1 Focal Point Angular Distribution

f/D = 1.1 Silica Tube Angular Distribution

18

20

100%

2000

90%

1800

80%

1600

1000

70%

1400

70%

800

60%

1200

60%

1000

50%

800

40%

1400 Frequency Cumulative %

1200

50%

Frequency

Frequency

1800

90% 70%

800

Frequency

100%

100% 90%

Frequency Cumulative %

80%

600

40%

400

30%

600

30%

20%

400

20%

10%

200

10%

200 0

0% 0

2.5

5

7.5

10 12.5 15 17.5 20 22.5 25 Incident Angle

0

0% 0

1.5

3

4.5

6

7.5

9 10.5 12 13.5 15 16.5

Incident Angle

Figure 4.7i Figure 4.7j Figure 4.7: Histograms of entrance and exit aperture angular distribution

Figure 4.8b: TIR tube Figure 4.8a: HIR tube Figure 4.8: Rays at entrance region of HIR and TIR tubes

46 At the air-glass interface, there will be Fresnel reflection losses that depend on the wavelength and incident angle of the ray. Equation 4.9 [22] describes this reflectance.

p (λ ) =

1  sin 2 ( β − γ ) tan 2 ( β − γ )  + ⋅  2  sin 2 ( β + γ ) tan 2 ( β + γ ) 

Equation 4.9

Using equation 4.9, the average transmission at the air-glass interface can be determined, as shown in equation 4.10. Figure 4.9 shows the percent reflection and transmission as a function of incident angle.

R

∫ 2 ⋅ π ⋅ r ⋅ (1 − p(λ ) )⋅ dr Equation 4.10

π ⋅ R2

Silica-Air Interface 100% 80% Percent

T (λ ) =

0

60%

Transmissivity Reflectivity

40% 20% 0% 0

15

30

45

60

75

Angle [deg]

Figure 4.9: Reflectivity and transmissivity versus incident angle

90

47 4.1.3 RayTrace Results

The raytrace results comparing the five different f/D ratios investigated are shown in Figures 4.10 and 4.11. In the first series of graphs, Figure 4.10, the minimum cell flux versus NI tube length-to-width ratio is shown. The minimum flux increases as the symmetry of the incoming rays is broken up, which happens with more reflections off the walls. As expected, the minimum flux on a cell in the HIR tube increases more rapidly than in the TIR tube. This is due to the fact that the rays straighten out in the TIR tube and act as though the primary mirror had a longer f/D ratio. For the shortest system analyzed, f/D = 0.3, there was a substantial difference between the transmission efficiencies of the HIR and TIR systems. The TIR system only had an efficiency of 86.6%, while the HIR system had an efficiency of 95.1%. This is obviously due to reflection losses at the entrance aperture of the silica tube. For the rest of the systems, the transmission efficiencies were all in the range of 95-97%. These high numbers are attainable since not all of the rays are reflected off the NI tube walls.

48 120000 100000

2

Flux [W/m ]

80000 60000 40000 HIR TIR

20000 0 0

1

2

3

4

5

6

Length/Width Ratio

Figure 4.10a: f/D = 0.3

120000 100000

2

Flux [W/m ]

80000 60000 40000 HIR TIR

20000 0 0

2

4 6 Length/Width Ratio

Figure 4.10b: f/D = 0.5

8

49 120000 100000

2

Flux [W/m ]

80000 60000 40000 HIR TIR

20000 0 0

2

4

6

8

10

Length/Width Ratio

Figure 4.10c: f/D = 0.7

120000 100000

2

Flux [W/m ]

80000 60000 40000 HIR TIR

20000 0 0

2

4

6

Length/Width Ratio

Figure 4.10d: f/D=0.9

8

10

50 120000 100000

2

Flux [W/m ]

80000 60000 40000 HIR TIR

20000 0 0

2

4

6

8

10

Length/Width Ratio

Figure 4.10e: f/D = 1.1 Figure 4.10: Minimum cell flux on the target PV array versus NI tube length/width ratio

In the next series of graphs, Figure 4.11, the minimum-to-average (min/avg) flux ratio versus the tube length-to-width ratio is shown. This ratio shows how well the system homogenizes the flux on the target plane. For the HIR system with the reflective inner walls, the average cell flux decreases linearly with tube length after the first reflection off of the wall, as shown in Figure 4.12, but for the TIR system the average flux is essentially constant along the length of the tube after the reflection losses at the entrance. Due to this fact, the location of the highest minimum cell flux in the HIR tube does not coincide with the highest ratio of min/avg flux; the peak min/avg ratio actually occurs further down the tube. In the TIR system, the highest minimum cell flux and peak min/avg flux ratio do coincide, due to the fact that the average flux remains constant in the TIR tube.

51 When designing an HIR tube, it would be a mistake to design only for the highest min/avg flux ratio, but designing for this in a TIR system would be acceptable.

1

Min/Avg Ratio

0.8

0.6

0.4 HIR TIR

0.2

0 0

1

2

3

4

5

6

Length/Width Ratio

Figure 4.11a: f/D = 0.3

1

Min/Avg Ratio

0.8

0.6

0.4 HIR TIR

0.2

0 0

2

4 Length/Width Ratio

Figure 4.11b: f/D = 0.5

6

8

52

1

Min/Avg Ratio

0.8

0.6

0.4 HIR TIR

0.2

0 0

2

4

6

8

10

Length/Width Ratio

Figure 4.11c: f/D = 0.7

1

Min/Avg Ratio

0.8

0.6

0.4 HIR TIR

0.2

0 0

2

4 6 Lenght/Width Ratio

Figure 4.11d: f/D = 0.9

8

10

53

1

Min/Avg Ratio

0.8

0.6

0.4 HIR TIR

0.2

0 0

2

4

6

8

10

Length/Width Ratio

Figure 4.11e: f/D = 1.1 Figure 4.11: Minimum-to-average flux ratio versus NI tube length-to-width ratio

140000

120000

2

Flux [W/m ]

100000

80000

60000

40000 HIR TIR

20000

0 0

50

100

150

200

250

300

350

400

NI Tube Length [mm]

Figure 4.12: Average flux versus NI tube length for f/D = 0.5

450

54 4.1.4 Conclusions

The results for the HIR and TIR systems are presented in Table 4.2. In this table, the peak minimum flux is given for each f/D ratio as well as the corresponding NI tube length-to-width (L/W) ratio, minimum-to-average flux ratio, and transmission efficiency. The main difference between the two systems is the required L/W ratio of the NI tube. The TIR tube requires approximately three to ten times the length as the HIR tube, depending on the f/D ratio of the primary mirror. The fact that with short f/D ratios there will be high reflection losses at the entrance aperture of the silica tube requires some attention. A possible solution would be the use of anti-reflective coatings on the entrance aperture. Steep entrance angles would not be desirable for most receivers, such as an array of PV cells, but dishes with short f/D ratios are desirable in some aspects.

TABLE 4.2: Non-Imaging Device Results f/D Ratio Tube Type

HIR

TIR

HIR

TIR

HIR

TIR

HIR

TIR

HIR

TIR

Peak Minimum Flux [W/m2]

114028

105514

116255

116215

114790

117175

114481

116587

113775

114159

Corresponding NI L/W Ratio

0.56

5.58

0.88

5.48

1.91

7.47

2.59

8.47

2.43

7.97

Min/Avg Ratio

0.97

0.98

0.97

0.99

0.97

0.99

0.97

0.98

0.95

0.96

Transmission Efficiency

95.1

86.8

96.9

95.1

95.8

96.0

95.7

95.8

96.5

95.9

0.3

0.5

0.7

0.9

1.1

The L/W ratio versus f/D ratio is shown in Figure 4.13. Both curves follow roughly the same shape, except in the short f/D region of the TIR tube where reflection losses at the

55 entrance change the angular distribution of the incoming rays, i.e. rays with larger incident angles at the entrance aperture are lost and therefore the rays that do enter the tube have an angular distribution closer to that of a system with a longer f/D ratio.

Preliminary tests show that the NI tube length-to-width ratio holds for TIR tubes with varying widths, but not for HIR tubes. This could be due to the fact that the flux is more homogenized in the TIR tube and therefore it is a more robust or stable system. At the very least the L/W ratio given in Figure 4.13 or Table 4.2 for TIR tubes can provide an estimate of the required tube length based on a certain f/D ratio and target plane width.

Length-to-Width Ratio vs. f/D Ratio 9.000 8.000 7.000

L/W Ratio

6.000 HIR TIR

5.000 4.000 3.000 2.000 1.000 0.000 0.3

0.5

0.7

0.9

f/D Ratio

Figure 4.13: Length-to-width ratio versus f/D ratio at the peak minimum flux point

1.1

56 One thing to note is that the lengths used here are from the focal point to the array plane. A shorter tube length can be used if the focal point is placed at a distance in front of the tube instead of directly at the entrance aperture. For a silica TIR tube, this would reduce the high concentration of energy at the entrance aperture and thus reduce the heat flux if it is a problem. However, having the focal point directly at the entrance aperture of the NI tube relaxes the tracking accuracy. Depending on the concentration ratio, the tracking accuracy can be reduced substantially which would lead to a more robust system.

For the full-spectrum collector/receiver, which has an f/D ratio of approximately 0.35, an HIR NI tube will probably be utilized, but more investigation will be performed on this exact system since the TPV array to be used is not square. The GaSb TPV cells with an anti-reflection coating can accept incident angles up to 60 degrees, so the incident angles at the exit aperture of the HIR system would be acceptable. The HIR system would also have the added benefit of keeping the entire collector more compact as well as less expensive. The required length of a solid TIR NI device would increase the weight at the antenna of the system and increase the torque on the structure and tracking mechanism.

57 4.2 Geometric Configuration of the First Generation Non-Imaging Device

4.2.0 Introduction

The benchmark full-spectrum solar collector/receiver system built at Oak Ridge National Laboratory (ORNL) has demonstrated efficient collection and transfer of the visible portion of the solar spectrum. The visible portion of the solar spectrum is separated from the IR and concentrated for transmittance of the day-light via fiber optics to hybrid luminaires or photobioreactors. The IR spectrum is concentrated and will be directed onto a TPV array for electric power generation.

TPV Array Non-Imaging Device Secondary Mirror

Primary Mirror

Fiber Optics

Figure 4.14: Modified Cassegrain full-spectrum collector/receiver with NI device

58 The collector/receiver is a modified Cassegrain system that uses a large parabolic mirror and a secondary mirror comprised of multiple planar segments, as shown in Figure 4.14. The secondary mirror’s segments have a spectrally selective cold mirror coating that lets IR energy pass through while reflecting the visible light. A sequential raytrace detailing this process is shown in Figure 4.15. In this sequence, the rays are shown: striking the primary mirror; being directed towards the secondary mirror; entering the fiber optic cables (visible spectrum); passing through the secondary mirror and entering the NI device (IR), eventually striking the TPV array.

Figure 4.15a: Incident on primary mirror

Figure 4.15b: Directed to secondary mirror

Figure 4.15c: Visible light directed into Figure 4.15d: IR energy passing through fiber optic cables secondary mirror into NI device Figure 4.15: Raytrace figures show path of solar irradiance through optics

59 4.2.1 Analysis

The TPV array requires uniform flux in order to function properly, so a NI device is required to un-focus and distribute the flux evenly on the array. A cylinder or circular funnel does not work well, since the key is to break up the rotational symmetry of the flux. A solid, square-shaped refractive NI device, as recommended in the literature [11], was investigated. However, due to the short f/D ratio of the prototype parabolic mirror, excessive reflection losses were expected, so HIR systems were investigated. Five different geometries have been analyzed here, four of which are shown in Figure 4.16. The fifth geometry, a cylindrical funnel, produced similar results to the cylinder.

Cylindrical Tube

“Octagonal” Tube

Silhouette Tube Rectangular Tube Figure 4.16: NI geometries investigated

60 The TPV array is comprised of 100 GaSb cells that are responsive from 0.7 < λ < 1.8 µm. The active area of the array is approximately 180 cm2. The cells are mounted on a thin dielectric material applied to a metal substrate in shingle fashion, as shown in Figures 4.17 and 4.18. The cells are wired in series, so maximum power output will be reached when all cells receive equal amounts of IR energy.

Figure 4.17: 100 cell GaSb TPV array

61

Figure 4.18: 100 cell GaSb TPV array side view

The analysis was performed using TracePro version 2.4, a raytracing optical design program that geometrically traces photons. A solid model of the collector/receiver system with the surface reflectivity and transmissivity properties shown in Figures 3.4 and 3.5 was built within TracePro. The solar spectrum at AM 1.0, as shown in Figure 4.19, was used as the ray source in the analysis. This represents the irradiance received at sea level at the equator at solar noon. The wavelengths were entered individually with the corresponding irradiance values to accurately represent the direct normal solar radiation. Approximately 100,000 rays per run were traced. These analyses were performed early in the development of the TracePro models, as shown by use of version 2.4 instead of 3.0, so the models weren’t quite as accurate as the current models and AM 1.0 was used instead of AM 1.5. Despite this fact, the data and conclusions presented in this section are still useful since they are mainly comparing the different geometrical options for the NI device. Better models were developed and actual energy transfer from the AM 1.5 source is presented in the next section.

62

800

1200 1000

600

800 400

600 400

200

200 0

Total Irradiance [W]

1400

2

Irradiance [W/m *micron]

Air Mass 1.0

0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Wavelength [µm] Figure 4.19: AM 1.0 direct normal solar irradiation curve

The NI device to be investigated was placed at the antenna of the parabolic dish, directly behind and in the shadow of the secondary mirror. The TPV array was moved down the NI device away from the focal point in 0.254 cm (0.1 in.) increments. A Scheme program was written that runs TracePro through these iterations and saves the results in text files, which are later analyzed. The whole analysis was set up and run for approximately 50 hours on a 1.6 Ghz Pentium 4 with 512 Mb RAM, for each NI device tested. The incident flux on each cell of the TPV array was accounted for and the results were compared to determine which tube geometry and array location provides the least amount of flux variation across the array surface. Three-dimensional flux maps are shown in Figure 4.20. The flux profile is shown to flatten out as the array is moved away from the focal point.

63

15.9cm

17.0 cm

18.5 cm

20.0 cm

23.6 cm

25.0 cm

Figure 4.20: Flux distributions at different lengths of the rectangular NI device

4.2.2 Results

A comparison of the absolute flux variation of the four configurations investigated is presented in Figure 4.21. Of the four systems, three quickly show a significant drop in the flux variation, then level out. Only the cylinder exhibits a significant rise in the

64 absolute flux variation after a minimum is reached. This is due to the fact that the other three geometries break up the rotational symmetry of the flux, while the cylinder does not. Figure 4.22 shows the same results without the cylinder for lengths from six to 31 cm, therefore illustrating the difference between the three non-cylindrical geometries.

Flux Difference vs. NI Tube Length 2500

Flux Difference [%]

2000

Rectangle Octagonal Silhouette Cylinder

1500

1000

500

0 0

5

10

15

20

25

NI Tube Length [cm]

Figure 4.21: Comparison of the four configurations investigated over the length of the NI device

30

65

Flux Difference vs. NI Tube Length 120

Rectangle Octagonal Silhouette

Flux Difference [%]

100

80

60

40

20

0 6

8

10

12

14

16

18

20

22

24

26

28

30

NI Tube Length [cm]

Figure 4.22: Comparison of the three non-cylindrical geometries

Figures 4.21 and 4.22 show the flux variation, which is the percent above average of the cell with the highest flux plus the absolute value of the percent below average of the cell with the lowest flux. A flux difference of 20% could also be stated as approximately ± 10%. While the flux difference gives an indication of how uniform the flux on the array surface is, it is not the key feature of a NI device designed for maximum energy transfer to the TPV array. The key features are how far below average the lowest flux is and, more importantly, what length of NI tube produces the maximum value of the minimum flux. The maximum value of the minimum flux is the optimum performance point for the TPV array. The minimum-to-average flux ratio is a key indication of how robust the NI

66 device is. A smaller difference between low and average flux represents a better NI device that will not be as susceptible to misalignment and tracking errors.

Of the four geometries, the rectangular tube produces the lowest difference between average and minimum flux, but the octagonal tube produces the highest minimum flux value. This is shown in Figures 4.23 and 4.24, respectively.

Minimum-to-Average Flux Ratio vs. NI Length 1.0 0.9

Min/Avg Flux Ratio

0.8 0.7 0.6 0.5 0.4 0.3

Rectangle Octagonal Silhouette Cylinder

0.2 0.1 0.0 5

10

15

20

25

NI Tube Length [cm]

Figure 4.23: Minimum-to-average flux ratio versus NI tube length

30

67

Minimum Flux vs NI Length 1.6

Minimum Flux [W/cm2]

1.4 1.2 1.0 0.8 0.6

Rectangle Octagonal Silhouette Cylinder

0.4 0.2 0.0 0

5

10

15

20

25

30

NI Tube Length [cm]

Figure 4.24: Minimum flux versus NI tube length

The minimum flux from the octagonal tube approaches 1.45 W/cm2, while the rectangular tube approaches 1.39 W/cm2. These numbers represent the highest value of the minimum flux that any cell on the array would receive, and minimum flux controls the output of the TPV array. This is obtained at NI tube lengths greater than 23 cm in length. The silhouette tube briefly reaches 1.43 W/cm2, but then falls back down to around 1.1 W/cm2. This could cause problems if it is too sensitive to location, because tracking and misalignment errors could affect it greatly. The rectangular, octagonal, and silhouette tube are all viable solutions to the problem, as shown in Table 4.3, but the rectangular tube would provide the best flux uniformity for a robust system with only a small loss in performance over the other systems considered.

68 Table 4.3: Rectangular, Silhouette, Octagonal, and Cylindrical Tube Results Rectangular Tube Component

Irradiance

Efficiency

439 W 320 W 250 W 45 W

73% 78% 18%

Primary Mirror Secondary Mirror Backside TPV Array* Electricity Generated Overall Optical Efficiency = 57%

Silhouette Tube Component Primary Mirror Secondary Mirror Backside TPV Array* Electricity Generated

Irradiance

Efficiency

439 W 320 W 257 W 46 W

73% 80% 18%

Overall Optical Efficiency = 58.5%

Octagonal Tube Component

Irradiance

Efficiency

Primary Mirror Secondary Mirror Backside TPV Array*

439 W 320 W 261 W

73% 82%

Electricity Generated

47 W

18%

Overall Optical Efficiency = 59.5%

Cylindrical Tube Component Primary Mirror Secondary Mirror Backside TPV Array* Electricity Generated

Irradiance

Efficiency

439 W 320 W 184 W 33 W

73% 58% 18%

Overall Optical Efficiency = 41.9% *Usable Irradiance = Min Flux x TPV Area

69 4.2.3 Conclusions and Recommendations

Simple, yet effective, NI devices have been shown to maximize the minimum flux any cell on the TPV array would receive. The minimum flux rises from zero to 1.45 W/cm2 in 23 cm of NI tube length. The total flux variation falls from extremely high at the focal point of the primary mirror down to below 20% after the NI device. This IR energy system, in combination with the visible lighting system to be used for day-lighting or photobioreactors, can better utilize the solar spectrum than standard day-lighting systems or PV cells alone.

Future iterations of the NI device and TPV array will produce better matched systems. A simple alternative to the first generation TPV array is an array with a rectangular or square shape. This would obviously have fewer losses due to space at the corners of the current array, where IR energy is striking the backing plate of the TPV cells.

The next section looks at work performed to compare the losses of TIR and HIR systems based on the conclusions of this section.

70 4.3 Refractive and Reflective Tubes for the Benchmark System Non-Imaging Device

4.3.0 Introduction

Work has been performed to determine the optimum shape of a NI device to homogenize the IR flux concentrated by the primary parabolic mirror. The results of that research show that a rectangular tube would perform the best as the NI device, with an octagonal tube a close second. The next step is to determine if a TIR or an HIR system would perform the best. The average incident angle at the focal plane is approximately 49 degrees, so reflection losses are expected at the entrance of the TIR tube. The HIR tube will not have the entrance aperture losses, but the advantage of the refractive TIR system is that the average incident angle at the exit aperture will decrease to 30.7 degrees, while the reflective HIR system will retain the higher angles.

To determine which type of NI device would perform the best for the benchmark TPV array, two different configurations have been investigated: an HIR and a TIR system with rectangular cross-sectional shape. The results of the detailed analysis have been used to determine which system has the highest energy transfer efficiency. A second generation TPV array is suggested. This array is close to square in cross-section and the HIR and TIR NI tubes will be used to compare this system to the benchmark or first generation system. It is expected that the second generation system will have a higher efficiency from the NI optics entrance to exit aperture due to more useable area at the exit aperture.

71 But, compared to the IR losses at the secondary mirror, this gain in NI optics efficiency may be negligible.

4.3.1 New Array Design

For more efficient energy transfer, a close to square-shaped TPV array is specified. Based on the test data from the original TPV array, each cell in the array has a voltage at the maximum power point of Vmax = 0.345 V and an open circuit voltage of Voc = 0.477 V. The dimensions of each cell are approximately 16.33 mm x 10.85 mm. Using this data, a possible array could have 96 cells, which will have Voc = 45.8 V and Vmax = 33.1 V, and outside dimensions of 13.07 cm x 13.02 cm. This array has been used in the analysis as a possible second generation TPV array. Other options are presented in Table 4.4. In Table 4.4, (a) and (b) represent the number of cells along each side of the array. Figure 4.25 shows the comparison of the 100 cell array and the proposed 96 cell array.

Table 4.4: TPV Array Configuration Options # Cells 60 63 70 77 80 88 96 104 108

a 6 7 7 7 8 8 8 8 9

b 10 9 10 11 10 11 12 13 12

h [cm] 9.799 11.433 11.433 11.433 13.066 13.066 13.066 13.066 14.699

w [cm] 10.846 9.761 10.846 11.93 10.846 11.93 13.015 14.1 13.015

Voc 28.632 30.064 33.404 36.744 38.176 41.994 45.811 49.629 51.538

Vmax 20.712 21.748 24.164 26.58 27.616 30.378 33.139 35.901 37.282

Area [cm2] Concentration 106.281 96.222 111.596 91.64 123.995 82.476 136.395 74.978 141.709 72.167 155.879 65.606 170.05 60.139 184.221 55.513 191.307 53.547

72

Figure 4.25a: 100 Cell Figure 4.25b: 96 Cell Figure 4.25: 100 cell and proposed 96 cell TPV arrays

4.3.1 RayTrace Results

The results from the raytrace analysis are presented below in tables 4.5 and 4.6. For both the 96 cell and 100 cell array the output from the two different NI tubes are comparable. From AM 1.5, there is approximately 395 W/m2 IR energy available, and the benchmark system collects about 404 W. The predicted outputs from the 100 cell array are 37 W from the HIR tube and 36 W from the TIR tube. The predicted outputs from the 96 cell array are 44 W from both the TIR and HIR tubes. This is an increase in power production of almost 19% by simply changing the shape of the TPV array. The optical system efficiency of the 100 cell array systems is about 51%, and for the 96 cell array systems it is about 60%. With the IR energy conversion efficiency of the TPV cells accounted for, the overall system efficiency for the 100 cell and 96 cell arrays are 9% and 11%, respectively.

73

Table 4.5: Comparison Between HIR and TIR Tubes for the 100 Cell TPV Array 100 Cell TPV Array Peak min/avg ratio Distance from focal point [mm] Length to width ratio Peak Minimum Cell Watts Distance from focal point [mm] Length to width ratio Maximum available power1 [W] Power Transfer Efficiency Maximum power output2 [W] Overall System Efficiency [%] 1 2

HIR Tube 0.97 190 1.34 2.05 190 1.34 205 51 37 9

TIR Tube 0.96 810 5.73 2.02 660 4.66 202 50 36 9

Minimum cell power multiplied by the number of cells Maximum power available multiplied by an efficiency of 18%

Table 4.6: Comparison Between HIR and TIR Tubes for the 96 Cell TPV Array 96 Cell TPV Array Peak min/avg ratio Distance from focal point [mm] Length to width ratio Peak Mininum Cell Watts Distance from focal point [mm] Length to width ratio Maximum available power1 [W] Power Transfer Efficiency Maximum power output2 [W] Overall System Efficiency [%] 1 2

HIR Tube 0.97 180 1.38 2.52 180 1.38 242 60 44 11

TIR Tube 0.97 800 6.13 2.55 800 6.13 245 61 44 11

Minimum cell power multiplied by the number of cells Maximum power available multiplied by an efficiency of 18%

74

CHAPTER 5 CONCLUSIONS

5.0 Introduction

A simple, yet effective, non-imaging (NI) device for the full-spectrum solar energy system has been developed and the procession of the development was presented in preceding chapters. In this chapter the conclusions from the study on primary mirror geometry are presented. Next, the conclusions of the development of the NI device for the full-spectrum solar energy system will be summarized. Finally, a test setup being built at the University of Nevada, Reno (UNR) for the NI optics will be described.

5.1 Square Refractive and Reflective Tubes for Non-Imaging Devices

Both hollow internal reflective (HIR) tubes and solid total internal reflecting (TIR) tubes work well as NI devices, but the primary mirror characteristics affect the transmission through the secondary optical device due to the effects of entrance angles. It was shown that as the angles at the focal plane increase, the required length of the NI tube increases as well.

75 For the most part, TIR and HIR tubes had similar transmission efficiencies due to nearperfect transmission of the rays inside the TIR tube and zero entrance losses at the entrance aperture of the HIR tube, as was shown in Figure 4.13 and Table 4.2. This is not the case as the focal length-to-diameter (f/D) ratio approaches 0.3, because reflective losses at the entrance aperture of the TIR tube increase substantially at short f/D ratios, causing the overall transmission efficiency of the system to decrease. This is not a problem with the HIR tube. However, the angles of the rays are preserved as they propagate down the hollow NI (NI) tube, so they will strike the exit aperture at higher angles than the rays that went through the refractive tube.

Both systems have their advantages and disadvantages. For the most robust system, a refractive (TIR) tube would perform best if the f/D ratio was long enough to reduce losses at the entrance. This system homogenizes the irradiance the best and is probably less susceptible to tracking or misalignment errors. However, the cost of this tube for large arrays, as well as the additional weight at the antenna of the collector, are drawbacks. The HIR tube is a relatively inexpensive, lightweight option that will produce comparable results if properly aligned. Highly reflective coatings are readily obtainable that can handle the high heat fluxes and temperatures seen inside a concentrating solar energy system such as this.

76 5.2 Non-Imaging Device for the Full-Spectrum Solar Energy System

The design of the NI device for the benchmark collector/receiver was the primary goal of this project. The prototype array provided to the research team is not square or rectangular in shape, so a study had to be performed to determine the best NI device for maximum performance.

The first tests performed compared rectangular, silhouette, octagonal, and circular shaped tubes that could be used as the NI device. A complete model of the benchmark system as built at Oak Ridge National Laboratory (ORNL) was built with TracePro and several tests were performed on each tube to determine which shape homogenized the flux the best as well as transmitted the highest amount of energy to the thermophotovoltaic (TPV) array. It was shown that the rectangular tube does the best job of distributing the flux over the TPV array and is the recommended shape of the NI device, even though there are slight losses at the corners of the TPV array. These losses only correspond to a decrease in transmission efficiency of a few percent when compared to the octagonal and silhouette shaped tubes, and the better flux distribution of the rectangular tube makes it a more desirable system.

After it was determined to use the rectangular tube, a comparison of hollow reflecting tubes and solid refracting tubes was performed. These tests compared a hollow tube with a 97% average reflective coating with a refractive tube of silica. Tests showed that the systems are comparable in their transmission efficiencies (51%) and in the minimum to

77 average flux ratio (0.97 for the HIR, 0.96 for the TIR). Given this fact, the research team will move on with the testing of an HIR tube since it will be less expensive and substantially lighter than the TIR tube. The proposed length of the NI tubes are 190 mm (7.5 in.) for the hollow reflective tube and 810 mm (31.9 in.) for the solid refractive tube. These lengths are measured from the focal point of the primary mirror. The dimensions of the entrance aperture of this tube are 152.4 mm (6 in.) by 130.9 mm (5.15 in). Of course, the entrance aperture of the NI tube does not have to start directly at the focal point. It can be placed past the focal point as long as all of the rays passing through the focal point still enter the tube. However, placing the entrance aperture directly at the focal point allows for misalignment or tracking accuracy mistakes which could otherwise affect the system.

In order to demonstrate the maximum potential power generation of the infrared (IR) energy that is transmitted through the secondary mirror, a better matched TPV array was proposed. This array is comprised of 96 cells instead of the 100 cells on the first array, which allows it to be configured in a nearly square shape. This TPV array was tested with both HIR and TIR tubes as well, and the results showed that an increase in power output of 16% is obtainable. It is recommended that this shape of array be used instead of the first TPV array built, to better demonstrate the technical feasibility of this combined full-spectrum solar energy system. The more power obtained from the IR portion of the system, the better the overall system performance becomes.

78 Future work will include a detailed analysis of the angular dependence of the Gallium Antimonide (GaSb) TPV array. In other words, the efficiency of the GaSb cells versus the incident angle of the photons would be very helpful in determining the effects of the primary mirror geometry and the type of NI device used. Also, if a TIR tube was used as the NI device, a study would be required to determine the best method of extracting the rays without severe reflection losses.

5.3 Non-Imaging Device Testing

5.3.0 Introduction

In order to demonstrate the use of an HIR NI device, a test system is currently being built at UNR and will be tested during Spring 2003. The results are not available at this time but will be published when they are obtained. The test system is based on a different parabolic mirror than utilized by the benchmark collector/receiver, but the results will be relevant because they will validate the use of a NI device with this TPV array. A tracking system was constructed so the performance of the TPV array can be tested for long periods of time.

79 5.3.1 Primary Mirror and Non-Imaging Device

The primary mirror used for the test system has a diameter of 46.5 in., a focal length of 21.5 in., and an f/D ratio of 0.46. A NI device will be built that has inner walls that have an enhanced aluminum coating with a 96% average reflectivity over the range 0.7 µm < λ < 1.8 µm. The test setup will look like Figure 5.1.

TPV Array Primary Mirror Non-Imaging Device

Figure 5.1: NI device test setup

The primary mirror was obtained from D.H. Satellite [23]. It is a spun aluminum mirror and came without coating on the front surface. The dish is shown in Figure 5.2 below.

80

Figure 5.2: 46.5 in. parabolic spun aluminum mirror from D.H. Satellite

The front surface was coated with ReflecTech, which was obtained from the National Renewable Energy Laboratory (NREL). This coating comes in a large sheet that has an adhesive backing, so individual gourds were cut and then laminated to the surface by hand. This material is highly reflective in the visible and IR spectrum so it is particularly suitable for our testing purposes. The final quality of the mirror does not come close to that of the glass parabolic mirror at ORNL, but is an inexpensive alternative with a tight enough spot size for the testing of the NI device. A picture of the mirror is shown in Figure 5.3. The spectral reflectivity of ReflecTech is shown in Figure 5.4.

81

Figure 5.3: Mirror with ReflecTech coating

ReflecTech

Reflectivity [%]

100 80 60 40 20 0 0.3

0.8

1.3

1.8

2.3

Wavelength [micron]

Figure 5.4: Spectral reflectivity of ReflecTech coating

82 5.4.1 Tracking System

A two-axis tracking system was purchased from Enhancement Electronics, Inc. [24]. This system utilizes the SolarTrak controller, which was developed at Sandia National Laboratory, to control a WattSun AZ-100 gear drive [25]. This is a microprocessorbased control system that calculates the position of the sun based on the date, time, latitude, longitude, drive unit parameters, tower tilt, etc. The tracker has a reported accuracy of Hole Edge : Default-Perfect Absorber Reflector Surface : Default-Flabeg Glass Mirror Outer Edge : Default-Perfect Absorber Backside : Default-Perfect Absorber

6180.806473 1100079.534 40888.89015 1148378.699

25423 17063546 511126 1

437.1064745 0.360555896 419.9263766 16.8195421 7.27E-06

0 0.360555896 40.38240945 16.8195421 7.27E-06

Junction Barrel : -> Surface 0 : Default-Perfect Absorber Surface 1 : Default-Perfect Absorber Surface 2 : Default-Perfect Absorber Surface 3 : Default-Perfect Absorber

8360.673405 16721.34681 2873.981483 2873.981483

0 237409 0 0

3.142364713 0 3.142364713 0 0

0 0 3.142364713 0 0

2nd Mirror Segment : IR -> SILICA Surface 0 : Default-Navitar Cold Mirror Surface 1 : Default-Navitar Cold Mirror Surface 2 : Default-Navitar Cold Mirror Surface 3 : Default-Navitar Cold Mirror Reflector : Default-Navitar Cold Mirror Surface 5 : Default-Navitar Cold Mirror

82.831686 335.7959137 319.1256 335.7959137 7019.17863 7019.17863

2585 36019 16291 35946 2929221 2778516

45.98778997 0.031420327 0.754399663 0.245786597 0.750575014 57.29752924 48.71576194

0 0.000314203 0.007543997 0.002457866 0.00750575 0.572975292 0.487157619

2nd Mirror Segment : IR -> SILICA Surface 0 : Default-Navitar Cold Mirror Surface 1 : Default-Navitar Cold Mirror Surface 2 : Default-Navitar Cold Mirror Surface 3 : Default-Navitar Cold Mirror Reflector : Default-Navitar Cold Mirror Surface 5 : Default-Navitar Cold Mirror

82.831686 335.7959137 319.1256 335.7959137 7019.17863 7019.17863

2563 35649 16225 35626 2932800 2784106

46.2238205 0.031314309 0.749616213 0.244928883 0.748830242 57.46710312 48.9625999

0 0.000313143 0.007496162 0.002449289 0.007488302 0.574671031 0.489625999