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Light transmissive variable thermal insulator based on nonimaging optics with potential application in… Valerio, Angel 2014

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LIGHT TRANSMISSIVE VARIABLE THERMAL INSULATOR BASED ON NONIMAGING OPTICS WITH POTENTIAL APPLICATION IN COLD CLIMATE GREENHOUSES  by Angel Valerio  B.Eng., Queretaro Institute of Technology, Mexico, 2006 M.Sc., Monterrey Institute of Technology, Mexico, 2008  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Interdisciplinary Studies)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) December 2014 © Angel Valerio, 2014   ii  Abstract Greenhouse structures have demonstrated success enhancing crop yields in farmlands, but the energy for thermal control and lighting make them impractical in cold weather locations because traditional greenhouse construction techniques result in a trade-off between light transmission and thermal insulation. The objective of the project described in this dissertation was to conceptualize, design and test a practical solution to the light transmission and thermal insulation trade-off challenge. The system that was developed is a variable light valve system that can be switched between two states – in one state the system acts as a sunlight transparent window and the other state the system acts as a highly thermally insulated ceiling capable of keeping the structure warm in cold weather conditions. Switching between the two states requires only a simple, low-cost rotation mechanism. The possibility of extending the hours of operation for the light valve system by adjusting the angular position of its light valve elements was also explored.  The light valve system when in its highly thermally insulated state, demonstrated a thermal insulation value above 3.33 W/m2K and 70% light transmittance when in its light transmissive state. In order to achieve this thermal insulation value, air mass transfer losses through the light valve structure were reduced by the implementation of low pressure seal. The experimental devices used to test the light valve system demonstrated it can be constructed using inexpensive and readily available materials. The project described in this dissertation has successfully confirmed a practical solution to reduce the energy use for heating in cold climate greenhouses while maintaining appropriate sunlight transmittance through their structure. The light valve system may represent a practical alternative for cold climate greenhouse horticulture. iii  Preface All of the work presented henceforth was conducted in the Sustainability Solutions Applied Physics Laboratory at the University of British Columbia, Point Grey campus, which provided equipment, knowledge, and both published [1] and unpublished optical design concepts.  The research described henceforth is a detailed scientific evaluation of some of those optical design concepts. The information included in the dissertation, and particularly Chapters 4, 5 and 6, has been submitted for publication (A. Valerio, M. Mossman and L. Whitehead, “Light Valve based on nonimaging optics with potential application in cold climate greenhouses”).  I was the lead investigator, responsible for design and assembly of test apparatuses and methods, data collection and analysis, and manuscript composition. Lorne Whitehead was involved throughout the project as my research supervisor, as a co-author of the publication, and in providing editorial guidance for the manuscript composition.   I was the lead investigator for the research presented in Chapter 3 (unpublished) for which I was responsible for design and assembly of test apparatuses and methods, data collection and analysis. Lorne Whitehead also provided editorial guidance for my dissertation. Additional guidance and advice was provided by the members of my departmental supervisory committee, and project collaborators Timothy Durance, Patrick McGinn, Mahesh K. Upadhyaya, Michele Mossman, Jon Scott, Douglas Campbell, Edson Sanchez, Deborah Henderson, Andres Torres and John Huizinga. iv  Table of Contents Abstract .......................................................................................................................................... ii Preface ........................................................................................................................................... iii Table of Contents ......................................................................................................................... iv List of Tables ............................................................................................................................... vii List of Figures ............................................................................................................................. viii List of Abbreviations ................................................................................................................. xiii Acknowledgements .................................................................................................................... xiv Dedication .....................................................................................................................................xv Chapter 1: Introduction ........................................................................................................... 1 1.1  Description of the Research Program ......................................................................... 1 1.2  State of the Art of Energy Efficient Greenhouses ...................................................... 6 Chapter 2: Background .......................................................................................................... 10 2.1  Optics Concepts ........................................................................................................ 10 2.2  Energy Transfer and Thermal Resistance ................................................................. 17 2.3  Photosynthesis and its Limiting Factors ................................................................... 20 Chapter 3: The Light Tube Composite Greenhouse ........................................................... 26 3.1  Light Tube Composite Greenhouse Conceptual Design ........................................... 26 3.2  Light Tube Composite Structure Subsystem ............................................................ 31 3.3  Single Slat Solar Tracker and Compound Parabolic Concentrator Subsystem ........ 38 3.4  Double Slat Solar Tracker and Compound Parabolic Concentrator Subsystem ....... 45 3.5  Discussion of the Light Tube Composite Greenhouse ............................................. 52 3.6  Early Experimentation with the Light Tube Composite Greenhouse ....................... 57 v  Chapter 4: The Light Valve ................................................................................................... 60 4.1  Conceptual Design of the Light Valve...................................................................... 60 4.2  Design Details of the Light Valve ............................................................................ 61 4.3  Ray tracing Analysis for the Light Valve ................................................................. 68 4.4  Light Valve Low Pressure Seal ................................................................................. 74 4.5  Irradiance Control Using the Light Valve ................................................................ 77 4.6  Discussion of the Light Valve Design using Pareto Frontier Analysis .................... 83 Chapter 5: Small Scale Experimentation with a Light Valve Device ................................ 87 5.1  Description of the Experimental Locations .............................................................. 87 5.2  Tools, Methods and Experimental Light Valve Device Construction ...................... 89 5.3  Optical Transmittance Experimentation with the Small Scale Light Valve Experimental Device ................................................................................................. 97 5.4  Thermal Resistance Experimentation with the Small Scale Light Valve Experimental Device ............................................................................................... 112 Chapter 6: Light Valve Experimentation in a Fully Functional Greenhouse ................. 126 6.1  Description of the Experimental Location .............................................................. 126 6.2  Tools, Methods and Experimental Light Valve Device Construction .................... 127 6.3  Optics Performance Experimental Results for the Light Valve Experiment in a Fully Functional Greenhouse ........................................................................................... 133 6.4  Thermal Performance of the Light Valve Experimental Device in a Fully Functional Greenhouse ............................................................................................................. 143 Chapter 7: Early Environmental and Economic Considerations for the Light Valve System Greenhouse ............................................................................................................... 153 vi  Chapter 8: Conclusion .......................................................................................................... 159 References .............................................................................................................................. 162 Appendix A – Light Valve Positioning Code ...................................................................... 174  vii  List of Tables Table 1 – Optical transmittance readings in the expeirmental light valve device. ..................... 139 Table 2 – KPU light valve experimental device thermal bridges summary. .............................. 150 Table 3 – Energy savings estimation for the light valve system. ................................................ 156 Table 4 – Material cost per square meter to construct a light valve system. .............................. 157  viii  List of Figures Figure 1 - Present day greenhouse design approaches. ................................................................... 3 Figure 2 – Sectional views of a compound parabolic concentrator. ............................................. 12 Figure 3 – Compound parabolic concentrator profile. .................................................................. 13 Figure 4 – Characteristic coordinate point of a compound parabolic concentrator. ..................... 14 Figure 5 - Acceptance angle of a compound parabolic concentrator. ........................................... 15 Figure 6 - Total equivalent thermal resistance value. ................................................................... 19 Figure 7 - Light absorption spectra of photosynthesis pigments .................................................. 21 Figure 8 - Typical photosynthesis response curves and limiting factors. ..................................... 23 Figure 9 – Generalized photosynthesis response curve. ............................................................... 24 Figure 10 - Light transmissive and highly insulating composite structure. .................................. 27 Figure 11 –Sectional view of a light tube composite structure. .................................................... 28 Figure 12 - Light tube composite greenhouse design. .................................................................. 30 Figure 13 - Light transmission and thermal insulation for light tube windows. ........................... 33 Figure 14 – Sectional view of the ray tracing set up for the light tube composite structure. ....... 34 Figure 15 - Composite structure optical performance. ................................................................. 35 Figure 16 – Light tube composite structure thermal insulation. ................................................... 37 Figure 17 - Light tube composite structure including a low precision solar tracker. ................... 39 Figure 18 - Design parameters of the low precision solar tracker. ............................................... 39 Figure 19 - Light ray projection. ................................................................................................... 42 Figure 20 – Single slat tracker ray tracing simulation setup. ........................................................ 42 Figure 21 - Ray tracing simulation results of the single slat solar tracker and CPC subsystem. .. 43 Figure 22 – Missed rays crossing the single slat low precision solar tracker. .............................. 45 ix  Figure 23 – Independent rotation double slat tracker design approach. ....................................... 46 Figure 24 - Independent rotation double slat solar tracker. .......................................................... 47 Figure 25 - Reflection modes of the double slat solar tracker. ..................................................... 48 Figure 26 – Double slat tracker ray tracing simulation setup. ...................................................... 49 Figure 27 – Tracking optimization for a double slat tracker. ....................................................... 50 Figure 28 - Solar tracker and CPC subsystem optical performance. ............................................ 51 Figure 29 - Optical performance of the light tube composite structure. ....................................... 53 Figure 30 – Optimal orientation of the light tube composite structure. ........................................ 55 Figure 31 – Light tube composite structure optical tranmittance for two characteristic days. ..... 56 Figure 32 - Ideal optical tranmittance of a light tube composite structure. .................................. 56 Figure 33 - Light tube composite structure experimental device. ................................................ 58 Figure 34 - Sectional views of the light valve system. ................................................................. 61 Figure 35 – Light valve general design. ........................................................................................ 63 Figure 36 – Optimization of the concentration ratio for the light valve design. ........................... 65 Figure 37 - The ideal installation of the light valve system. ......................................................... 68 Figure 38 – Light valve ray tracing simulation setup. .................................................................. 69 Figure 39 - Direct radiation light transmittance of the light valve system. .................................. 70 Figure 40 - Ray-tracing sources for direct and downward diffuse radiation. ............................... 71 Figure 41 – Optimal orientation of the light valve system. .......................................................... 71 Figure 42 – Light valve optical tranmittance for two characteristic days. .................................... 73 Figure 43 - Ideal optical transmittance of a light valve design. .................................................... 73 Figure 44 - Light valve design prototype. ..................................................................................... 75 Figure 45 - Optics performance of the light valve system with low pressure seal. ...................... 75 x  Figure 46 - Air exfiltration experimental setup ............................................................................ 76 Figure 47 – Light valve optical transmittance control ray tracing setup. ..................................... 78 Figure 48 – Light transmittance control with the light valve system. .......................................... 79 Figure 49 - Optical transmittance of the light valve system when working as a solar tracker. .... 80 Figure 50 - Optimal rotation of the valve elements when tracking. ............................................. 81 Figure 51 – Solar tracking light valve optical tranmittance for two characteristic days. ............. 82 Figure 52 - Ideal optical transmittance of a solar tracking light valve design. ............................. 82 Figure 53 – Thermal resistance and optical transmittance comparison using Pareto frontiers. ... 84 Figure 54 – The UBC Vancouver campus experimental site. ...................................................... 88 Figure 55 – The UBC Okanagan campus experimental site. ........................................................ 89 Figure 56 - Light valve experimental device design. .................................................................... 90 Figure 57 – Computer model of a valve element. ......................................................................... 90 Figure 58 - Sectional view of the prismatic film. ......................................................................... 91 Figure 59 - Light valve experimental device assembly ................................................................ 92 Figure 60 - Lamination of aluminized polyethylene film on expanded polystyrene foam. .......... 93 Figure 61 – Inner view of the light valve experimental device. ................................................... 94 Figure 62 - Spectral response of the corrected TSL254R irradiance sensor. ................................ 96 Figure 63 – 3D ray tracing simulation setup of the light valve experimental device. .................. 98 Figure 64 – Light valve experimental device ray tracing setup .................................................... 99 Figure 65 – Ray tracing optical transmittance for the light valve experimental device ............. 100 Figure 66 – Rays rejected in the prismatic film by total internal reflection ............................... 101 Figure 67 – View of the interior of the light valve experimental device .................................... 103 Figure 68 - Predicted and experimental irradiance comparison in the experimental device. ..... 104 xi  Figure 69 - Predicted and experimental irradiance comparison from Aug. 27 to Sep. 2, 2012. . 106 Figure 70 - Experimental irradiance control with the light valve device. .................................. 109 Figure 71 - Average daily light integral. ..................................................................................... 111 Figure 72 – Analog thermal circuit of the UBC Okanagan light valve experiment. .................. 113 Figure 73 - Air exfiltration experiment of the small scale experimental device. ....................... 118 Figure 74 - Heating and cooling tests for the thermal model. .................................................... 121 Figure 75 - Thermal decay experiment (Okanagan February 21 to 27, 2014). .......................... 123 Figure 76 - Thermal decay experiment (Okanagan March 19th to 22nd, 2013). .......................... 125 Figure 77 – KPU experimental greenhouse location (KPU Langley campus). .......................... 127 Figure 78 - The experimental device used for the KPU experiment. ......................................... 128 Figure 79 – Space between the greenhouse structural trusses. ................................................... 129 Figure 80 - Actuation mechanism of the KPU light valve module experimental device. .......... 130 Figure 81 – Insulating chamber of the KPU experiment. ........................................................... 131 Figure 82 – Installation of the light valve modules. ................................................................... 132 Figure 83 - The Light Valve system during a test of the automatic control. .............................. 133 Figure 84 – Ray tracing optical transmittance prediction for the light valve KPU experiment. 134 Figure 85 – Direct light ray tracing optical transmittance prediction. ........................................ 136 Figure 86 – Experimental irradiance mesurements in the KPU light valve device. ................... 137 Figure 87 - Irradiance control in the light valve experiment. ..................................................... 142 Figure 88 – Equivalent thermal circuit of the KPU light valve experiment. .............................. 144 Figure 89 - Thermal performance experiment from October 15th  to October 21st , 2013. ........ 149 Figure 90 - Thermal behaviour of the KPU light valve exprimental device. ............................. 151 Figure 91 – Crops grown in the light valve experimental device. .............................................. 152 xii  Figure 92 - Potential locations where the light valve system can be more beneficial. ............... 155  xiii  List of Abbreviations CPC – Compound parabolic concentrator: Nonimaging optical device formed by combining two rotated parabolas. KPU – Kwantlen Polytechnic University Langley campus. LV – Light valve system: Variable insulation light valve with potential applications in greenhouse agriculture. R-value – Thermal resistance value. PAR – Photosynthetically active radiation: Spectral range which maximizes photosynthesis        (400 nm – 700 nm). UBC – The University of British Columbia, Vancouver campus. UBCO – The University of British Columbia, Okanagan campus.     xiv  Acknowledgements  I would like to express my gratitude to all those people who directly and indirectly have contributed to this dissertation. First and foremost, I would like to express my deepest gratitude to Dr. Lorne Whitehead for his continuous support, guidance and ideas. Lorne, from you I learned that the most important characteristics of a good scientist are aimed hard work, convinced effort, and empathy to others. Thank you for helping me to become a better person. My forever gratitude to you for all the learning experiences you shared with me.  I am grateful to my lab manager Dr. Michele Mossman. Michele, you are the most professional, caring, and reliable lab manager one can have the pleasure to work with. Thank you for all your efforts to help me to succeed in my doctoral program. I am grateful to my thesis committee members Dr. Timothy Durance, Dr. Patrick McGinn and Dr. Mahesh Upadhyaya. I will treasure forever everything I have learned from you. I am grateful to Dr. Andrzej Kotlicki, Jon Scott, Douglas Campbell and John Huizinga for their valuable technical inputs and knowledge to help me succeed in my doctoral program. I am grateful to NSERC, UBC Vancouver, the ISGP, the SSAP lab, and the UBC Physics Department for their financial support that helped me to sustain my family during my studies. I would like to express all my love and gratitude to my wife Claudia Cambero for her decided support to my person. You are the best person I know and the best influence in my life.  I am deeply grateful to my parents Angelica and Adolfo. You were always there for me. I am grateful to my lab friends Edson Sanchez, Jason Radel, Megan Ogilvie, Debbie Eeltink, Jakob Emmel and Sepideh Khosravi, you guys made better these four years of my life. xv  Dedication Para Claudia y mis padres Angelica y Adolfo.  Gracias por compartirme su amor, paciencia y sueños.    1  Chapter 1: Introduction Greenhouse structures have been demonstrated to be successful in extending the growing season and enhancing crop yields [2,3], but three main factors have restricted their application in cold climate locations: (1) the sustainable use of limited natural resources, (2) adverse climatic conditions that result in impractical energy investments for operation and (3) an inherent conflict between sunlight transmission and thermal insulation of the greenhouse covers [3].   1.1 Description of the Research Program Cold climate greenhouse growers are forced in winter to increase the insulation of their greenhouses and invest significant amounts of energy in order to maintain adequate environmental conditions for agriculture. Heating and lighting are the most energy consuming parameters to control in greenhouses during winter time, the reason is that greenhouse structures result in a trade-off between light transmission and thermal insulation [4]. However, governmental pressure on greenhouse growers has been applied recently in order to reduce their energy use, alternate energy-efficient approaches are needed [5]. An example is the case of the Dutch Greenhouse Growers Association, which in conjunction with the Dutch government in 2010 set an aggressive goal to limit their energy usage to 35% of the 1980 standards [5]. Heating represents 30% to 40% of the operation budget in the average commercial greenhouse, so the most efficient technique to reduce energy loads in commercial greenhouses is by increasing the thermal insulation properties of the structure. The ideal cold climate greenhouse has two requirements to achieve: (1) high thermal insulation when the sun is not shinning, and (2) optimal sunlight transmission when the sun shines [6].  2  Thermal insulation is achieved in present day greenhouse structures by adding layers of poorly optically transmissive insulation. On the other hand, optical transmission is achieved by increasing the exposure area of light transmissive but poorly thermally insulated materials. The conflicting light transmission and thermal insulation objectives for present day greenhouse structures is a fundamental trade-off. The greenhouse industry has come up with two design approaches to address this light transmission and thermal insulation trade-off. One approach is to sacrifice light transmission to gain enough thermal insulation to save heating expenses at night time or to extend by a couple of months the growing season [7]. An example is the use of triple or quadruple layer polycarbonate covers which increase the thermal resistance of the structure (the term thermal resistance is defined in Section 2.2) from 0.17 m2K/W (equivalent thermal conductance of 5.9 W/m2K) of single glass covers to above 0.42 m2K/W (equivalent thermal conductance of 2.4 W/m2K) [7,8] . The thermal conductance is the inverse of the thermal resistance and is defined as the ability of a material to transfer heat [9]. The compromise is a reduction of the useful sunlight from 90% transmission of perpendicular direct sunlight using single glass covers to 65% using quadruple layer windows [7]. In most of the cases this design approach is not practical because the yield gained by extending the growing season for about a month and/or the heating energy savings are less than the yield lost by incomplete photosynthesis during the growing peaks in summer [10]. The second approach is constructing the greenhouse cover with a poorly insulated but highly light transmissive material, which in most cases is glass or polycarbonate (90% of perpendicular sunlight transmission). Thermal insulation is gained by the use of movable thermal screens with thermal resistance values of 0.33 m2K/W [11]. The compromise of this approach is the high initial and operation investment of the movable screens compared with the not very  3  significant thermal insulation gained [11]. Another practical problem of this approach is the light blocked by the thermal screens when in its light transmissive state. Light losses of about 15% have been reported in the literature because of light blocked by non-deployed thermal screens and instruments [12].  Figure 1 - Present day greenhouse design approaches either sacrifice light transmission (a) to improve their thermal insulation, or make use of poorly insulated thermal screens to reduce light losses (b). The ideal greenhouse structure for cold climates is the one which can efficiently switch from highly thermally insulated, when there is no sunlight available, to highly optically transmissive when the sun shines (c).  Both design approaches (Figure 1a and 1b) make economically impractical the use of greenhouse structures for commercial purposes in cold climates where thermal resistance values  4  above 3.33 m2K/W and useful photosynthetically active sunlight transmittances above 70% are required. The thermal resistance value estimation (3.33 m2K/W) for cold climate greenhouse operation, considers the extreme scenario of maintaining temperatures in the greenhouse above freezing for more than one week during a winter storm without supplemental heating (a simplification of the model described in Section 5.4.1 was used for this calculation).  The central objective of the project discussed in this dissertation was to design and test a practical solution to reduce the energy use for heating in cold climate greenhouses while conserving appropriate light transmission through their structure. This objective was achieved by the design, construction and testing of a variable insulation system which combines nonimaging concentrators and low cost thermal insulation which, by means of a simple two-state mechanism, transforms the structure from completely enclosed and highly thermally insulated to an efficient optically transmissive structure. The hypothesis of the research presented in this dissertation is that thermal resistance values above 3.33 m2K/W and light transmittances above 70% can be achieved with the new variable insulation system design in a practical fashion (using readily available and inexpensive materials, instruments, and construction techniques). The ideal variable insulation structure would act as the roof of a greenhouse with a highly light transmissive cover on top (shown in Figure 1c); this top would protect the greenhouse environment from external elements like rain, wind, pests and/or diseases; when this ideal structure is in its light transmissive state, temperature is gained by the greenhouse effect as any other greenhouse. The walls of the greenhouse would be made of solid insulation blocks. The potential light losses by the solid insulation walls are expected to be insignificant considering the roof/wall area ratio of large greenhouse clusters; for example, in a ten acre greenhouse cluster, the walls represent less than 5% of the total light transmission area.   5  The novel variable insulation light valve design discussed in this dissertation can efficiently transmit sunlight rays within its acceptance angle (േ30°). While this approach does depend on the angle of the solar rays and therefore will not be highly transmissive to sunlight in all geographical locations at all times of year, the detailed ray-tracing analysis presented in Chapter 4 shows that when properly designed and installed, it can achieve high sunlight transmission for a considerable portion of the day in most locations. It was also studied and reported in Section 4.5 that the light valve design can incorporate solar tracking when practical. The particular objectives of the research program presented in this document are: (1) to develop the detailed design of the new light valve concept, (2) to conduct the numerical optical transmittance simulation and theoretical thermal resistance calculation of the new light valve design, (3) to design and construct the experimental devices to verify the performance of the new light valve design, (4) to design, execute, process and analyze the data obtained with the optical and thermal experimental verifications in the light valve experimental devices, and (5) to preliminarily evaluate the opportunity of the light valve system to be implemented in a realistic greenhouse scenario. It was experimentally verified that the light valve system can provide acceptable photosynthetically active radiation transmittance values for plant growth applications (ideal optical transmittances above 70%) and also to have a thermal resistance value above 3.33 m2K/W compared to 0.17 m2K/W of common glass panels [7,8]. The experimental devices presented in this document demonstrate the feasibility of the construction of the light valve design using inexpensive and readily available materials and its practicality to be installed in a fully functional greenhouse.  6  The success of the development and application of the light valve system may represent for the agriculture industry, (1) the possibility to use land that has not been considered for agriculture because of its poor climatic conditions to grow food, and (2) the opportunity to increase the productive season by largely decoupling the greenhouse energy operation cost (heating and lighting) and the climatic conditions (ambient temperature).  1.2 State of the Art of Energy Efficient Greenhouses Typical large greenhouse operations (more than 4,000 m2) use a considerable amount of energy. Their operation is completely automated, and their climate is controlled for heating and cooling; almost all of them have hydroponic growing systems [13]. Single greenhouse units can be as big as 80,000 m2 where 95% of the effective greenhouse exposed area represents the roof of the structure. The most common cover materials used for large greenhouses are glass and polycarbonate panels [13]. Thermal control is a key factor to increase the greenhouse production profit. Heating in cold climates represents a quarter of the total annual operation budget [14]. The heating cost in greenhouses is directly related to the quality and cost of the fuel used. The most common fuel options for greenhouse heating are fuel-oil, natural gas, electricity, and/or biomass pellets. A less explored but promising alternative to traditional fuels is the use of landfill biogas [15]. Heating in large commercial greenhouses is commonly achieved by using hot water pipes heated with natural gas. Large greenhouse operations use CO2 enrichment (liquid CO2 or CO2 recovery from the hot water boiler). The use of containers filled with water is the most common greenhouse energy storage technology for maintaining warm interior temperatures during nighttime operation [3]. The most  7  common places to locate the thermal masses are the north face of the greenhouse for the case of water tanks, and on the path rows along the ground surface and near the plants for the plastic bags, tubes, and/or pipes [3].  For short-term thermal mass storage, commonly achieved by the use of water containers, the standard in commercial greenhouses is from 0.040 m3/m2 to 0.065 m3/m2 [3,12].  Artificial lighting is crucial for greenhouses in high latitude and cloudy locations where ambient irradiance is an important limiting factor for crop photosynthesis. The accepted standard for greenhouses is to provide artificial supplemental lighting when the irradiance on the crop drops below 90 W/m2 in the photosynthetically active radiation spectrum (90 PARW/m2) [16]. The most common greenhouse lighting technologies are discharge lamps. The average power to light efficiency of metal halide lamps is 80 - 90 lm/W and 117 lm/W for sodium lamps [16]. When the objective of artificial lighting is to replace ambient sunlight, metal halides are preferred because of their wide spectrum in the photosynthetically active radiation (PAR) region (400 nm – 700 nm). On the other hand, if the objective is just supplemental lighting, sodium lamps are preferred because of their high light to power efficiency. In the last decade there has been increased interest in finding a sustainable solution to improve the low energy performance of present day greenhouse structures in cold climates as a result of their light transmission and thermal insulation trade-off. Some examples of recent mechanical and non-mechanical solution approaches to improve the low energy performance of present day greenhouses in cold climates are: insulated walls that move to expose glazed windows (mechanical) [17], multilayer greenhouse panels (non-mechanical) [18], removable thermal screens (mechanical) [19], systems that inject foam (mechanical) [20,21] or soap bubbles  8  (mechanical) [14] in a gap between sealed glass panes, and completely automated indoor greenhouses (non-mechanical) [22]. Despite their contribution to the state of the art, the previously described approaches fail to provide a practical solution to improve the low energy performance of present day greenhouse structures in cold climates caused by their light transmission and thermal insulation trade-off, some of the reasons why some of those approaches have not been widely implemented in commercial greenhouse operations are excessive amounts of labor required to operate them, their non-renewable energy usage, the high capital investment or a combination of all. The most holistic approach to the solution of the poor energy performance of cold climate greenhouses has been the German Zineg project [23]. This project has been for the last decade the role model to follow for energy efficient greenhouses design. The Zineg project is an aggressive initiative whose final objective is to reduce by 90% the energy consumption of the average German greenhouse [23]. Tantau et al [24] determined that the use of double glazed windows for the Zineg greenhouse was not optimal because of the reduced light transmittance and low thermal performance. Meyer [25] proposed three technical innovations for the Zineg greenhouse: (1) a highly insulated multi-layer film plastic cover (photosynthetically active radiation transmittance of 57%), (2) the use of optimized thermal screens (three screens; aluminized material, light transmissive screen as day screen and a highly insulated black out screen), and (3) a wood pellet heating system with heat recovery and CO2 recycling. It has been found that this design theoretically reduces by 80% the annual energy consumption compared with a single layer glass greenhouse even when the reduced light transmission by the structure and thermal screens is compensated by artificial lighting [23-25].   9  The two most important limitations of the use of the Zineg greenhouse [25] in cold commercial applications are: (1) the high cost of the components considered for the design, and (2) the thermal resistance measured for the Zineg [24,25] greenhouse structure is below         1.17 m2K/W which does not satisfy the thermal requirements for cold climate greenhouse operation defined for the purposes of the project discussed in this dissertation (3.33 m2K/W).  Most of the work done on energy efficiency in greenhouses has been concentrated in movable thermal screens. One of the first reports on thermal screens for greenhouses is the one by von Zabeltitz [12] where various materials for thermal screens were tested in commercial greenhouses. It was found that the optimal material for these devices is insulated aluminized curtains. Sanford [26] analyzed later the thermal properties of these curtains experimentally finding a thermal conductance of 2.5 W/m2K. In 1981 Roberts et al. [27] experimented with a rigid one inch polystyrene foam movable insulation system in a closed greenhouse. It was found that this experimental device reduced the heat transfer coefficient to 1.03 W/m2K, and succeeded in maintaining proper growing conditions without artificial heating at nighttime in mild weather conditions [26]. The mechanism used for this experimental device was not successful for commercial applications mainly because of three reasons, (1) the light blockages when in its open position, (2) the complex and high maintenance dependent mechanism, and (3) the large amount of energy required for operation. The work presented in this dissertation, is focused on the characterization of a practical solution to reduce the energy use for heating in cold climate greenhouse structures while conserving proper light transmission through their cover structure.  10  Chapter 2: Background The development of a light transmissive structure which achieves high thermal insulation when needed is an interdisciplinary problem that requires diverse background foundations. This chapter has been divided in three sections covering the basic concepts in optics, thermal energy and plant energetics.  2.1 Optics Concepts The objective of this section is to introduce the basic optics concepts used for the research program presented in this dissertation. The particular focus topics of this section are radiometry, non-imaging optics theory and Monte Carlo ray tracing analysis.  2.1.1 Radiometry Radiometry involves the measurement of electromagnetic radiation for the situation where energy flows are constant over time intervals longer than the typical period of the electromagnetic oscillating field [28]. This condition is also known as dynamic steady state condition. Radiation power in radiometry can be distributed in three ways [28]:  Spatially (over area) – The term irradiance describes how the radiation spreads out over area and the international system units are W/m2.  Directionally (over solid angle) – The solid angle is commonly defined as the pack of angles that will be described by an area on the surface of a sphere from its center [28]. The value of the solid angle is the ratio of the area over the square of the sphere radius  11  and the international system units are steradians (sr). The radiant intensity describes the distribution of the radiation over solid angle which international units are W/sr.  Spatially and directionally (Over area and solid angle) – The radiance measures the radiation distribution over solid angle and area and the international units are W/m2/sr. The radiance remains constant for a plane perpendicular to the ray along the ray path even when the ray changes its special or directional distribution. An important concept in radiometry is that it is not possible to reduce both spatial and directional distribution of light; decreasing one will automatically increase the other [28]. This postulate defines the conservation of the étendue. The étendue is the product of the solid angle and the cross sectional area of a light beam. By definition, the étendue has to be conserved as light travels along a particular ray path. For example, a light concentrator reduces the effective spatial distribution of light from a large to a smaller area, the concentration process by definition, increases the directional distribution of light. This concept is important for the purposes of the project discussed in this dissertation to establish the limitation of the designed optical devices to concentrate truly diffuse radiation.  2.1.2 Nonimaging Optics Theory and the Compound Parabolic Concentrator Figure 2 shows a 3D computer design of a three dimensional compound parabolic concentrator with constant cross section. The design of nonimaging concentrators is based on the “edge ray principle”, which states that the rays entering at the edge of the concentrator’s aperture have to be concentrated on the edge of the absorber as shown in the section view of Figure 2a [29]. The solid arrows presented in the sectional view of Figure 2a represent the extreme rays of  12  the concentrator and the angle formed by its intersection is defined as the acceptance angle (2ߠ୫ୟ୶). Rays within the compound parabolic concentrator acceptance angle will be concentrated, and those outside the acceptance angle will be rejected. In Figure 2b, the green dashed and the red dotted lines represent rays inside and outside of the acceptance angle of the concentrator respectively.   Figure 2 – Sectional views of a 3D computer design of a compound parabolic concentrator (concentration ratio of two). The sectional views show (a) the extreme angles of the concentrator and (b) rays in and out of the accetance angle.  As shown in Figure 3, the general geometry of a compound parabolic concentrator is a pair of rotated parabolas with their focus at the opposite edge of the concentrator and axis rotated to an angle equal to half acceptance angle (ߠ୫ୟ୶). Considering ܻܺ as the coordinate system in which the compound parabolic concentrator axis is collinear with the vertical (Y axis), the  13  coordinates of the compound parabolic reflector points shown in Figure 4 for 90 െ ߠ୫ୟ୶ ൑ ߮ ൑90 ൅ ߠ୫ୟ୶ are shown in Equation 1, where the focal length ( ୐݂) is given by Equation 2 [29].  ሺܺେ୔େ, େܻ୔େሻ ൌ ቆ2 ୐݂ sinሺ߮ െ ߠ୫ୟ୶ሻ1 െ cos߮ െ ܽ,2 ୐݂ cosሺ߮ െ ߠ୫ୟ୶ሻ1 െ cos߮ ቇ (1) ୐݂ ൌ ܽሺsin ߠୟ ൅ sin ߠ୭୳୲ሻ (2)   Figure 3 – The compound parabolic concentrator profile is formed by a rotated parabola [29].   14   Figure 4 – Characteristic coordinate point of a compound parabolic concentrator [29]  Compound concentrators achieve the maximum concentration for any given light divergence or acceptance angle permitted by the second law of thermodynamics [29,30] achieving high performances for solar applications [31]. The concentration ratio of a 2D compound parabolic concentrator (C) is related to the half maximum acceptance angle (ߠ୫ୟ୶) and the refraction index of the medium in which the concentrator is submersed (n) as shown Equation 3 and Figure 4 [31]. ܣ and ܽ are the aperture and absorber half characteristic lengths of the concentrator (Figure 2a).   ܥ ൌ ܽܣ ൌ݊sin ߠ୫ୟ୶ (3)   15   Figure 5 - Acceptance angle of a compound parabolic concentrator for different concentration ratios  Rabl [32] and Winston [33] calculated the isotropic diffuse radiation light transmittance limit for a compound parabolic concentrator with perfect reflectors as ଵ஼ where C is the concentration ratio. For example, a compound concentrator with a concentration ratio of two can transmit as much as 50% of the incident truly isotropic diffuse radiation. Entropy is defined as ܵ ൌ ߢ୆ ln ߛ, where  ߢ୆ is the Boltzmann constant, and ߛ is the number of degrees of freedom for the system. The étendue (݁́) is defined as ݁́ ൌ dߗ cos ߠ dܤ, where dܤcosߠ is the projection of the light beam cross-sectional area (dܤ) on a plane whose normal is at an angle ߠ with the direction of the light propagation, dߗ is the solid angle of the light. Winston [34] related the definition of entropy with étendue as ܵ ൌ ߢ୆ ln ߛ ൎ ߢ୆ lnሺdߗ cos ߠ dܤሻ [34]. For the case of a completely diffuse photon gas (truly isotropic radiation), its solid angle (ߗ) is maximized and therefore the entropy is already in a maximum state. In other words, diffuse light cannot be concentrated by any mechanism which conserves entropy (lenses or reflectors). Thus, compound  16  parabolic concentrators, as any other concentration device are not capable of concentrating truly isotropic diffuse radiation [32].  2.1.3 Ray Tracing Analysis Ray tracing in optics is a method for which the path of electromagnetic radiation waves (incident sunlight for the purposes for the project discussed in this dissertation) is traced through a system with defined optical properties such as refractive index and/or surface reflectance, transmittance and absorbance values [35]. The method works by idealizing that the incident sunlight wave can be simplified as a large number of very narrow beams or rays traveling through the system. The interaction of the rays with optical objects such as lenses or reflectors results in adjustments of the path of each ray. The ray tracing process has to be performed with as many rays as are necessary in order to reach an adequate level of uncertainty.  TraceProTM is a commercially available ray tracing optical engineering software using 3D computer aided design (CAD) environments [36]. The design process in TraceProTM starts with the construction of a 3D model of the optical device either in the TraceProTM CAD interface or by importing a 3D model from another CAD application such as SolidWorksTM. Once the model has been successfully imported in TraceProTM, ray sources and material/surface properties have to be defined; TraceProTM provides libraries with predefined material and surface properties or the user can define their own. Finally, rays are traced and reports can be generated to find the energy distribution on a surface or energy flux through space. For the purposes of the project discussed in this dissertation, the final objective of the ray tracing analysis was to track the energy flux transmitted through the designed optical devices. TraceProTM uses the Monte Carlo method for its ray tracing [36].  17  The Monte Carlo method is an algorithm based on repeated random sampling where the objective is to obtain a numerical value of a probabilistic event, for example if a ray is transmitted or not through a concentrator [36]. TraceProTM uses ray sources which generate random rays, the rays interact with the optical devices and their paths are determined by the probability of absorption, reflection, transmission, refraction and scattering on each interaction. The optical devices designed for this project were analyzed by using TraceProTM, where ray sources which emulate the angular divergence of direct solar radiation (0.5°) were implemented. The uncertainty of a ray tracing simulation is inversely proportional to the number of rays used. The more rays used in a ray tracing simulation, the more accurate it will be but larger processing times would be required. A balance between processing time and target accuracy has to be assessed for the specific application of the ray tracing analysis. In general, for optical devices such as the ones designed for the project discussed in this dissertation, it is generally accepted that a level of uncertainty no larger than 5% will ensure manageable simulations considering the computational resources of a desktop computer [37].  2.2 Energy Transfer and Thermal Resistance The simplest model of the thermal energy exchange between a system and its surroundings is shown in Equation 4, where E is the internal energy of the system [J], t is the elapsed time [s] and ∆ ሶܳ  is the net heat transfer rate between the system and the surroundings [W]. The internal energy of the system can be characterized by Equation5, where m is the mass of the system [kg], ܿ୮ is its specific heat at constant pressure [J/kgK] and T is its temperature [K].  18  ݀ܧ݀ݐ ൌ ∆ ሶܳ  (4) ܧ ൌ ݉ܿ௣ܶ (5)  Fourier’s law is widely used in the construction industry to provide a first estimate on the net heat transfer between structures and their surroundings [38]. The simplest form of Fourier’s law assumes one dimensional steady state heat transfer. In large enclosed structures exposed to uniform ambient conditions, for example in a greenhouse, the predominant heat transfer occurs in one dimension and the temperature fluctuations occur over a sufficient long time to replicate steady state conditions so Fourier’s law approximation seems valid. The structural heat transfer then can be defined as shown in Equation 6, where ୧ܶ୬ and ୭ܶ୳୲ are the temperatures in and out of the structure [K] and Reff is its effective thermal resistance [K/W].  ሶܳ ൌ ୧ܶ୬ െ ୭ܶ୳୲ܴୣ୤୤  (6)  The thermal resistance value (R-value) is a parameter used to measure the insulation properties of a material [39]; large R-values represent materials with high insulation properties. The R-value is commonly presented in imperial units (ft2Fh/Btu) and by industrial convention the units are omitted and the accepted format is R-X.X, for example 3.5 ft2Fh/Btu is equivalent to R-3.5. The international units of the R-value are m2K/W and 1 m2K/W is equal to R-5.68. For the purposes of the project discussed in this dissertation, thermal resistance values are presented in international units followed by the imperial conversion in brackets, for example a thermal resistance of 5 m2K/W is presented as 5 m2K/W (R-28.4).  19  The total thermal resistance of a system containing a boundary formed by different materials can be calculated by using an electrical resistance analogy. Materials aggregated in series sum their thermal resistances, and the total thermal resistance of materials aggregated in parallel is the inverse of the sum of the thermal resistance inverse of each material. As shown in Figure 6 materials R1 and R2 are aggregated in parallel while materials Ra, Rb, and Rc are in series, the total thermal resistance (ܴ୘) of the system is shown in Equation 7.  1ܴ୘ ൌ1ܴଵ ൅1ܴଶ ൌ1ܴଵ ൅1ܴୟ ൅ ܴୠ ൅ ܴୡ (7)    Figure 6 - Total equivalent thermal resistance value  of components with different individual thermal resistance values aggregated in series and parallel.  The main purpose of a thermal insulation material is to increase the thermal resistance of the insulated system’s boundary [38]. The most effective and common thermal insulation materials are formed by micro and macro structures filled with air. Those air filled structures  20  reduce the air bulk convection and take advantage of the thermal conduction resistance of static air [38]; expanded polystyrene foam is a common example of those insulation materials.  2.3 Photosynthesis and its Limiting Factors The purpose of this section is to provide a general understanding of the photosynthesis process and its theoretical performance in order to differentiate what portion of the incoming sunlight energy is used for the plant for growing and what portion is rejected ultimately in the form of heat. Photosynthesis is a photochemical process by which carbon dioxide (CO2) is chemically reduced to carbohydrate (CH2O) using energy and reducing power derived from sunlight as described by Equation 8 [40]. The three most important photosynthesis pigments are the Chlorophyll a, Chlorophyll b and the carotenoids whose absorption spectrum ranges from 400 nm to 700 nm, the range known as photosynthetically active radiation (PAR) [40] (Figure 7).  6COଶ ൅ 12HଶO ൅ photons → C଺HଵଶO଺ ൅ 9Oଶ ൅ 6Hଶ (8)  Photosynthesis, as any other photochemical process, operates more efficiently under certain environmental conditions which have to be achieved by the ideal greenhouse cover design. An ideal greenhouse cover is not the one which maximizes every environmental parameter linked to the photosynthesis process but the one which optimizes them in the most economically feasible fashion in accordance with the intrinsic limitations of the photosynthesis process. The total theoretical efficiency of the photosynthesis process is 11.3% [40]. Real life efficiencies average values of around 1.5%. The reasons of those lower real life photosynthesis  21  efficiencies are, among others, saturation, photo-respiration and poor light absorption [41]. Red and far-red radiation is particularly important for plants. Germination and flowering control, photoperiods and photo-morphogenesis (leaf size, orientation and chloroplast density) are strongly controlled by light from that part of the spectrum. The pigment responsible for managing the plant photoperiods and morphologic processes is a pigment called phytochrome. The phytochrome is an organic switch which can detect red (more abundant during daytime) and far-red light (abundant during dawn and dusk) to measure the length of the days and nights and to promote flowering, germination and other metabolic processes. These photoperiods can be manipulated with artificial lighting to accelerate the morphological processes [41].  Figure 7 - Light absorption spectra of the three most important photosynthesis pigments [40]  The three main greenhouse control parameters which may limit photosynthesis are the PAR intensity, the carbon dioxide concentration in air and the temperature of the plant.  22  Blackmann formulated in 1905 the law of limiting factors [42]. This law states that the rate of photosynthesis in a plant will be limited by the factor which is in shortest supply. Any change on the limiting factor will change the response rate of the photosynthesis system.  When light is the limiting factor, more photons incident on the leaf will represent more chlorophyll pigments ionized and more basic sugars produced. At high PAR intensity exposure during extended periods of time, some plant species suffer damage in their chlorophyll pigments (photooxidative stress) [43] or photoinhibition [44] resulting in an abrupt interruption of the photosynthetic response [43]. These adverse effects in plants are complex reactions that depend on other factors, for example water stress [44]. For the practical purposes of the project discussed in this dissertation, it is considered that the harmful effect on the plant photosynthesis response caused by prolonged high PAR irradiance exposure may occur at PAR intensities above direct full sunlight (> 450 PAR W/m2) [44]. As shown in Figure 8, when light is the limiting factor, the increase of the photosynthetic response is directly proportional to the increase of the PAR intensity up to the point where the photosynthesis response is limited by another factor, commonly CO2, this point represents the transition between light limited and light saturated photosynthesis responses [45]. The irradiance at the onset of light saturation is a complex parameter that depends on various factors such as the plant species [46], climate used to grow the crop (temperature, CO2 concentration, humidity, etc.) [47], acclimation to the irradiance level (open sky cultivation, greenhouse cultivation, shadowed cultivation, etc.) [45], separation between plants and foliage [48], etc. Acceptable irradiance levels for greenhouse crops of 130 PAR W/m2 [49] and 150 PAR W/m2 [50] have been reported in the literature for ambient CO2 concentrations and temperatures between 20°C and 30°C. For greenhouse cultivation, proper growing conditions for tomato plants can be  23  achieved with irradiances between 90 - 110 PAR W/m2 [51,52]. Other optimum irradiance values for different greenhouse crops are 80 PAR W/m2 for pepper [53], 160 PAR W/m2 for cucumber [46], 50 PAR W/m2 for roses [54] and 110 PAR W/m2 for chrysanthemums [55]. For the practical purposes of the project discussed in this dissertation, irradiance values between 100 PAR W/m2 to 150 PAR W/m2 are considered as optimal for greenhouse crop cultivation under ambient CO2 concentrations and temperatures between 20°C and 30°C.   Figure 8 - Typical photosynthesis response curves for PAR intensity, carbon dioxide concentration and temperature as limiting factors.   When CO2 is the limiting factor, a higher carbon concentration in the air enables more carbon fixation and consequently more sugars produced. Plants can take advantage of higher than ambient CO2 concentrations. It is a common practice in commercial greenhouses to enrich air with CO2 reaching concentrations as high as 1000 ppm [56]; the average atmosphere CO2 concentration is around 390 ppm [57]. Yield increases above 20% have been reported when CO2 enriched air is used and light is not a limiting factor [56]. CO2 concentrations above 1500 ppm  24  can cause permanent damage in plants like chlorosis (insufficient chlorophyll production), necrosis and curling [56]. Dark photosynthesis reactions, specifically CO2 fixation, are performed by enzymes with specific optimal temperature ranges. When the optimal temperature for these enzymes is not achieved, temperature becomes the limiting factor for photosynthesis. Cockshull [58] estimated that the chemical reactions in the plant are reduced by about 50% every 10°C above or below the optimal temperature point, which for greenhouse crops it is in average 25°C [58]. It is well known that most photosynthesis reactions stop at temperatures below 5°C and above 40°C [58].   Figure 9 – Generalized photosynthesis response curve [59]. Under ambient air CO2 concentration (390 ppm [57]) the PAR intensity is a limiting factor for photosynthesis until it reaches a value of 100-150 PAR W/m2.   25  Figure 9 compares the photosynthesis response of different CO2 concentrations and PAR intensity levels based on the CO2 assimilation studies presented by Heschel et al. [60]. In    Figure 9 it can be noticed that under ambient CO2 concentrations (about 390 ppm [57]), the PAR intensity is the limiting factor for photosynthesis until it reaches a value of 100-150 PAR W/m2. After that intensity, and maintaining optimal temperature conditions (25°C), CO2 now becomes the limiting factor for photosynthesis [60]. Therefore, for ambient CO2 concentrations, plants only can take advantage of the 35% of the total available PAR radiation in a clear sunny day (1000 W/m2 or 450 PAR W/m2).      26  Chapter 3: The Light Tube Composite Greenhouse The light tube composite structure was the first design approach aiming to reduce the energy use for heating of present day greenhouses while maintaining appropriate light transmittance through their structure. The original application of this design was microalgae photobioreactors but the design concept can also be applied in the construction of greenhouse structures. In this chapter the light tube composite greenhouse idea is presented from its conceptual design to the detailed performance simulations and calculations.   3.1 Light Tube Composite Greenhouse Conceptual Design Figure 10 shows a conceptual design of a highly insulating and light transmissive composite structure. In this approach, insulation blocks are alternated with light tubes. A light tube is defined for the purposes of the project discussed in this dissertation as a reflective cylinder with highly transmissive windows on each end. The effective thermal resistance of the composite structure presented in Figure 14 depends on the individual thermal resistance contributions of the insulation blocks and light tubes in parallel. It follows from this that the resulting thermal performance of the light tube composite structure is inversely proportional to the portion of the total area covered by light tubes. For example, quadruple glass layer commercial windows report thermal insulation values between 0.83 m2K/W to 1.33 m2K/W (R-4.7 to R-7.6) [61,62], whereas 0.15 m expanded polystyrene foam insulation blocks have thermal insulation values between 3.78 m2K/W to    5.41 m2K/W (R-21.5 to R-30.7) [63]. Assuming a light tube composite structure, like the one shown in Figure 10, where the light tubes and insulation blocks have a thermal resistance equal to 0.80 m2K/W (R-4.7) and 5.00 m2K/W (R-28.4) respectively, the effective thermal resistance  27  value of the composite structure would be 3.33 m2K/W (R-18.9) if the light tube area represents just 10% of the total surface area. On the other hand, if the light tube area goes up to 50%, the effective thermal resistance value of the composite structure goes down to 1.43 m2K/W (R-8.1). Therefore, the thermal resistance optimization goal of the light tube composite structure is to minimize the area covered by light tubes. This optimization objective is in conflict with the light transmission optimization goal which is to maximize the light tube coverage area.   Figure 10 - Light transmissive and highly insulating composite structure.  One practical approach to reduce the impact of the light transmission and thermal insulation trade-off for the light tube composite structure is the use of light concentration.   Figure 11 shows the coupling of compound parabolic concentrators (CPC) on one end of the  28  composite structure. The absorber of the compound concentrators is located on top of each light tube window (Figure 11b), and the concentration ratio (ܥେ୔େ) is given by the portion of the total heat transfer area covered by light tubes (ݔ୐୘) as shown in Equation 9.  ܥେ୔େ ൌ 1ݔ୐୘ (9)   Figure 11 –Sectional view (a) and sectional representation (b) of compound parabolic concentrators coupled on a light tube composite structure. A CPC concentration ratio of five is used for the sectional view (a).   29  The integration of the array of compound parabolic concentrators on top of the light tube composite structure increases the optical active area of the light tube system to the entire exposed surface as shown in Figure 11a for any ray within the acceptance angle of the concentrators. As has been established before, in order to maximize the thermal resistance of the composite structure, the light tube area has to be minimized and consequently the concentration ratio of the compound parabolic concentrators has to be the maximum which is practical for the design. As discussed in Section 2.1.2, the acceptance angle of a nonimaging concentrator depends on its concentration ratio and therefore the increase of the concentration ratio reduces the acceptance angle of the light tube composite structure. Small acceptance angles combined with the solar altitude variability in a day results in a large number of rays rejected by the compound parabolic concentrators, decreasing the daily overall light energy transmitted by the light tube composite structure for most greenhouse applications. For example, the solar elevation range of an average winter day in latitude 40°N is 0° to 27°, and it goes up to 0° to 72° in summer. For the case of the composite structure design shown in Figure 11 with a concentration ratio of five and with a maximum acceptance angle of 22.6° (20% of the total exposed area covered by light tubes), the range of solar elevations in the previously described location (latitude 40°N) would result in a large amount of light rejected by the light tube composite structure. To maximize optical transmittance for extended periods of time each day with the light tube composite structure, the use of a solar tracking technology is required. A solar tracking device is a mechanical element formed by an array of reflectors, lenses or other optical components that adjust their position based on the solar geometry of the installation site. The cost of the tracker depends on the tracking precision of the device. The wide acceptance angle of  30  the compound parabolic contractors used for the light tube composite structure design, compared to any other concentrating device, permits the use of low precision solar tracking. Taking as an example the design discussed previously, for compound parabolic concentrators with a concentration ratio of five, the angular uncertainty of the tracking device can be as high as േ5° with no significant impact on the overall performance of the system (all rays still within the concentrator’s acceptance angle).   Figure 12 - Solar tracker and compound parabolic concentrator subsystem (a), and light tube composite structure subsystem (b) of the light tube composite greenhouse design.  In the following sections the detailed design of the light tube composite structure, compound parabolic concentrators and tracker is discussed. To simplify the analysis, the light tube composite system was divided in two subsystems, (1) the solar tracker and compound  31  parabolic concentrator subsystem (section view Figure 12a), and (2) the light tube composite structure subsystem (section view Figure 12b). The total thermal response of the light tube composite design is determined by the thermal properties of the light tube composite structure subsystem, and the total optical transmittance of the design is the product of the optical transmittances of the solar tracker and compound parabolic concentrator subsystem and the light tube composite structure subsystem. In Section 3.2 the detailed design of the light tube composite subsystem is discussed and in Section 3.3 the solar tracker and compound parabolic concentrator subsystem design is detailed. In Section 3.4 the improvements to the solar tracker design are analyzed.  3.2 Light Tube Composite Structure Subsystem As shown in Figure 13 and discussed in the previous section, high concentration ratios for the compound parabolic array represent less exposed light tube window area for the structural composite and therefore higher thermal resistance for the structure. However, high concentration ratios for the compound parabolic concentrators also mean restricted acceptance angles as shown in Figure 5 requiring a more precise solar tracker. The optimization objective for the concentration ratio of the compound parabolic concentrators is to maximize its value while conserving practical tracking precision for the solar tracker. Low cost microcontrollers and actuators can easily achieve angular tracking precisions lower than േ5° when coupled in a solar tracker and, preliminary experimentation using inexpensive linear actuators [64] and microcontrollers [65] has demonstrated angular precision of േ2.5° for the elements of a tracking device. Assuming a desired tracking precision of േ5° for the tacking elements, a concentration ratio of five for the compound parabolic concentrators would result in no significant optical  32  transmittance impact for the light tube composite design. Ray tracing analysis demonstrates that the energy flux transmittance variation of a compound parabolic contractor with a concentration ratio of five (acceptance angle of േ11.5°) and a tracking precision of േ5° (േ10° effective light redirection uncertainty) is less than 2.5% of the energy flux achieved by perfectly collimated rays entering to the concentrator with a direction perpendicular to the CPC aperture. For the analysis purposes the project discussed in this section, the width of the compound parabolic concentrator aperture (2A) shown in Figure 2 was chosen to be 0.125 m; this aperture width results in a convenient height for the concentrator (H) less than 0.50 m (concentration ratio of five). By definition, the compound parabolic array designed in this Section can transmit 20% of the total incident isotropic downwards diffuse radiation when 100% specular reflective reflectors are used (1 ܥൗ ൌ 0.20) [32,33]. After concentration by the compound parabolic array, the rays enter the light tube composite structure by passing through the first light tube window as shown in Figure 11a. In Figure 13 it is shown that the normal transmittance of the light tube windows decreases with the number of glass layers but, at the same time, the thermal resistance of the window increases [66]. The example shown in Figure 13 summarizes the case when uncoated low iron glass with a refraction index of n = 1.51 at 550 nm is used (no antireflective coatings) [67,68]. As shown in Figure 13, it was calculated that a double layer low iron glass window with no antireflective coating can achieve a light transmittance value in the PAR spectrum above 80% with an approximate thermal resistance of 0.40 m2K/W (R-2.3); the thermal resistance calculations shown in Figure 13 consider 0.003 m glass layers with a thermal resistance equal to              0.025 m2K/W for every 0.025 m of material thickness [69], 0.005 m air gaps between the glass layers with a thermal resistance equal to 0.066 m2K/W [70], and the air film insulation effect on  33  the glass surfaces (0.11 m2K/W inner surfaces and 0.05 m2K/W for outer surfaces) [66,71]. For the design exercise presented in this chapter, double glazed windows are used for the light tube design; other applications may require an optimization of the light tube window design. In the following section, ray tracing simulations are used to optimize the light transmission of the light tubes in the composite structure, different reflective coatings for the light tubes and antireflective coatings for the window glass surfaces are explored.   Figure 13 - Correlation between light transmission and thermal insulation for light tube windows with various 0.003 m low iron glass layers [8,72] separated by air gaps.  3.2.1 Light Tube Composite Structure Subsystem Ray Tracing Optimization Figure 14 shows the section view of the ray tracing set up used for the optimization discussed in this section. The light transmittance of the light tubes is defined as the ratio of the  34  light flux incident on the plane after and before the composite structure. Both planes are identical to each other and parallel to the light tube composite structure. For the case of the results summarized in Figure 15, the optical transmittance is defined as the ratio of the light flux on the transmitted sunlight plane after the light tube composite structure (IT) over the incident sunlight flux after the CPC concentration plane (ICPC). This plane is located before the first light tube window as shown in Figure 14. The sunlight entering the light tubes has been previously concentrated by a compound parabolic contractor with a concentration ratio of five.   Figure 14 – Sectional view of the ray tracing set up for the light tube composite structure.  Four combinations of double low iron glass windows (n = 1.51 at 550 nm) and light tube reflective coatings were studied: 1) Triple layer antireflective film [73] low iron glass windows [74] and 98% multi-layer enhanced specular reflective film [75] coated light tubes [76] (shown as “3L AR ESR” in Figure 15).  35  2) Single layer antireflective film [77] low iron glass windows and 98% multi-layer enhanced specular reflective film [75] coated light tubes (shown as “1L AR ESR” in Figure 15). 3) Uncoated low iron glass windows and 98% multi-layer enhanced specular reflective film [75] coated light tubes (shown as “ESR” in Figure 15). 4) Uncoated low iron glass windows and 90% specular reflective aluminized biaxially-oriented polyethylene terephthalate film [78] coated light tubes (shown as “Mylar” in Figure 15).  Figure 15 - Composite structure optical performance for different composite structure widths (D).  Figure 15 shows the light tube composite structure optical transmittance calculated using ray tracing analysis for different composite structure widths (shown as D in Figure 14). The number of reflections required by the average ray transmitted through the structure increase with  36  the light tube composite structure width (D). As shown in Figure 15, the effects of light lost in the composite structure can be reduced by using antireflective coatings [73] on the glazed surfaces and high performance reflective films like the 98% specular reflective multi-layer film [75] for the light tubes. The effective composite structure optical transmittance is reduced mainly by three factors: (1) by the use of non-enhanced reflectance materials as reflective coating for the light tubes (e.g. aluminized polyethylene film [79] with a specular reflectance value of 90% for the PAR spectrum shown as “Mylar” in Figure 15), (2) by the use of fewer layers of antireflective coatings [73] on the light tube low iron window glass [74], and (3) by increased light tube transmission lengths (D). The optimal combination of light tube composite structure width (D) and light tube materials depends on the specific thermal insulation and light transmittance requirements of the target application.   3.2.2 Light Tube Composite Structure Subsystem Thermal Analysis As described before, for the light tube design discussed in this chapter, a concentration ratio of five for the compound parabolic concentrators was used, representing 20% of the total structure area covered by light tubes. Ignoring air mass exfiltration thermal losses for the light tube composite greenhouse, the effective thermal resistance of the composite structure (ܴ୉) as a function of the thermal resistances of the light tubes (ܴ୐୘) and insulation material (୍ܴ), and the portion of the total heat transfer area covered by light tubes (ݔ୐୘) as shown in Equation 10.  ܴா ൌ ܴ୐୘୍ܴܴ୐୘ሺ1 െ ݔ୐୘ሻ ൅ ୍ܴݔ୐୘ (10)  37  If the optimization goal for the light tube composite structure width (D) is a light transmittance for the light tube no lower than 80% while maximizing the thermal resistance of the structure, a 0.15 m thick light tube composite structure (D = 0.15 m) using triple layer antireflective coatings on the low iron double glass light tube windows with multi-layer enhanced specular reflective film [75] coated light tubes is a design that can achieve this design goal (shown as “3L AR ESR” in Figure 15). Selecting D = 0.15 m, ୍ܴ is then the thermal resistance of the 0.15 m thick insulation blocks. The material of those insulation blocks is considered to be expanded polystyrene rigid foam insulation because of its availability, cost and its ability to be fabricated into desired shapes [63]. For practical purposes, it is assumed that 0.15 m thick expanded polystyrene foam rigid insulation has a thermal resistance value of 5.00 m2K/W (R-28.4) [80].  Figure 16 – Light tube composite structure thermal insulation as a function of the relative area covered by the light tubes. Thermal resistance values of 0.97 m2K/W (R-5.5) and 5.00 m2K/W (R-28.4) were used for the light tubes and thermal insulation respectively.  38  ܴ୐୘ can be calculated by adding the individual thermal resistances of the double glazed light tube windows calculated in Section 3.2.1 (0.40 m2K/W (R-2.3) each), and the thermal resistance of the air contained in the light tube where, a thermal resistance value of 0.17 m2K/W (R-1) is recommended for air contained in a 0.12 m gap [70]. Therefore, the total thermal resistance of the light tubes is 0.97 m2K/W (R-5.5); Figure 16 summarizes the effective thermal resistance decay of a light tube composite structure as function of the total heat transfer area covered by the light tubes. As shown in Figure 16, a thermal resistance value of 2.73 m2K/W (R-15.5) can be expected for a light tube composite structure design with 20% of its effective area covered by light tubes (CPCs with a concentration ratio of five).  3.3 Single Slat Solar Tracker and Compound Parabolic Concentrator Subsystem In this section, the detailed design of the light tube solar tracker and compound parabolic concentrator subsystem is discussed. The main objective of the section is to describe a practical design for the light tube single slat solar tracker and to investigate its optical properties. For the purposes of the project discussed in this dissertation, the objective of the designed tracking devices is to adjust the angularity of the downward sunlight radiation such that it enters perpendicularly to the aperture of the compound parabolic concentrators as shown in Figure 17. The sunlight angular adjustment can be achieved by an array of single reflective slats as shown in Figure 17. The inclination (߬) of the whole light tube composite structure and solar tracker can be adjusted as shown in Figure 17 depending on the geographical location and the relative position of the structure (latitude and orientation). This adjustment may result in better light  39  transmittances compared with a horizontal design (߬ ൌ 0). The optimal angle of inclination (߬) can be inferred by using ray tracing analysis.   Figure 17 - Light tube composite structure including a low precision solar tracker.   Figure 18 - Design parameters of the low precision solar tracker.  40  The most important design parameters for the low precision solar tracker are the length (L) and separation (S) of the reflective slats shown in Figure 18. The optimization objective for both parameters is to maximize the number of rays that interact with the slats and to minimize the shading of adjacent slats. A rough approximation of the optimal spacing of adjacent slats for a low precision single axis solar tracker system can be calculated by Equation 11. ߙୟ୴ୣ is the average solar altitude of the site measured from the horizontal.  ܵ ൌ ܮ ቎sin ቀߙୟ୴ୣ ൅ ߬ ൅ 90°2 ቁtanሺߙୟ୴ୣ ൅ ߬ሻ െ cos ൬ߙୟ୴ୣ ൅ ߬ ൅ 90°2 ൰቏ (11)  3.3.1 Single Slat Solar Tracker and Compound Parabolic Concentrator Subsystem Ray Tracing Analysis To investigate the benefits of the single slat low precision solar tracking system, a simple ray tracing experiment was designed and simulated. For this simulation, a horizontal system was used (߬ ൌ 0) and the full range of solar elevations was investigated (െ90° ൑ α୒ ൑ ൅90°). This generalized ray tracing analysis and the projection of the solar elevation angles using as reference the normal axis of the system, open the opportunity to infer specific light transmittance values for the light tube system when its orientation (߬) is optimized. The surface property used for the compound parabolic reflectors (concentration ratio of five) and solar tracker slats was a specular reflectance of 90% over the PAR spectral range (10% absorbance). It was assumed, for the purposes of this ray tracing analysis, that the reflectance of the surfaces has no meaningful dependency on the light wavelength or incidence angle. The material thicknesses used for the design exercise presented in this Section were   0.002 m and  41  0.003 m for the CPC reflectors and tracker slats respectively. Specular reflective surfaces for the top and bottom of the tracker slats were considered.  A light source with the same angular divergence as that of the direct solar beam (0.5°) was used in TraceProTM for the ray tracing simulation. Different ratios of slats separation divided by their length (S/L) were tried for the ray tracing analysis. The angular rotation of the slats from the horizontal (ߚ) shown in Figure 18, is presented in Equation 12 where ߙ is the projected solar altitude measured from the horizontal.  ߚ ൌ ߙ ൅ ሺ90° െ ߬ሻ2  (12)  Two dimensional solar elevation ray projections were used to describe the solar geometry for the ray tracing simulations presented in this and later chapters. The 3D ray tracing analyses discussed in this chapter and Chapter 4 consider the case where longitudinal symmetric optical elements are sufficiently long that structural shading losses are insignificant. In other words, the system can be characterized solely by the projection of the solar altitude on the optical element active plane as shown in Figure 19. For the case of a horizontal light tube system (߬ ൌ 0), the projected solar altitude on the active optics plane measured from the horizontal (ߙ) can be calculated by using Equation 13. ߪ is the offset angle of the plane where the optical device is contained, ߱ is the hour angle (sun’s angular direction relative to the solar noon) [81], ߜ is the solar declination, and λ is the latitude of the site. The solar elevation angle (ߩ) is calculated as sin ߩ ൌ sin ߜ sin ߣ ൅ cos ߜ cos ߣ cos߱ [81].   42    Figure 19 - Light ray projection on the CPC profile plane for a South (S), East (E) and Vertical (V) coordinate system.   Figure 20 – Single slat tracker ray tracing simulation setup for a horizontal light tube system (࣎ ൌ ૙).   43  Figure 19 shows an example of this angular projection for the case of a compound parabolic concentrator (CPC). For convenience, the light transmittance values in this section are reported as a function of the solar elevation projection on the plane where the light tube system CPC profiles are contained (Figure 19), measured from the normal of the system (ߙ୒) as shown in Figure 20 for the case of a horizontally positioned light tube system (߬ ൌ 0). An ideal light tube installation is the one which optimizes the angular position of the system (߬) as described in Section 3.3 and is East-West aligned ሺߪ ൌ 0ሻ.  tan ߙ ൌ sin ߩcos ߩ cosሺ߱ ൅ ߪሻ (13)   Figure 21 - Ray tracing simulation results of the single slat solar tracker and compound parabolic concentrator subsystem for L = 0.032 m and three S/L ratios (CPC concentration ratio of five).  44  Figure 21 summarizes the ray tracing light transmittance results obtained with the simulation of the single slat solar tracker and compound parabolic concentrator subsystem. The light transmittance parameter is defined for the ray tracing simulations as the ratio of the light flux incident on the planes after (Io) and before (IT) the optical devices as shown in Figure 20, both planes are identical each other and perpendicular to the normal of the optical devices. Therefore, the optical transmittance reported in Figure 21 is the ratio of the light flux on the transmitted sunlight plane after the CPCs absorber (IT) divided by the light flux on the incident sunlight plane before the solar tracker (Io) as shown in Figure 20. An important improvement in light transmittance can be observed with the single slat tracker as shown in Figure 21. The acceptance angle of the compound parabolic concentrators used for this simulation was 23° and any ray outside of this angular acceptance range will be rejected as shown in Figure 21 for the case when no solar tracker is used (“CPCs without tracker”). For the rays within the compound parabolic concentrator acceptance angle (െ11.5° ൑ߙ୒ ൑ 11.5°), the transmittance difference between the system with and without solar tracker is the light rejected by the width of the slats shown as W in Figure 18. One hundred thousand rays were used for the ray tracing simulations discussed in this section; an uncertainty of less than 1% of the ray tracing optical transmittance values was observed. It is unrealistic to optimize the S/L ratio for every solar altitude so an average solar altitude is used to generalize the S/L ratio for the tracker design as discussed in the previous section. The low transmittance of the single slat tracker and CPC array for rays between 11.5° ൏ߙ୒ ൑ 30° and െ30° ൑ ߙ୒ ൏ െ11.5° is the result of this generalization where the angular direction of most of the rays (already out of the CPCs acceptance angle) is not redirected by the  45  tracker as shown in Figure 22 (and therefore rejected by the concentrators). Alternative tracking approaches were considered as described in the following section.   Figure 22 – Missed rays (dashed lines) crossing the single slat low precision solar tracker and not interacting with any slat.  3.4 Double Slat Solar Tracker and Compound Parabolic Concentrator Subsystem An independent rotation double slat tracker has the flexibility to behave as a low S/L ratio tracker to efficiently redirect high sunlight elevations (Figure 23a) or a high S/L ratio tracker when redirecting low sunlight elevations (Figure 23c). A portion of high sunlight elevation rays incident on single slat high S/L ratio trackers (Figure 23b) are missed as described in Figure 22. However, single slat low S/L ratio trackers (Figure 23d) shade portion of the already redirected low sunlight elevation rays reducing the sunlight transmittance of the system (fewer rays reach the compound parabolic concentrators within their acceptance angle). The use of multiple slat redirectors (more than two) was explored, but it was found that there was no significant  46  improvement in the resulting optical transmittance of the system compared to the double slat tracker approach.   Figure 23 – An independent rotation double slat tracker improves the light redirection performance of a single slat tracker for high (a) and low (c) sunlight elevations. Single slat trackers with high S/L ratio (b) miss portion of the high sunlight elevation rays and low S/L single slat trackers (d) shadow portion of the redirected low sunlight elevation rays.   47   Figure 24 - Independent rotation double slat solar tracker.  The typical path of a ray in the double slat tracking light tube composite system starts at the double slat tracker where the light is redirected parallel to the compound parabolic concentrator normal direction (Figure 24). The double slat solar tracker adjusts the angular position of its pair of identical independent rotation slats shown in Figure 24 (ߚଵ and ߚଶ) for  48  three main tracking modes described in figure 25. The algorithms used for the tracking modes 1, 2 and 3 are given in Equations 14, 15 and 16 where ߚଵ and ߚଶ are the angular positions of the independent rotation slats (Figure 24), ߙ is the projected solar altitude, and ߬ is the inclination of the light tube system (Figure 17). Other more complex tracking modes were tested for the double slat tracker but no significant improvement was found compared with the three main modes for most of the cases.  ߚଵ ൌ ߚଶ ൌ ߙ ൅ ሺ90° െ ߬ሻ2  (14) ߚଵ ൌ ߙ ൅ ሺ90° െ ߬ሻ2 and ߚଶ ൌ 90° െ ߬ (15) ߚଵ ൌ ߚଶ ൌ ߙ (16)   Figure 25 - Reflection modes of the double slat solar tracker. In Mode 1, light is redirected by a single reflection on parallel slats, in Mode 2 the light redirected by the first slat and the second slat remains parallel to the direction of the reflected light, and in Mode 3, both slats are parallel to the light direction.   49  3.4.1 Double Slat Solar Tracker and Compound Parabolic Concentrator Subsystem Ray Tracing Analysis For this simulation, a horizontal system was used (߬ ൌ 0) and the full range of solar elevations was investigated (െ90° ൑ α୒ ൑ ൅90°), as mentioned in Section 3.3.1, the results of this analysis will help to infer specific light transmittance values for the light tube design when its angular orientation (߬) is optimized. Figure 26 shows the sectional view of the ray tracing simulation set up used where the optical transmittance is the ratio of the light flux on the transmitted sunlight plane after the CPCs absorber (IT) divided by the light flux on the incident sunlight plane before the solar tracker (Io).    Figure 26 – Double slat tracker ray tracing simulation setup.   50   Figure 27 – Tracking optimization for a double slat tracker with L = 0.032 m (2L = 0.064 m) and S/L = 0.6.  The optimal rotation algorithm of the slats is given by the rotation mode which maximizes the overall transmittance of the solar tracker and compound parabolic concentrator subsystem for each solar elevation as shown in Figure 27 for the case of a double slat tracker with L = 0.032 m and S/L = 0.6. Figure 28 summarizes the results obtained with the ray tracing analysis of the double slat solar tracker and compound parabolic concentrator subsystem for three S/L ratios (the S/L ratio was calculated based on the dimensions described in Figure 24).  For the results presented in Figure 28 it was considered L = 0.032 m and three S/L ratios (0.3, 0.6 and 1.6). As expected, high optical transmittances (above 70% for the three S/L ratios) were achieved when the projected solar altitude is within the acceptance angle of the compound parabolic concentrators (േ11.5° from the normal direction). Rotation mode three is the most effective for this range where the main source of light loss is absorption by the 0.003 m slat  51  width (shown as W in Figure 18); more spacing between slats (S) represents higher optical performances for this solar altitude range.    Figure 28 - Solar tracker and CPC subsystem optical performance results for different S/L ratios.  A decrease of the light tube design performance was identified for angles higher and in the vicinity of the acceptance angle of the CPCs (11.5° ൏ α୒ ൏ 30° and െ30° ൏ α୒ ൏ െ11.5°). The reason of this behavior is that, as explained in Section 3.4 and Figure 23, the solar tracker ratio S/L was not optimized for every single solar elevation (the double slat tracker permits this optimization for two solar elevations), therefore, an important portion of the rays out of the CPC acceptance angle are not redirected by the tracker as shown in Figure 23b and consequently rejected by the CPC array. For the rest of the angles, a combination of rotation modes one and two provide the highest optical performances for the light tube design. For rotation modes one  52  and two, the two main sources of light loss are (1) rays which are not redirected by the double slat solar tracker and then rejected by the compound parabolic concentrators (11.5° ൏ α୒ ൏ 30° and െ30° ൏ α୒ ൏ െ11.5°), and or (2) multiple reflections by adjacent slats (60° ൏ α୒ ൏ 90° and െ90° ൏ α୒ ൏ െ60°).  3.5 Discussion of the Light Tube Composite Greenhouse The ray tracing analysis and theoretical thermal resistance calculation results for the light tube greenhouse structure are encouraging in relation to the potential of the design to improve present day technology in light transmissive and thermally insulated greenhouse covers. Figure 29 compares the light tube design total sunlight transmittance (light tube composite structure and solar tracker and compound parabolic concentrator subsystems) with and without solar tracking, and as can be seen, a clear improvement in the optical transmittance of the system is achieved by the use of a double slat tracker. The light tube greenhouse theoretically can achieve optical transmittances above 48% for the full range of solar altitudes studied (-90° ൑ ߙ୒ ൑ 90°) while achieving thermal resistance values of 2.73 m2K/W (R-15.5) with 20% of its effective area covered by light tubes. Presently, highly thermally insulated greenhouses use quadruple layered acrylic or polycarbonate covers with a thermal resistance value of about 0.63 m2K/W (R-3.6) and normal light transmittance values above 70% for the PAR spectrum (quadruple acrylic walls [82]). The light tube design increases more than four times the thermal insulation expected for this quadruple layer greenhouse cover. By using this quadruple layer cover technology, it would be required to use four of those covers in series in order to reach the same level of insulation than the light tube  53  design; this would result in a normal light transmittance value of 24% of the PAR spectrum which is less than half of what the light tube design achieves.   Figure 29 – Generalized optical performance of the light tube greenhouse.  For the light tube design proposed in this section, the use of an ethylene tetrafluoroethylene (ETFE) membrane (n=1.40 at 550 nm) [83] parallel to the plane of the compound parabolic concentrators’ aperture on top of the light tube composite structure was modeled as the protective cover (shown in the section view of Figure 30). The objective of this ETFE cover [83] is to protect the optics of the system against rain, wind, snow, dirt, etc. Three important properties have to be achieved by the protective cover: (1) low Fresnel losses and light absorption in the PAR spectrum, for example a thin film with a refractive index lower than the  54  refractive index of low emissivity fused silica glass (n = 1.45 at 550 nm) [84], enough structural strength to withstand high wind loads, for example a category two hurricane conveys maximum wind speeds of 50 m/s and maximum wind loads on flat surfaces of 2.15 kPa (Saffir–Simpson hurricane wind scale [85]), and the capacity to support at least 1m of snow load (minimum 75 kg/m2) [86]. Ethylene tetrafluoroethylene (ETFE) membranes [83,87] are good candidates for this purpose, these membranes have low Fresnel losses because of their low refractive index (n = 1.40 at 550 nm) [83] compared to glass (n = 1.52 at 550 nm) [74] or polycarbonate (n=1.59 at 550 nm) [88] and high tensile strengths over 39,000 kPa (ASTM D882 [83]). Another advantage of the use of these membranes is their light weight compared with glass, acrylic or polycarbonate. Waaijenberg et al [89] found that the weight of a greenhouse ETFE structural cover was one tenth of the same single glass cover. Less weight represents less structural loads for the greenhouse. Figure 31 shows the optical transmittance of the light tube design using the ETFE protective cover, the double slat solar tracker and compound parabolic concentrators subsystem and the 0.15 m light tube composite structure subsystem (shown as “3L AR ESR” in Figure 15). The orientation of the light tube composite system used for this comparison is shown in      Figure 30 for a location at latitude 50°N, facing South and East-West aligned ሺߪ ൌ 0ሻ. Figure 31 contrasts the expected light transmission per active optics area for different inclinations (߬) during a characteristic summer and winter day. The transmitted irradiance (IT) reported in Figure 31 is defined as the irradiance on the transmitted sunlight plane shown in Figure 30. Both comparisons consider ambient irradiance values equal to 450 W/m2 all the time when measured perpendicular to the solar elevation. The red dotted red line marks the optimal irradiance level  55  for photosynthesis under ambient CO2 concentrations (390 ppm [57]) and temperatures between    20 – 25°C.   Figure 30 – Optimal orientation of the light tube composite structure where the inclination (߬ሻ	has to be optimized in accordance with the geographical location of the site. The light tube design is oriented in a north (N), south (S), east (pointing in the page) and west (pointing into the page) coordinate system.  Figure 32 compares for different days, the optical transmittance of a 40° tilted light tube composite structure design (߬ ൌ 40°), situated in a 50°N latitude location and positioned as shown in Figure 30. It is well known that at times close to dusk or dawn almost all available sunlight is diffuse. The ratio between direct and diffuse light during the day depends on specific local atmospheric characteristics. For the purposes of this comparison no atmospheric diffusion  56  was considered in Figures 31 and 32 and only direct radiation was assumed all the time (0.5° divergence).  Figure 31 – Light tube composite structure optical tranmittance for two characteristic days, one in summer and the other in winter for a location at latitude 50° N.   Figure 32 - Optical tranmittance of a light tube composite structure with an inclination equal to 40° (τ=40°) facing South and East-West aligned for a location 50°N latitude.  57  It was calculated, based on the thermal characteristics of the materials selected for the light tube design, a theoretical thermal resistance value equal to 2.73 m2K/W (R-15.5) (Section 3.2.2) and ray tracing PAR light transmittance values greater than 48% for a wide range of solar altitudes (-50° ൑ ߙ୒ ൑ 50°), and exceeding 60% for solar elevations between the acceptance angle of the compound concentrators of the light tube design (-12° ൑ ߙ୒ ൑ 12°) as described in Section 3.4. Very high performance windows (triple layer low iron glass filled with argon [61]) achieve similar average transmittance values (above 50% for the PAR spectrum) for thermal resistance values of 0.77 m2K/W (R-4.4) [61]. The light tube composite structure ideally achieves more than three times the thermal insulation of these high performance windows for a comparable light transmission.  In comparison, for a fiber optics lighting system [90], one may expect light transmittance values of above 50% and thermal resistance values of 3 m2K/W (R-17) when the structure is assumed to be 0.1 m thick expanded polystyrene foam rigid insulation [80]. The optical performance of fiber optics lighting systems is similar to that obtained with the light tube design. The most important limitation on the large scale application of fiber optics lighting systems is their cost (more than $500 per m2 of collection area [91]), which is more than five times the prototype cost of the light tube design based on a very conservative estimate ($90 per m2 of collection area; the prototype cost of the light tube design is expected to be similar to the prototype cost of the light valve system calculated in Chapter 7).   3.6 Early Experimentation with the Light Tube Composite Greenhouse A light tube experimental greenhouse device using this design was constructed and tested. The objective of this experimental device was to verify the theoretical optical  58  transmittance and thermal insulation value calculated in this chapter. The results of this experimental device suggest that this design concept has merit by demonstrating that it can be constructed with readily available materials as shown in Figure 33.   Figure 33 - Light tube composite structure experimental device.   59  Optical transmittance experimentation was carried out with the experimental device measuring optical transmittances above 40% for solar elevation ranges of 40°. The thermal resistance properties of the device were also experimentally tested finding thermal resistance values between 2.0 m2K/W (R-12) and 2.4 m2K/W (R-14). Only preliminary experiments with the light tube design were conducted, because it was determined that the light valve design, discussed in the following chapter, offers a better solution to reduce the energy use for heating in cold climate greenhouses while conserving proper transmission of sunlight. The work done with the light tube composite structure system represents the base for the conceptualization of the light valve. The light valve system is the main interest of this dissertation and it is discussed in detail in the following chapters.    60  Chapter 4: The Light Valve The light valve system successfully transitions between a highly thermally insulated structure and a light transmissive structure by using switchable optical devices. This practical approach to reduce the heating energy use in greenhouses while conserving appropriate light transmissions through their structure is introduced in this chapter.  4.1 Conceptual Design of the Light Valve  A roof level variable structure has been developed that can be switched between the two states shown in Figure 35. In the light transmissive state (Figures 34a and 34a1), rays within the acceptance angle of the system (solid orange and dashed green arrows shown in Figure 34a) will be transmitted and rejected otherwise (red dotted arrows in Figure 34a). In the highly thermally insulated state, the valve elements rotate to nest against one another, creating a highly thermally resistive structure (Figures 34b and 34b1). The system extends like a canopy under a weather-tolerant, sunlight transparent roof. The rotating light valve elements shown in Figure 35 have a highly insulating core and are coated so the resulting surfaces are specular reflective. The valve elements are shaped such that when the valve is open, adjacent valve elements form compound parabolic concentrating passages between the elements that cause sunlight to be efficiently transmitted into the greenhouse. For maximum light transmission, the light valve should be properly oriented relative to its geographical location such that the acceptance angle of the curved profile valve elements (2ߠ୫ୟ୶) maximizes light transmission through the day depending on the sun position. When closed, the specially designed shape of the valve elements enables to nest against one another  61  and seal to form a semi-rigid layer of highly thermal insulating material, as shown in Figure 34b1.   Figure 34 - Sectional (a, b) and isometric (a1, b1) views of the light transmissive (a, a1) and highly thermally insulated (b, b1) states of the light valve system.  4.2 Design Details of the Light Valve The sectional profile of each light valve element is composed by four parabolic segments [33] presented in Figure 35 as S1, S2, S3, and S4. θmax is half acceptance angle of the compound parabolic concentrator formed by two adjacent reflectors (S1 and S2). The angle between any point of the compound parabolic reflector profile ሺݔୗ, ݕୗሻ and the axis of its basic parabola is ߮. A and a are the half characteristic lengths of the inner and outer apertures, b is the length of the valve element tip and G is the valve element height. The focal length of the origin parabola is represented as ୐݂ [33]. The concentration ratio (C) for the light valve design (2D longitudinal symmetric compound parabolic concentrator) is equal to the inverse sine of θmax ቀܥ ൌ ஺௔ ൌ 62  ଵୱ୧୬ఏౣ౗౮ቁ [31]. The upper light valve profiles S1 and S2 are described by Equations 17 and 18 respectively, the origin of those equations is the center of rotation (Figure 35) of the light valve elements. The light valve constitutive equations are adaptations of the compound parabolic concentrator polar equation [33].   ሺݔୗଵ, ݕୗଵሻ ൌ ቆ2 ୐݂ sinሺ߮ െ ߠ୫ୟ୶ሻ1 െ cos߮ െ ܽ െ ܣ െܾ2 ,2 ୐݂ cosሺ߮ െ ߠ୫ୟ୶ሻ1 െ cos߮ ቇ (17) ሺݔୗଶ, ݕୗଶሻ ൌ ቆെ2 ୐݂ sinሺ߮ െ ߠ୫ୟ୶ሻ1 െ cos߮ ൅ ܽ ൅ ܣ ൅ܾ2 ,2 ୐݂ cosሺ߮ െ ߠ୫ୟ୶ሻ1 െ cos߮ ቇ (18)  The lower light valve profiles S3 and S4 are calculated so when the light valve is in its thermally insulated state, it results in a perfect match between adjacent valve elements (Figures 35 and 34b1). In order to fully define the valve element profiles S3 and S4, it is necessary to select values for the tip of the valve element (b), the absorber half width (A) and the light valve concentration ratio (C). An important structural consideration for the light valve design is the minimum valve element tip width (b). From an optical transmittance perspective, the ideal light valve design is the one which minimizes the width of the parameter b, but on the other hand, it cannot be vanishingly small because it would compromise the structural integrity of the light valve design. For the purposes of the design exercise presented in this dissertation, expanded polystyrene foam blocks were selected as the material for the insulating core of the valve elements. It was found that a valve element tip width of b = 0.01 m resulted in strong enough valve element structures which can endure long term cyclic operation for the light valve system. It is expected that the light valve system would operate with contact compression pressures  63  between valve elements no larger than 50 Pa and two opening and closing actuations per day (1,000 cyclic actuations per year); the valve element design with a tip width of b = 0.01 m experimentally demonstrated to endure those conditions.   Figure 35 – Light valve general design. S1 and S2 are the profiles of a cylindrical compound parabolic concentrator with a concentration ratio of two. S3 and S4 are the resulting parabolic profiles required for a perfect nest of the valve elements.  The concentration ratio (C) and the width of the aperture (2A) have to be selected so the target maximum acceptance angle (2θmax) and thermal insulation values are achieved while  64  conserving practical height for the light valve elements (shown as G in Figure 35). For the thermal design of the light valve system, the most important parameter is the resulting thickness of the rotated valve elements when in their highly thermally insulated state (shown as L in  Figure 35); this parameter is directly proportional to the thermal resistance of the structure. For the case of the specific application studied in this dissertation (greenhouse operation in cold climates), and considering the extreme scenario of a two-week long winter storm with temperatures below -20°C, preliminary calculations have shown that a design thermal resistance value of 4.00 m2K/W (R-22.7) for the light valve greenhouse structure is practical to maintain indoor greenhouse air temperatures above freezing. For this extreme scenario (two-week long winter storm), it was assumed that the light valve system stayed closed all the time and electric lighting was used to provide PAR lighting to the plants (electric lighting heating was not considered for the thermal calculation). Minimum long term lighting conditions for plant survival of 4 PAR W/m2 to 10 PAR W/m2 have been reported in the literature [92-94].  Figure 36 shows the concentration ratio of the light valve system as a function of the total height of the valve elements (shown as G in Figure 35). For the analysis presented in Figure 36, the parameter L was defined as 0.13 m in order to ensure a thermal insulation value of           4.00 m2K/W (R-22.7); expanded polystyrene foam valve elements with a thermal resistance value of 0.78 m2K/W (R-4.4) for every 0.025 m of material thickness were considered for this study. As shown in Figure 36, the concentration ratio which minimizes the valve element height (G) is C = 2. The minimization of the valve elements height (G), results in a minimum amount of materials used for the construction of the valve elements and power for the operation of the light valve system for any given thermal insulation value.   65  The target locations for the implementation of the light valve system are places with cold but predominantly sunny weather, typically located around latitude 50° N where the maximum solar elevation ranges from 20° to 65° in winter and summer respectively. Most of the sunlight rays in those target locations can be efficiently transmitted by the light valve system for a design with an acceptance angle of 2θmax = 60° which is ideally achieved by a concentration ratio of two (C = 2). A concentration ratio of two for the light valve design also optimizes the height of the valve elements (red cross Figure 36).   Figure 36 – Optimization of the concentration ratio for the light valve design for an effective thermal insulation value of 4.00 m2K/W (R-22.7).  Based on the analysis previously discussed, the design parameters for the light valve system were chosen to be b = 0.01 m, C = 2, L = 0.13 m, G = 0.46 m, and 2A = 0.20 m. As  66  mentioned before, the valve element tip (b) represents the first source of light losses for the light valve design due to the fact that the incident light on this surface will be prevented from entering to compound parabolic concentrators. Assuming that a perfect mirror coating is used for the light valve reflectors, the transmittance of the light valve system is 1 െ ௕ଶ஺ for any ray within the light valve acceptance angle and 0 otherwise. The selected dimensions for the aperture represent in average 5% of the light transmission sacrificed due to the light valve element tip (b). To compare the impact of losing 5% of the light because of the light valve element tip, the common light blocked in commercial greenhouses because of its structural frame and instruments, is about 15% of the total light available [95]. For the particular interest of the design exercise discussed in this dissertation, the valve elements were designed such that they could be installed and tested in an existing greenhouse. In this case, valve element lengths (G) smaller than 0.50 m were appropriate, assuming that the optimal installation space for the system is between the greenhouse structural trusses (the average greenhouse structural truss is 0.50 m tall). The profile of the lower compound parabolic reflectors S3 and S4 shown in Figure 35 can be found by rotating the upper compound parabolic reflectors (S1 and S2) using as center of rotation the middle of the line that links their lower points so they match as shown in Figure 35. For the design parameters chosen before, the approximate equations that define the profiles S3 and S4 are Equations 19 and 20 respectively  ሺݔୗଷ, ݕୗଷሻ ൎ ቆെ2 ୐݂ sinሺ߮ െ ߠ୫ୟ୶ሻ1 െ cos߮ ൅ ܽ ൅ܣ2 െ 0.66ܾ,2 ୐݂ cosሺ߮ െ ߠ୫ୟ୶ሻ1 െ cos߮ െ 0.78ܪቇ (19) ሺݔୗସ, ݕୗସሻ ൎ ቆ2 ୐݂ sinሺ߮ െ ߠ୫ୟ୶ሻ1 െ cos߮ െ ܽ െܣ2 ൅ 0.66ܾ,2 ୐݂ cosሺ߮ െ ߠ୫ୟ୶ሻ1 െ cos߮ െ 0.78ܪቇ (20)  67  Where H is the height of the compound parabolic concentrator profiles as described in Figure 35 and defined by Equation 21.  ܪ ൌ ܽ ൅ ܣtanሺߠ୫ୟ୶ሻ (21)  A ray entering to the light valve system within its acceptance angle has four possible ray paths as shown in Figures 34a and 39a: 1) It can pass in between the valve elements without any reflection. 2) It can have a first reflection on the valve element profiles S1 or S2 and then been transmitted without any other reflection. 3) It can have a first reflection on the valve element profiles S1 or S2 and then a second reflection on S3 or S4 and then been transmitted without any other reflection. 4) It can have a first reflection on the valve element profiles S1 or S2 and then transmission after multiple reflections between S3 and S4. For the case of a light valve system with perfect specular reflectors (100% reflectance), the maximum transmittance of completely isotropic diffuse downward radiation is ଵ஼ ቀ1 െ௕ଶ஺ቁ. Considering the current design parameters, the expected light valve diffuse radiation transmittance when 100% specular reflectors are used is 47.5%. It is expected that the diffuse light transmittance characteristics of the light valve system do not significantly impact its overall optical performance in predominately sunny locations where more than 85% of the incident light is direct [96].  68  The light valve system can be properly tilted depending on the geographical location such that it maximizes light transmission for most of the year taking advantage of its design acceptance angle. The optimal tilt angle for the light valve (τ), depends on the specific location where the device is installed, the design of the greenhouse structure, and the required illumination level. A detailed solar geometry study [97] is recommended to find the optimal light valve tilt angle (τ). For example, if the optimization target is to maximize the annual transmittance of the system, an initial approach could be to consider ߬ ൌ 90° െ ߙୟ୴ୣ, where ߙୟ୴ୣ is the annual average solar elevation of the location as shown in Figure 37.   Figure 37 - The ideal light valve system is tilted (τ) in a way such that most of the solar elevations in a year (r) are captured by the acceptance angle of the design (2θmax).  4.3 Ray tracing Analysis for the Light Valve  For the ray tracing analysis presented in this chapter, it has been considered that the length of the valve elements is long enough that shade effects of each element cross section and  69  the frame in which the system is contained are negligible. Also, it was considered that the surface of the light valve reflectors is 90% specular reflective and 10% absorptive for the photosynthetically active radiation spectrum. A ray source which emulates the angular divergence of direct solar radiation (0.5°) was designed in TraceProTM to study the light valve system.   Figure 38 – Light valve ray tracing simulation setup.  The light transmittance through the light valve (IT/Io) was defined for the ray tracing simulations presented in this section as the ratio of the light flux incident on the planes after and before the light valve, both planes are identical to each other and parallel to the aperture plane of the light valve. Consequently, the optical transmittance reported in Figure 39 is the ratio of the light flux on the transmitted sunlight plane after the light valve (IT) divided by the light flux on the incident sunlight plane before the light valve (Io) as shown in Figure 38.   70   Figure 39 - Direct radiation light transmittance of the light valve system for different projected solar altitudes (ߙN). Rays within the light valve acceptance angle (േ30°) are efficiently transmitted and rejected otherwise.  Figure 39 summarizes the light transmittance through the light valve for direct radiation. For convenience, the light transmittance values in this chapter are reported as function of the projected solar altitude measured from the normal of the system (ߙ୒) as shown in Figure 39. The horizontal error considers the angular uncertainty of the rays from the ray tracing source (0.5°). One hundred thousand rays were used for the ray tracing simulations discussed in this section; an uncertainty of less than 1% of the optical transmittance values (IT/Io) for the ray tracing analysis was observed. As expected, efficient transmission occurs when the projected solar altitude (ߙ୒ሻ is within the light valve acceptance angle (െ30° ൑ ߙ୒ ൑ 30°), this acceptance angle is determined by the concentration ratio of the light valve constitutive compound parabolic concentrators (concentration ratio of two). As shown in Figure 39a the light transmittance of the light valve decreases for rays in the vicinity of its acceptance angle (ߙ୒ ൌ േ30°) mainly as result  71  of multiple reflections of the light rays on the reflective surfaces while transmitted through the system.    Figure 40 – Ray tracing sources for (a) direct (10°) and downward diffuse radiation (b).   Figure 41 – Optimal orientation of the light valve system where the inclination (߬ሻ	has to be optimized in accordance with the specific geographical location of the installation site. The light valve system is oriented in a north (N), south (S), east (pointing in the page) and west (pointing into the page) coordinate system.  72  The isotropic diffuse radiation transmission characteristics of the light valve system were studied. The diffuse radiation source designed for this purpose was calibrated by ray tracing the light valve system for 100% specular reflective valve elements resulting in an isotropic diffuse radiation transmittance value of 0.479 ± 0.005 (IT/Io); this transmittance value is consistent with the theoretical prediction for the light valve design when 100% specular reflective surfaces are used under downward completely isotropic diffuse radiation (0.475) [32,33]. Figure 40 shows the light valve system ray tracing setup accepting rays coming from both, the direct radiation source (40a) and the isotropic radiation source (40b). It has been found that the light valve system isotropic diffuse radiation transmittance is 0.411 ± 0.004 (IT/Io) when the surfaces of the compound parabolic reflectors are 90% specular reflective.  Figure 42 contrasts the expected light transmission of the light valve for different inclinations (shown as ߬ in Figure 41) during characteristic summer and winter days in a location 50° N latitude. The transmitted irradiance (IT) reported in Figure 42 is defined as the irradiance on the transmitted sunlight plane shown in Figure 41. Both comparisons consider ambient irradiance values equal to 450 W/m2 at all times when measured perpendicular to the direction of the incident sunlight. The red dotted line marks the optimal irradiance level for photosynthesis under ambient CO2 concentrations (390 ppm [57]) and temperatures between 20°C – 25°C. The orientation of the light valve system used for this comparison is shown in the isometric view in Figure 41 (light valve facing South and East-West aligned). As in previous sections, for the realistic scenarios in Figures 42 and 43, the use of an ethylene tetrafluoroethylene (ETFE) membrane (n = 1.40 at 550 nm) [83] parallel to the plane of the light valve aperture was considered as protective cover (shown in the section view of Figure 41). The objective of the ETFE cover [83] is to protect the optics of the system against environmental hazards (rain, wind  73  or snow) and it has been used for the simulations in Figures 42 and 43 to represent a realistic ray tracing setup.  Figure 42 – Light valve optical tranmittance for two characteristic days one in summer and the other in winter for a location at latitude 50° N.   Figure 43 - Optical transmittance of a light valve design with an inclination equal to 50° (τ=50°) facing South and East-West aligned  for a location 50° N latitude.  74  Figure 43 compares for different days the optical transmittance of a 50° tilted light valve design (߬ ൌ 50°) situated in a 50° N latitude location as shown in the isometric view in Figure 41. The light valve system has been optimized for direct radiation so no atmospheric diffusion was considered for the analysis in Figures 42 and 43. The light valve ray tracing analysis has shown optical transmittances above 80% for a considerable portion of the day in our target locations.  4.4 Light Valve Low Pressure Seal An important technical feature of the light valve design is the implementation of a low pressure seal to minimize air mass heat exfiltration. Air exfiltration results in considerable heat loss, and so it follows that an air tight structure is desirable for good thermal insulation.  For the construction of the light valve low pressure seal design, a compressible elastic material is used to produce the contact seal between valve elements (shown in yellow in Figure 44). The desirable properties for this elastic compressible material are low fatigue deformation and high thermal resistance. For the specific experimental device shown in Figure 44 fiberglass batting [98] was used as the seal material because of its good thermal insulation properties           (0.66 m2K/W or R-3.7 for every 0.025 m of material thickness) and low permanent deformation by cyclic compression (less than 15% after 15,000 cycles for 40% volume compression per cycle). Cyclic compression is defined for the purposes of the project described in this section as the action of compressing by contact with an adjacent valve element once the sealing material of the low pressure seal by closing and opening the light valve system. This low pressure seal design results in a total volumetric compression of 40% for the sealing material.    75   Figure 44 - The light valve design is shown in its transmissive state (a) and in its high thermal resistance state (b). The fiberglass low pressure seal is shown in yellow for both pictures.   Figure 45 - Optics performance comparison of the light valve system with and without low pressure seal.  The low pressure seal profile was designed to fit inside the overall light valve profile as shown in Figure 42. Ray tracing optimization was used to optimize the dimensions of the low  76  pressure seal profile and therefore minimize light obstructions by rejected rays and/or absorption due to multiple reflections. Figure 45 compares the light valve optical transmittance with and without the optimized low pressure seal design. Optical transmittance losses for the light valve of less than 3% where measured using ray tracing analysis as a result of the optimization of the low pressure seal profile. This analysis confirms that the incorporation of the low pressure seal material does not meaningfully alter the optical transmittance of the light valve element structure. It is important to clarify that the low pressure seal is entirely coated with the same highly reflective aluminized polyethylene film [99] used to be laminated on the light valve elements.     Figure 46 - Air exfiltration experimental setup  The effectiveness of this low pressure seal was tested experimentally using the setup shown in Figure 46. For this experimental setup, an air blower [100] pressurized a plastic bag attached to the lower portion of the light valve system. An anemometer [101] measured the volumetric air exfiltration ( ሶܸ ) through the contact of the low pressure seal and the valve elements. A barometer [102] measured the equilibrium manometric pressure (P) in the airbag  77  attached to the light valve system. The air conductance was calculated using the Equation 22, air conductance rates as low as 5.5E-6 m3/sPa per m2 after 1,000 actuation cycles for the light valve system have been measured experimentally.  ܥܣ௅௏ ൌሶܸܲ (22)  For the hypothetical scenario of a 3 m tall greenhouse with an air temperature difference in and out of the structure equal to 30°C (for example, 15°C inside the structure and -15°C outside), and outdoor wind blowing at 1 m/s, the expected air pressure difference between the air in and out of the greenhouse is 5 Pa assuming the validity of the stack or flue effect model. Using experimental air conductance measurements for the light valve, the exfiltration rate was calculated to be 2.75E-5 m3/s per m2 and the effective thermal loss is 0.022 W/K. This air exfiltration thermal loss represents 10% of the light valve design thermal conductance         (0.250 W/K).  4.5 Irradiance Control Using the Light Valve Solar tracking can be implemented in the light valve design by rotating the valve elements to follow the position of the sun through the day. The solar tracking characteristics of the light valve design open the opportunity of both, irradiance control during a heat wave and operation when optimal positioning of the light valve is not practical.   78  4.5.1 Optical Transmittance Control with the Light Valve The rotation of the light valve elements makes the light valve assembly able to track the sun in two dimensions as shown in Figure 47. The optical transmittance of the light valve system can be smoothly varied by rotating the light valve elements as can be seen in Figure 48. The light transmittance through the light valve (IT/Io) was defined for the ray tracing simulations presented in this section as the ratio of the light flux incident on the planes after and before the light valve, both planes are identical to each other and parallel to the aperture plane of the light valve. Subsequently, the optical transmittance reported in Figure 48 is the ratio of the light flux on the transmitted sunlight plane after the light valve (IT) divided by the light flux on the incident sunlight plane before the light valve (Io) as shown in Figure 47.   Figure 47 – Light valve optical transmittance control ray tracing setup.  There is an angular position for the light valve system which maximizes the optical transmittance of the design for every projected solar altitude. Figure 49a shows that even  79  projected solar altitudes out of the light valve design acceptance angle in the non-tracking mode can be efficiently transmitted by rotating the valve elements. For example, rays at 35° from the normal of the light valve aperture (ߙ୒ ൌ 35°) are captured by rotating the valve elements 15° (߮ ൌ 15°). Lower solar altitudes can be efficiently transmitted by rotating the light valve elements even further. Figure 49b exemplifies how projected solar altitude rays at ߙ୒ ൌ	60° can be transmitted with less than three average reflections when the light valve elements are rotated ߮ ൌ 44°.   Figure 48 – Light transmittance control with the light valve system by rotating the light valve elements (߮) for different solar altitudes (ࢻN).  The optimized optical transmittance of the light valve design for two dimensional solar tracking is presented in Figure 49 for direct and isotropic diffuse radiation (90% specular  80  reflective and 10% absorptive light valve reflectors). For the diffuse radiation analysis, it was concluded that the diffuse light transmission of the light valve decays with the angular position of the valve elements (߮) from its maximum diffuse light transmittance value (IT/Io = 0.411 ± 0.004) to IT/Io = 0 when the valve elements are completely closed at ߙ୒ ൌ േ90° (߮	= 74°). For completely isotropic diffuse light, the optimal position of the light valve elements is at ߮	ൌ	0°	ሺIT/Io = 0.411 ± 0.004).   Figure 49 - Optical transmittance comparison of the light valve system when working as a solar tracker.  Figure 50 presents the optimized rotation algorithm (߮) for the light valve elements when tracking the solar elevation (ߙN). This rotation algorithm is successfully implemented in Chapter 6 in a commercially available microcontroller [65] to code the tracking control for the valve elements. The commented code is included in the Appendix A of this dissertation.   81   Figure 50 - Optimal rotation of the valve elements (߮) when tracking the projected solar elevation (ࢻNሻ.  Figure 51 shows the optical transmittance of the solar tracking light valve design for a location 50° latitude N, facing South and East-West aligned as shown in Figure 41. Figure 51 contrasts the expected light flux transmission through the light valve (shown as IT in Figure 41) per active optics area for different inclinations (shown as ߬ in Figure 41) during characteristic summer and winter days. Both comparisons assume ambient irradiance values equal to 450 W/m2 at all times when measured perpendicular to the direction of the incident sunlight. The red dashed line marks the optimal irradiance level for photosynthesis under ambient CO2 concentrations and temperatures between 20°C and 25°C. Figure 52 compares for different days the optical transmittance of a 50° tilted solar tracking light valve (߬ ൌ 50°) located in a 50° N latitude site. No atmospheric diffusion was considered for Figures 51 and 52.   82   Figure 51 – Solar tracking light valve optical tranmittance for two characteristic days in summer and the winter for a location latitude 50° N.   Figure 52 - Optical transmittance of a solar tracking light valve design with an inclination equal to 50° (τ=50°) facing south and east-west aligned  for a location latitude 50° N.   83  The ray tracing analysis demonstrates a substantial improvement in the performance of the light valve design by rotating the valve elements to track the sunlight; the solar tracking capabilities of the adjustable angular position valve elements extend the use of the light valve system beyond the acceptance angle of the design for the non-tracking scenario. As in previous sections, for the realistic scenarios presented in Figures 51 and 52, the use of an ethylene tetrafluoroethylene (ETFE) membrane (n = 1.40 at 550 nm) [83] parallel to the plane of the light valve aperture was considered as a protective cover (shown in the section view of Figure 41).   4.6 Discussion of the Light Valve Design using Pareto Frontier Analysis The most important achievement with the light valve design is that its optical properties are independent of the effective insulation of the structure when closed. This characteristic of the light valve system largely decouples the thermal and optical responses of the structure providing a practical solution to maintain proper light transmission trough the greenhouse structure while reducing its energy use for heating. The development of the light valve system opens the opportunity of accessing high thermal resistances while conserving desirable light transmittances. Figure 53 shows a thermal and optical performance comparison between present day polycarbonate windows, the light tube composite structure design and light valve system design. Thermal and optical performances, defined as conflicting objectives for polycarbonate window technology are contrasted simultaneously using Pareto optimal frontiers. A Pareto optimal frontier is a multi-objective optimization in which a particular set of optimal solutions is used to define design limits for two or more correlated and contrasting parameters [103]. By definition,  84  the Pareto frontier is considered optimal because, for a given set of conditions, there is no other combination of correlated parameters which produce superior responses to all objectives [103].   Figure 53 – Thermal resistance and optical transmittance of polycarbonate windows, light tube composite structure and light valve designs are compared using Pareto optimal frontiers. The dotted portion of the lines (small dots) represent the region which is not practical for greenhouse farming applications.  An increase of the thermal resistance properties of polycarbonate covers can be achieved by adding layers of material which is a common practice in the greenhouse construction industry. In Figure 53 the dotted lines (small dots) represent the region of the Pareto optimal frontier in which the design is not practical for plant growth environments. Covers made of four layers of material are used in experimental high performance greenhouses [23], and for the purposes of the project discussed in this dissertation are considered as the practical limit for polycarbonate  85  covers. Quadruple layer polycarbonate covers have light transmittance values above 65% and thermal resistance values above 0.50 m2K/W (R-2.9) [104]. The light tube composite structure design extends the Pareto optimal frontier of the polycarbonate covers achieving thermal resistances of 2.73 m2K/W (R-15.5) for light transmittances above 34% when aluminized polyethylene film [79] is applied as coating material for the light tubes and low iron glass windows (n = 1.51 at 550 nm) [67,68] is used (shown as “Light Tube Mylar+LIG” in Figure 53). This level of insulation represents a 0.15 m thick light tube composite structure with 0.45 m tall compound parabolic concentrators; those dimensions are practical for the light tube composite structure to be installed below the greenhouse structural trusses and the compound parabolic concentrators in the space between trusses; to the best of knowledge of the author, the height of the space between trusses in a commercial greenhouse is not larger than 0.50 m. Thermal resistance values below 0.50 m2K/W (R-2.9) are also not practical for the light tube composite structure (polycarbonate covers offer a better solution for those thermal resistance values). Optical transmittances above 58% can be achieved for the same insulation level when the light tubes are coated with multi-layer enhanced specular reflective film [75] and low iron glass [67,68] light tube windows coated with triple layer antireflective films [73] (shown as “Light Tube ESR+LIG+3ARL” in Figure 53). As shown in Figure 53, the light valve design does not just move the Pareto optimal frontier, but largely decouples the light transmittance to the thermal insulation of the structure. Consequently, a wide range of insulation values can be achieved using the light valve design while also conserving an ideal average direct radiation optics performance above 80% most of the time in our target applications (-30° ൑ ߙ୒ ൑ 30°). For practical purposes, the best location for the installation of the light valve system is in the space between structural trusses in the  86  greenhouse (0.50 m). 0.46 m high valve elements represent a theoretical thermal resistance value of 4.00 m2K/W (R-22.7) for the design discussed in Section 4.2. As mentioned before, very high performance windows (triple layer low iron glass filled with argon [61]) achieve ideal average transmittance values above 50% for thermal resistance values of 0.77 m2K/W (R-4.4) [61]. The light valve system ideally achieves more than five times the thermal insulation of these high performance windows and 60% more of their peak light transmittance values. In comparison, the ideal light transmittance of the light valve system is 60% higher than the transmittance of a fiber optics lighting system [90,91]. For the theoretical comparison presented in Figure 53, the use of an ethylene tetrafluoroethylene (ETFE) membrane (n = 1.40 at 550 nm) parallel to the planes of the light valve and light tube composite structure aperture has been taken into consideration for an accurate comparison with the polycarbonate window greenhouse (those protective ETFE covers are shown in the section views of Figures 30 and 41) [83]. Recent case studies have demonstrated success on the application of EFTE membranes in the construction industry where it has been forecasted an important production cost reduction for those materials in the near future [105,106]. In Chapter 7, it is discussed that the materials selected for the construction of both, the light valve and light tube composite structure designs are inexpensive, accessible and readily available.  The results of this Pareto optimal frontier analysis provide evidence that this new light valve system exceeds the performance of present day greenhouse covers and represents a practical variable light transmission and thermal insulation control system for cold climate locations. The experimental work with the light valve design is detailed in Chapters 5 and 6.   87  Chapter 5: Small Scale Experimentation with a Light Valve Device The objective of the small scale experimentation presented in this chapter is to characterize the thermal and optical properties of an experimental light valve device. The data presented in this chapter support the theoretical and numerical predictions done in Chapter 4 and support the conclusion that the light valve system could help to reduce the energy use for heating in present day greenhouses while keeping appropriate sunlight transmission levels.  5.1 Description of the Experimental Locations The first experimental location was the experimental greenhouse at the University of British Columbia (UBC) Vancouver campus shown in Figure 54a (49.26° N, 123.25° W). The UBC Vancouver campus location offered the advantage to test the system under natural sunlight and real-life greenhouse ambient conditions. For this location, the experimental device shown in Figure 54c was located in the south greenhouse compartment of UBC’s Horticulture Greenhouse. This experiment started on April 2012 and finalized on January 2013. As discussed in Chapter 2, the target locations for the application of the light valve technology are places with heating season temperatures below the average farmer economic feasibility threshold (0°C), but sunny enough to provide sufficient sunlight both for plant growth and thermal heating. Our second location for the light valve greenhouse experiment was an open space on the campus at the University of British Columbia Okanagan campus shown in Figure 55a (49.93° N, 119.39° W). The Okanagan Valley, specifically the city of Kelowna BC Canada, presents the characteristic climatic conditions of the target locations for the application of the light valve system with heating season ambient temperatures below 0°C and average irradiance values during the cold season above 100 W/m2. The main interest with the UBC Okanagan  88  campus experiment (Figure 55b) is to test the thermal response of the light valve under sub-zero temperature conditions. This experiment ran from March 2013 to March 2014.   Figure 54 – Satellite view (a) of the experimental greenhouse at the University of British Columbia (UBC) Vancouver campus (49.26° N, 123.25° W), the East-West offset angle of this greenhouse is ࣌ ൌ ૛૞°. The light valve experimental device (c) was contained in the south compartment of the greenhouse (c).     89   Figure 55 – Satellite view (a) of the alley of the engineering department building at the University of British Columbia Okanagan campus (49.93° N, 119.39° W), the experimental device (b) was East-West alligned (࣌ ൌ ૙°).  5.2 Tools, Methods and Experimental Light Valve Device Construction The small scale light valve experiment consisted of three main elements: (1) the light valve module, (2) the insulating box in which the light valve module was installed, and (3) sensors and electronics used for data collection and to control the opening and closing of the valve elements. Figure 56 presents the computer aided design model of the light valve module in its light transmissive and thermally insulating states. The valve element profiles (Figure 57a) were cut with a computer controlled hot wire using expanded polystyrene foam (Figure 57b) with a thermal resistance value of 0.73 m2K/W (R-4.1) for every 0.025 m of material at 23°C (density equal to 22 kg/m3) [63]. Figure 57c shows the feature designed to contain the low pressure sealing material (detailed in Section 4.4).   90   Figure 56 - Light transmissive and thermally insulated states of the light valve experimental device design.   Figure 57 – Computer model of a valve element (a) showing the sealing material profile (c). A computer controlled hot wire was used to cut the foam valve elements (b).  In order to simplify the design, manufacture and installation of the light valve experimental device, the inclination angle of the system (shown as ߬ in Figure 41) was not  91  optimized for the geographical conditions of the experimental locations in Vancouver and Kelowna, Canada (approximately ߬ ൌ 50°), a horizontal light valve design was used (߬ ൌ 0°). The greenhouse where the experimental device was installed has a 25° East-West offset angle as shown in Figure 54a (ߪ ൌ 25° in Figure 19), because of the limited available space in the greenhouse it was not practical to correct this offset for the experimental device. Solar tracking control for the valve elements was not implemented for this experiment.  Figure 58 - Sectional view of the prismatic film (a) and its installation on top of the light valve experiment (b).  Not optimally tilting the light valve experimental device and/or implementing solar tracking for the valve elements results in an important portion of the rays during a standard day to be rejected because of their entrance angle to the system (shown as ߙ୒ in Figure 38) is out of the light valve acceptance angle (െ30° ൐ ߙ୒ ൐ 30°). In order to correct the angular direction of those rays (ߙ୒) to meet the light valve acceptance angle (െ30° ൑ ߙ୒ ൑ 30°), a prismatic film with prisms at an angle of 70° [107] (Figure 58a) was used on top of the experimental device as shown in Figure 58b (n = 1.59 at 550 nm). The prismatic film profile was installed co-planar  92  with the light valve profile and on top of a 0.005 m polycarbonate protective cover (n = 1.59 at 550 nm) [88].   Figure 59 - Light valve experimental device assembly  A 2.1 m3 insulating box (1.7 m X 1.1 m X 1.1 m) shown in Figure 59c was constructed to emulate a structure in which the roof is the light valve module (Figure 59a). The material used for the construction of the box was 0.15 m thick expanded polystyrene foam blocks (EPS foam) [63]. The inner walls of the light valve insulating foam box were coated with 90% reflective surfaces (specular reflective for the East and West walls [108] and diffuse reflective for the  93  South and North walls [109]) as shown in Figure 61 to emulate the light distribution one may expect in a full size greenhouse structure.   Figure 60 - Lamination of aluminized polyethylene film on expanded polystyrene foam.  Aluminized polyethylene film [78] was used as the reflective coating for the valve elements; this material does not change the spectral distribution of the light (PAR spectrum) as a result of reflecting from it [110,111]. Ideal specular reflectance values ranging from 85% to 95% (visible spectrum) for the aluminized polyethylene film have been reported in the literature [79,112-114]. This reflectance value was verified experimentally obtaining an average specular reflectance for the aluminized polyethylene film of 88% ± 3% using a 650nm laser at 45° incidence angle. The aluminized polyethylene film was laminated on the light valve foam profiles (Figure 60a) using polyurethane adhesive. The optimized lamination process developed for this purpose accomplished uniform surfaces as can be seen in Figure 60b.   94  The light valve module frame shown in Figure 59b was positioned on top of the light valve insulating foam box to contain the valve elements. An angular uncertainty for the position of the light valve elements when in their light transmissive state was estimated to be േ2°; this angular position uncertainty results from a combination of the relative angular offset of each valve element (േ1.5°) and the angular uncertainty of the hard stop (േ0.5°) used to fix the position of the valve elements in their open state as shown in Figure 56a.   Figure 61 – Inner view of the light valve experimental device.  The light valve module inner walls were coated with fiberglass covered with a diffuse reflective (70% diffuse reflectance) polytetrafluoroethylene film (white Teflon® film) [115]. The objective of this film is to act as a low friction cover for the low pressure seal on the inner walls of the light valve module (Figure 61). The low pressure seal of the light valve module intends to reduce the air exfiltration losses through the contact between the extreme faces of the valve elements and the inner surface of the light valve module’s walls. Fiberglass batting was used as compressible sealing material for the light valve module low pressure seal; a detailed description  95  of the use of this material in low pressure seals can found in Section 4.4. An appropriate contact between the light valve module inner walls and the valve element extreme faces was achieved by the low friction and low pressure seal as shown in Figure 61.  The actuator used to rotate the valve elements from its light transmissive to its highly insulating state was a 12V compact DC gear-motor (5.5 Nm at 0.6 RPM). The DC gear motor was coupled to the central valve element and the torque was transmitted by a four bar mechanism attached to the lower region of the valve elements as shown in Figure 56. The total actuation time for opening and closing the light valve experimental device was 30 seconds with this design. Commercial off-of-the-shelf sensors were used to measure temperature and irradiance in the light valve experiment. A data acquisition card model NI USB6008 12Bit controlled by LabView was used to collect data from the sensors at a sampling rate of 0.1 Hz; the data logging error of the data card is equal to 5 mVrms for the range of voltages measured. The temperature in the experimental device was measured using precision integrated-circuit temperature sensors (LM61) [116] with a measurement range of -30°C to 100°C. The LM61 temperature sensor response is linearly proportional to the temperature in Celsius degrees where a maximum uncertainty of ±2°C for the full temperature operation range is recommended by the manufacturer [116]. In order to minimize the thermal radiation interference on the temperature sensors, a multi-plate radiation shield [117,118] was used. The irradiance was measured using a precision high-speed light to voltage converter combining a photodiode and a transimpedance amplifier (TSL254R) whose response is proportional to the irradiance level [119]. The systematic uncertainty of the TSL254R was measured to be ± 4.8% with dark state fluctuations of ± 2.5 W/m2 by using an incandescent halogen light source [120]. Diffuse acrylic, glass and infrared reflective films (hot mirrors by  96  Edmund optics) were used to correct the cosine error of the sensor (diffuse acrylic) [121], and to reduce the ultraviolet (glass) and infrared (hot mirror) [122] contributions narrowing the sensor response to the PAR spectrum (400 nm to 700 nm) [40]. Figure 57 shows the spectral response comparison of the corrected TSL254R sensor versus a commercial LI-190 PAR sensor [123]. The dotted line represents the original spectral response of the TSL254R light to voltage converter and the red solid line represents the response after spectral correction using the acrylic, glass and hot mirror. The dashed line represents the spectral response of a commercial LI-190 PAR sensor [123].   Figure 62 - Spectral response comparison of the corrected TSL254R irradiance sensor and a commercial LI-190 PAR sensor [123].  When operating in automatic actuation, the position of the light valves was controlled using an Arduino microcontroller [65]. The opening and closing of the light valve experimental  97  device was determined by the ambient irradiance. Two irradiance thresholds were used to trigger the opening and closing actuation of the light valve experimental device, the first threshold at 25 PAR W/m2 where for irradiances above this value the system keeps or transitions to its light transmissive state (open state). The second threshold at 25 PARW/m2 where for irradiances below this value the system keeps or transits to its highly thermal resistive state (closed state). An actuation time delay was coded to prevent unwanted actuation of the system. The ambient irradiance had to be above or below the thresholds for more than five minutes to trigger the actuation.  5.3 Optical Transmittance Experimentation with the Small Scale Light Valve Experimental Device To understand the specific characteristics of the optics of the small scale experimental device, a ray tracing analysis using the same parameters of the experiment was analyzed.  5.3.1 Detailed Ray Tracing Simulations of the Experimental Device The ray tracing analysis presented in this section incorporates the use of the prismatic film and a polycarbonate cover on top of the light valve experimental device (Figure 63b). The optical characteristics of the wall surfaces of the insulating box and light valve elements were taken into consideration for the ray tracing analysis. The properties of the materials used for this ray tracing simulation are detailed in Section 5.2.  The prismatic film and the polycarbonate sheet are refractive optical devices which are strongly dependent on the incidence angle of the light. A full 3D ray tracing analysis was performed on the light valve experimental device model as shown in Figure 63a; the 3D solar  98  geometry [124] has been defined by a pair of two dimensional solar elevation ray projections in perpendicular planes as shown in Figure 64. The projected solar elevation angles ߙ and ߛ can be modeled by Equations 23 and 24 respectively where ߪ is the East-West offset angle of the light valve experimental device (shown in Figure 54), ߱ is the hour angle (sun’s angular direction relative to the solar noon) [81], ߩ is the solar altitude angle (defined by Equations 25 and 26), δ is the solar declination and λ is the latitude of the site.   Figure 63 – 3D ray tracing simulation setup of the light valve experimental device (a) where the use of the prismatic film and polycarbonate sheet is detailed.  The light valve experimental device was ray traced using both direct and diffuse radiation sources (as detailed in Section 4.3). Figure 65 shows the resulting direct radiation optical transmittance for the light valve experimental device using the ray tracing setup shown in Figure  99  64. The light transmittance through the light valve (IT/Io) was defined for the ray tracing simulations presented in this section as the ratio of the total light flux incident on top of the inner bottom surface of the experimental device (shown in Figure 64 as IT) divided by the light flux incident on the horizontal plane before the prismatic film (shown in Figure 64 as Io), both planes are identical each other and parallel to the aperture plane of the light valve.   Figure 64 – Light valve experimental device ray tracing setup  tan ߙ ൌ sin ߩcos ߩ cosሺ߱ ൅ ߪሻ (23)  100  tan ߛ ൌ sin ߩcos ߩ cosሺ90° ൅ ߱ ൅ ߪሻ (24) ߩ ൌ 90° െ ߚ (25) cos ߚ ൌ sin ߜ sin ߣ ൅ cos ߜ cos ߣ cos߱ (26)   Figure 65 – Ray tracing direct radiation optical transmittance for the light valve experimental device.  Low optical transmittance values (IT/Io) have been measured in the ray tracing model of the light valve experimental device for high solar altitudes (ߙ), because some rays are rejected by total internal reflection (TIR) in the prismatic film (Figure 66). The diffuse radiation ray tracing optical transmittance (IT/Io) was measured to be 0.220 ± 0.002. One hundred thousand rays were  101  used for the ray tracing simulations discussed in this section; an uncertainty of less than 1% of the optical transmittance values (IT/Io) for the ray tracing analysis was observed. The theoretical ray tracing light transmittance of the light valve experimental device (ܶ) has to be calculated considering both, the diffuse ( ୢܶ୧୤୤୳ୱୣ) and direct ( ୢܶ୧୰ୣୡ୲) light transmittance contributions as described in Equation 27, where z is the diffuse radiation portion for a specific day and time as a function of the latitude, altitude, wavelength and other particle and aerosol (colloidal suspension of particles) characteristics (0 ൑ ݖ ൑ 1) [125].  ܶ ൌ ሺ1 െ ݖሻ ୢܶ୧୰ୣୡ୲ ൅ ሺݖሻ ୢܶ୧୤୤୳ୱୣ (27)   Figure 66 – Rays rejected in the prismatic film by total internal reflection  The model used to calculate the proportion of diffuse (z) and direct light (1 - z) under clear sky conditions was a broadband simplification of the Solis model [125]. For example, in a  102  clear day during the first days of autumn in Vancouver, Canada, ݖ ranges from z = 0.1 to z = 0.2 for most of the day (10 to 20% of the available ambient sunlight is diffuse and 80% to 90% is direct), and then increases up to z = 0.5 after 7 pm. approaching to z = 1 in the vicinity of the dusk.  5.3.2 Optical Transmittance Measurements in the Small Scale Light Valve Experimental Device Optical transmittance measurements were taken in the light valve experimental device from August 2012 to September 2012 at the UBC Vancouver campus experimental location. The optical transmittance experimentation with light valve consisted of keeping the valve elements in its light transmissive state (open state) while measuring the horizontal irradiance on top of the inner bottom surface of the experimental device (plane shown as IT in Figure 64) and out of the experimental device on top of the prismatic film (plane shown as Io in Figure 64). Four points were selected to measure the irradiance on the inner bottom surface of the experimental device and one point was used to measure the ambient irradiance on top of the experimental device. All the sensors were set to take data with a frequency of 0.1 Hz, storing the average irradiance value every five minutes in memory for later retrieval.  Figure 67 shows the interior of the experimental device during the optical transmittance experiments. The experimental optical transmittance measured in the light valve from August 14, 2012 to September 2, 2012 was compared with the ray tracing model predictions for the same days and times as shown in Figures 68 and 69. The red dots in Figures 68 and 69 represent the average irradiance readings of the four selected sensors positioned on the inner bottom surface of the light valve experimental device and the black solid line is the prediction of the ray tracing  103  model. The horizontal uncertainty of the measured data (red points) is the data logger averaging time. The vertical uncertainty of the measured data points (Figure 69a) has been assumed to be the standard error of the readings of the four light sensors.  Figure 67 – View of the interior of the light valve experimental device from below of the light valve elements. The color dispersion noticed in the picture was caused by the prismatic film. The reflective material, used to construct the light valve experimental device, does not change the spectral distribution of the reflected light.  The predicted irradiance in the experimental device was calculated by multiplying the ambient irradiance measured on top of the experimental device times the predicted ray tracing optical transmittance of the specific time of the day (shown as ܶ in Equation 27). The two black dotted lines in Figure 69a represent the error of the irradiance model which is a function of the ambient irradiance sensor uncertainty and the effective ray tracing uncertainty. The ray tracing uncertainty was calculated by considering the ray tracing simulation uncertainty (± 1.0% of the optical transmittance value), the measured angular position error of the light valve elements (± 1.1% of the optical transmittance value) and the spatial positioning error of the light valve experimental device (± 0.5% of the optical transmittance value).   104   Figure 68 - Predicted and experimental irradiance comparison for a week of measurements in the Vancouver experimental device. Selected portions of the data from each day were omitted (11:55 pm - 12:35 pm) due to uncharacteristically high irradiance values.  From 1:00 pm to 3:00 pm each day for August 14 to 21, 2012 and from 10:00 am to 11:00 am each day for August 30 to September 2, 2012 the UBC Vancouver greenhouse shade screens were deployed; the shade screens were assumed 50% shading in the ray tracing model. From 2:00 pm to 4:00 pm each day from August 14 to 21, 2012 and from 3:00 pm to 5:00 pm each day from August 30 to September 2, 2012 a curtain in the UBC’s Horticulture Greenhouse blocked the ambient irradiance sensor resulting in erroneous irradiance predictions (as shown in Figure 69a from 3:00 pm to 5:00 pm). In order to test the ray tracing model for those times of the day, historical ambient irradiance measurements (UBC Climate Station [126]) were used to simulate the predicted irradiance in the experimental device from 3:00 pm to 5:00 pm for    105  Figure 69a (shown as a black dotted line). The data before 6:00 am and after 6:00 pm was not included (dawn and dusk). Selected data points from 12:00 pm to 1:15 pm were omitted because of uncharacteristically high irradiance values measured as result of inadvertent concentration by the experimental device. In Figure 69a, a discrepancy between the ray tracing model and the measured data from 8:00am to 9:00am can be noticed; it is suspected that this is the result of partial shading by nearby greenhouse structural elements. The performance of the experimental device is dependent on the solar elevation and it varies with the position of the sun during the day (Figure 65). The highest optical transmittance values under clear sky conditions were measured from 10:00 am to 11:00 am for the data set presented in Figure 68 and from 11:00 am to 12:00 pm for the one presented in Figure 69. The average of the optical transmittance readings in the experimental device from 10:00 am to 11:00 am (August 15 to 17, 2012) was 0.518 ± 0.105 in agreement with the average ray tracing optical transmittance prediction of 0.497 ± 0.009 for the same data points. For the data set presented in Figure 69 the average optical transmittance measured in the experimental device from 11:00 am to 12:00 pm (August 31 to September 2, 2012) was 0.445 ± 0.035 in agreement with the ray tracing prediction of 0.439 ± 0.037 for the same data points. The ray tracing optical transmittance model predicts that from 1:00 pm to 3:00 pm most of the incident direct light was rejected by total internal reflection in the prismatic film on top of the experimental device (Figure 66). The predicted sunlight transmittance by the model from 1:30 pm to 3:00 pm (August 31 to September 2, 2012) was 0.115 ± 0.046 and the average transmittance measured for the same days and times was 0.078 ± 0.030. Similarly, the predicted sunlight transmittance by the model from 1:00 pm to 2:00 pm (August 15 to 17, 2012) was 0.071 ± 0.009 and the average transmittance measured for the same data points was 0.053 ± 0.008.  106   Figure 69 - Predicted and experimental irradiance comparison with the light valve experimental device from Aug. 27 to Sep. 2 (Vancouver). Selected portions of the data from each day were omitted (12:00 pm to 1:15 pm) due to uncharacteristically high irradiance values. The zoom-in view of Sep. 2 (b) shows the error bars of the measurements and the expected uncertainty of the ray tracing model (dashed lines).  107  The fractional difference between the measured transmittance and the predicted transmittance by the model for each data point was measured to be about 12% for the data sets taken from August 15 to 20, 2012 and from August 27 to September 20, 2012. This fractional difference indicates that in average, the ray tracing model predictions are off by about 12% from the measured data in accordance with the expected uncertainty of the model and the experimental measurements (combined uncertainty of about 10%). For the data sets presented in Figures 68 and 69 the coefficient of determination (r2) was calculated finding values of r2 = 0.90 (data set Figure 68) and r2 = 0.89 (data set Figure 69) indicating that about 90% of the variation in the model can be explained by the variation of the measured irradiance. It results very difficult to define a threshold value for the determination coefficient that validates a ray tracing model, but based on the definition of the determination coefficient [127], a determination coefficient of 0.9 signifies that the standard deviation of the ray tracing model’s errors is one third the size of the standard deviation of the errors one may expect by using an intercept-only model. This gives confidence that the ray tracing model was a useful tool for the prediction of the light transmittance in the experimental device. As expected, considering the clear sky model used to predict the portion of direct and diffuse ambient radiation (Solis model [125]), the ray tracing model has demonstrated to be a better predictor for clear sky days where the fractional difference between the measured transmittance and the predicted transmittance by the model for each data point goes down to about 10% from August 15 to August 17, 2012 and from August 31 to September 20, 2012. The correlation and determination coefficients were also improved during predominantly sunny and clear sky days, for example, a value of r2 = 0.93 was calculated from August 31 to September 2,  108  2012 in contrast with days with more cloudy periods observed (August 27 to 29, 2012) where a value of r2 = 0.80 was calculated. The optical transmittance values achieved by the light valve experimental device are lower than what one may achieve in a target application mainly because of the simplified design used for the experimental device. The horizontal light valve design required the use of a prismatic film to redirect the incident light resulting in important Fresnel losses for low and high solar elevations (total internal reflection). Moreover, the UBC Horticulture Greenhouse where the experimental device was contained forced a 25° offset for the experimental device relative to the north-south axis. However, since the measured irradiance values in the experimental device compares well with the predicted irradiance by the ray tracing model under the same conditions, we are confident that the direct optical transmittance of the light valve can exceed values of 70% (IT/Io ≥ 0.7) for most of the solar elevations in our target locations (-30° ≤ αN ≤ 30°). The objectives of the experimental device presented in this chapter were to demonstrate the application of the light valve in a physical device and to validate the ray tracing analysis done for the light valve system. While the experimental device geometry is not ideal, the results obtained with it are meaningful because they verified that the ray tracing model predicts the optical behavior of the light valve system well and that the light valve design can be implemented in a physical device.  5.3.3 Optical Transmittance Control with the Small Scale Light Valve Experimental Device The optical transmittance control of the light valve experimental device was tested measuring the transmitted irradiance on top of the inner bottom of the experimental device  109  (shown as “Transmitted Sunlight Plane (IT) in Figure 64) while the system was transitioned from the open to the close state. The frequency of the data sampling for this experiment was 25 Hz. Figure 70 describes the transition of the light valve elements angular position (߮ሻ from their completely open state at ߮ൌ0° (70a), to their highly insulating and completely closed state at ߮ =74° (70c). The black line represents the irradiance inside the experimental device (IT). Figure 70b is the optimal angular position of the light valve which maximizes its transmittance for the specific day and time of the experiment (߮ൌ35°).   Figure 70 - Experimental irradiance control with the light valve device.  Stable intermediate irradiance values were achieved with the light valve experimental device by rotating the valve elements to an angular position different than the optimal transmission angle as shown in Figure 70. The experimental observations presented in this section provide empirical evidence of the smooth light transmittance control opportunities with  110  the light valve system. Chapter 6 describes experimentation with the light valve system in a fully functional greenhouse where the experimental device was designed to actively track the solar position by changing the angular position of the valve elements as described in Section 4.5.1.  5.3.4 Day Light Integral in the Small Scale Light Valve Experimental Device In greenhouses, the daily light integral is defined as the total photosynthetically active radiation (PAR) energy incident on the crops plane per day per unit area. The uniformity of the daily light integral is one of the most important parameters in the design of commercial greenhouses; it determines the total energy incident on the crops and it has to be as uniform as possible over the total growing area in order to guarantee evenness of crop growth [128]. Commercial greenhouses are designed so the daily light integral of the darkest spot in the structure is at least 70% of that of the brightest spot (red dotted line Figure 71) [95]. The bars in Figure 71 show the experimental average daily light integral of the readings of four light sensors for two weeks of operation, the sensors were positioned on the inner bottom surface of the light valve experimental device (shown as “Transmitted Sunlight Plane (IT) in Figure 64). The average daily light integral of the darkest point in the experiment (Position 2) represents 63% (Week 1) and 73% (Week 2) of the average light integral of the brightest point in the experiment (Position 3). Acceptable uniform daily light integral distributions can be achieved with the light valve experimental device based on the empirical evidence presented in this section.   111   Figure 71 - Average daily light integral of the readings of four sensors in the light valve experimental device.  5.3.5 Durability Study of the Specular Reflective Surfaces on the Light Valve Elements The interior air in a greenhouse typically contains water vapor, fertilizers, dust and organic matter [129]. Scratches caused by friction of particles on the light valve element surfaces as result of its cyclic actuation may represent a reduction in the specular reflective properties of the system. As mentioned in Section 5.2, the reflective valve element surfaces were achieved by the lamination of a specular reflective aluminized polyethylene film [79] on the light valve foam elements. The specific aluminized polyethylene film used for the construction of the light valve experimental device consists of a 125 ߤm thick transparent polyethylene film metalized on both sides using aluminum deposition. After lamination, the transparent polyethylene film serves as a protective cover for the reflective aluminum deposition cover on the inside surface of the film.  112  A long term operation of the light valve system equivalent to opening and closing the system twice per day for 20 years (15,000 opening and closing cycles) was simulated by opening and closing the light valve system once every 90 seconds for a period of time equal to seven days in the UBC’ Horticulture Greenhouse. At the end of this accelerated long term operation experiment, the scratches on the valve element reflective surfaces where identified and studied. It was measured that the average scratch has a depth of 50 ߤm after 15,000 light valve actuation cycles and the scratches cover less than 4% of the reflective surfaces. The empirical evidence gives confidence that the transparent polyethylene film (125 ߤm) is not penetrated by the abrasive particles and therefore the reflective aluminum deposition on the inner surface of the laminated polyethylene film [79] is not compromised.   5.4 Thermal Resistance Experimentation with the Small Scale Light Valve Experimental Device The thermal resistance of the small scale experimental device was studied using a customized thermal model and experimental thermal decay measurements.  5.4.1 Thermal Energy Model for the Analysis of the Light Valve Experimental Device The thermal properties of the small scale experimental device structure were studied by measuring the decay of the air temperature in the experiment when containing a well-known thermal mass. For this experiment, the light valve device was kept closed (high thermal resistance state) and 0.08 m3 of hot water were introduced in four 0.02 m3 containers. The air temperature inside and outside of the experiment was measured with a frequency of 0.1 Hz.   113   Figure 72 – Analog thermal circuit of the UBC Okanagan light valve experiment.  A simplified thermal model of the heat transfer interactions in the experiment was used to compare the thermal resistance of the light valve inferred from the experimental observations with the theoretical prediction. The simplified thermal model presented in this section has two objectives to accomplish: (1) to understand the dominant heat transfer mechanisms of the light valve experimental device and (2) to infer an early estimate of the thermal resistance of the light valve experimental device structure. This model considers three thermal masses, (1) the light valve structure, (2) the air contained in the experimental device and (3) the water used as thermal  114  mass. For the formulation of the thermal model presented in this section, an electrical analogy for the heat transfer interactions was used. In analogy to an electric circuit, the heat flux corresponds to the current, the temperature difference corresponds to the voltage difference, the thermal resistance corresponds to the electrical resistance, the heat capacity of a material corresponds to the electrical capacitance, Ohm’s law corresponds to Fourier’s law of heat transfer, and the circuit reduction techniques used for electric circuits apply [9]. Figure 72 shows the simplified thermal circuit used for the model where ୶ܶ represents average absolute temperatures (K), ܴ୶ thermal resistances (K/W), ܳୣ୶ heat losses by exfiltration (W), ܳୱ୵୰ short wavelength radiation heat transfers (W), ܳ୪୵୰ long wavelength radiation heat transfers (W), ܭ୶ heat capacities of the thermal mass systems (J/K) and ܫୱ୭୪ is the horizontal irradiance measured on top of the experimental device (W/m2). Equations 28, 29 and 30 represent the energy balances of the three thermal mass systems studied. These were containers filled with hot water (w), air contained in the experimental device (air) and the structure of the experimental device (st).  ܭ୵ d ୵ܶdݐ ൌ ܳ୪୵୰,୵,ୱ୲ ൅ ܳ୵,ୟ୧୰ (28) ܭୟ୧୰ d ୟܶ୧୰dݐ ൌ ܳୟ୧୰,ୱ୲ െ ܳ୵,ୟ୧୰ െ ܳୣ୶ (29) ܭୱ୲ d ୱܶ୲dݐ ൌ ܳ୭୳୲,ୣ୯ െ ܳ୪୵୰,୵,ୱ୲ െ ܳୟ୧୰,ୱ୲ (30)  The solution of the energy balances presented in Equations 28, 29, and 30 is calculated every five minutes assuming steady state conditions and single dimensional heat transfer  115  mechanisms for conduction, convection and radiation. The sign convention used for the energy flux is positive for the energy leaving the mass system and negative for the entering energy. As shown in Figure 72, two heat fluxes define the energy balance of the hot water thermal mass (Equation 28): the equivalent long wavelength radiation heat transfer from the hot water thermal mass to the experimental device structure (ܳ୪୵୰,୵,ୱ୲) and the heat transfer from the hot water thermal mass to the air contained in the experimental device (ܳ୵,ୟ୧୰). On the other hand, three heat fluxes define the energy balance of the air contained in the experimental device as shown in Equation 29: the heat transfer from the hot water thermal mass to the air contained in the experimental device (ܳ୵,ୟ୧୰), the heat transfer from the air contained in the experimental device to the experimental device structure (ܳୟ୧୰,ୱ୲) and the air exfiltration heat losses (ܳୣ୶). Likewise, the thermal balance of the experimental device structure mass system (Equation 30) is defined by the equivalent heat transfer from the structure to the surroundings (ܳ୭୳୲,ୣ୯), the equivalent long wavelength radiation heat transfer from the hot water thermal mass to the experimental device structure (ܳ୪୵୰,୵,ୱ୲) and the heat transfer from the air contained in the experimental device to the experimental device structure (ܳୟ୧୰,ୱ୲). Assuming that the only effect of the resulting internal energy variations defined by the energy balances in Equations 28, 29 and 30 are temperature differences in the three thermal mass systems (containers filled with hot water, air contained in the experimental device and experimental device structure), the time dependent temperatures of the three thermal mass systems can be approximated by solving those energy balances for n discrete time periods (∆ݐ). For the specific case of the model presented in this section, the duration of each time period is five minutes (∆ݐ ൌ 300s). Defining that the heat capacity of each thermal mass system (ܭ୶) is  116  the product of its specific heat capacity (ܿ୶), volume ( ୶ܸ) and density (ߩ୶), the temperatures of the three thermal mass systems at the period n can be calculated using Equation 31 for the containers filled with hot water assumed to have a uniform temperature for the whole thermal mass ( ୵ܶ௡), Equation 32 for the air contained in the experimental device assuming a uniform temperature for the whole thermal mass ( ୟܶ୧୰௡) and Equation 33 for the experimental device structure at the middle plane between its outside and inside surfaces ( ୱܶ୲௡).  ୵ܶ௡ ൌ ୵ܶ௡ିଵ ൅ܳ୪୵୰,୵,ୱ୲௡ିଵ ൅ ܳ୵,ୟ୧୰௡ିଵܿ୵ ୵ܸߩ୵ ሺ∆ݐሻ (31) ୟܶ୧୰௡ ൌ ୟܶ୧୰௡ିଵ ൅ܳୟ୧୰,ୱ୲௡ିଵ െ ܳ୵,ୟ୧୰௡ିଵ െ ܳୣ୶ܿୟ୧୰ ୟܸ୧୰ߩୟ୧୰ ሺ∆ݐሻ (32) ୱܶ୲௡ ൌ ୱܶ୲௡ିଵ ൅ܳ୭୳୲,ୣ୯௡ିଵ െ ܳ୪୵୰,୵,ୱ୲௡ିଵ െ ܳୟ୧୰,ୱ୲௡ିଵܿୱ୲ ୱܸ୲ߩୱ୲ ሺ∆ݐሻ (33)  The equivalent long wavelength radiation heat transfer from the hot water thermal mass to the experimental device structure (ܳ୪୵୰,୵,ୱ୲) is defined by Equation 34 where ୱܶ୲ is the temperature at the middle plane of the experimental device outside and inside surfaces and ୵ܶ is the average temperature of the hot water thermal mass. ܴୣ୯,୵,ୱ୲ is the equivalent long wavelength radiation thermal resistance between the experimental device structure and the hot water thermal mass defined in Equation 35 where ܴୱ୲ is the thermal resistance of the experimental device structure from its surface to its middle point fitted by the thermal model, ܣ୵ is the surface are of the water containers (ܣ୵ = 1.12 m2) and ݄୰,୵,ୱ୲ is the effective radiation conductance between the hot water thermal mass and the experimental device structure. Equation 36 shows the  117  simplified calculation used for the effective radiation conductance (݄୰,୵,ୱ୲) [9] where ߝ୵ is the fitted emissivity of the hot water containers and ߪ is the Stefan–Boltzmann constant                  (5.67 = ߪE-8 W/m2K4). For the purposes of the model described in this section, the emissivity of all long wavelength radiation emitting surfaces was assumed to be constant [130,131]. A more complex model for ܳ୪୵୰,୵,ୱ୲ can be defined by measuring the temperature of the inner surface of the experimental device structure for every time period. Nevertheless, this simplified method has demonstrated experimentally to reproduce well the thermal behavior of the long wavelength radiation heat flux between the hot water thermal masses and the experimental device structure as discussed in the following section.  ܳ୪୵୰,୵,ୱ୲ ൌ ሺ ୱܶ୲ െ ୵ܶሻܴୣ୯,୵,ୱ୲  (34) ܴୣ୯,୵,ୱ୲ ൌ ܴୱ୲ ൅ 1ܣ୵݄୰,୵,ୱ୲ (35) ݄୰,୵,ୱ୲ ൌ ߝ୵ߪሺ ௪ܶ ൅ ௦ܶ௧ሻ൫ ௪ܶଶ ൅ ௦ܶ௧ଶ൯ (36)  The heat transfer from the hot water thermal mass to the air contained in the experimental device (ܳ୵,ୟ୧୰) is defined by Equation 37 where ୟܶ୧୰ is the average temperature of the air contained in the experimental device and ܴ୵,ୟ୧୰ is the fitted air film thermal resistance of the hot water containers. The heat transfer from the air contained in the experimental device to the experimental device structure (ܳୟ୧୰,ୱ୲) is defined by Equation 38. ܴୣ୯,ୟ୧୰,ୱ୲ is defined by Equation 39 where ܣୱ୲ is the effective heat transfer surface area of the experimental device (ܣୱ୲ = 10m2)  118  and ݄ୟ୤,୧୬ is the fitted thermal conductance of the air film on the inner surface of the experimental device.  ܳ୵,ୟ୧୰ ൌ ሺ ୟܶ୧୰ െ ୵ܶሻܴ୵,ୟ୧୰  (37) ܳୟ୧୰,ୱ୲ ൌ ሺ ୱܶ୲ െ ୟܶ୧୰ሻܴୣ୯,ୟ୧୰,ୱ୲  (38) ܴୣ୯,ୟ୧୰,ୱ୲ ൌ ܴୱ୲ ൅ 1ܣୱ୲݄ୟ୤,୧୬ (39)   Figure 73 - Air exfiltration experiment of the small scale experimental device.  The air exfiltration heat losses (ܳୣ୶) were calculated by using Equation 40 where ∆ܲ is the pressure differential of the air inside and outside the experimental device assuming that the Stack effect is the main air exfiltration mechanism [132-134]. ܺୱ୲ is the air conductance of the structure and it was measured using the experimental setup shown in Figure 73. The experimental procedure was to pressurize the experimental device and to measure the air exfiltration rate under steady state pressure conditions. An air conductance value of 4.3E-4 m3/sPa was measured in the experimental device (ܺୱ୲ = 4.3E-4 m3/sPa).  119  ܳୣ୶ ൌ ܺୱ୲∆ܲܿୟ୧୰ߩୟ୧୰ (40)  As seen in Figure 72, three heat transfer mechanisms define the heat flux from the external surface of the experimental device to the surroundings and vice versa (ܳୱ୲,୭୳୲) (Equation 41): (1) The short wavelength heat flux of the incident sunlight radiation on the experimental device (ܳୱ୵୰,ୱ୭୪) defined in Equation 42 where ߙୱ୲ is the fitted absorbance of the experimental device structure for sunlight radiation, ݌ୱ୭୪ is the average portion of the experimental device exposed to direct radiation (about 50%), this parameter also corrects the irradiance difference between vertical and horizontal exposed surfaces (cosine correction) considering that the irradiance values used for the model were measured horizontally (݌ୱ୭୪ = 0.85) and ܫୱ୭୪ is the horizontal irradiance measured on the top horizontal plane of the experimental device. (2) The heat transfer from the external surface of the experimental device to the ambient air as modeled in Equation 41 where ݄ୟ୤,୭୳୲ is the fitted thermal conductance of the air film on the external surface of the experimental device, ୭ܶ୳୲ is the measured ambient temperature and ୱܶ୲,୭୳୲ is the average temperature of the external surface of the experimental device. Finally, (3) the long wavelength radiation heat transfer between the external surface of the experimental device and the protective cover (ܳ୪୵୰,ୱ୭,ୱ୲) defined by Equation 43 where ߝୱ୲ represents the emissivity of the external surface of the experimental device, and ∆ܧୱ୲,ୱ୭ is the long wavelength radiation heat transfer between the external surface of the experimental device and the protective cover. ∆ܧୱ୲,ୱ୭ is a complex parameter to calculate considering that the external surface of the experimental device receives radiation not just from the protective cover but from surrounding objects and the  120  ground as well, the ASHRAE manual [66] provides a guidance on the selection of this parameter for diverse scenarios.  ܳୱ୲,୭୳୲ ൌ ܳୱ୵୰,ୱ୭୪ ൅ ݄ୟ୤,୭୳୲൫ ୭ܶ୳୲ െ ୱܶ୲,୭୳୲൯ െ ܳ୪୵୰,ୱ୭,ୱ୲ (41) ܳୱ୵୰,ୱ୭୪ ൌ ߙୱ୲݌ୱ୭୪ܫୱ୭୪ (42) ܳ୪୵୰,ୱ୭,ୱ୲ ൌ ߝୱ୲∆ܧୱ୲,ୱ୭ (43)  In order to simplify the calculation of the heat transferred from the structure to the surroundings (ܳୱ୲,୭୳୲), it has been assumed that there is a hypothetical equivalent air temperature ( ୣܶ,୭୳୲ in Equation 44), which in the absence of any radiation heat exchange results in the same heat flux defined in Equation 41 (Equation 45) [66]. Therefore, the equivalent heat transfer from the structure to the surroundings (ܳ୭୳୲,ୣ୯) is defined by Equation 46 where ܴୣ୯ is the equivalent thermal resistance between the middle plane of the experimental device structure and the surroundings described by Equation 47.  ܳୱ୲,୭୳୲ܣୱ୲ ൌ ݄ୟ୤,୭୳୲൫ ୣܶ,୭୳୲ െ ୱܶ୲,୭୳୲൯ ൌ ߙୱ୲݌ୱ୭୪ܫୱ୭୪ ൅ ݄ୟ୤,୭୳୲൫ ୭ܶ୳୲ െ ୱܶ୲,୭୳୲൯ െ ߝୱ୲∆ܧୱ୲,ୱ୭ (44) ୣܶ,୭୳୲ ൌ ୭ܶ୳୲ ൅ ߙୱ୲݌ୱ୭୪ܫୱ୭୪݄ୟ୤,୭୳୲ െߝୱ୲∆ܧୱ୲,ୱ୭݄ୟ୤,୭୳୲  (45) ܳ୭୳୲,ୣ୯ ൌ ൫ ୣܶ,୭୳୲ െ ୱܶ୲൯ܴୣ୯  (46) ܴୣ୯ ൌ ܴୱ୲ ൅ 1ܣୱ୲݄ୟ୤,୭୳୲ (47)   121   Figure 74 - Heating and cooling tests for the thermal model.  The thermal model was tested by using a square wave temperature function for heating and cooling as shown in Figure 74 (black dashed line). The objective of this test was to verify the expected time dependent thermal responses of the air and water systems under a well-known energy transfer scenario. For an abrupt change of the ambient temperature out of the experimental device, it is expected that the temperature increase or decrease of the air contained in the experimental device (solid line in Figure 74) will be more rapid for a period of time and then it stabilizes with the dominant thermal mass which are the containers filled with water (dotted line in Figure 74).  5.4.2 Experimental Thermal Resistance of the Small Scale Light Valve Experiment Five successful thermal decay experiments were performed in the experimental light valve device from September 2012 to March 2014. The air temperatures in the experimental device ( ୟܶ୧୰) predicted by the thermal model fitted well the experimental observations for an average thermal resistance value (2ܴୱ୲) of the experimental device structure (light valve module  122  and insulated chamber) equal to 4.16 Km2/W േ	0.16 Km2/W (R-23.6 േ R-0.9). The predicted average temperature of the middle plane of the light valve experimental device structure ( ୱܶ୲) for the five experimental data sets was 23°C, assuming that the expanded polystyrene foam used to construct the experimental device has an average thermal resistance value of 0.73 m2K/W for every 0.025 m of material thickness at 24°C (expanded polystyrene foam type II [63]), the expected thermal resistance of the light valve experimental device (light valve module and insulated chamber) would be 4.25 Km2/W (R-24.1). The minimum theoretical thermal resistance value expected for the light valve experimental device (light valve module and insulated chamber) is 4.06 Km2/W (R-23.1) considering that the minimum thermal resistance value reported for the expanded polystyrene foam used at 24°C is 0.70 m2K/W [63]. Figures 75 and 76 show the optimized fit of the thermal model for two thermal decay experiments conducted in the UBC Okanagan experimental location. The optimization objective for the thermal model was to minimize the sum of the squared of the temperature difference of each data point between the measured air temperature in the experimental device and the predicted air temperature by the thermal model ( ୟܶ୧୰). The average relative difference between the air temperature measured in the experimental device and the one predicated by the thermal model ( ୟܶ୧୰) after optimization for the data sets presented in Figures 75 and 76 was calculated to be 3.7% and 1.9% respectively. In Figures 75 and 76 the red line represents the air temperature measured in the light valve experimental device, the blue dots are the air temperatures measured out of the experimental device ( ୭ܶ୳୲), and the black dashed line is the optimized fit obtained using the thermal model described in the previous section. The vertical uncertainty of the measured temperature data points was assumed to be the statistical error of the averaging over five minutes of the 0.1 Hz readings of the temperature sensor.  123   Figure 75 - Thermal decay experiment (Okanagan February 21 to 27, 2014). The peaks in the graph are the result of solar gains through the structure.  After optimization of the thermal model, the fitted values obtained for the thermal conductance of the air films on the inner (݄ୟ୤,୧୬) and outer (݄ୟ୤,୭୳୲) surfaces of the experimental device and the water containers (݄୵,ୟ୧୰) were: ݄ୟ୤,୧୬ = 9.0 W/m2K, ݄ୟ୤,୭୳୲ = 17.0 W/m2K and       124  ݄୵,ୟ୧୰ = 6.5 W/m2K. Those values are consistent with the ones reported by the literature for similar experiments, which, for the internal surfaces of the insulating structure, the air film thermal conductance values range from 5 – 9 W/m2K [71,135] and 13 – 25 W/m2K for external surfaces [71,136]. The emissivity of the water containers and the light valve experimental device structure was fitted to ߝୱ୲ = ߝ୵	= 0.9 which is consistent with the emissivity values used for thermal models previously reported [137,138]. The short wavelength radiation absorbance (sunlight radiation) of the external walls of the light valve experimental device structure (dark gray painted) was fitted to ߙୱ୲ = 0.6 in accordance with the short wavelength absorbance values reported in the literature for dark colored walls in building applications (0.5 ൑ ߙ ൑ 0.8) [139-142].  The ASHRAE manual [66] recommends to neglect the contribution of the long wavelength heat transfer (∆ܧୱ୲,ୱ୭) between vertical surfaces and surrounding objects, ground and buildings and to use a value of about 63 W/m2 for surfaces exposed to the clear sky (i.e. roofs). The model disregards the contribution of the parameter ∆ܧୱ୲,ୱ୭ for predominantly overcast days and uses a value of 12 W/m2 for predominately clear sky days (considering the geometry of the light valve system and the protective cover). The average temperature difference between the inner surface of the protective cover and the external surface of the experimental device should be between 0°C ≤ ୱܶ୭ ≤ 2.9°C based on the values of ∆ܧୱ୲,ୱ୭, this temperature difference range seems reasonable considering that the external surface of the protective cover is exchanging long wavelength radiation directly with the sky.  125   Figure 76 - Thermal decay experiment (Okanagan March 19th to 22nd, 2013). The peaks in the graph are the result of solar gains through the structure.      126  Chapter 6: Light Valve Experimentation in a Fully Functional Greenhouse The objective of the experiment discussed in this chapter was to characterize the thermal and optical behavior of the experimental light valve system in a fully functional greenhouse. The data presented in this chapter support the theoretical and numerical predictions done in Chapter 4 and provide evidence of the capability of the light valve system to be integrated in an already constructed fully functional greenhouse structure.  6.1 Description of the Experimental Location The location selected for this experiment was the Sustainable Horticulture Research Greenhouse at the Langley campus of the Kwantlen Polytechnic University (KPU) (49.11° N, 122.64° W). This location shown in Figure 77 provided a real life scenario for the experimentation with the light valve system. All the necessary services in the greenhouse were operational for the duration of the experiment. The experimental setup in this greenhouse required the construction of a 29.7 m2 light valve experimental device composed of six 2 m x 2 m solar tracking light valve modules (24 m2 covered by light valves and 5.7 m2 covered by instruments, mechanism and the KPU greenhouse structure). The light valve modules were contained in an expanded polystyrene foam thermally insulated chamber (4.5 m x 6.6 m x 5.5 m) whose function was to thermally isolate the inner environment of the experimental device from the rest of the greenhouse. The sensors used for this experiment were customized for this specific application using commercial components as described in Section 5.2. The East-West axis of the Sustainable Horticulture Research Greenhouse at Kwantlen Polytechnic University is 25° off the geographical east-west axis as  127  shown in Figure 77; this axial offset was taken into consideration solar geometry calculations [124] done for the ray tracing analysis.   Figure 77 – KPU experimental greenhouse location (KPU Langley campus).  6.2 Tools, Methods and Experimental Light Valve Device Construction The light valve modules (Figure 78b) used to construct the experimental device (Figure 78a) were customized to be installed at the roof of the KPU greenhouse without disrupting any existing structural elements or services. After a detailed analysis of the most feasible location for  128  the light valve experimental device in the greenhouse unit, it was decided that the experimental device would cover one fourth of the total greenhouse unit area, which also made practical from a cost perspective to isolate the light valve modules for detailed thermal and optical transmittance experimentation (Figure 78).   Figure 78 - The experimental device used for the KPU experiment covers one fourth of the total greenhouse unit where the light valve modules are intalled as the roof of a thermally insulated chamber.  In order to successfully fulfill the installation challenges in the KPU greenhouse, the original design of the light valve modules was scaled down by 25% so they could fit in the free  129  space between the structural trusses shown in Figure 79. This space was the most practical location for the experiment considering the KPU greenhouse structure, its mechanisms and the instruments used to control its services. For this experiment, six light valve modules each with a total area of 4 m2 (3.6 m2 of effective light valve area and 0.4 m2 of frame area) were constructed using aluminized polyethylene film [79] laminated on expanded polystyrene foam [80] valve element structures. To facilitate the design effort, a fully functional 3D computer model depicted in Figure 78 was developed. The optimal design of the light valve modules used for this experiment is about 70% lighter compared to the experimental device detailed in Chapter 5 to reduce the complexity of the installation process for the experimental device; this optimized light valve modules weighted 25 kg each.  Figure 79 – A photograph of the space between the greenhouse structural trusses where the light valve modules were installed.  The rotation mechanism of the light valve modules was improved and simplified for this experimental device by moving the actuation from the side of the central valve element, as in the  130  small scale experimental device detailed in Chapter 5, to a linking bar connected to the central lower portion of each valve element by a pin/connector mechanism shown in Figure 80. For this experimental device, the actuation was powered by inexpensive linear actuators [64] whose maximum travel was controlled by hard stops and electromechanical devices to prevent damage resulting from uncontrolled actuation. The design of the light valve modules includes a mechanical safety factor of two; in other words, the mechanical loads used for the design of the elements and mechanisms are twice the maximum expected loads under normal operation of the system.    Figure 80 - Actuation mechanism of the KPU light valve module experimental device.  The first stage of the installation in the KPU greenhouse was the construction of a 0.1 m thick insulation chamber, shown in Figure 81. Once the enclosure was completed, modules were suspended from the roof (Figure 82) using lightweight steel cables. The six fully installed light valve modules used for the experimental device are shown from below (Figure 82b) and above (Figure 82c). The experiment was equipped with four temperature [117,143] and four irradiance sensors [119,121] installed inside and outside of the chamber (eight sensors in total). The  131  sensors, data card and data acquisition protocols are the same as the ones used for the UBC experiments and described in Chapter 5.   Figure 81 – Insulating chamber of the KPU experiment viewed from east to west (a) and west to east (b).  The modules were controlled by a custom-designed automated control system that is compatible with the environmental conditions of the greenhouse and includes fail-safe features such as redundant position and control verification protocols in the software, and power break features and fuses if uncharacteristic operation parameters are measured by the control system. The light valve modules were independently controlled and monitored using an inexpensive microcontroller [65] that provides solar tracking capabilities to the design. The solar tracking  132  protocol adjusts, by means of a potentiometer feedback connected to the linear actuator [64], the angular position of the valve elements once per hour to the appropriate position depending on the known sun position and the optical transmittance optimization results (Section 4.5.1). The commented code designed to automatically position the valve elements is provided in the appendix of this document. Two web cameras and an internet based remote control system [144] were installed in the experimental device for monitoring purposes.  Figure 82 – Installation of the light valve modules (a). Top (b) and bottom (c) views of the KPU installation.  Figure 83a shows the six light valve modules in the open or light transmissive state, Figure 83b shows five of the light valve modules in their closed or highly thermally insulated state and one in its open or light transmissive state. For this experiment the geometry of the  133  greenhouse roof structure made it impractical to tilt the light valve experimental device to its optimal angular position (shown as ߬ in Figure 37) based on the geographical location of the KPU greenhouse.    Figure 83 - The Light Valve system during a test of the automatic control (a). In this photo, five of the modules are kept in the high insulation state while one is set to the light transmissive state (b).  6.3 Optics Performance Experimental Results for the Light Valve Experiment in a Fully Functional Greenhouse A detailed model to predict the light transmission of the light valve in the experimental device was developed based on the ray tracing optical transmittance predictions reported in Section 4.5 (light valve system working as a solar tracker). The model was calibrated to consider the optical losses caused by the greenhouse structure and the diffuse and direct sunlight transmission in the system based on the modified Solis model [125]. The optical transmittance experiments consisted of measuring the horizontal irradiance incident on the experimental device  134  and the irradiance below the light valve modules approximately 0.45 m below the light valve modules where the light obstruction by the structure and crops was minimized. All sensors were set to take data with a frequency of 0.1 Hz. The position of the valve elements was adjusted once per hour to the optimal angular position based on the analysis presented in Section 4.5. Detailed light transmittance measurements were also taken at the level of the growing trays (shown in Figure 81).  Figure 84 – Ray tracing optical transmittance setup for the light valve KPU experiment.  135  The optical transmittance model uses a detailed 3D solar geometry calculation [97], the objective of which is to assign two projections of the solar altitude angle on the active planes of the experimental device; those two angles (shown in Figure 84 as ߙ and ߛ) are used to infer a global optical transmittance value (T) as a function of the direct ( ୢܶ୧୰ୣୡ୲ሺߙ, ߛሻ) and diffuse ( ୢܶ୧୤୤୳ୱୣሺߙ, ߛሻ) transmittances for each experimental data point. The optical transmittance value predicted by the model is then multiplied by the ambient irradiance measured on top of the experimental device to predict the intensity of the transmitted light into the experimental device.  In an ideal case, where the assumptions are that the valve elements are infinitely long, there are no surrounding obstructions and the light valve frame walls are highly reflective, the predicted direct radiation optical transmittance function ( ୢܶ୧୰ୣୡ୲ሺߙ, ߛሻ) is characterized by the direct light transmittance of the light valve system when working as a solar tracker (reported in Figure 48 Section 4.5). Therefore, the projected solar angle ߛ (Figure 84) has no significant impact on the overall transmittance of the light valve system. For the case of the experimental device studied in this section, the resulting direct light shading by the light valve frame, valve element sides and surrounding structural greenhouse elements was considered in the optical transmittance analysis. As shown in Equation 48, the shading losses by the light valve frame and structural elements are assumed to be a function of the height of the effective light valve module frame walls and structural blockages (shown as h in Figure 84), the effective transmittance of the light incident on the light valve module frame walls ( ୣܶ୯.୵ୟ୪୪), and the solar elevation projection on the projection plane #1 (shown as ߛ in Figure 84). For the purposes of this analysis, the light blockages by the light valve module frame and surrounding KPU greenhouse structural elements have been approximated using an effective height for the light valve modules frame (h), where  136  this effective height is the sum of the contributions of the height of the light valve module frame walls (0.25 m) plus an equivalent height on top and below the light valve module which shading effect on the light valve module as a function of the solar elevation is equivalent to the effective light blocked by the surrounding structural elements in the KPU greenhouse.  ୢܶ୧୰ୣୡ୲ሺߙ, ߛሻ ൌ ୢܶ୧୰ୣୡ୲ሺߙሻ ൭1 ൅ ݄ tanሺ90 െ ߛሻܮୟୡ୲୧୴ୣ ൫ ୣܶ୯.୵ୟ୪୪ െ 1൯൱ (48)   Figure 85 – Direct light ray tracing optical transmittance prediction.  Figure 85 shows the direct radiation optical transmittance values (IT/Io) predicted by the ray tracing model as a function of the solar elevation projections ሺߙ, ߛሻ [97]. The light transmittance through the light valve (IT/Io) reported in Figure 85 is defined here  as ratio of the  137  light flux on the transmitted sunlight plane 0.45 m below the light valve (IT) divided by the light flux on the incident sunlight plane before the light valve (Io) as shown in Figure 84.   Figure 86 – Comparison of the experimental irradiance mesurements in the KPU light valve device and the predictions of the ray tracing model for the light transmittance by the light valve measured 0.45 m below the light valve modules from (a) February 19 to 21,2014 and (b) February 25 to 28, 2014 (b).  138  For the analysis of the data set presented in Figure 86 (February 16 to March 6, 2014), the ray tracing model assumes that the parameter h is 0.75 m in total, this value considers the height of the light valve frame (0.12 m in average) and the structural elements in the KPU greenhouse surrounding the light valve modules. The most important light obstructions in the greenhouse structure are the trusses with an average height of 0.58 m. On the other hand, for the parameter ୣܶ୯.୵ୟ୪୪ (effective transmittance of the light incident on the light valve module frame walls), it was assumed that (1) the light incident on the greenhouse trusses and other structural light blockages was 10% diffusely reflected (black paint [97]), (2) the reflectance of the inner light valve frame walls is 90% specular [79], and (3) 50% of the light incident on the inner light valve frame walls is rejected as result of the arbitrary specular reflections caused by the irregular surfaces and wrinkles of the light valve frame low pressure seal.  The experimental optical transmittance of the light valve system was compared with the ray tracing model predictions in Figure 86 where the red dots represent the irradiance measured in the experimental device. The vertical uncertainty of the measured data points was assumed to be the statistical error of the averaging over five minutes of the 0.1 Hz irradiance readings of the light sensor used to measure the irradiance in the experimental device. The black solid line in Figure 86 represents the predicted irradiance in the experimental device by the model where the two black dotted lines represent the expected uncertainty of the model as a function of the ambient irradiance sensor uncertainty and the effective ray tracing uncertainty. The effective ray tracing uncertainty was calculated by considering the ray tracing simulation uncertainty (±1.0% of the optical transmittance value), the measured angular position error of the light valve elements (±2.5% of the optical transmittance value) and the spatial positioning error of the installation of the light valve experimental device (±0.7% of the optical transmittance value).  139  As discussed in Chapters 4 and 5, the transmission value of the experimental device depends on the solar elevation and it varies with the position of the sun during the day (Figure 85). Table 1 summarizes the average optical transmittance measured under predominantly clear sky conditions in the light valve experimental device and compares it with the predicted transmittance by the ray tracing model for the same data points. Selected data points from 10:50 am to 11:05 am, 11:30 am to 11:45 am were omitted because of uncharacteristically high irradiance values measured as result of inadvertent concentration by the experimental device. A rapid and atypical decrease of the irradiance values in the experimental device was observed from 12:00 pm to 12:20 pm during predominantly clear days (and until 12:50 pm on February 25, 2014), presumably caused by partial shading by the structural elements in the greenhouse on the transmitted irradiance sensor. Those data points were not included in the analysis.  From To Experimental Experimental Std. Dev. Ray Tracing Prediction Ray Tracing Pred. Std. Dev. 10:00 AM 11:00 AM 0.483 0.129 0.516 0.036 11:00 AM 12:00 PM 0.541 0.106 0.537 0.018 12:00 PM 1:00 PM 0.311 0.137 0.459 0.027 1:00 PM 2:00 PM 0.294 0.096 0.364 0.035 2:00 PM 3:00 PM 0.145 0.070 0.245 0.039 3:00 PM 4:00 PM 0.152 0.061 0.143 0.018  Table 1 – Comparison of the predicted and measured optical transmittance readings in the expeirmental light valve device from 10:00 am to 3:00 pm from February 19 to 21, 2014 and from February 25 to 28, 2014.  The fractional difference between the measured transmittance and the predicted transmittance by the model for each data point was calculated to be 9% for predominantly clear sky days from 10:00 am to 3:00 pm (from February 19 to 21, 2014 and from February 25 to 28,  140  2014) in accordance with the expected uncertainty of the model and the experimental measurements (combined uncertainty of about 10%). The determination coefficient was also calculated for those days finding a value of r2 = 0.84. In contrast, during predominantly overcast days (February 16 to 18 and 22 to 24, 2014 and March 1 to 6, 2014) values of r2 = 0.61 were calculated. The horizontal irradiance of the KPU light valve experimental device at growing tray level (1.3 m above ground) was measured before the planting of the crops in the experimental device on August 20 and August 21, 2013 (totally clear sky days) from 11:00 am to 12:00 pm (times when the shading of the surrounding greenhouse structure on the light valve experimental device was minimized). The experimental protocol followed for this measurement was to adjust the angular position of the light valve modules in order to maximize their transmittance (based on the ray tracing predictions described in Section 4.5). The horizontal irradiance was measured every 0.5 meters on the five growing trays shown in Figure 81 and on top of the experimental device using a light meter [145]. The average measured irradiance value for the KPU experimental device for August 20 and August 21, 2013 from 11:00 am to 12:00 pm was 107 PAR W/m2 ± 11 PAR W/m2 in agreement with the irradiance value predicted by the ray tracing model for the same days and times (114 PAR W/m2 ± 8 PAR W/m2). The measured irradiance at growing tray level in the experimental device for August 20th and 21st, 2013 from 11:00 am to 12:00 pm is higher than the critical point where the light intensity is a limiting factor for photosynthesis under ambient CO2 concentrations (about 100 PAR W/m2). For this comparison, the ray tracing model was modified by including the optical properties of the inner walls of the insulating chamber and the ground. For the case of the reflective inner walls of the insulating chamber (specular reflective mirrors  141  [79] covered two thirds of the insulating chamber inner wall area and the rest was painted with white paint [109]), it was assumed that 10% of the light was absorbed by the walls and 90% was diffusely reflected in one third of the surface and specular reflected for the rest of the wall area. For the case of the ground, it was assumed a diffuse reflectance of 45%. Certainly, the transmittance values achieved in the KPU experimental device are lower than what would be achieved in one of the target locations described in Sections 2.2 and 4.5 where the light valve system is properly tilted, east-west aligned and the structural blockages are minimized. Since the measured irradiance values in the experimental device compares well with the predicted irradiance by the ray tracing model under the same conditions, it can be inferred that under ideal installation conditions in a target location, the direct light transmittance of the light valve could exceed values of 70% for most of the solar elevations (-75° ≤  αN ≤ 75°) and it can go up to above 80% (IT/Io ≥ 0.8) for the characteristic solar elevation range of the target locations (-30° ≤  αN ≤ 30°). The objectives of the experimental device presented in this chapter were to demonstrate the application of the light valve system in a real world scenario and to validate the ray tracing analysis. While the experimental device geometry is not ideal, the results obtained with it are meaningful because they verified that the ray tracing model predicts well the optical behavior of the light valve system and that the light valve design can be implemented in a real world greenhouse application. The irradiance control capabilities of the light valve experimental device where verified as shown in Figure 87 with similar results than the ones obtained and reported in Section 5.3.3. The average actuation time was measured to be 10 seconds. This is a substantially faster response than achieved by average commercial shade screens which deploys in 600 seconds. For  142  some crops, rapid light control is preferred to prevent plants from overheating [146], and this level of light control is not achieved by present day technology. Figure 87 describes the transmittance as the angular position (߮ሻ	of	the	valve	elements	is	varied	from the completely open state at ߮	ൌ	0° (70a), to their highly insulating and completely closed state at ߮	= 74° (70c). Figure 70b is the optimal angular positions of the light valve which maximizes its transmittance for the specific day and time of the experiment (August 22, 2014).   Figure 87 - Irradiance control in the light valve experiment by the rotation of the valve elements form (a) their completelly open state to (c) their completlly closed state. The optimal angular position of the valve elements is shown in (b).  As mentioned before, the valve elements optimize their angular position each hour to adapt for the solar altitude variation. This angular reposition was set to occur hourly in order to be compatible with the memory limitations of the Arduino microcontroller used [65]. It has been  143  estimated that this hourly tracking results in an average transmittance decay of 10% compared with the case of the light valve tracker re-positioning the valve elements every minute. In a given application, the central control of the greenhouse can be set to achieve one minute valve element re-positioning if desired, though in most applications it is anticipated that this would not be required. After the completion of the experiment discussed in this chapter (one year of operation of the light valve experimental device), the impact on the reflectance of the light valve surfaces caused by dirt accumulation was assessed. Through the course of this experiment, top light valve surfaces were directly exposed to open ventilation windows and in a horizontal position most of the time. This operation characteristic resulted in those surfaces to be the ones with the highest dirt accumulation for the duration of the experiment; maximum reflectance reductions of 25% were measured on those surfaces after one year of operation. This operation characteristic of the experimental device did not significantly impact the overall performance of the system because those surfaces are not optically active when the light valve system operated in tracking mode. It was found a maximum reflectance reduction caused by dirt accumulation of no more than 5% for the optically active surfaces of the light valve system after one year of operation (not directly exposed surfaces). In an ideal operation, those optical losses will be reduced by encapsulating the light valve modules in protective light transmissive structures  6.4 Thermal Performance of the Light Valve Experimental Device in a Fully Functional Greenhouse The thermal insulation properties of the light valve system were evaluated using temperature profiles measured inside and outside of the experimental chamber while the desired  144  thermal conditions were set by heating the interior of the chamber with an electric heater. The thermal model described in Section 5.4.1 was modified to include contributions from the ground and electric heater for this experiment. This modified model considers two thermal masses, (1) the light valve structure and (2) the air contained in the experimental device. Most of the nomenclature used in this Section has been described in detail in Section 5.4.1, so for the purposes of this section just the newly introduced parameters are defined.   Figure 88 – Equivalent thermal circuit of the KPU light valve experiment.  Figure 88 shows the simplified thermal circuit used in this model where ୶ܶ represents average absolute temperature (K), ܴ୶ thermal resistances (K/W), ܳୣ୶ heat losses by exfiltration  145  (W), ܳୱ୵୰ short wavelength radiation heat transfers (W), ܳ୪୵୰ long wavelength radiation heat transfers (W), ܭ୶ heat capacities of the thermal mass systems (J/K), ܳ୤ is the heat flux from the fans in the experimental chamber (W), ܳ୦ is the heat flux from the electric heaters (W) and ܫୱ୭୪ is the horizontal irradiance measured on top of the experimental device (W/m2). Equations 49 and 50 describe the energy balance of the two thermal mass systems studied, which were the air contained in the experimental device (air) and the structure of the experimental device (st).  ܭୟ୧୰ d ୟܶ୧୰dݐ ൌ ܳୟ୧୰,ୱ୲ െ ܳ୥ୟ െ ܳୣ୶ ൅ ܳ୤ ൅ ܳ୦ (49) ܭୱ୲ d ୱܶ୲dݐ ൌ ܳ୭୳୲,ୣ୯ െ ܳ୪୵୰,୥,ୱ୲ െ ܳୟ୧୰,ୱ୲ (50)  As shown in Figure 88, five heat flux quantities define the energy balance of the air contained in the experimental device as shown in Equation 49: the heat flux from the hot water thermal mass to the air contained in the experimental device (ܳ୵,ୟ୧୰), the heat transfer from the air contained in the experimental device to the experimental device structure (ܳୟ୧୰,ୱ୲), the heat flux from the fans in the experimental chamber (ܳ୤), the heat flux from the electric heaters (ܳ୦)  and the air exfiltration heat losses (ܳୣ୶). Likewise, the thermal balance of the experimental device structure mass system (Equation 50) is defined by the equivalent heat transfer from the structure to the surroundings (ܳ୭୳୲,ୣ୯), the equivalent long wavelength radiation heat transfer from the ground to the experimental device structure (ܳ୪୵୰,୥,ୱ୲) and the heat transfer from the air contained in the experimental device to the experimental device structure (ܳୟ୧୰,ୱ୲). The  146  temperatures of the air ( ୟܶ୧୰௡) and structure ( ୱܶ୲௡) thermal mass systems at the period n can be calculated by using Equations 51 and 52.  ୟܶ୧୰௡ ൌ ୟܶ୧୰௡ିଵ ൅ܳୟ୧୰,ୱ୲௡ିଵ െ ܳ୥ୟ௡ିଵ െ ܳୣ୶ ൅ ܳ୤ ൅ ܳ୦ܿୟ୧୰ ୟܸ୧୰ߩୟ୧୰ ሺ∆ݐሻ (51) ୱܶ୲௡ ൌ ୱܶ୲௡ିଵ ൅ܳ୭୳୲,ୣ୯௡ିଵ െ ܳ୪୵୰,୥,ୱ୲௡ିଵ െ ܳୟ୧୰,ୱ୲௡ିଵܿୱ୲ ୱܸ୲ߩୱ୲ ሺ∆ݐሻ (52)  The equivalent long wavelength radiation heat transfer from the ground to the experimental device structure (ܳ୪୵୰,୥,ୱ୲) is defined by Equation 53 where ୥ܶ is the temperature at the surface of the ground in the experimental chamber and ܴୣ୯,୥,ୱ୲ is the equivalent long wavelength radiation thermal resistance between the experimental device structure and the ground.  ܳ୪୵୰,୥,ୱ୲ ൌ൫ ୱܶ୲ െ ୥ܶ൯ܴୣ୯,୥,ୱ୲  (53)  The heat transfer from the ground to the air contained in the experimental device (ܳ୥ୟ) is defined by Equation 54 where ୥ܶ is the measured temperature 0.1 m below ground and ܴ୥ୟ is the effective thermal resistance of the ground defined in Equation 55. ܣ୥ is the heat transfer surface area of the ground (ܣ୥ = 28.7 m2), ܴ୥ is the conduction thermal resistance of the ground       (0.66 m2K/W for 0.1 m of dry gravel [147]) and ݄ୟ୥,୧୬ is the fitted thermal conductance of the air film on the ground.  147   ܳ୵,ୟ୧୰ ൌ൫ ୟܶ୧୰ െ ୥ܶ൯ܴ୥ୟ  (54) ܴ୥ୟ ൌ ܴ୥ ൅ 1ܣ୥݄ୟ୥,୧୬ (55)  An air exfiltration experiment was performed in the experimental device to measure the air conductance of the experimental device (ܺୱ୲) and calculate the exfiltration heat losses (ܳୣ୶) by using Equation 56. The air conductance of the experimental device was measured to be equal to 0.012 m3/s per unit of pressure (ܺୱ୲ = 0.012 m3/sPa).   ܳୣ୶ ൌ ܺୱ୲∆ܲܿୟ୧୰ߩୟ୧୰ (56)  As described in Section 5.4.1 (Equation 41), three heat transfer mechanisms define the heat flux from the external surface of the experimental device to the surroundings (ܳୱ୲,୭୳୲). For the case of the short wavelength heat flux of the incident sunlight radiation into the experimental device (ܳୱ୵୰,ୱ୭୪), it was assumed that the absorbance of the experimental device structure for sunlight radiation (ߙୱ୲) was equal to 0.1 considering that the external walls were painted with 90% diffusely reflective white paint and the light valve elements are coated with 90% specular reflective aluminized polyethylene film. The long wavelength radiation heat transfer between the external surface of the experimental device and the KPU greenhouse cover (ܳ୪୵୰,ୱ୭,ୱ୲) was assumed to be negligible considering the low emissivity values of the aluminized polyethylene film used to construct the light valve elements (emissivity values lower than 0.05 [99]), and that  148  the long wavelength radiation heat transfer between the external surface of the experimental device and the protective cover (∆ܧୱ୲,ୱ୭) is insignificant for the vertical walls of the insulating chamber [9]. The total heat transfer area of the experimental device has been assumed to be 145 m2 (ܣୱ୲ = 145 m2). The thermal testing of the light valve experimental device was conducted in October 2013. The air temperatures ( ୟܶ୧୰) predicted by the thermal model compared favorably to the experimental observations for average total thermal resistance values (2ܴୱ୲) of the experimental device structure (light valve modules and thermally insulated chamber) of 1.53 m2K/W ± 0.37 m2K/W (R-8.7 ± R-2.1). Because of the complexity of the thermal interactions in the KPU experiment, this range of thermal resistance values was the best estimate offered by the thermal model. Assuming that the expanded polystyrene foam used to construct the experimental device has a minimum thermal resistance value of 0.75 m2K/W (R-4.1) for the light valve modules and between 0.55 m2K/W (R-3.3) and 0.76 m2K/W (R-4.3) for the thermally insulated chamber for every 0.025 m of material thickness at 24°C (expanded polystyrene foam [80,148]), the expected thermal resistance under ideal conditions for the light valve experimental device would be 2.15 m2K/W ± 0.30 m2K/W (R-12.2 ± R-1.7).  Figure 89 shows the fit of the thermal model for a data set taken from October 15 to October 21 2013. The optimization objective for the thermal model was to minimize the sum of the squared absolute temperature difference of each data point between the measured air temperature in the experimental device and the predicted air temperature by the thermal model ( ୟܶ୧୰). The percentage difference between the air temperature measured in the experimental device and the one predicated by the thermal model ( ୟܶ୧୰) for the data set presented in Figure 89 was calculated to be 2%. In Figure 89 the red line represents the air temperature measured in the  149  light valve experimental device, the black dashed line is the optimized fit obtained using the thermal model and the long dashed line represents the effective heat flux from the fans and electric heater (ܳ୤ ൅ ܳ୦). The vertical uncertainty of the measured temperature data points was assumed to be the statistical error of the averaging over five minutes of the 0.1 Hz readings of the temperature sensor.    Figure 89 - Thermal performance experiment from October 15th  to October 21st , 2013. The peaks in the graph are the result of the electric heater gains.  After optimization of the thermal model, the fitted values obtained for the thermal conductance of the air films on the inner (݄ୟ୤,୧୬) and outer (݄ୟ୤,୭୳୲) surfaces of the experimental device were: ݄ୟ୤,୧୬ = 10 W/m2K, ݄ୟ୤,୭୳୲ = 22 W/m2K. Those values are consistent with the ones reported by the literature for similar experiments (5 W/m2K to 25 W/m2K [71,135,136]). The  150  thermal bridges in the experimental device were also taken into account for the thermal model. A thermal bridge is defined as the penetration of a thermally insulated structure by a highly thermal conductive material reducing the effective insulation of the structure. The effective thermal conductance calculated for those thermal bridges is summarized in Table 2.  Feature Thermal conductance [W/K] Rail pipes 1.28 Roof pipes 10.84 Fertilization pipes 0.14 Irrigation pipes 0.14 Truss 5.58 Gutters 0.08 Screws 0.02 Caulking 2.06  Table 2 – KPU light valve experimental device thermal bridges summary.  Figure 90 shows the general behavior of the experimental device when working in automatic actuation tracking the sun every hour during daytime and closing the valve elements at nighttime. The dashed blue line and the solid red line represent the temperature outside and inside the experimental device respectively. As can be seen in Figure 90a, when the valve system was closed at 6:00 pm, a rapid temperature increase occurred as result of the heating by the supplemental lighting and the high thermal resistance of the light valve system. At nighttime, the  151  KPU greenhouse compartments (inside and outside of the highly insulating experimental device) were supplied with the same amount of supplemental heating. The temperature difference shown in Figure 90b at nighttime, when the supplemental lighting was off, was the result of the highly thermal resistive properties of the light valve experimental device. The lights were turned on at 5:00 am and the temperature in the experimental device rapidly increased while the light valve system was still closed (Figure 90c). At 8:00 am, the light valve system opened and started tracking the sun; the temperature in the chamber rapidly decreased to reach equilibrium with the air temperature out of the experimental device (Figure 90d).   Figure 90 - Thermal behaviour of the KPU light valve exprimental device for automatic actuation in a fully functional greenhouse.  For seven months small crops of gerbera flowers and strawberries (Figure 91) were grown in the experimental chamber (from October 9, 2013 to April 21, 2014). At the end of this experimental evaluation it was observed that all plants were alive and in apparent good conditions. Both crops completed five growth cycles with regular harvesting. Supplemental  152  lighting was used to overcome the low ambient irradiance levels during overcast days and at night. A detailed analysis on the impact of the light valve system on the physiological development and plant energetics of the crops should be conducted in future studies.    Figure 91 – Gerberas and strawberries where planted in the experimental device (a). Crops grown in the light valve experimental device (b).    153  Chapter 7: Early Environmental and Economic Considerations for the Light Valve System Greenhouse The variety of different greenhouse styles, energy requirements for crops and local markets makes it complex to set economic limits which, combined with the photosynthesis limiting factors, make present day commercial greenhouse operations economically profitable. The objective of this chapter is not to define those limits but to provide an educated guess of the regions whose climates are beneficial for the implementation of the light valve system. Traditional greenhouses combined with enough heaters and lamps can provide the required conditions to grow food. The energy used to power present day greenhouses has a cost which increases with time; also the energy resource is not widely available restricting the economically viable locations for a commercial greenhouse operation. The most important photosynthesis limiting factor for a cold climate greenhouse is temperature (heating costs). The average heating season temperatures (October to April in the northern hemisphere) of the coldest commercial greenhouse clusters are around 2.5°C. It seems practical to consider that the locations where the light valve system may be more beneficial are those where present day commercial greenhouses are not installed because of their cold ambient temperatures. It seems correct to identify that those locations are the ones with temperatures below 0°C for the heating season. The irradiance of those sub-zero locations where the light valve system may be more beneficial has to be enough to grow food and to maintain the temperature in the greenhouse to acceptable levels at day time when the light valve greenhouse is in its low thermal insulation and light transmissive state. The investment limit on artificial lighting for high latitude greenhouses  154  is about 50 PAR W/m2 [149]. Considering  to be 15% below the optimal photosynthesis PAR intensity under ambient CO2 concentrations (85 PAR W/m2) and also assuming that                  50 PAR W/m2 are supplied by artificial lighting, the minimum acceptable ambient irradiance after transmission through a structure with 80% average PAR transmittance is 35 PAR W/m2 (100 W/m2 of sunlight). There is no upper limit for irradiance considering the light valve can control the solar energy flux entering the greenhouse structure. If supplemental CO2 is practical for the greenhouse operation, natural ventilation is not required to overcome CO2 depletion by the photosynthesis performed by the plants, but in order to identify a realistic scenario for the implementation of the light valve system, where supplemental CO2 is not practical, it is possible to estimate a lower temperature limit for the light valve system where natural ventilation does not affect the greenhouse operation. Using a simple energy balance, it can be calculated that a reasonable estimation of the minimum practical ambient temperature for the light valve system, in a fully planted greenhouse, is -30°C to maintain a temperature of 20°C for the indoor air when natural ventilation is used to replace the CO2 photosynthesis depletion. It was assumed that ventilation can be provided by the same natural and mechanical ventilation techniques used in present day greenhouse operations [11,132,150,151]. Based on the considerations discussed before, and for the case when supplemental CO2 is not practical, Figure 92 shows the regions on a map which comply with the climatic parameters discussed before. These regions represent the area with temperatures above -30°C but below 0°C from October to April [152] and locations with annual irradiance averages above 100 W/m2 [153]. The intersection of those regions (green area in Figure 92), are the locations where it is assumed, that the light valve system designed in this dissertation, can be more beneficial. As can  155  be seen in Figure 92 an important region in North America, Europe and Asia may share the climatic conditions that could propitiate a successful implementation of the light valve system. As mentioned before, to accurately define those locations, it is necessary to also consider detailed socio-economic characteristics of the potential locations where the light valve system may be implemented. The objective of this Chapter is not to accurately define those locations, but to identify the portion of cold but sunny locations whose climatic conditions favor the implementation of the light valve system over present day greenhouse structures.     Figure 92 - World map showing locations with average temperatures above -30°C and below 0°C and annual irradiance above 100 W/m2. The locations in green are considered the potential locations where the light valve system can be more beneficial.  The light valve system has demonstrated thermal insulation values above 3.33 m2K/W (R-18.9) when expanded polystyrene foam [63] is used for the light valve elements compared to  156  0.55 m2K/W (R-1.7) of a double polycarbonate greenhouse (0.29 m2K/W or R-1.7) plus a thermal screen (0.26 m2K/W or R-1.5) [154]. The expected energy saved by the light valve system is about 0.7 GJ/m2 per year for the previously identified locations in Figure 92. This under-estimation does not include the solar thermal energy captured and stored by the thermal masses in the greenhouse.  Energy source Heat conversion factor [%] Energy cost [$/GJ] Thermal savings per year [$/m2] Natural gas 70% $13 $10 Propane 70% $25 $18 Fuel oil 70% $16 $11 Electricity 100% $21 $15  Table 3 – Energy savings estimation for the light valve system based on the information provided by the Government of Manitoba Canada [154].  The four most important energy sources used in greenhouses for heating are natural gas, propane, fuel oil, and electricity; Table 3 summarizes the energy cost per unit of usable energy for each source based on the information provided by the Government of Manitoba Canada [154]. A conservative estimate of the energy consumption by the light valve system per year is 0.01 GJ/m2 (an average electric consumption of 50 W/m2 with a daily actuation/operation time of 600s). Based on this rough calculation, the light valve system is expected to consume $0.23 per square meter per year if an electricity cost of $21 per GJ is considered. As can be seen, the economic thermal energy savings by the light valve system are at least one order of magnitude higher than the expected investment on electric energy for its operation. Based on the considerations mentioned before and the information in Table 3, the expected net monthly  157  savings by the light valve system, just considering supplemental thermal energy reduction, are between $0.5 and $1.5 per square meter. The energy savings estimate presented in Table 3 are just an approximation based on generalized energy prices taken from only one source [154], a more detailed energy savings analysis, of course out of the reach of this dissertation, has to consider the fluctuation of the fossil fuels price for different geographical regions and as a function of time. A rough estimate of the geographical fossil fuels price fluctuation is a variation by a factor of 4 for natural gas [155-158] and by a factor of 2 for oil derived fuels like heating oil and propane [159-163]. Table 3 shows the estimated savings per year for greenhouse heating considering that the light valve system reduces by 1.9 GJ/m2 per year the heating energy usage in the greenhouse.  Description Material Unit Cost Quantity per m2 Total Foam elements EPS foam [148] $80 / m3 0.13 m3 $10 Reflective film Aluminized polyethylene film [79] $2 / m2 10 m2 $20 Low pressure seal Fiberglass insulation [98] $1 / m 10 m $10 Frame structure and mechanism Aluminum [164] $2 / kg 12.5 kg $25 Actuator and electronics Linear actuator with feedback [165] $15 / m2 1 m2 $15 Others Fastening and joining $10 / m2 1 m2 $10 Total per m2 $90  Table 4 – Material cost per square meter to construct a light valve system.   158  If only the heating energy savings are considered, and the assumed payback time of the light valve greenhouse project is 15 years, the estimated total savings achieved by a farmer in the central Manitoba greenhouse corridor using the light valve system range from $150/m2 to $350/m2 compared to a classic double polycarbonate greenhouse structure with thermal screens. It is expected that the energy savings calculated before will fully cover the production cost of the light valve system. Assuming a large scale production operation, where the production cost is largely driven by the cost of the materials, a rough estimate of the cost per square meter for the light vale system is $90 per m2. Table 4 summarizes the cost of the materials used to construct the light valve system in a per square meter basis; the unit cost reported in Table 4 is for small quantity orders and it is anticipated that a volume purchase would reduce it. On the other hand, transportation expenses from mild weather farmlands can be cut by producing the food nearby the target locations of the light valve system. The most common vehicle used for fresh produce transportation is the heavy duty diesel truck (10 tons; 90 km/h) with refrigeration and gas controlled cardboard boxes [166]. Considering again the central Manitoba greenhouse corridor, and the three most important fresh produce exporters to Canada (California USA, Florida USA and Sinaloa MEX), the average transportation savings for the final consumer are $0.15/kg of fresh produce and the CO2 emissions reduction would be of 0.3 kilograms of CO2 equivalent units per kilogram of fresh produce [167,168]. The use of the light valve system would signify for those communities a 25% final retailer cost reduction. The successful experimental implementation of the light valve technology in a fully functional greenhouse structure opens the discussion on the potential benefits this technology may represent for cold climate greenhouse growers.   159  Chapter 8: Conclusion In this dissertation a new approach to reduce the energy use for heating in cold climate greenhouses while conserving appropriate sunlight transmission through their structure. The system developed is a variable canopy system that can be switched between two states – in one state the system acts as a sunlight transparent window and the other state the system acts as a highly thermally insulated ceiling capable of keeping the structure warm in cold weather conditions. This variable canopy system uses readily available and inexpensive materials, and switching between the two states requires only a simple, low-cost rotation device. Based on the work presented in this dissertation, it can be concluded that: 1) The light valve system, when in its high thermal resistance state, results in a thermal insulation value above R-18.9, (3.33 W/m2K) for the current design. 2) The optical transmittance of the light valve system is expected to be above 80% for projected solar altitudes within the compound parabolic reflectors acceptance angle for 90% specular reflective valve elements (when the system is properly installed in the target locations). 3) The light valve system exceeds the thermal insulation and light transmittance Pareto limits of present day construction materials, thermal screens, and windows, resulting in a practical solution to improve the low energy performance of present day greenhouse structures in cold climates caused by their light transmission and thermal insulation trade-off. 4) The light valve system can be constructed using inexpensive and readily available materials taking advantage of commercial and scalable manufacture techniques.  160  5) The low pressure seal designed for the light valve system has been successful preventing   excessive air mass exfiltration rates. 6) The light valve system when working as a solar tracker can extend the hours of operation achieving optical transmittances above 70% for most of the solar elevations in our target locations; this also enables intermediate irradiance control. The project discussed in this dissertation has successfully demonstrated a practical solution to reduce the energy use for heating in cold climate greenhouses while maintaining proper sunlight transmittances. Further experimental work is recommended for the light valve greenhouse design in order to optimize the length of the valve elements. Longer valve elements represent less light lost by the light valve frame but, at the same time, they would compromise the structural integrity of the system by excessive bending. Experimentation with different light valve frame designs and valve element lengths can provide evidence on the dimensional limits of the light valve system. For the purposes of the present dissertation, the efforts were focused on cold climate locations. For future work, the exploration of the light valve greenhouse application in hot climates is recommended. The potential benefit in those climates of a structure with the characteristics of the light valve system is a reduction of the cooling loads by controlling independently the infrared and the PAR from the incoming sunlight. A more detailed characterization of plant growth using the light valve system is recommended. The experiments presented in this dissertation were not focused on the growth characteristics of the crops under the light valve system. Certainly, experimentation with  161  extended growing cycles could provide more information on the physiological effects of growing food under the light valve system. Also it may be useful to replicate a large commercial greenhouse operation under the light valve system in order to determine if the stress caused by large commercial greenhouse operations, combined with the light valve operational characteristics, may impact on the growth performance of the plants. 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Ecological economics research trends 2008;1:1-11.    174  Appendix A – Light Valve Positioning Code The code described in this section was used for the optimal positioning of the valve elements based on our ray-tracing simulations. The present code was written in collaboration with Edson Sanchez. The program starts assuming solar tracking, and can change depending on signal from data card.  //////////////////// Time Communication with the computer////////////////////// /////////This section of the code was downloaded from ///// http://playground.arduino.cc/Code/time #include <Time.h>   #define TIME_MSG_LEN  11   // time sync to PC is HEADER followed by unix time_t as ten ascii digits #define TIME_HEADER  'T'   // Header tag for serial time sync message #define TIME_REQUEST  7    // ASCII bell character requests a time sync message  ///////////////////////////////////////////////////////////////////////////////////////////////////  /////////////////////// Setting up Control Protocol /////////////////////////////////////  //Array for looking up multiplier int Batches[31] = {1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10};  //lookup table int AnglesCorrected[2879] = { optimalanglesarray.xls  //Variables for Actuator +/- pins int ActuatorOnePot = 0; int ActuatorTwoPot = 1; int ActuatorThreePot = 2; int ActuatorFourPot = 3; int ActuatorFivePot = 4; int ActuatorSixPot = 5;  int ActuatorOnePlus = 52; int ActuatorOneMinus = 53; int ActuatorTwoPlus = 50; int ActuatorTwoMinus = 51; int ActuatorThreePlus = 48;  175  int ActuatorThreeMinus = 49; int ActuatorFourPlus = 46; int ActuatorFourMinus = 47; int ActuatorFivePlus =44; int ActuatorFiveMinus = 45; int ActuatorSixPlus = 42; int ActuatorSixMinus = 43;  //Variables for sensed values double VoltageReadOne = 0.0; double VoltageReadTwo = 0.0; double VoltageReadThree = 0.0; double VoltageReadFour = 0.0; double VoltageReadFive = 0.0; double VoltageReadSix = 0.0;  double PotOne = 0.0; double PotTwo = 0.0; double PotThree = 0.0; double PotFour = 0.0; double PotFive = 0.0; double PotSix = 0.0;  //Variables for target values double Angle = -1.0; double Resistance = 0.0; double Distance = 0.0;  //variables for time int CurrentDay = 0; int CurrentHour = 0; int CurrentMonth = 0; int TotalHours = 0;  //variables and pins for changing mode boolean SOLARMODE = true;  boolean keepgoing = false; int SolarModePin = 8;  int ClosePin = 10;  void setup() {   // Open the serial port:   Serial.begin(9600);   pinMode(ActuatorOnePlus, OUTPUT);   pinMode(ActuatorOneMinus, OUTPUT);  176    pinMode(ActuatorTwoPlus, OUTPUT);   pinMode(ActuatorTwoMinus, OUTPUT);   pinMode(ActuatorThreePlus, OUTPUT);   pinMode(ActuatorThreeMinus, OUTPUT);   pinMode(ActuatorFourPlus, OUTPUT);   pinMode(ActuatorFourMinus, OUTPUT);   pinMode(ActuatorFivePlus, OUTPUT);   pinMode(ActuatorFiveMinus, OUTPUT);   pinMode(ActuatorSixPlus, OUTPUT);   pinMode(ActuatorSixMinus, OUTPUT);  ////////////////////////////////// Time connection with the computer////////////////////////////////   setSyncProvider( requestSync);  //set function to call when sync required   Serial.println("Waiting for sync message"); ///////////////////////////////////////////////////////////////////////////////////////////////    } ///////////////////////////// Running Control Protocol /////////////////////////////////////// void loop() {   if( analogRead(SolarModePin) > 1000 ) { //check if solar tracking mode is on       SOLARMODE = true;   }     if( SOLARMODE == true ) {       //////////////////// Time Stuff ////////////////////       if(Serial.available() )          {           processSyncMessage();         }         if(timeStatus()!= timeNotSet)            {           digitalWrite(13,timeStatus() == timeSet); // on if synced, off if needs refresh             //digitalClockDisplay();           }         delay(1000);       ///////////////////////////////////////////////////         CurrentHour = hour();          CurrentDay = day();         CurrentMonth = month();          //calculating number of hours till present time         TotalHours = (CurrentMonth-1)*240 + (Batches[CurrentDay-1]-1)*24 + CurrentHour -1;         //looking up angle from table         Angle = AnglesCorrected[TotalHours];         //Calculate distance actuator rod has to travel         Distance = (sqrt(1300000.0*Angle + 45949641.0)-3621.0)/260.0;         //Calculate resistance corresponding to distance of travel  177          Resistance = (-.296*Distance +10.062)*1000.0;       if(Angle > -1){    //if statement to prevent actuation until user enters angle for the first time         //Read voltage from potentiometers         VoltageReadOne = analogRead(ActuatorOnePot)*5.0/1023.0;         VoltageReadTwo = analogRead(ActuatorTwoPot)*(5.0/1023.0);         VoltageReadThree = analogRead(ActuatorThreePot)*5.0/1023.0;         VoltageReadFour = analogRead(ActuatorFourPot)*5.0/1023.0;         VoltageReadFive = analogRead(ActuatorFivePot)*5.0/1023.0;         VoltageReadSix = analogRead(ActuatorSixPot)*5.0/1023.0;         //Convert voltage to resistance         PotOne = 1960.0*VoltageReadOne;         PotTwo = 1960.0*VoltageReadTwo;         PotThree = 1960.0*VoltageReadThree;         PotFour = 1960.0*VoltageReadFour;         PotFive = 1960.0*VoltageReadFive;         PotSix = 1960.0*VoltageReadSix;         //Adjust rod distance         //////////////////// Actuator 1 ////////////////////         if((Resistance - 100) >PotOne ) {//if target greater than current pot value: open valve elements           digitalWrite(ActuatorOnePlus,LOW);           digitalWrite(ActuatorOneMinus,HIGH);               }         if((Resistance+100) < PotOne ){ //if target lower than current pot value: close valve elements           digitalWrite(ActuatorOnePlus,HIGH);           digitalWrite(ActuatorOneMinus,LOW);         }         if(PotOne < (Resistance +100) && (PotOne > Resistance -100)){           digitalWrite(ActuatorOnePlus,LOW);           digitalWrite(ActuatorOneMinus,LOW);         }        //////////////////// Actuator 2 ////////////////////         if((Resistance - 100) >PotTwo ) {//if target greater than current pot value: open valve elements           digitalWrite(ActuatorTwoPlus,LOW);           digitalWrite(ActuatorTwoMinus,HIGH);               }         if((Resistance+100) < PotTwo ){ //if target lower than current pot value: close valve elements           digitalWrite(ActuatorTwoPlus,HIGH);           digitalWrite(ActuatorTwoMinus,LOW);         }         if(PotTwo < (Resistance +100) && (PotTwo > Resistance -100)){           digitalWrite(ActuatorTwoPlus,LOW);  178            digitalWrite(ActuatorTwoMinus,LOW);         }        //////////////////// Actuator 3 ////////////////////         if((Resistance - 100) >PotThree ) {//if target greater than current pot value: open valve elements           digitalWrite(ActuatorThreePlus,LOW);           digitalWrite(ActuatorThreeMinus,HIGH);               }         if((Resistance+100) < PotThree ){ //if target lower than current pot value: close valve elements           digitalWrite(ActuatorThreePlus,HIGH);           digitalWrite(ActuatorThreeMinus,LOW);         }         if(PotThree < (Resistance +100) && (PotThree > Resistance -100)){           digitalWrite(ActuatorThreePlus,LOW);           digitalWrite(ActuatorThreeMinus,LOW);         }        //////////////////// Actuator 4 ////////////////////         if((Resistance - 100) >PotFour ) {//if target greater than current pot value: open valve elements           digitalWrite(ActuatorFourPlus,LOW);           digitalWrite(ActuatorFourMinus,HIGH);               }         if((Resistance+100) < PotFour ){ //if target lower than current pot value: close valve elements           digitalWrite(ActuatorFourPlus,HIGH);           digitalWrite(ActuatorFourMinus,LOW);         }         if(PotFour < (Resistance +100) && (PotFour > Resistance -100)){           digitalWrite(ActuatorFourPlus,LOW);           digitalWrite(ActuatorFourMinus,LOW);         }        //////////////////// Actuator 5 ////////////////////         if((Resistance - 100) >PotFive ) {//if target greater than current pot value: open valve elements           digitalWrite(ActuatorFivePlus,LOW);           digitalWrite(ActuatorFiveMinus,HIGH);               }         if((Resistance+100) < PotFive ){ //if target lower than current pot value: close valve elements           digitalWrite(ActuatorFivePlus,HIGH);           digitalWrite(ActuatorFiveMinus,LOW);         }         if(PotFive < (Resistance +100) && (PotFive > Resistance -100)){           digitalWrite(ActuatorFivePlus,LOW);  179            digitalWrite(ActuatorFiveMinus,LOW);         }         //////////////////// Actuator 6 ////////////////////         if((Resistance - 100) >PotSix ) {//if target greater than current pot value: open valve elements           digitalWrite(ActuatorSixPlus,LOW);           digitalWrite(ActuatorSixMinus,HIGH);               }         if((Resistance+100) < PotTwo ){ //if target lower than current pot value: close valve elements           digitalWrite(ActuatorSixPlus,HIGH);           digitalWrite(ActuatorSixMinus,LOW);         }         if(PotSix < (Resistance +100) && (PotSix > Resistance -100)){           digitalWrite(ActuatorSixPlus,LOW);           digitalWrite(ActuatorSixMinus,LOW);         }       }     }     if( analogRead(ClosePin) > 1000 ) { //check if system has to close completely       SOLARMODE = false;       keepgoing = true;     }     if( SOLARMODE == false ) {         if(keepgoing == true ) { //close all actuators (keep power on for 45 seconds to make sure they close)           digitalWrite(ActuatorOnePlus,HIGH);           digitalWrite(ActuatorOneMinus,LOW);           digitalWrite(ActuatorTwoPlus,HIGH);           digitalWrite(ActuatorTwoMinus,LOW);           digitalWrite(ActuatorThreePlus,HIGH);           digitalWrite(ActuatorThreeMinus,LOW);           digitalWrite(ActuatorFourPlus,LOW);           digitalWrite(ActuatorFourMinus,LOW);           digitalWrite(ActuatorFivePlus,HIGH);           digitalWrite(ActuatorFiveMinus,LOW);           digitalWrite(ActuatorSixPlus,HIGH);           digitalWrite(ActuatorSixMinus,LOW);           delay (45000);           keepgoing = false;         }         if( keepgoing == false ) { //turn all actuators off           digitalWrite(ActuatorOnePlus,LOW);           digitalWrite(ActuatorOneMinus,LOW);           digitalWrite(ActuatorTwoPlus,LOW);  180            digitalWrite(ActuatorTwoMinus,LOW);           digitalWrite(ActuatorThreePlus,LOW);           digitalWrite(ActuatorThreeMinus,LOW);           digitalWrite(ActuatorFourPlus,LOW);           digitalWrite(ActuatorFourMinus,LOW);           digitalWrite(ActuatorFivePlus,LOW);           digitalWrite(ActuatorFiveMinus,LOW);           digitalWrite(ActuatorSixPlus,LOW);           digitalWrite(ActuatorSixMinus,LOW);         }     } } ////////////////////////// Time Functions ////////////////////////////////////////////// void digitalClockDisplay(){   // digital clock display of the time   Serial.print(hour());   printDigits(minute());   printDigits(second());   Serial.print(" ");   Serial.print(day());   Serial.print(" ");   Serial.print(month());   Serial.print(" ");   Serial.print(year());    Serial.println();  } void printDigits(int digits){   // utility function for digital clock display: prints preceding colon and leading 0   Serial.print(":");   if(digits < 10)     Serial.print('0');   Serial.print(digits); } void processSyncMessage() {   // if time sync available from serial port, update time and return true   while(Serial.available() >=  TIME_MSG_LEN ){  // time message consists of a header and ten ascii digits     char c = Serial.read() ;      Serial.print(c);       if( c == TIME_HEADER ) {              time_t pctime = 0;       for(int i=0; i < TIME_MSG_LEN -1; i++){            c = Serial.read();                   if( c >= '0' && c <= '9'){              pctime = (10 * pctime) + (c - '0') ; // convert digits to a number      181          }       }          setTime(pctime);   // Sync Arduino clock to the time received on the serial port     }     } } time_t requestSync() {   Serial.write(TIME_REQUEST);     return 0; // the time will be sent later in response to serial mesg. }   

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