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Heat and Mass Transfer of a Low Pressure Mars Greenhouse: Simulation and Experimental Analysis


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HEAT AND MASS TRANSFER OF A LO W PRESSURE MARS GREENHOUSE: SIMULATION AND EXPERIMENTAL ANALYSIS By INKA HUBLITZ A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2006

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Copyright 2006 by Inka Hublitz

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I dedicate this dissertation to my parent s, Melitta and Bruno Hublitz, who have always supported my adventures and endeavors. Th eir love and guidance encouraged me to follow my dreams and to reach innumerable goals.

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iv ACKNOWLEDGMENTS First and foremost, I would like to expr ess my deepest gratitude to my major advisor, Dr. Ray Bucklin, for giving me th e unique opportunity to complete my Ph.D. program under his guidance. Furthermore, I am thankful that Dr. Bucklin encouraged me to participate in various conf erences and international events such as the International Space University’s Summer Session Program in Australia. With his help I have constantly increased my network of colleague s working in relevant fields. Dr. Bucklin’s help in realizing my stay at NASA’s Kennedy Space Center was also highly appreciated. I also acknowledge the members of my supervisory committee for their huge amount of support and advice. I es pecially would like to thank Dr. Jim Leary for his positive attitude that helped me enrich my people skills. Dr. Khe Chau for providing me with lab space. Dr. Raymond Wheeler for introducing me to Dr. Bucklin during my master’s thesis research and for helping to organize my stay at NASA’s Kennedy Space Center. Dr. David Hahn for his quick responses to all my questions and for being much more involved in the project than an external committee member generally is. I am grateful to Dr. Sencer Yeralan for sh aring his great exper tise in the field of microcontrollers. At NASA’s Kennedy Space Ce nter I thank Dr. Vadim Rygalov, Dr. Phil Fowler and Dr. John Sager for their support I am thankful to Dr. Hartwell Allen for teaching me how to grow plants and provi ding me with the right equipment. Bob Tonkinson’s, Billy Duckworth’s and Steve F eagle’s hard work was always greatly appreciated.

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v My family and my husband, Sharath Cuga ti, deserve special thanks for their emotional and technical support. My gratitude al so extends to my friends Dr. Peter Eckart and Dr. Kristian Pauly, for introducing me to the field of space life support systems and biospherics.

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vi TABLE OF CONTENTS page ACKNOWLEDGMENTS.................................................................................................iv LIST OF TABLES.............................................................................................................ix LIST OF FIGURES...........................................................................................................xi ABSTRACT....................................................................................................................... xv CHAPTER 1 INTRODUCTION........................................................................................................1 Low Pressure Mars Greenhouses..................................................................................1 Structure of the Dissertation.........................................................................................3 2 LITERATURE REVIEW.............................................................................................4 Advanced Life Support.................................................................................................4 Mars Environment........................................................................................................6 Plant Requirements and Environment Control...........................................................10 Temperature.........................................................................................................11 Temperature effect.......................................................................................11 Temperature control.....................................................................................12 Relative Humidity...............................................................................................12 Relative humidity effect...............................................................................12 Relative humidity control.............................................................................13 Atmospheric Pressure and Composition.............................................................13 Carbon dioxide effect...................................................................................13 Carbon dioxide control.................................................................................14 Oxygen effect...............................................................................................14 Oxygen control.............................................................................................15 Vapor pressure effect and control................................................................15 Pressurizing gas............................................................................................15 Ventilation...........................................................................................................15 Radiation..............................................................................................................16 Radiation effects...........................................................................................16 Radiation control..........................................................................................17 Growth Area........................................................................................................19

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vii Low Pressure Plant Growth Studies...........................................................................19 3 OBJECTIVES OF THIS STUDY..............................................................................23 4 EXPERIMENTAL WORK........................................................................................24 System Description.....................................................................................................24 Instrumentation and Sensor Calibration.....................................................................28 Leakage Testing..........................................................................................................32 Leakage of Vacuum Chamber.............................................................................32 Leakage of Greenhouse Dome............................................................................34 Data Acquisition and Control System........................................................................36 Greenhouse Dome Environmental Control................................................................37 Gas Composition and Total Pressure Control Algorithm....................................37 Air Temperature Control Algorithm...................................................................39 Heat and Mass Transfer E xperiments without Plants.................................................41 Heat and Mass Transfer Experiments with Plants......................................................50 Medium-term Plant Experiment i nvolving Buttercrunch Lettuce.......................50 Long-term Plant Experiment involving Galactic Lettuce...................................56 5 MATHEMATICAL MODEL DEVELOPMENT......................................................65 Effect of Low Pressure on Heat and Mass Transfer...................................................65 Convection Heat Transfer....................................................................................65 Laminar flow over a horizontal plate...........................................................67 Turbulent flow over a horizontal plate.........................................................68 Laminar free convection on a vertical plate.................................................69 External free convection for a sphere...........................................................70 Mass Transfer by Evaporation.............................................................................71 Development of Low Pressure Psychromet rics for Non-Standard Atmospheres.......72 Gas Theory..........................................................................................................73 Equation of state...........................................................................................73 Dry gas mixture............................................................................................74 Water vapor component...............................................................................75 Construction of Modified Psychrometric Chart..................................................75 Saturation line..............................................................................................75 Humidity isolines.........................................................................................77 Specific enthalpy isolines.............................................................................78 Specific volume isolines...............................................................................78 Vapor pressure isolines................................................................................79 Adiabatic saturation temperature isolines....................................................79 Dew-point temperature isolines...................................................................80 One–dimensional Steady State Heat Tr ansfer Model of the Greenhouse Dome........83 Overall Thermal Resistance Model.....................................................................83 Individual Thermal Resistances and Thermal Coefficients.................................84 Total Thermal Resistance....................................................................................90 Comparison of Radiation and Convection in the Chamber at Mars Pressure.....92

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viii Transient Heat Transfer Model fo r Greenhouse Temperature Simulation.................93 6 RESULTS AND CONCLUSION...............................................................................98 7 FUTURE WORK......................................................................................................100 APPENDIX A STRUCTURAL ANALYSIS OF DOME SHELL, BASE PLATE AND CYLINDRICAL CALIBRATION CHAMBER......................................................102 Structural Analysis of th e Spherical Greenhouse Dome..........................................102 Structural Analysis of Ba se Plate for Greenhouse Dome.........................................103 Structural Analysis of the Base Plate without Additional Bracings..................104 Structural Analysis of the Base Plate with Additional Bracings.......................106 Structural Analysis of Cylinder us ed as Sensor Calibration Chamber.....................112 Maximum Allowable Pressure..........................................................................112 Short cylinder behavior..............................................................................113 Intermediate cylinder behavior...................................................................113 Long cylinder behavior..............................................................................114 Axial Buckling...................................................................................................114 Wall Yielding....................................................................................................115 B SENSOR CALIBRATION.......................................................................................116 Pressure.....................................................................................................................11 6 Temperature..............................................................................................................117 Relative Humidity.....................................................................................................117 Carbon Dioxide Concentration.................................................................................118 Oxygen Concentration..............................................................................................119 Load Cells.................................................................................................................121 Radiation...................................................................................................................122 Amplification of Low Voltage Sensors....................................................................123 LIST OF REFERENCES.................................................................................................124 BIOGRAPHICAL SKETCH...........................................................................................129

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ix LIST OF TABLES Table page 2-1 Human metabolism values per crew me mber and per day (CM-d) for average activity level...............................................................................................................5 2-2 Environment properties..............................................................................................8 2-3 Atmosphere composition by volume..........................................................................8 2-4 Plant environment requirements...............................................................................10 2-5 Advanced life support crop growth conditions........................................................11 4-1 Sensors used to measure environmen tal parameters, the sensor ranges and accuracies.................................................................................................................29 4-2 Steady state temperature distribution under different fr eezer temperature, light and heating power conditions...................................................................................44 4-3 Buttercrunch lettuce environmen tal conditions and their control............................53 4-4 Evaporation rates per scale with scales 2-5 containing two le ttuce plants each......55 4-5 Galactic lettuce environmenta l conditions and their control....................................57 5-1 Effect of reduced pressure on convect ive heat transfer coefficient and mass diffusion coefficient.................................................................................................71 5-2 Psychrometric parameters of a low pressure atmosphere (76% N2, 20% O2, 4% CO2) with initial conditions of 20 kPa dry air at 20C and a constant specific volume of 0.004138m/kg........................................................................................80 5-3 Steady state temperature data of the long-term experiment involving Galactic lettuce plants.............................................................................................................86 5-4 Thermal resistances and coefficients ba sed on the data obtained of the long-term experiment involving Gal actic lettuce plants...........................................................87 5-5 Simulated temperatures based on the thermal resistance model..............................89 5-6 Comparison of measured and simulated temperature values...................................90

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x 5-7 Comparison of convection heat transfer to radiation heat transfer in the chamber at a pressure of 0.6 kPa.............................................................................................93 A-1 Structural analysis of base plate without and with additional bracings.................112

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xi LIST OF FIGURES Figure page 1-1 "Astronaut" approaching University of Florida’s Mars Greenhouse Dome..............2 2-1 Martian spectral irradiance (Ls=250, 15S, noon) vs. te rrestrial spectral irradiance....................................................................................................................9 2-2 Average solar irradiance of Mars compared to Earth...............................................10 2-3 Photosynthetic efficiency.........................................................................................16 4-1 Dome used to protect plants from th e simulated low pressure, low temperature Mars environment. A) Empty dome. B) Do me with sensors, scales and flasks installed....................................................................................................................25 4-2 Vacuum chamber used to simulate the low pressure Mars environment (less than 1% of Earth’s atmosphere).......................................................................................26 4-3 Industrial walk-in freezer ensures lo w temperature of the vacuum chamber (simulated Mars environment).................................................................................26 4-4 Schematic of experimental setup..............................................................................28 4-5 Cylinder used for calibration of pressu re-sensitive sensors and for initial gas mixing control algorithm development....................................................................30 4-6 Comparison of Honeywell capacitan ce RH sensors to the HMP 237 reference RH sensor for pressures of 0 to 25 kPa....................................................................31 4-7 Forces on chamber window. A) Vacu um chamber at 0.6 kPa with top window bulging in. B) Gasket drawn into the chamber due to pressure difference..............33 4-8 Dome and chamber leakage with gas resupply and vacuum pumps turned off at a temperature of -10 C...............................................................................................35 4-9 Comparison of vacuum chamber and gr eenhouse dome leak rate s to values of other low pressure plant growth studies (leak rate is presented in logarithmic scale)......................................................................................................................... 35 4-10 Gas mixing of dome greenhouse atmosphe re without plants (oxygen set point at 4.0 kPa and carbon dioxide set point at 0.5 kPa).....................................................38

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xii 4-11 Pressure control of vacuum chamber (set point 0.6 kPa) and greenhouse dome (set points 20 kPa)....................................................................................................39 4-12 Air temperature control of gr eenhouse dome (set point at 20 C)............................40 4-13 Sensor locations for heat and mass transfer experiments without plants.................41 4-14 Preparation of the steady state experime nts. A) Bottom of dome base with foam insulation. B) Side view of greenhous e dome with the sensors and scales installed. C) Top view of greenhouse dom e without shell. D) Installation of greenhouse dome into the vacuum chamber............................................................42 4-15 Temperature readings until steady state is achieved. (0 C freezer temperature, 26 W heating power and light switched off)............................................................43 4-16 Steady state temperatures versus power of heater at seven different locations (T1-T7). Freezer temperature is 0 C and the growth light is switched off...............44 4-17 Steady state temperatures versus power of heater at seven different locations (T1-T7). Freezer temperature is -10 C a nd the growth light is switched off...........45 4-18 Steady state temperatures versus power of heater at seven different locations (T1-T7). Freezer temperature is -20 C a nd the growth light is switched off...........45 4-19 Steady state temperatures versus power of heater at seven different locations (T1-T7). Freezer temperature is -10 C a nd the growth light is switched on............46 4-20 Steady state temperatures versus power of heater at seven different locations (T1-T7). Freezer temperature is -20 C a nd the growth light is switched on............46 4-21 Steady state air temperatures (T3) versus power of heater for freezer temperatures of 0 C, -10 C and -2 0 C (growth light switched off).......................47 4-22 Freezer temperature versus power of h eater for steady state air temperatures (T3) of 15 C, 20 C and 25 C.........................................................................................48 4-23 Condensation inside of greenhouse she ll with a greenhouse air temperature of 20 C. A) Freezer temperature at 0 C. B) Freezer temperature at -20 C.....................50 4-24 Buttercrunch lettuce in Ehrlenmeyer fl ask. A) The average height of the shoot zone is 15 cm. B) Putty and a stopper prevent evaporati on of the hydroponic solution as they separate the root from the shoot zone............................................51 4-25 Installation of flasks containing the lettuce plants onto the scales...........................52 4-26 Constant temperature distribution and varying relative humidity during the buttercrunch lettuce experiment...............................................................................53

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xiii 4-27 Plant evapo-transpiration rates of pl ants from 5 to 10 hours after the beginning of the experiment......................................................................................................55 4-28 Lettuce plants after an exposure of 36 hours to the controlled Mars greenhouse environment. Healthy plant without any vi sible physical damage on the left side, wilted plant with roots that do not reac h water and nutrient supply on the right side........................................................................................................................... 56 4-29 Galactic lettuce plant for long-term expe riments with an average height of 8 cm..57 4-30 Sensor locations for the long-term expe riments with galactic lettuce plants...........58 4-31 Temperature variations during the lo ng-term galactic lettuce experiment..............59 4-32 Comparison of steady state temperature di stribution of the day cycle to the night cycle during the long-term plant experiments..........................................................60 4-33 Relative humidity variation during the day and night cycle....................................61 4-34 Gas composition control of the green house atmosphere. Set points are 20 kPa for total pressure, 4 kPa for oxygen part ial pressure and 0.8 kPa for carbon dioxide partial pressure............................................................................................62 4-35 Water evaporation measured on scale 2 and 3 during the galactic lettuce plant experiment................................................................................................................63 4-36 Galactic lettuce plants after exposure of seven days to the low pressure Mars greenhouse environment..........................................................................................63 4-37 Visible damages of the plants. A) an d B) Wilting/drying of the plant leaves..........64 5-1 Effect of pressure on the saturation line of an open system with standard atmosphere composition...........................................................................................72 5-2 Psychrometric chart of low pressure atmosphere (76% N2, 20% O2, 4% CO2) with initial conditions of 20 kPa dry air at 20C and a constant specific volume of 0.004138m/kg.....................................................................................................82 5-3 Heat transfer of greenhouse dom e and thermal resistance circuit............................84 5-4 Emissivities of the polycarbonate dome and the stainless steel chamber (light off)........................................................................................................................... .87 5-5 Emissivities of the polycarbonate dome and the stainless steel chamber (light on)............................................................................................................................ .88 5-6 Required heating power versus temperat ure difference of the dome air to the freezer. Slope of linear regression is the to tal thermal resistance (light off)...........91

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xiv 5-7 Required heating power versus temperat ure difference of the dome air to the freezer. Slope of linear regression is the total thermal resistance (light on)............91 5-8 Simulation of greenhouse atmosphere, dome and vacuum chamber temperatures (light off, 51W heating power, -10 C freezer temperature)....................................96 5-9 Simulation of greenhouse atmosphere, dome and vacuum chamber temperatures (light off, 77 W heating power, -10 C freezer temperature)...................................96 5-10 Simulation of greenhouse atmosphere, dome and vacuum chamber temperatures (light off, 103 W heating power, -10 C freezer temperature).................................97 5-11 LabView front panel of ove rall model for simulation..............................................97 7-1 Ice building up on the bottom part of the greenhouse shell. A) Overview. B) Detailed view of the ice-crystals............................................................................101 A-1 Bottom view of greenhouse dome base..................................................................103 A-2 Triangular load over full beam...............................................................................104 A-3 Trapezoidal load over part of the beam..................................................................106 A-4 First part of superposi tion: uniform load for x>a...................................................107 A-5 Second part of superpositi on: triangular load for x>a............................................108 A-6 Bending moments of beam for trapezoidal load varies with the distance a of the additional bracing...................................................................................................110 B-1 Pressure sensor #1 calibration................................................................................116 B-2 Pressure sensor #2 calibration................................................................................117 B-3 Carbon dioxide sensor calibration..........................................................................118 B-4 Carbon dioxide sensor calibration..........................................................................119 B-5 Oxygen sensor #1 calibration.................................................................................120 B-6 Oxygen sensor #1 calibration.................................................................................120 B-7 Oxygen sensor #2 calibration.................................................................................121 B-8 Oxygen sensor #2 calibration.................................................................................121 B-9 Load cell calibration...............................................................................................122 B-10 Amplifier circuit.....................................................................................................123

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xv Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy HEAT AND MASS TRANSFER OF A LO W PRESSURE MARS GREENHOUSE: SIMULATION AND EXPERIMENTAL ANALYSIS By Inka Hublitz May 2006 Chair: Ray A. Bucklin Major Department: Agricultural and Biological Engineering Biological life support systems based on pl ant growth offer the advantage of producing fresh food for the crew during a long surface stay on Mars. Greenhouses on Mars are also used for air and water regene ration and waste treatment. A major challenge in developing a Mars greenhouse is its in teraction with the thin and cold Mars environment. Operating a Mars greenhouse at lo w interior pressure reduces the pressure differential across the structur e and therefore saves structural mass as well as reduces leakage. Experiments were conducted to analyze th e heating requirements as well as the temperature and humidity distribution within a small-scale greenhouse that was placed in a chamber simulating the temperatures, pressu re and light conditions on Mars. Lettuce plants were successfully grown inside of the Mars greenhouse for up to seven days. The greenhouse atmosphere parameters, includi ng temperature, total pressure, oxygen and

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xvi carbon dioxide concentration were controlled tightly; radiation level, relative humidity and plant evapo-transpirati on rates were measured. A vertical stratification of temperat ure and humidity across the greenhouse atmosphere was observed. Condensation form ed on the inside of the greenhouse when the shell temperature dropped below the dewpoint. During the night cycles frost built up on the greenhouse base plate and the lower part of the shell. Heat loss increased significantly during the night cycle. Due to the placement of the heating system and the fan blowing warm air directly on the upper greenhouse shell, condensation above the plants was avoided and therefore the photosynthe tically active radiati on at plant level was kept constant. Plant growth was not affected by the temperature stratification due to the tight temperature control of the warmer upper section of the greenhouse, where the lettuce plants were placed. A steady state and a transien t heat transfer model of the low pressure greenhouse were developed for the day and the night cycl e. Furthermore, low pressure psychrometric relations for closed systems and modified at mospheres were generated to calculate the properties of the moist air in order to predic t condensate formation. The results of this study improve the design of the environmental control system leading to an optimization of plant growth conditions.

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1 CHAPTER 1 INTRODUCTION Low Pressure Mars Greenhouses Mars greenhouses are important co mponents of the human Mars mission infrastructure as plant-based life support systems offer self-s ufficiency and possibly cost reduction. Resupply is prohibitive for long dur ation Mars missions as it increases the launch mass and consequently the launch costs. Relying on frequent resupply from Earth also increases risk to the astronauts. Greenhouses produce edible biomass as well as regenerate the air and wa ter through photosynthesis. The atmospheric surface pressure on Mars is on average 0.61 kPa, i.e., below 1% of Earth’s standard atmospheric pressure ( NASA, 2004). Operating a greenhouse at low interior pressure reduces the pressure differential across the structure and therefore saves structural mass as well as reduces leakage. Studies have shown that plant growth is feasible at pressures as low as 20 kPa; pl ants even survive short-term exposure to pressures as low as 10 kPa (A ndre and Richaud, 1986; Fowler et al. 2002). Inflatable greenhouse structures are being studied as th ey offer the advantage of a high volume to mass ratio, and can be packed efficiently for the transit, reducing the number of launches (Clawson et al. 1999; Kennedy, 1999; Hublitz, 2000). A major challenge in developi ng a Mars greenhouse is its interaction with the thin and cold Mars environment. The environmen tal conditions inside the greenhouse have to be controlled within th e ranges where plants are highly pr oductive. Transparent structures capture day-time solar radiation that is re quired for photosynthesis and heating of the

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2 greenhouse, whereas during the night they have to be covered with multi-layered insulation to avoid heat loss (Hublitz, 2000). Most experimental Mars greenhouse studies ha ve focused on the ability of plants to grow at reduced pressures with non-standard atmosphere compositions, but little research has been done on the thermal interactions of the greenhouse with the Mars environment. The heat and mass transfer analysis is an important step in the design of the thermal control system that provide s the climatic environment essential for plant growth. Figure 1-1. "Astronaut" approaching Universi ty of Florida’s Mars Greenhouse Dome.

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3 Structure of the Dissertation Chapter 1 introduces the importance of res earch on the heat a nd mass transfer of low pressure Mars greenhouses and gives an ou tline of this dissertation. Chapter 2 states the objectives of advanced life support systems, summari zes the fundamental knowledge of the Mars environment and reviews the lite rature on low pressure plant growth studies. The objectives of this dissertation are disc ussed in Chapter 3. Ch apter 4 describes the setup of the experimental work, the data acq uisition and the control system. Data of the heat and mass transfer experiments with and without plants are presented. The mathematical model development and simula tion results are discussed in Chapter 5. Chapter 6 gives results and conclusions; Ch apter 7 states recomme ndations for future studies. The structural analys es of the greenhouse dome and sensor calibration cylinder as well as the sensor calibration are included in the appendices.

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4 CHAPTER 2 LITERATURE REVIEW Advanced Life Support The goal of NASA’s Advanced Life Suppor t (ALS) Project (National Aeronautics and Space Administration (NASA), 2002), is to “provide life support self-sufficiency for human beings to carry out research and expl oration productively in space for benefits on Earth and to open the door for extended onorbit stays and planetary exploration.” For long-duration missions open loop life s upport systems have to be replaced by closed loop life support systems, in order to avoid the high costs associated with the launch and storage of consumables and high risk of relying on frequent resupply missions. Advanced life support systems shoul d not only provide a high degree of closure of the air and water loop, but also begi n to close the food loop (Eckart, 1996). In contrast to the life support system s for the current short-duration missions, biological processes, in additi on to physico-chemical proce sses, such as food production utilizing higher plants will be implemen ted for long-duration missions (Duffield, 2003). Valuable chemicals will be recovered by processing solid waste. In-situ resources, where available, may also be used to replenish life support consumables. Consumables for human space missions amount to approximate ly 31 kg of oxygen, water and food per astronaut and per day as listed in Table 2-1. Simultaneously, the same amount of waste is created. Physico-chemical life support systems can provide oxygen, reduce carbon dioxide and recycle water, whereas biologi cal life support systems can fulfill all these functions and additionally produce food (Eckart, 1996).

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5 Table 2-1. Human metabolism values per crew member and per day (CM-d) for average activity level. Consumable Units Needs Effluents Air Carbon Dioxide Load kg/CM-d 1.00 Oxygen Consumed kg/CM-d 0.84 Food Mass of Consumed Food (dry basis) kg/CM-d 0.62 Energy of Consumed Food MJ/CM-d 11.82 Potable Water Consumed (incl. water in food) kg/CM-d 3.91 Thermal Sensible Metabolic Heat Load MJ/CM-d 6.31 Latent Metabolic Heat Load MJ/CM-d 5.51 Waste Fecal Solid Waste (dry basis) kg/CM-d 0.03 Perspiration Solid Waste (dry basis) kg/CM-d 0.02 Urine Solid Waste (dry basis) kg/CM-d 0.06 Water Fecal Water kg/CM-d 0.09 Respiration and Perspiration Water kg/CM-d 2.28 Urine Water kg/CM-d 1.89 Hygiene Water Hygiene Water (Flush, Hand Wash, Shower, Laundry, Dish Wash) kg/CM-d 25.58 Greywater kg/CM-d 25.58 Total Mass kg/CM-d 30.95 30.95 Total Energy MJ/CM-d 11.82 11.82 Source: Hanford, 2004. The objectives of ALS systems based on plant growth are to (NASA, 2002) Produce food that meets human requirement s for nutrition, sensory acceptability and food safety. Provide the environmental and cultural re quirements to produce crops, including efficient environmental control (temperature, relative humidity, gas composition), the lighting intensity and spectral com position, the growth area, and nutrient delivery system. Provide post-harvest processing, material s handling and storage of harvested products. Utilize resources recovered from other life support systems, including carbon dioxide, waste water and solid wastes. Provide non-food products to other life support systems for utilization, further processing or disposal, including oxygen, tr anspired water, heat and inedible biomass.

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6 Minimize required involvement of th e crew in life support operations. Minimize the impact of life suppor t on planetary environments. For the development of bioregenerative life support systems for Mars, it is critical to develop models to predict system beha vior in the planetary environment and to evaluate the performance through experime nts in a simulated Mars environment. Mars Environment The Mars environment differs from that on Earth in several significant ways including lower gravity, very low density at mosphere rich in carbon dioxide, reduced light levels and very cold ambient temperatures. The Mars atmosphere is highly variable on a daily, seasonal a nd annual basis. The thinness of the atmosphere and the lower solar constant (which is 43% of the terrestrial value) guarantee a large daily temperature ra nge at the surface unde r clear conditions. On an annual basis, the atmospheric pressure at the surface changed from 0.69 to 0.9 kPa at the Viking 1 lander site due to c ondensation and sublimation of CO2 (NASA, 2004). The mean atmospheric pressure is estimated at 0.64 kPa. Although Mars has no liquid water and its at mospheric pressure is approximately 1.0 percent that of Earth, many of its meteorological features are similar to the terrestrial ones. Water ice clouds, fronts with wind shif ts and associated temperature changes similar in nature to those on Earth can be found. The main differences between the Earth and the Mars atmosphere are that the Mars at mosphere does not transfer as much heat by conduction and convection as the Earth atmosphe re and it cools much faster by radiation. Mars’ diurnal temperature cycle is larger than Earth’s: 184 to 242 K during the summer but stabilized near 150 K (CO2 frost point) during the wi nter (Kaplan, 1988; NASA, 2004). Water ice clouds occur due to many di fferent causes just as on Earth. Nighttime

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7 radiation cooling produces fogs ; afternoon heating causes draf ts which cool the air and cause condensation; flow over topography causes gravity clouds; and cooling in the winter polar regions ca uses clouds (Kaplan, 1988). Mars has local dust storms of at least a few hundred kilometers in extent. The duration and extent of Martian dust storms va ry greatly. Dust storms of planetary scale may occur each Martian year with a velocity of up to 30 m/s. Unfortunately, neither Earth based nor spacecraft observations have been systematic enough to quantify the frequency of dust storm occurrence or ev en the true extent of many individual storms. There is no reliable method for prediction of great dust storms. They mainly occur during southern spring and summer. Local dust storms have b een observed on Mars during all seasons, but they are most likely to occur during the same periods as the great dust storms. The physical grain size of the drifting material is estimated to be 0.1 to 10 m. It has the characteristics of very fine grained, porous materials with low cohesion (Kaplan, 1988). The dust raised into the atmosphere by dus t storms and the ordinary atmospheric dust always present in the atmosphere settle out of the atmosphe re onto any horizontal surface. Measurements made by the Pathfinde r Mission showed a 0.3% loss of solar array performance per day due to dust obscuration (Kaplan et al. 2000). This dust deposition could be a significant problem for a gree nhouse operated with solar light for long duration missions, unless a tech nique is developed to rem ove the dust periodically or prevent settled dust from co ating the greenhouse surface. The Mars atmosphere consists mainly of carbon dioxide (95.3%). Photosynthesis requires carbon dioxide which c ould be taken out of the pl anet’s carbon dioxide rich

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8 atmosphere, in case of an autonomous greenhous e that is pre-deployed before the first humans arrive. In Table 2-2 the Mars environment prope rties are summarized. Table 2-3 describes the composition of the atmosphere of Mars in terms of the gases present by volume. Table 2-2. Envir onment properties. Property Value Mars Value Earth Orbit period 687 days 365 days Rotation period (day length) 24.62 hours 23.93 hours Gravity 3.69 m/s 9.81 m/s Surface Pressure ~ 0.64 kPa (variable, depending on season and location) 0.69 to 0.9 kPa at Viking 1 lander site (22 N lat.) 101.4 kPa (at sea level) Surface density ~ 0.020 kg/m 1.217 kg/m Average temperature ~ 210 K 288 K Diurnal temperature range 184 to 242 K (summer) 150 K (winter) 283 to 293 K Wind speeds 2 to 7 m/s (summer) 5 to 10 m/s (fall) 0 to 100 m/s Solar irradiance in orbit 589 W/m 1368 W/m Drifting material Size Cohesion 0.1 to 10 m 1.61.2 kPa Source: Carr, 1981; Kaplan, 1988; NASA, 2004. Table 2-3. Atmosphere composition by volume. Gas Value Mars Value Earth Carbon Dioxide (CO2) 95.32 % 0.035 % Nitrogen (N2) 2.7 % 78.084% Argon (Ar) 1.6 % 0.93% Oxygen (O2) 0.13% 20.946% Carbon Monoxide (CO) 0.08% Water (H2O) 210 ppm Highly variable (typically 1%) Nitrogen Oxide(NO) 100 ppm Neon (Ne) 2.5 ppm 18.18 ppm Hydrogen-Deuterium-Oxygen (HDO) 0.85 ppm Krypton (Kr) 0.3 ppm 1.14 ppm Xenon (Xe) 0.08 ppm Helium (He) 5.24 ppm CH4 1.7 ppm Hydrogen (H2) 0.55 ppm Source: NASA, 2004.

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9 The solar irradiance varies as a function of season, latitude, time of day and optical depth of the atmosphere. The solar irradiance incident on the surface of Mars consists of two components: the direct beam and th e fuse component. The fuse component comprises the scattering by small particles in the atmosphere and the diffuse skylight. The solar radiation on Mars va ries according to the eccentric ity of the Mars orbit. The mean solar radiation in Mars orbit is 589 W/m The ultraviolet radiation that reaches the Mars surface is much greater than on Earth, because the Martian atmosphere is more tenuous and there is very little ozone. The u ltraviolet radiation is mainly absorbed by carbon dioxide; all ultrav iolet radiation with a wavelength less than 200 nm is absorbed by the atmosphere (Kaplan, 1988). The availa ble photosynthetically active radiation (PAR) changes throughout the Mars season. Th e average PAR is estimated to be 20.8 mol/(m day) (Gertner, 1999). Figure 2-1 depicts the spectrum of the sola r radiation on Mars. Du st affects both the intensity and the spectral content of the s unlight. The solar irradiance on the surface of Mars during a global dust storm is comparab le to the one of a cloudy day on Earth (see Figure 2-2). Figure 2-1. Martian spectral irradiance (Ls=250, 15S, noon) vs. te rrestrial spectral irradiance (Rettberg et al. 2004)

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10 6.5% 13% 22% 43% 5.7% 56.6% 100% 0 200 400 600 800 1000 1200 1400 1600Earth OrbitEarth Surface (Clear) Earth Surface (Cloudy) Mars OrbitMars Surface (Clear) Mars Surface (Cloudy Local Storm) Mars Surface (Cloudy Global Storm)Average Solar Irradiance [W/m] Figure 2-2. Average solar irradiance of Mars compared to Earth (Clawson et al. 1999). Plant Requirements and Environment Control High yields in plant growth chambers can be achieved by contro lling temperature, relative humidity, atmosphere pressure and composition, ventilation, light intensity and spectral quality, water and nut rient delivery. Table 2-4 lists the minimum, maximum and optimum environmental parameters. The optim al growth conditions depend on the type of crop. A list of crops identified for ALS application and the re quired environmental condition is shown in Table 2-5. Table 2-4. Plant environment requirements. Parameter Unit Low Value High Value Optimal Value Temperature C +5.0 +35 +20 to +27 Atmospheric Pressure kPa 10.0 (?) 100 100 Photosynthetically active radiation W/m 50 500 150 to 200 Partial Pressure CO2 kPa 0.03 3.0 to 5.0 0.1 to 0.2 Partial Pressure O2 kPa 5.0 27 to 30 10(?) to 22 Relative Humidity % 55 100 70 to 85 Source: Rygalov et al. 2000.

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11 Table 2-5. Advanced life support crop growth conditions. Crop Photosynthetic Photon Flux [mol/m-d] Diurnal Photoperiod [h/d] Growth Period [days after planting] Air Temperature Day [C] Air Temperature Night [C] Cabbage 17 85 >25 Carrot 17 75 16-18 Chard 17 16 45 23 23 Celery 17 75 Dry Bean 24 18 85 28 24 Green Onion 17 50 Lettuce 17 16 28 23 23 Onion 17 50 Pea 24 75 Peanut 27 12 104 26 22 Pepper 27 85 Radish 17 16 25 23 23 Red Beet 17 16 38 23 23 Rice 33 12 85 28 24 Snap Bean 24 85 28 24 Soybean 28 12 97 26 22 Spinach 17 16 30 23 23 Strawberry 22 12 85 20 16 Sweet Potato 28 12 85 26 22 Tomato 27 12 85 24 24 Wheat 115 20-24 79 20 20 White Potato 28 12 132 20 16 Source: Hanford, 2004. Temperature Temperature effect Temperature is an important physical parame ter for controlling plant growth. It has a direct effect on biochemical reaction rates in the various metabolic processes and can indirectly contribute to water stress by e nhancing transpiration (Downs and Hellmers, 1975). The various biochemical reactions have different mini mum, maximum and optimum temperatures. Up to 30 C temperat ure affects plant growth positively by more rapid leaf expansion and increa sed root initiation (Albright et al. 2001). In general, most plants grow well at a temperature from 10 to 30 C. Excessive temperatures result in heat damage; temperatures below this range l ead to chilling and/or freeze damage. The

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12 severity of the damage increases with incr easing temperature difference and the time the plant spends in this unfavorable condition. Temperature control In order to control the ai r temperature of a Mars gr eenhouse, it is essential to analyze the heat and mass balance of the green house and its environment. Heat received by the greenhouse through solar radiation or wa ste heat of internal electric equipment may lead to a rise of the temperature. C onvective, conductive and ra diative heat loss of the greenhouse to the environment may re sult in a decreasing internal greenhouse temperature. Furthermore, the addition and removal of latent heat by evaporation and condensation of water directly affect the plant as well as the greenhouse temperature. Air temperature can be increased by additi on of heat to the greenhouse such as by turning on the heating system. Temperature is decreased by removing heat from the greenhouse such as by utilizati on of cooling coils or maximizing heat emission of the greenhouse structure to the Mars environm ent. Temperature uniformity within a greenhouse is achieved by vertical ventilation. Relative Humidity Relative humidity effect Relative humidity is an indicator of potenti al water loss from the plants as it is a function of the water vapor pre ssure. Transpiration ra tes of plants increase as the vapor pressure deficit between the cells of the l eaf and the atmosphere increases. At a given temperature, the vapor pressure deficit incr eases rapidly with d ecreasing humidity. The balance and dynamics of water loss by tr anspiration and gain by root absorption determine the plant water status. Water stre ss and possibly wilting can be caused by a high transpiration rate and vapor pressure deficit.

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13 Humidity also reduces the incident radi ation on plants through absorption of infrared radiation leading to a higher sp ecific heat of the ai r. Condensation and evaporation affect the energy balance and therefore the air temperature. 70-85% relative humidity is c onsidered to be the optimal range for plant growth (Tibbitts, 1979). Low relative humidity levels cause wilting of the plants; high relative humidity levels lead to de velopment of fungus and mold. Relative humidity control In a closed environment, humidity is increased by evaporation of open water sources or evapo-transpiration of the plants. Humidity levels are reduced by condensation. Humidity control can be achieved by studying the underlying psychrometric relationships which are explained in detail in the psyc hrometrics section at the end of Chapter 5. Atmospheric Pressure and Composition The greenhouse atmosphere is composed of essential gases required for plant growth (such as carbon dioxide, oxygen and water vapor) and some non-essential gases (such as nitrogen) for pressu rizing the greenhouse structure. The total pressure of the greenhouse atmosphere is the sum of th e partial pressures of the gases. Carbon dioxide effect Apart from light and water, carbon dioxi de is required fo r photosynthesis and therefore plant growth. Plant response to increased/decreased carbon dioxide levels depends on plant species, development stag e, irradiance, temperature and mineral nutrition (Langhans and Tibbitts, 1997). Slightly elevated carbon dioxide during the day may lead to increased biomass production, wher eas highly elevated ca rbon dioxide levels can be toxic for plants. As net photosynthesi s increases with elevated carbon dioxide

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14 concentration (up to 0.5 kPa), tr anspiration may decrease due to stomatal closure and leaf temperatures could rise (Wheeler, 2000). Thus benefits from elevated carbon dioxide concentrations can be reduced by higher leaf temperatures. On the other hand, studies showed that at super-elevat ed levels of carbon dioxide c oncentration (0.5-1.0kPa) leaf transpiration and plant water use increased significantly for some species (Wheeler, 2000). Plant photosynthesis and hence growth responses to carbon dioxide generally show near linear increases at the low concen trations (up to 0.15 kP a), after which rates either saturate or eventually taper off. Carbon dioxide c oncentration below terrestrial ambient levels (370 ppm) decreases photos ynthesis and plant growth (Langhans and Tibbitts, 1997). Carbon dioxide control If carbon dioxide is not c ontrolled in a plant growth chamber, it will decrease during the day when it is used for photosynthe sis. During the night the amount of carbon dioxide increases due to plant respiration. Carbon dioxide th at is taken up by the plants for photosynthesis has to be replenished to the greenhouse atmosphere. In case of an autonomous greenhouse, pre-deployed before human arrival, carbon dioxide is not available as a byproduct of the human metabo lism and should be taken out of the carbon dioxide rich Mars atmosphere. Oxygen effect Oxygen is important for respiration, es pecially at night when there is no photosynthetically generated oxygen. Probably at least 5 kPa of oxygen is needed to sustain plant growth (Quebedeaux and Ha rdy, 1973). Partial pressure of oxygen is especially critical for the r oot-zone respiration. The upper li mit of oxygen partial pressure

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15 can be set at 23.5%, because above this there are safety concerns related to fire risks (Lacey et al. 2000). Oxygen control Photosynthesis produces oxygen and therefor e the oxygen levels will build up in a greenhouse over time. Thus, oxygen has to be sc rubbed out of the atmosphere or used by humans in order to keep the oxygen level constant. Vapor pressure effect and control The effect and control of relative humid ity have been described above. Under Earth atmospheric pressure in an open system, the ch ange in vapor pressure has minimal effect on total pressure, but in a totally closed syst em at low pressure, fluctuations in vapor pressure will significantly infl uence total pressure (Bucklin et al. 2004). This effect is explained in detail in the psychr ometrics section in Chapter 5. Pressurizing gas Nitrogen and argon are two inert gases that may be used as pressurizing gases. In case of a Mars greenhouse both of the gases c ould be used, as they are available in the Mars atmosphere, so they could be extrac ted locally. Nitrogen a nd argon are biologically inert. They would be used as make-up gase s in order to increase the total pressure required for the inflatable structure. Ventilation The ventilation system ensures a homogenous gas mix in terms of gas composition, temperature and humidity inside of the gr eenhouse. Furthermore, ventilation provides a minimum air velocity over the plants to facilitate gas exchange required for photosynthesis. On the other hand, excessi ve air movement through the crop canopy leads to increased transpiration a nd potential water stress (Albright et al. 2001).

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16 Radiation Radiation effects Electromagnetic radiation is the energy source for plant growth. Radiation controls photosynthesis not only through the intensity but also through the sp ectral distribution and photoperiod. For photosynthesis, plants require phot osynthetically active radiation in the wavelengths between 400 and 700 nm. Photosynt hetic efficiency decreases in the region of 500 to 600 nm where radiation is not absorbed well by the chlorophyll, giving the plants their characteristic gr een appearance (see Figure 2-3). Figure 2-3. Photosynthetic effi ciency (Eckart, 1996). The radiation intensity required to saturate C3 plants is around 300 mol/m-s for a daily photoperiod of 16 hours; C4 plants require at least 500 mol/m-s for a daily photoperiod of 16 hours (Langha ns and Tibbitts, 1997). Shade leaves tend to be larger, thinne r, and contain more chlorophyll per unit weight than do sun, i.e., bri ght light-grown leaves (Board man, 1977). But sun leaves have higher photosynthetic capacities. As a cons equence, low levels of photosynthetically active radiation result in bi gger leaves, elongation of inte rnodes and less dry weight,

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17 whereas high light levels lead to stimulation of auxiliary br anch growth and possibly to photodestruction of chlorophyll. Excess radiat ion may cause heating of the leaves and desiccation due to water loss (Langhans and Tibbitts, 1997). Radiation control Shading can lower radiation intensity and filters can change the spectrum. On Mars the low levels of solar radiation may have to be supplemented by li ght collection systems or by electric light. Options fo r electric lights suitable for plant growth are: Incandescent lamps, fluorescent lamps, high-intensity disc harge lamps (e.g. metal halide lamps, high pressure sodium lamps), xenon lamps and light emitting diodes. Incandescent light is blackbody radiation as it is created by a heated body. The spectrum depends on the temperature of the h eated element. Most of the energy from incandescent lights is in the infrared-region. The infra-red radiation is not useful for photosynthesis and must be dissipated from the growth chamber. The spectrum can be shifted by changing the voltage to the lamp; th e higher the voltage the lower the ratio of infra-red to visible radiation. Another method of alte ring the spectrum is th e use of filters. Wavelengths not useful for photosynthesis can be filtered out. The disadvantage of this method is that the overall radiation is re duced. Incandescent lamps have a very low efficiency, not more than 10% of the output radiation is within th e visible wavelengths (Langhans and Tibbitts, 1997). Fluorescent Lamps have many advantages over incandescent lamps. The radiation output is continuous, generally uniform and the photosynthetically active radiation is high. Their optimal operation temperature is only about 38 C. In order to alter the spectrum of the fluorescent lamps the inner wa ll of the tubes, which emits the radiation, can be coated with different phosphors. Most fluorescent plant growth lamps are coated

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18 with a special phosphor mix to provide an e nhanced blue and red spectrum. Cool white lamps are the most efficient fluorescent lamp s, with efficiencies of around 20%. Output of very high output lamps decreases to 70% after the lamps have been operated for 1 year, 16 hours per day (Langhans an d Tibbitts, 1997; Schwarzkopf, 1990). High-intensity discharge lamps excite elements in the arc in order to emit characteristic wavelengths. Their spectrum is uniform but not continuous. Irradiances are higher than those of inca ndescent and fluorescent lamps. Two commonly used highintensity discharge lamps are metal halide and hi gh-pressure sodium lights. In contrast to fluorescent lamps the output radiation of me tal halide lamps is not affected by the ambient temperature. Most of the radiati on output is in the 400-700 nm but output can shift with lamp age. The efficiency of metal halide lamps is around 22%. The radiation output of high pressure sodium lamps is c oncentrated in the 550-650 nm range, and very scarce in the 400-550 nm range. High pressure sodium lights are useful in combination with alternative lighting options such as metal halide, blue phosphor and cool-white fluorescent lamps. High pressure sodium lights ar e very efficient with efficiencies of 25% (Langhans and Tibbitts, 1997; Schwarzkopf, 1990). Xenon lamps are rarely used for plant gr owth chambers even though they have a spectrum similar to the solar spectrum. Th eir disadvantages incl ude the high cost and their emission of ultraviolet radiation, which leads to development of ozone. Furthermore, the high infra-red radiation incr eases the cooling load of the plant growth chamber (Langhans and Tibbitts, 1997). Light emitting diodes (LEDs) are very useful for plant growth as certain LEDs have specific outputs required for photosynthesis. Moreover, they are solid state devices and

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19 have a long operating life. Blue and red LEDs can be combined to fulfill the plant needs (Langhans and Tibbitts, 1997). Growth Area The size of the Mars greenhouse depends on the number of astronauts and the desired amount of food grown locally vs. sh ipped from Earth. The required plant-growth area per person can be estimated at 50 m to fulfill 100% of the food requirements (Wheeler et al. 2001). Food, if grown on-site, can regene rate some or all of the crew’s air and water. If more than about 25% of the food, by dry mass, is produced locally, all the required water can be regenerated by the sa me process. If approximately 50% or more of the food, by dry mass, is produced on site, all the required air can be regenerated by the same process depending on the cr op and growth conditions (Wheeler et al. 2001; Hanford, 2004). Low Pressure Plant Growth Studies Operating a greenhouse on Mars at low inte rnal pressure reduces the pressure differential across the structur e and therefore saves structural mass as well as reduces leakage. The literature contai ns a variety of studies on the plant responses to low pressure. The lower limits of oxygen, carbon di oxide, water vapor and inert gases that plants can tolerate and th rive in are a key in the development of hypobaric Mars greenhouses. Studies on plant responses to low pressu re date back to the 1960s, when NASA first considered the implementation of bi ological life support syst ems. These studies include research at Brooks Air Force Base where the plant environment pressure was dropped to 51 and 93 kPa and other research Wright-Patterson Air Force Base with an

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20 even lower pressure of 1/3 atmosphere. No adverse effects on plant growth due to low pressure were observed (Corey et al. 2002). Further studies focused on the effect of the different atmosphere components on the seed germination, seedling development and plant growth. Andre and Richaud (1986) and Andre and Massimino (1992) evaluated if an inert gas such as nitrogen is necessary for plant growth by studying barley at 7 kP a. They concluded th at nitrogen is not necessary for plant growth. An increased tr anspiration rate was observed at this low pressure. Furthermore, these studies demonstrat ed that growth of wheat is possible at a total pressure as low as 10 kPa. Wheat grow th at 20 kPa was greater than at 10 kPa and even greater than at atmospheric pressure levels. Musgrave at al. (1988) found enhanced growth of mungbean at 21-24 kPa total pressure atmospheres with a low oxygen level of 5kPa. A study by Schwartzkopf and Mancinelli (1991) confirmed that an oxygen partia l pressure of at least 5 kPa is necessary for seed germination and initial plant growth, as seeds failed to germinate at atmospheres with a partial pressure of oxyge n lower than 5 kPa. With a total pressure of 6 kPa and therefore an oxygen concentra tion of 83%, this study was we ll above the oxygen level of 23.5% that is the upper limit considered to be safe regarding fire hazards (Lacey et al. 2000). Although others have operated system s at high oxygen concentration, e.g. Goto et al. (2002) operated the growth chamber at a high level of 91% oxygen (21 kPa partial oxygen pressure, 23 kPa total pressure). Spanarkel and Drew (2002) reported that le ttuce grown at 70 kPa total pressure was normal in appearance, and that photosynthesi s was unaffected compared to plant growth

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21 at ambient pressure. Oxygen levels were maintained at 21 kPa and carbon dioxide at 66.5–73.5 Pa during both ambient and hypobaric conditions. Research by Daunicht and Brinkjans (1996) compared plant growth at 100 kPa to 70 kPa and 40 kPa total pressure with equal carbon dioxide concentration. Photosynthetic rate increased at 70 kPa compared to 100 kPa and was similar at 40 kPa and 100 kPa. Furthermore, plant morphology was affected by the reduced pressures. Experiments conducted in the variable pr essure growth chambers at different NASA centers tested wheat under 70 kPa a nd lettuce under a progressive reduction of pressure down to 20 kPa (Corey et al. 1996; Corey et al. 1997b, Corey et al. 2002). Lettuce, as well as the wheat experienced increased transpiration at reduced total pressures. An effect of the oxygen partia l pressure on the photosynthesis was also observed. Photosynthesis increased with decreasing oxygen partial pressure and decreased if oxygen was inje cted into the chamber. Studies at Texas A&M also tested the pe rformance of wheat and lettuce at low pressures ranging from 30 to 101 kPa (He et al. 2003). Low pressure increased plant growth and did not alter germ ination rate. Low oxygen con centration inhibited ethylene production of lettuce. Low total pressure in hibited ethylene producti on of wheat, whereas oxygen reduction did not have an influe nce on ethylene production for wheat. The University of Tokyo performed a series of studies on spinach and maize in a reduced pressure plant growth chamber (Goto et al. 1996; Iwabuchi et al. 1996; Iwabuchi and Kurata, 2003). Similar to the ot her studies described above, they observed increased photosynthesis and tr anspiration rates at reduced pressures. Furthermore, stomatal size and aperture of leaves were si gnificantly smaller at reduced total pressures.

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22 Ferl et al. (2002) describes the adaptation and plant responses to low pressure environments. Plant stress includes hypoxic st ress, drought stress and heat shock that may alter plant morphology. For th is research genes were analyzed to understand the fundamental processes that involve gene re sponses to environmental signals. Genetic engineering will lead to plants that can to lerate and thrive in extreme environments. In a study by Wilkerson (2005) evapo-tran spiration rates of radishes increased significantly at a low atmospheric pressu re of 12 kPa and a carbon dioxide partial pressure of 40 Pa. Furthermore, this rese arch concluded that increasing the carbon dioxide partial pressure from 40 Pa to 150 Pa is an effective countermeasure to wilting of the plants at low atmosphe ric pressures because the stomata close at higher carbon dioxide concentrations and theref ore transpiration rates decrease. The studies described above indicate that plant gr owth is possible under low atmospheric pressure. Neverthele ss, more detailed research is necessary on the response of plants to the environment properties es pecially for more than one life cycle. Additionally, studies on plant growth chambers exposed to the Martian environmental conditions are necessary in case of transparen t greenhouse structures, as the local climate has a huge effect on the plant growth condi tions. Operating a greenhouse in the Mars environment may lead to st ratification of te mperature and humidity, condensation resulting in lower light levels, as well as de gradation of transparent greenhouse materials leading to a change of the spectrum of the photosynthetically active radiation. Last but not least, genetic engineering will play an important role in the selection of the crop suited for advanced life support.

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23 CHAPTER 3 OBJECTIVES OF THIS STUDY This study can be divided into the theo retical (mathematical) simulation and the experimental work. The objectives of the experimental part were Design of simulated Mars environment and low pressure greenhouse for plant growth. Development of control-algorithm to mainta in total pressure and temperature of vacuum chamber (simulated Mars environment). Development of control-algorithm to mainta in total pressure, temperature and gas composition (CO2, O2 and N2 concentration) of greenhouse dome. Monitoring of stratification of temperat ure and relative humidity in greenhouse dome. Monitoring of condensation pattern on inte rior of greenhouse do me and its effect on light reduction. Monitoring of plant evapo-tr anspiration in low pressure greenhouse that is exposed to low temperature environment. The objectives of the simulation were Development of low pressure psychrometri c relationships for closed systems and non-standard atmospheres. Prediction of temperatures of greenhous e atmosphere, greenhouse floor, interior and exterior greenhouse shell by creating a ma thematical model to simulate the heat and mass transfer. Prediction of occurrence of condensa tion on interior of greenhouse dome. Comparison of theoretical and experime ntal results to deduce conclusions.

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24 CHAPTER 4 EXPERIMENTAL WORK System Description A careful selection of equipment for th e set-up of the experimental work was required in order to fulfill the objectiv es listed in Chapter 3. A polycarbonate hemispherical dome with a diameter of 1 meter served as the Mars greenhouse (see Figure 4-1). The dome was clamped to a re-inf orced aluminum base with the help of a silicon rubber gasket to ensure the enclosur e of the system. A 10 cen timeter thick layer of polyurethane foam was fixed to the bottom of the aluminum dome base for insulation. Feed-throughs in the dome base were used for data transfer, power and gas supply. The maximum pressure differential that the dome structure could withst and without failure was estimated to be 50 kPa. The structural analysis of the dome and its base plate is presented in Appendix A. A dome similar to the one that was ut ilized as a greenhouse model for this study had been used at NASA’s Kennedy Space Center as an autonomous low pressure growth chamber. In a preliminary test lettuce was grown at a pressure of 25 kPa for 45 days (Fowler et al. 2002; Bucklin et al ., 2004). However, during this lettuce growth experiment at NASA the dome was not exposed to simulated Mars conditions as in the experiments described in this document. A large stainless steel vacuum chamber was used to simulate the Mars atmosphere of 0.6 kPa. Its interior volume was comprise d by an area of 1.2 mete r by 1.2 meter with a

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25 height of 1 meter. The chamber was cu stom-made by Chicago Wilcox based on the following requirements: The vessel should be able to hold a pressure of 0.1 kPa with no significant leakage. It should be big enough for the green house dome (0.5 m radius) to fit in. It should have a window on top to allow grow th light to penetrat e into the chamber. It should have 12 ports on the side fo r data transfer, power and gas supply. It should have a door to move equipment in and out. The stainless steel chamber was braced on the bottom and on all sides (except for door) to avoid deflection of the walls because of the huge pressure difference. A 1.27 cm thick polycarbonate sheet serv ed as a window pane. A grid of steel bars supported the polycarbonate window (see Figure 4-2). An industrial freezer shown in Figure 4-3 ensured the low temperature of the vacuum chamber (simulated Mars environment) The interior temperature of the freezer could be dropped down to as low as –34 C. In itially, jacketing the vacuum chamber with a heat exchanger was discussed as an opti on to reduce the temper ature inside of the chamber, but putting the entire vacuum chamber in a freezer had the advantage that the temperature distribution was more uniform especially at the chamber window. A) B) Figure 4-1. Dome used to protect plants from the simulated low pressure, low temperature Mars environment. A) Em pty dome. B) Dome with sensors, scales and flasks installed.

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26 Figure 4-2. Vacuum chamber used to simulate the low pressure Mars environment (less than 1% of Earth’s atmosphere). Figure 4-3. Industrial walk-in freezer ensure s low temperature of the vacuum chamber (simulated Mars environment).

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27 Two vacuum pumps were installed outside the freezer. A powerful two-stage rotary vane vacuum pump (DUO 10, Pfeiffer Vacuum ) with a volumetric flow rate of 10 m/hour was connected to the vacuum ch amber; a two-stage vacuum pump (DV-85N, J/B Industries) with a volumetric displace ment of 5 m/hour was connected to the greenhouse dome. During the experiments the pum ps were always turned on and the air flow was controlled by two solenoid valves that were installed between the pumps and the chamber/dome. Three mass flow controllers ensured the correct gas mixture that was fed into the greenhouse dome. The mass flow c ontrollers were connected to bottles of nitrogen, oxygen and carbon dioxide. Scale 1 was located on the bottom of the greenhouse. It measured the amount of water that ran off the greenhouse shell and the recollection funnel. Four scales (Scale 2 to Scale 5) were installed in the upper part of the dome. They measured the amount of water that the plants evaporated and transpired. Two flasks, each containing one lettuce plant, were placed on each of these four scales, leading to a total number of 8 flasks. A 512W/110V cooking range coil was placed in the center of the greenhouse dome and served as the heater. A 24V fan ensured mixi ng of the air and minimized temperature, gas composition and relative humidity stratification. A high pressure sodium growth light ( 1000W HPS, Hortilux) was installed above the vacuum chamber. Two I/O boards, one for data acquisition and one for control, were connected to the sensors and actuators. Th ey were connected to the computer for programming and as user interface. Figure 44 gives an overview of the experimental setup.

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28 Figure 4-4. Schematic of experimental setup. Instrumentation and Sensor Calibration Most commercially available sensors fo r the measurement of environmental parameters contain a data sheet with calib ration information under standard atmospheric conditions. However, in this project, the pr essure and gas composition of the environment that the sensors were exposed to differed si gnificantly from the standard atmosphere. Therefore, the sensors were carefully selected according to the environmental conditions and a re-calibration of the sensors was perfor med against a standard sensor that was not affected by pressure or gas composition. DS18B20 (Dallas Semiconductor) digital thermometers were selected for temperature measurements. They were shielded to avoid measurement errors caused by direct radiation onto the sensors. Relativ e humidity (RH) was monitored by HIH-3602-L (Honeywell) capacitance type sensors capable of measuring RH in the range of 0-100%

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29 (non-condensing). LI-COR’s LI-190 SA qua ntum sensor monitored the level of photosynthetically active radiation insi de the greenhouse dome. The carbon dioxide concentration was measured by Vais ala’s infrared GMP 221 sensor, oxygen concentration by Maxtec’s Max 250 galvan ic cell type sensor. The mass of the recollected water and the masses of the indi vidual plants were measured by Vishay Celetron’s LPS-2 kg load cells. Table 4-1 list s the environmental parameters that were monitored and their corresponding sensors. Table 4-1. Sensors used to measure envir onmental parameters, the sensor ranges and accuracies. Parameter Type Range Accuracy Temperature DS18B20 digital thermometer (Dallas Semiconductor) -55 to +125 C 0.5 C Relative Humidity HIH-3602-L capacitance type RH sensor (Honeywell) 0 to 100% 2% Light LI-190SA quantum sensor (LI-COR Inc.) 0 to 10,000 mol/m2/s 5% Pressure ASCX15AN (Sensym ICT) 0 to 15 psi 0.5% Carbon Dioxide GMP 221 (VAISALA) 0 to 10 % 0.02% Oxygen Max 250 (MaxTec) 0 to 100% 1.0 % Water / Plant Mass LPS-2 kg Load Cell (Vishay Celtron) 0 to 2 kg 0.1 g A transparent acrylic cylinder with an aluminum base served as calibration chamber for the sensors. It had an interi or diameter of 20.32 cm, a wall thickness of 0.64 cm and a height of 30.48 cm. The cylinder was supported by an aluminum base containing feed-throughs for data transfer, power and gas supply. An O-ring minimized

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30 leakage of air into the cylinder. The structur al analysis of the cy linder is presented in Appendix A. The calibration data of all sensors is found in Appendix B. Figure 4-5. Cylinder used for ca libration of pressure-sensitive sensors and for initial gas mixing control algorithm development. The performance of the temperature sens ors, light sensor and load cells was unaffected by changes in total pressure. The sensors affected by low pressure, including relative humidity (RH), carbon dioxide concentration and oxy gen concentration, had to be calibrated for low pressures. Carbon di oxide and oxygen were calibrated by a method similar to the one described by Mu (2005). Rygalov et al. (2002) compared various types of RH sensors under low atmospheric pressure to RH readings from a chilled mirror/dew point hygrometer that is unaffected by pressure changes. This study concluded that the dr y-bulb/wet-bulb method was not adequate for low pressures as not enough air mass moves over the sensor. In

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31 contrast to this, the readings of the ca pacitance type RH se nsor did not change significantly at diffe rent pressures. As the accuracy of the relative humidity m easurements was of major importance to the study described in this di ssertation, further experiment s were conducted to confirm the independence of the output of the capacitanc e type RH sensor at different pressures. The RH values of the capacitance sensors were compared to th e output of Vaisala’s HMP 237 by exposing the sensors to a wide range of humidities and pressures. The HMP 237 is also a capacitance RH sensor, but especially designed to measure RH and temperature in both pressurized as well as v acuum chambers. The difference in RH of the Honeywell sensors from Vaisala’s low pressure RH sensor never ex ceeded 3%. Thus, the RH values obtained by the Honeywell RH se nsors were not corrected for pressure. 81 82 83 84 85 86 87 88 8182838485868788Reference Relative Humidity (HMP 237) [%]Relative Humidity (Capacitance Sensors RH1 RH5) [%] RH1 RH2 RH3 RH4 RH5 Target RH conf +3% RH conf -3% Figure 4-6. Comparison of Honeywell capacita nce RH sensors to the HMP 237 reference RH sensor for pressures of 0 to 25 kPa.

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32 Leakage Testing In low pressure plant growth chambers, involving the measurement of gas exchange rates and evapo-transpiration, it is important to minimize the leakage and to account for the occurring leakage by making the necessary corrections (Corey, 1997a). Leakage is defined as t P P P Li1440 1000 0 (4-1) where: L = leak rate [% vol/day] Pi = end pressure [kPa] Po = initial pressure [kPa] t = time interval [min] Leakage of Vacuum Chamber Initial leak tests of the freshly shipped vacuum chamber, showed very high leak rates of 2.5 kPa/hour. Due to the high leak ra te it was not possible to pump the chamber down to a pressure lower than 4 kPa. Ch anging the plastic tubing to copper tubing, attaching C-clamps to the chamber door, seal ing ports additionally with Loctite glue, utilizing high vacuum rated Swaglok valves and installing a powerful new two-stage rotary vane vacuum pump (DUO 10, Pfeiffer Vacuum) with a volumetric flow rate of 10 m/hour, led to a reduction of the leakage to 1.65 kPa/hour. Even at this lower leakage the target Mars equivalent pressure of 0.6 kPa could not be reached in the chamber. Further leak tests utilizing he lium gas and a helium gas detect or revealed that the gas was mainly leaking through the chamber window. Th erefore, the window was taken off and a second layer of gasket was cut out and inst alled, so that the po lycarbonate window would

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33 be sandwiched in between the two gaskets. Thus, the window could deflect more, without causing gaps for the gas to leak in. Figure 4-7 depicts the strong forces that act upon the window when the chamber is at low pressure: Photo A depicts the bul ging of the polycarbonate window at low pressures; in Photo B the window gasket is drawn inside by th e large pressure difference. Additionally, vacuum grease wa s applied to the window a nd the door. Finding the right amount of vacuum grease is the key to success: enough to fill the gaps and reduce the gas leakage but not so much, that lack of fricti on causes the gasket to dislocate. Finally, a pressure of 0.07 kPa was achieved, well belo w the required pressure of 0.6 kPa. A) Figure 4-7. Forces on chamber window. A) V acuum chamber at 0.6 kPa with top window bulging in. B) Gasket drawn into the ch amber due to pressure difference.

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34 B) Figure 4-7. continued Leakage of Greenhouse Dome The greenhouse dome was installed in the 0.6 kPa vacuum chamber. Therefore, gas leaked from the dome into the vacuum chambe r, causing the dome pressure to drop. This leakage was minimized by applying vacuum grease on the dome gasket, tightening the 36 screws of the dome and sealing the feed-throughs with additional glue. Figure 4-8 presents the data of a combined leak test of the va cuum chamber and the greenhouse dome. The dome leakage was found to be -0.375 kPa/hour (45 vol%/day) at 20 kPa; the chamber leakage 0.243kPa/hour (9 72 vol%/day) at 0.6 kPa. Figure 4-4 compares the leak rates of the vacuum ch amber/greenhouse dome to other low pressure

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35 plant growth systems. This comparison shows that the leak rates of this large system compared relatively well with the much smaller bell jar or tube systems. 19 19.1 19.2 19.3 19.4 19.5 19.6 19.7 19.8 19.9 20 015294560 Time [min]Greenhouse Dome Pressure [kPa]0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2Mars Chamber Pressure [kPa] Greenhouse Dome Pressure [kPa] Mars Chamber Pressure [kPa] Figure 4-8. Dome and chamber leakage with gas resupply and vacuum pumps turned off at a temperature of -10 C. 0.01 0.1 1 10 020406080100 Pressure [kPa]Leak Rate [kPa/hour] Chamber / Dome Mu (2005) Wilkerson (2005) Brown & Lacey (2002) Figure 4-9. Comparison of vacuum chamber a nd greenhouse dome leak ra tes to values of other low pressure plant growth studies (leak rate is presented in logarithmic scale).

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36 Data Acquisition and Control System The distributed control system for this project was developed by Rigel Corporation, especially for low pressure pl ant growth experiments, with the aims of maximizing the inputs and outputs while being very flexible yet low cost. This control system, described in detail in Mu (2005), was modified and adapte d after it had been used for previous plant growth studies. Two control boards were ut ilized: one for data acquisition and a second one to execute the control signals. The two boards combined had a large number of analog and digital inputs/outputs 16 digital inputs for temperature sensors 16 analog inputs especially for thermocouples 32 single ended (16 diffe rential) analog inputs 32 digital outputs for operating the relays 16 analog outputs for the control of the ac tuators (such as mass flow controllers) 8 digital outputs designed for pulse widt h modulation (e.g. utilized for the control of the heating system) The data board and the contro l board were both connected to the PC via the serial port. The data acquisition and control softwa re was separated into two parts: The lowlevel programming of the microcontrollers was done by Rigel Corporation utilizing Assembly and C language. These low-level pr ograms, loaded onto the microcontrollers, received the data from the sensors and sent out control commands to the actuators. For the high-level programming LabView was chos en as it provides an excellent userinterface and is comprised of many built-in functions. As LabView is a graphic programming language it also facilitated multiusers to work with the same program and to understand it quickly. The LabVie w programs communicated with the microcontrollers, contained the cont rol logic and managed the data.

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37 Greenhouse Dome Environmental Control Gas Composition and Total Pressure Control Algorithm The dry atmosphere of the greenhouse was comprised of three gases: oxygen, carbon dioxide and nitrogen. Oxygen and carbon di oxide are the essent ial gases required for photosynthesis and therefore plant grow th. Nitrogen was used to fill up the atmosphere to the desired total pressure as total pressure is defined as the sum of the partial pressures of all gases. The oxyge n and carbon dioxide concentration of the greenhouse dome were directly measured by sensors. Nitrogen was calculated by measuring the total pressure and subtracti ng the partial pressures of oxygen and carbon dioxide. Three mass flow controllers were ut ilized to control the resupply of oxygen, carbon dioxide and nitrogen sepa rately. Resupply of the indivi dual gas was shut off if the partial pressure of the gas was higher than th e set point partial pressure. If the measured partial pressure of the gas was lower than the set point, gas was resupplied. The required mass flow of each gas was calcu lated by determining the mass of the gas to be resupplied into the greenhouse dome, re sulting in the following gas control algorithm: t gas t gas Mass gas Mass t gas Flowactual set ) ( ) ( ) ( ) ( (4-2) where: ) ( t gas Flow = gas flow rate [m/s] air dome set setT R V gas Pp gas M gas Mass ) ( ) ( ) ( = mass of gas required [kg] air dome actual actualT R V t gas Pp gas M t gas Mass ) ( ) ( ) ( = actual mass of gas [kg] M ( gas ) = Molecular mass of gas [kg/mol] Ppset( gas ) = partial pressure of gas at setpoint [Pa]

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38 Ppactual( gas ) = actual partial pre ssure of gas [Pa] Vdome = volume of dome [m] R = universal gas constant [8.3144J/(mol K)] Tair = air temperature [K] ( gas )= gas density [kg/m] t = length of control cycle [s] Total pressure of the greenhouse dome was maintained constant by controlling oxygen, carbon dioxide and nitroge n pressures separately as described above. Total pressure of the vacuum chamber was kept c onstant by controlling a solenoid valve that was connected to the vacuum pump. If the vacuum chamber pressure was above the setpoint, gas was pumped out. If it was be low the setpoint the pump was stopped. Figure 4-10 depicts the oxygen and carbon diox ide partial pressures during a test of the gas mixing control system that lasted 1 hour. Figure 4-11 shows th e total pressures of the vacuum chamber and the greenhouse dome. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 015304560 Time [min]Oxygen Partial Pressure [kPa]0 0.2 0.4 0.6 0.8 1 1.2 1.4Carbon Dioxide Partial Pressure [kPa] Oxygen [kPa] Carbon Dioxide [kPa] Figure 4-10. Gas mixing of dome greenhouse atmosphere without plants (oxygen set point at 4.0 kPa and carbon dioxi de set point at 0.5 kPa).

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39 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 015304560 Time [min]Chamber Pressure [kPa]15 16 17 18 19 20 21 22 23 24 25Dome Pressure [kPa] Mars Chamber Pressure [kPa] Dome Greenhouse Pressure [kPa] Figure 4-11. Pressure contro l of vacuum chamber (set point 0.6 kPa) and greenhouse dome (set points 20 kPa). Air Temperature Control Algorithm Maintaining the air temperature in a ra nge where the plants are productive is essential in the cold Mars environment. Air temperature was kept c onstant by the heating coil that was installed in the center of the gr eenhouse dome at plant le vel. The heater was controlled by pulse width modulation with duty cycles of 0%-100%. At 100% the maximum power output was calculated to be 512.7 W: W V R V P 7 512 6 23 ) 110 (2 2 max (4-3) where: Pmax = heating power [W] V = voltage [V] R = resistance [ ] To maintain the air temperature T3 at a certain set point, the required power of the heating system was calculated by adding the required steady state power (determined in

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40 the following section: see equa tions 4-5 & 4-6) to a proportiona l control term with a gain of 1/ T3air,set: ) ( 3 3 1 ) 3 ( ) (, ,t T T T Light T T P t Pset air set air set air freezer ss req (4-4) where: Preq( t ) = required heating power [W] Pss( Tfreezer, T3air,set, Light ) = steady state heating power [W] T3air,set = air set point temperature [C] T3air( t ) = actual air temperature T3 [C] Figure 4-12 gives an example of how the temperature control algorithm regulated the air temperature. A constant air temperat ure of 20 C was maintained by varying the heating power. When the light was turned on the required heating power was much less than when the light was turned off. 0 5 10 15 20 25 060120181 Time [min]Air Temperature T3 [C]0 50 100 150 200 250 300Heating Power [W] Light on Light off Light off Figure 4-12. Air temperature control of greenhouse dome (set point at 20 C).

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41 Heat and Mass Transfer Experiments without Plants The first step of modeling the heat and ma ss transfer of this Mars greenhouse was to analyze the heat transfer without the pl ants. Figure 4-13 shows the location of the sensors for measuring the environmental parameters. The CO2, O2 and light sensors were installed at the plant level. Temperat ure was measured at seven locations T1 at the aluminum dome base T2 at the water collection slope T3 is the air temperature at the plant level T4 is the temperature of the exha ust air of the fan and heater. T5 is the temperature of the exterior of the transparent greenhouse shell T6 is the temperature of the vacuum chamber window T7 is the temperature of the vacuum chamber wall Relative humidity sensors were installed at the location of T3 and T4. Furthermore, total pressure was measured in the dome and in the vacuum chamber. Figure 4-13. Sensor locations for heat and mass transfer experiments without plants.

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42 A) B) C) D) Figure 4-14. Preparation of the steady state e xperiments. A) Bottom of dome base with foam insulation. B) Side view of gree nhouse dome with the sensors and scales installed. C) Top view of greenhouse dom e without shell. D) Installation of greenhouse dome into the vacuum chamber. An exact understanding of the temperatur e distribution at the different locations illustrated in Figure 4-13 was important to calculate the thermal resistances in Chapter 5. The greenhouse dome was subjected to a combin ation of different freezer temperatures, heating power levels and growth light states: Freezer temperatures at 0 C, -10 C and -20 C. Heating power levels at 0 W, 26 W, 51 W, 77 W and 103 W. Growth light switched on/off. Useless combinations such as a heating pow er of 0W and the growth light switched off were left out, as well as combinations that resulted in very high dome temperatures

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43 (e.g. 0 C freezer temperature, 103 W heati ng power and growth light switched on). Figure 4-15 depicts the trend of the seven different temperatures for a freezer temperature of 0 C, a heating power of 26 W and the gr owth light switched off. Temperature T6 at the window and temperature T7 at the chamber wall oscillated as the freezer temperature was controlled at 0 C within a band of +1 C and -1 C. The time required to achieve steady-state temperatures was always at least 10 to 12 hours. The steady state temperatures at the seven locations for the di fferent combination of freezer temperatures, heating power levels and growth light state are given in table 4-2. Each experiment was conducted two times to minimize errors. Figu res 4-16 to 4-20 depi ct the temperature distributions. It can be observed that the temperatures inside the dome increase linearly with the increased in heati ng power. The chamber window (T6) and wall (T7) temperatures increased only slightly with in creasing heating power. On the other hand, T6 and T7 increased significantly when th e growth light was turned on. 0 2 4 6 8 10 12 14 16 0100200300400500600 Time [min]Temperature [C] T1 Base T2 Slope T3 Air/Plant T4 Fan Exhaust T5 Outside Shell T6 Window T7 Wall Figure 4-15. Temperature readings until steady state is achieved. (0 C freezer temperature, 26 W heating pow er and light switched off).

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44 Table 4-2. Steady state temper ature distribution under different freezer temperature, light and heating power conditions. Freezer Temp. [C] Lights (0=off, 1=on) Heating Power [W] Base T1 [C] Slope T2 [C] Air/ Plant T3 [C] Fan Exhaust T4 [C] Shell Outside T5 [C] Window Outside T6 [C] Wall Outside T7 [C] 0 0 26 4.34 10.35 12.74 13.72 10.43 0.90 0.01 0 0 51 5.96 15.29 19.17 20.75 15.68 1.83 0.34 0 0 77 6.98 18.93 24.06 26.11 19.69 2.28 0.49 0 0 103 8.56 24.09 30.25 32.60 24.49 2.39 0.11 -10 0 26 -3.44 2.68 5.29 6.38 2.81 -7.56 -9.63 -10 0 51 -3.06 6.61 10.76 12.40 7.17 -8.00 -9.94 -10 0 77 0.34 12.95 18.44 20.59 13.51 -7.00 -9.44 -10 0 103 2.84 17.73 24.01 26.61 17.96 -6.44 -9.38 -20 0 51 -10.81-0.94 3.38 4.94 -0.03 -17.25 -19.13 -20 0 77 -10.313.44 9.06 11.12 4.29 -17.06 -19.31 -20 0 103 -7.19 9.32 15.51 17.96 9.60 -15.94 -18.88 -20 0 128 -4.13 14.39 21.34 24.32 14.14 -15.00 -18.63 -10 1 0 9.47 18.74 16.76 18.96 19.88 8.74 -6.22 -10 1 26 10.12 23.66 25.74 27.08 25.22 9.28 -6.74 -10 1 51 10.61 28.59 32.17 34.15 30.62 9.81 -6.66 -10 1 77 11.96 32.50 38.27 39.56 34.63 10.56 -6.31 -20 1 0 -5.06 6.13 5.60 6.09 7.73 -5.56 -15.38 -20 1 26 1.75 15.37 17.52 18.18 16.76 -5.25 -14.38 -20 1 51 5.09 19.88 23.39 24.48 20.88 -5.06 -14.13 -20 1 77 9.81 27.22 32.73 34.95 29.17 -3.08 -13.85 -20 1 103 11.63 31.73 38.98 41.22 33.68 -3.88 -13.20 0 C Freezer Temperature Light off 0 5 10 15 20 25 30 35 050100150200 Heating Power [W]Steady State Temperature [C] T1 Base T2 Slope T3 Air/Plant T4 Fan Exhaust T5 Outside Shell T6 Window T7 Wall Figure 4-16. Steady state temperatures versus po wer of heater at seven different locations (T1-T7). Freezer temperature is 0 C and the growth light is switched off.

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45 -10 C Freezer Temperature Light off -10 -5 0 5 10 15 20 25 30 050100150200 Heating Power [W]Steady State Temperature [C] T1 Base T2 Slope T3 Air/Plant T4 Fan Exhaust T5 Outside Shell T6 Window T7 Wall Figure 4-17. Steady state temperatures versus po wer of heater at seven different locations (T1-T7). Freezer temperature is -10 C a nd the growth light is switched off. -20 C Freezer Temperature Light off -20 -15 -10 -5 0 5 10 15 20 25 30 050100150200 Heating Power [W]Steady State Temperature [C] T1 Base T2 Slope T3 Air/Plant T4Fan Exhaust T5 Outside Shell T6 Window T7 Wall Figure 4-18. Steady state temperatures versus po wer of heater at seven different locations (T1-T7). Freezer temperature is -20 C a nd the growth light is switched off.

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46 -10 C Freezer Temperature Light on -10 -5 0 5 10 15 20 25 30 35 40 050100150200 Heating Power [W]Steady State Temperature [C] T1 Base T2 Slope T3 Air/Plant T4 Fan Exhaust T5 Outside Shell T6 Window T7 Wall Figure 4-19. Steady state temperatures versus po wer of heater at seven different locations (T1-T7). Freezer temperature is -10 C a nd the growth light is switched on. -20 C Freezer Temperature Light on -20 -10 0 10 20 30 40 50 050100150200 Heating Power [W]Steady State Temperature [C] T1 Base T2 Slope T3 Air/Plant T4 Fan Exhaust T5 Outside Shell T6 Window T7 Wall Figure 4-20. Steady state temperatures versus po wer of heater at seven different locations (T1-T7). Freezer temperature is -20 C a nd the growth light is switched on. Figure 4-21 depicts the stea dy state air temperature T3 of the greenhouse dome for different heating power and freezer temper atures. The steady state air temperature

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47 increases linearly with increasing heater power. The linear equations for the freezer temperatures of 0 C, -10 C and -20 C are shown in Figure 4-21. According to the equations, the steady state air temperature is not equal to the freezer temperature when the heating system is switched off. This diffe rence results from the waste heat that is introduced by running the fan continuously and the difference of freezer temperature and wall temperature of the vacuum chamber T7 (see Table 4-2). Combining these three equations into one, the power of the heater required to heat the air to temperature T3 with a freezer temperature of Tfreezer can be calculated as follows: 23047 0 ) 000598 0 ( 741 7 ) 831 0 (, 3 freezer freezer airT T T Pss (4-5) where: Pss = power of heater [W] T3,air = steady state temperature of air T3 [C] Tfreezer = temperature of freezer [C] T3ss(0 C) = 0.2240*W + 7.2000 R2 = 0.9975 T3ss(-10 C) = 0.2490*W 1.3350 R2 = 0.9954 T3ss(-20 C) = 0.2353*W 8.7930 R2 = 0.9994 0 5 10 15 20 25 30 35 050100150 Heating Power[W]Steady State Air Temperature T3 [C] 0 C Freezer / Light off -10 C Freezer / Light off -20 C Freezer / Light off Figure 4-21. Steady state air temperatures (T3) versus power of heater for freezer temperatures of 0 C, -10 C and -2 0 C (growth light switched off).

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48 When the light is switched on, the power of the heater required to heat the air to temperature T3 with a freezer temperature of Tfreezer can be calculated as following: 2146 0 ) 00526 0 ( 27 26 ) 951 0 (, 3 freezer freezer airT T T Pss (4-6) Figure 4-22 depicts the heating power requirement depending on the freezer temperature for steady state air temperatures T3 of 15 C, 20 C and 25 C. When the growth light was switched off and if the freezer temperature was -20 C, e.g., the required heater power was 95.5 W, 116.2 W and 136.8 W to achieve a steady state air temperature of 15 C, 20 C and 25 C resp ectively. If the growth light was switched on, the required heating power was reduced significantly. At a freezer temperature of -20 C and an air temperature of 20 C, the heating power wa s reduced by 79.8 W, with the light switched on. 0 50 100 150 200 250 300 350 -40-35-30-25-20-15-10-50 Freezer Temperature [C]Heating Power [W] Air Temperature = 15C / light on Air Temperature = 20C / light on Air Temperature = 25C / light on Air Temperature = 15C / light off Air Temperature = 20C / light off Air Temperature = 25C / light off P(20C)= 79.8 W Figure 4-22. Freezer temperature versus power of heater for steady state air temperatures (T3) of 15 C, 20 C and 25 C.

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49 If the interior temperature of the gr eenhouse dome shell decreased below the dew point of the air temperature, condensation could occur. Figure 4-23 shows two photos of condensation on the inside of the greenhouse dome. High condensation occurred for low freezer temperatures (Photo B) as those low temperatures resulted in a lower greenhouse shell temperature. These photos also clearly show a stratific ation of temperature within the greenhouse dome. The top of the dome wa s warmed by radiation of the growth light and the air from the heating system that the fan blew across the inside shell. As the greenhouse shell was colder close to the water recollection funnel (black surface) condensation was more likely to occur ther e. The bottom of the greenhouse dome near the aluminum base showed less condensation, because the relative humidity was less in the lower part of the dome as the flasks were installed in the upper level. The curvature of the dome shell and the slope of the recollecti on funnel led to runoff of the water to the collection container located on scale 1 (see Figure 4-13). Under certain conditions, ice crystals had been observed on the aluminum base as temperatures may have dropped below 0C, even though the dome base was well insulated. During the long-term experiments involving le ttuce plants (see ne xt section) water evaporated from the collection container and the relative humidity in the bottom part of the greenhouse increased. Condensate and fr ost formed on the lower part of the greenhouse shell and the dome base plate due to the low temperatures. This can be clearly observed in the two photos shown in Figure 7-1, which were taken after the vacuum chamber was opened at the end of the 7 day experiment.

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50 A) B) Figure 4-23. Condensation inside of greenhous e shell with a greenhouse air temperature of 20 C. A) Freezer temperature at 0 C B) Freezer temperature at -20 C. Heat and Mass Transfer Experiments with Plants Medium-term Plant Experiment involving Buttercrunch Lettuce Selection criteria for the plants involved in the Mars greenhouse experiments were a short growth period, high evapo-transpiration rate, tolerance to co ld temperatures, low Condensation line

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51 light requirements, suitability for hydroponic growth in 150 ml Ehrlenmeyer flasks and dome height constraints. Buttercrunch lettuce ( Lactuca Sativa cv. Buttercrunch) was selected as lettuce is one of NASA’s baseli ne crops (see Chapter 2) and it fulfills the criteria mentioned above. Six weeks old le ttuce plants grown in soil under atmospheric conditions were transplanted into flasks f illed with 50% water a nd 50% nutrient solution. The flasks were wrapped in aluminum foil to avoid growth of algae caused by direct radiation onto the nutrient solution. One hol e of the stopper was cut open from the side and the plant was carefully inserted. Evaporation of th e hydroponic solution was avoided by sealing the gap between the plant and the st opper with putty as shown in Figure 4-24. Eight flasks were placed in to the greenhouse dome; two on ea ch scale (see Figure 4-25). A) B) Figure 4-24. Buttercrunch lettuce in Ehrlenme yer flask. A) The average height of the shoot zone is 15 cm. B) Putty and a stopper prevent evaporation of the hydroponic solution as they separate th e root from the shoot zone.

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52 Figure 4-25. Installation of flasks containing the lettuce plants onto the scales. The plants were exposed to a controlle d environment inside the greenhouse dome for 36 hours. The environment conditions and their control methods are summarized in Table 4-3. The air temperature and the ga s composition were tightly controlled by actuators. A total pressure of 25 kPa was selected as plants s till were to be productive at this low pressure level. The partial pressure of oxygen was set to 4 kPa, resulting in an oxygen level of 16%, lower than on Earth be cause oxygen is a very precious resource during a space mission on Mars: it must be shippe d from Earth as it is barely available in the Mars atmosphere and will be mainly used for human breathing. The partial pressure of carbon dioxide was set to a high level of 0.8 kPa, as carbon dioxide can easily be extracted from the Mars atmosphere. High le vels of carbon dioxide are known to enhance plant growth. The greenhouse humidity was passively controlled by the equilibrium between evaporation of the water from the plants and the open water surfaces versus the

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53 condensation of water on the cold surfaces. The variation of the humidity in the time range of 5 to 10 hours after the experiment had been started can be observed in Figure 4-26. The light was switched on during the comp lete experiment and the radiation level was measured to be at a constant value of 684 mol/(ms) at plant level. Therefore, no condensation occurred on the greenhouse su rface directly below the growth light. Table 4-3. Buttercrunch lettuce envir onmental conditions and their control. Parameter Value Controlled by Greenhouse Dome Air/Plant Temperature 20 C heating coil freezer temperature Greenhouse Dome Relative Humidity variable plant evaporation (passive control) condensation on cold surface (passive control) Greenhouse Dome Total Pressure 25 kPa N2, O2 and CO2 mass flow controllers vacuum pump (& passively by leakage) Greenhouse Dome Oxygen Partial Pressure 4 kPa O2 mass flow controller vacuum pump (& passively by leakage) Greenhouse Dome Carbon Dioxide Partial Pressure 0.8 kPa CO2 mass flow controller vacuum pump (& passively by leakage) Greenhouse Dome Radiation Level 684 mol/(ms) growth light on growth light off (& p assively by condensation) Vacuum Chamber Total Pressure 0.6 kPa leakage (passive control) vacuum pump Freezer Temperature -20 C ( 1C) thermostat on freezer thermostat on freezer -20 -10 0 10 20 30 40 50 60 300350400450500550600 Time [min]Temperature [C] / Relative Humidity [%] T3 Air/Plant T4 Fan Exhaust T6 Window T7 Wall Relative Humidity Figure 4-26. Constant temperature distribu tion and varying relative humidity during the buttercrunch lettuce experiment.

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54 Figure 4-27 depicts the rates of plant ev apo-transpiration from the scales 2-5. Scale 1 measured the water in the recollec tion container. It had been filled with 245 grams of water before the experiment in order to keep the humidity high at the beginning of the experiment. The change of the mass value of scale 1 is the difference between water evaporating from the open water surface and recollected water dripping into the container. A positive slope indicates more water was recollected than evaporated, a negative slope leads to the conclusion that more water was evaporated than re-collected. Surprisingly, in this experiment the sl ope of scale 1 had a negative value of –0.0661. Thus, the recollection system pr oved to be inefficient as less water was recollected than had evaporated. This resulted in higher humidities in the lower greenhouse part and therefore water condensati on on the cold dome aluminum base. The plant evapotranspiration can be calculated by dividing the water evapora tion rate of the scale by the plant leaf area per scale. In order to calculate the plan t leaf area, the leaves were cut off the plants at the end of the experiment and the silhouettes we re drawn on a white sheet of paper. The silhouettes were scanned togeth er with a calibration square. The pictures were converted to black and white images and the silhouettes were filled with black ink. The pictures were read into matlab and an image processi ng code determined the ratio of white to black pixels. The resulting values of the plan t leaf areas per scale are given in Table 4-4. Plant evapo-transpiration varied from 1.6 g/(min m) to 2.87 g/(min m). Evapotranspiration rates for lettuce under atmospheri c conditions are given as 1.23 g/(min m) in NASA’s Baseline Values and Assumptions Document (Hanford, 2004). Low pressure increases evaporation rates and therefore the evapo-transpiration values calculated in the

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55 research described in this document seem r easonable. It should be noted that evapotranspiration rates are further affected by ot her factors, including relative humidity, air temperature, leaf temperature, radiation leve l and lettuce cultivar, making it difficult to compare the values of different experiments. m1 = -0.0661*t + 249.99 R2 = 0.8428 m4 = -0.1187*t + 392.48 R2 = 0.8827 m2 = -0.1382*t + 379.57 R2 = 0.9692 m3 = -0.1308*t + 370.65 R2 = 0.9279 m5 = -0.1052*t + 348.2 R2 = 0.9003 200 220 240 260 280 300 320 340 360 380 400 300350400450500550600 Time [min]Mass [g] Scale 1 Scale 2 Scale 3 Scale 4 Scale 5 Figure 4-27. Plant evapo-tran spiration rates of plants from 5 to 10 hours after the beginning of the experiment. Table 4-4. Evaporation rates pe r scale with scales 2-5 contai ning two lettuce plants each. Scale 1 Scale 2 Scale 3 Scale 4 Scale 5 Evaporation/Time [g/min] 0.0661 0.1382 0.1308 0.1187 0.1052 Leaf Area Plant 1 [m] 0.0423350.0234 0.039542 0.032599 Leaf Area Plant 2 [m] 0.0332190.02215 0.023296 0.033002 Total Leaf Area [m] 0.0755540.045549 0.062838 0.065601 Evapo-transpiration Rate[g/min/m] 1.83 2.87 1.89 1.60 At the end of the experiment, seven out of the eight plants app eared to be healthy and without visible damage. One plant started wilting after the water level inside the flask

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56 decreased to a point where the roots could not reach the remaining water and nutrient solution (see Figure 4-28). Figure 4-28. Lettuce plants after an expos ure of 36 hours to the controlled Mars greenhouse environment. Healthy plant w ithout any visible physical damage on the left side, wilted plant with root s that do not reach water and nutrient supply on the right side. Long-term Plant Experiment involving Galactic Lettuce For the long-term plant experime nts Galactic lettuce plants ( Lactuca Sativa cv. Galactic) were selected (see Figure 4-29). The plants were grown from seeds in the departmental environment-controlled growth chamber under atmospheric conditions with a day-night cycle of 12 hours. Af ter four weeks, measuring an average height of 8 cm, the lettuce plants were transplanted into th e flasks filled with the hydroponic nutrient solution. Similar to the previous experiment eight plants were installed into the greenhouse dome, two per scale. Table 4-5 lists the environmental conditions the plants were exposed to and their control. All envir onmental parameters except of the total dome

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57 pressure were kept the same as in the bu ttercrunch lettuce experiments. The greenhouse dome total pressure was lowered to 20 kPa. Figure 4-29. Galactic lettuce pl ant for long-term experiments with an average height of 8 cm. Table 4-5. Galactic lettuce environm ental conditions and their control. Parameter Value Controlled by Greenhouse Dome Air/Plant Temperature 20 C heating coil freezer temperature Greenhouse Dome Relative Humidity variable plant evaporation (passive control) condensation on cold surfaces (passive control) Greenhouse Dome Total Pressure 20 kPa N2, O2 and CO2 mass flow controllers vacuum pump (& passively by leakage) Greenhouse Dome Oxygen Partial Pressure 4 kPa O2 mass flow controller vacuum pump (& passively by leakage) Greenhouse Dome Carbon Dioxide Partial Pressure 0.8 kPa CO2 mass flow controller vacuum pump (& passively by leakage) Greenhouse Dome Radiation Level 0 or 684 mol/(ms) growth light on growth light off (& p assively by condensation) Vacuum Chamber Total Pressure 0.6 kPa leakage (passive control) vacuum pump Freezer Temperature -20 C ( 1C) thermostat on freezer thermostat on freezer

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58 Figure 4-30 shows the locations of the sensors for the second set of plant experiments. Various temperat ure sensors were added or moved from their previous position: T2 was moved from the recollection funnel to the inside of the greenhouse dome shell, T5 was moved to the side of th e exterior greenhouse shell, T6 was fixed to the inside of the vacuum chamber wall, T7 on the outside of the chamber wall at medium height, T8 at the bottom of th e chamber wall and T9 measured the freezer air temperature. Figure 4-30. Sensor locations for the long-term experiments with galactic lettuce plants. Plants were exposed to the low pressu re controlled greenhouse environment for 7 days. Initially they were exposed to the growth light for 24 hours until steady state of all parameters was reached, the following days the day-night cycle was set to 12 hours. Figure 4-31 illustrates the temperature changes over time during the experiment. The air

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59 temperature at plant level was controlled at 20 C, the freezer temperature was controlled at -20 C ( 1C). Figure 4-32 depict s the steady state temperatures during the day and night cycle, when the growth light was switc hed on/off, respectively. A heating power of 40 Watts was required to maintain an air temp erature of 20 C at the plant level during the day cycle, a heater power of 119 Watts dur ing the night cycle. The temperature of the fan exhaust was higher for the night cycle as more heating was required, all other temperatures were lower when the growth li ght was switched off compared to when the growth light was switched on. -30 -20 -10 0 10 20 30 024487296120144168 Time [hours]Temperature [C] T3 Air/Plant T4 Fan Exhaust T2 Inside Shell T5 Outside Shell T6 Chamber Wall Inside T7Chamber Wall Outside Middle T9 Air Freezer T8 Chamber Wall Outside Bottom Light ON Light ON Light ON Light ON Light ON Light ON Light OFF Light OFF Light OFF Light OFF Light OFF Light OFF Light ON Figure 4-31. Temperature varia tions during the long-term ga lactic lettuce experiment.

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60 -20 -15 -10 -5 0 5 10 15 20 25Air/PlantTemp. T3 Fan Exhaust Temp. T4 Shell Inside Temp. T2 Shell Outside Temp. T5 Inside Wall Temp. T6 Outside Wall Middle Temp. T7 Outside Wall Bottom Temp. T8 Chamber Air Temp. T9 Steady State Temperature [C] Light off (119 W Heating) Light on (40 W Heating) Figure 4-32. Comparison of stea dy state temperature distribution of the day cycle to the night cycle during the long-te rm plant experiments. Figure 4-33 shows the variation of the re lative humidity during the day and night cycle. Before the experiment started, wh en the greenhouse dome was closed but the freezer not switched on yet, the relative humidity rose to 70%. This high humidity was due to addition of water vapor to the atmo sphere by plant evapotranspiration and the lack of water vapor removal by condensation as the temperatures of th e all surfaces of the greenhouse were at temperat ures above 20 C and ther efore above the dew-point. Relative humidity decreased to 35% during th e first 24 hours when the growth light was switched on. During the following day-night cy cles the relative humidity varied between a maximum of 35% when the growth light was switched on and a minimum of 28% when the growth light was switched off. Relative humidity was low during the night cycle as more condensation occurred due to the lowe r temperatures of th e greenhouse surfaces.

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61 Relative humidity was high during the day due to less condensation and more evapotranspiration of the plants. 0 10 20 30 40 50 60 70 80 024487296120144168 Time [hours]RH [%] Light ON Light ON Light ON Light ON Light ON Light ON Light ON Light OFF Light OFF Light OFF Light OFF Light OFF Light OFF Figure 4-33. Relative humid ity variation during the day and night cycle. Figure 4-34 shows the effectiv eness of the gas composition control, resulting in a constant gas composition even when all other environmental parameters were subject to great variations. Changes in temperature, re lative humidity and ra diation level did not affect the gas composition of 20 kPa total pr essure, 4 kPa oxygen partial pressure and 0.8 kPa carbon dioxide partial pressure.

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62 0 2 4 6 8 10 12 14 16 024487296120144168Time [hours]Dome Partial Pressures [kPa] N2 O2 CO2 Figure 4-34. Gas composition control of the greenhouse at mosphere. Set points are 20 kPa for total pressure, 4 kPa for oxyge n partial pressure and 0.8 kPa for carbon dioxide partial pressure. Figure 4-35 shows the mass values of the scal es that were measured from 5 to 10 hours after the galactic lettuce plant experiment ha d started. For this experiment only two out of the five scales were connected to the data acq uisition system due to the limited amount of available channels because of the added te mperature sensors. The evapo-transpiration rates of the plants were dete rmined with the same leaf area calculation method described earlier in this Chapter. The evapo-transpira tion rates were found to be 3.71 g/min/m for scale 2 and 4.84 g/min/m for scale 3. These eva poration rates are slig htly higher than the ones in the Buttercrunch lettuce experiments. One possible reason is th at the pressure was reduced from 25 kPa to 20 kPa, leading to an increase in mass diffusivity and therefore higher evaporation rates.

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63 m3 = -0.1132*t + 314.83 R2 = 0.9801 m2 = -0.1128*t + 303.16 R2 = 0.9572 200 210 220 230 240 250 260 270 280 290 300360420480540600 Time [min]Mass [g] Scale2 Scale3 Figure 4-35. Water evaporation measured on scale 2 and 3 during the galactic lettuce plant experiment. Figure 4-36 shows the galactic lettuce plan ts after they were exposed to the low pressure Mars greenhouse environment for 7 days. They showed only slight visible physical damage such as minor signs of water stress (see Figure 4-37 A and B). Figure 4-36. Galactic lettuce pl ants after exposure of seven da ys to the low pressure Mars greenhouse environment.

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64 A) B) Figure 4-37. Visible damages of the plants. A) and B) Wilting/drying of the plant leaves.

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65 CHAPTER 5 MATHEMATICAL MODEL DEVELOPMENT Effect of Low Pressure on Heat and Mass Transfer Operating the greenhouse dome at a reduced pressure in the low pressure Mars environment has a huge influence on the heat a nd mass transfer. Of the three heat transfer modes conduction, convection and ra diation, convective heat tran sfer is the one that is most dependent on the total pressure. Regardi ng the mass transfer, evaporation rates have to be analyzed for pressure dependency. Furthe rmore, the effect of the low pressure on psychrometric relations should be studied, in orde r to be able to determine the state of the moist air. Convection Heat Transfer Convection is defined as heat transfer between a surface and a fluid moving over the surface. Convective heat tran sfer at low pressures is analyzed based on the equations given in Incropera and DeWitt (2002). The convection heat transfer depends on the convection coefficient and on the temperatur e difference of the moving fluid and the surface: ) ( T T h qs (5-1) where: q = heat flux [W/m] h = convection coefficient [W/(m2 K)] Ts = surface temperature [K] T = fluid temperature [K]

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66 If there is a temperature difference betw een the fluid stream and the surface a thermal boundary layer develops. The loca l heat flux may be obtained by applying Fourier’s Law to the heat flux at the surface where y = 0. As there is no fluid motion at the surface, energy transfer occurs only by conduction: 0 y f sy T k q (5-2) Combining both equations leads to the following convection coefficient: T T y T k hs y f 0 (5-3) In order to find out if th e boundary layer is laminar or turbulent the Reynolds number has to be calculated: L uL Re (5-4) where: ReL = Reynolds number [-] = density [kg/m] u = velocity [m/s] = absolute viscosity [N s/m] L = characteristic length [m] The critical Reynolds number for which tr ansition from laminar to turbulent flow occurs is 5x105. A parameter that provides a measure of the convection heat transfer is the dimensionless temperature gradient, the Nusselt Number: Pr) Re ( 0 * L x f y y T f k hL Nu (5-5)

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67 where: s T T s T T T = dimensionless temperature L y y = dimensionless variable The average Nusselt number represents the average heat transfer independent of location: Pr) (ReL f Lf k L h Nu (5-6) The Prandtl number is the ratio of the properties / : f k p c Pr (5-7) where: = dynamic viscosity [m/s] = thermal diffusivity [m/s] cp = specific heat [kJ/(kg K)] kf = conduction coefficient [W/(m K)] Laminar flow over a horizontal plate For laminar flow, the Reynolds number has to be below the critical Reynolds number of 5x105: 5 ,10 5 Re L ucritical L (5-8) For laminar flow the Nusselt number may be obtained from: 6 0 Pr 3 / 1 Pr 2 / 1 Re 664 0 L f k L h L Nu (5-9) Inserting Equations 5-4 and 57 into Equation 5-9, results into the following convection coefficient:

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68 6 0 Pr 2 / 1 3 / 2 ) ( 3 / 1 ) ( 6 / 1 2 / 1 ) ( 664 0 L f k p c ) ( u L h (5-10) Therefore, convective heat transfer depends on the following parameters: High density, specific heat and thermal conductiv ity increase heat transfer. Low absolute viscosity increases heat transfer. Specific heat as well as absolute viscosity are independent of density, i.e., pressure. They are only dependent on temperature. Therma l conductivity is also independent of the air pressure. Thus, the convecti on transfer coefficient decreases with the square root of density/pressure. 2 / 1) ( ~ pressure hLfor ) ( ~ const T pressure density (5-11) Thus, the convection coefficient of a gas at a pressure of 20 kPa is 44.7 % of the convection coefficient of gas at a pressure of 100 kPa for laminar fluid flow with same velocity and temperature: ) 100 ( 447 0 ) 100 ( 100 20 ) 20 (2 / 1kPa h kPa h kPa hL L L (5-12) Turbulent flow over a horizontal plate For turbulent flow, the Reynolds number ha s to be above the critical Reynolds number of 5x105. For turbulent flow the Nusselt number may be obtained from: 3 / 1 5 / 4Pr Re 037 0L f L Lk L h Nu (5-13) Inserting the Reynolds and the Pr andtl number into Equation 5-13: 5 / 1 3 / 2 ) ( 3 / 1 ) ( 15 / 7 5 / 4 ) ( 037 0 L f k p c ) ( u L h (5-14)

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69 Thus, the convection transfer coefficient decreases with decreasing density, i.e. pressure. The convection coefficient of a gas at a pressure of 20 kPa is 27.6 % of the convection coefficient of a gas at 100 kPa for turbulent fluid flow with the same velocity and temperature: ) 100 ( 276 0 ) 100 ( ) 100 / 20 ( ) 20 (5 / 4kPa h kPa h kPa hL L L (5-15) Laminar free convection on a vertical plate For laminar free convection on a vertical plate, the Nusselt number is defined as: (Pr) 4 / 1 4 3 4 f L Gr f k L L h L Nu (5-16) where: 4 / 1 2 / 1 2 / 1Pr) 238 1 Pr 221 1 0609 0 ( Pr 75 0 (Pr) f The Grashof number is the ratio of the buoyancy to the viscous force: 2 3) ( L T T g Grs L (5-17) where: g = gravitational constant [m/s] = 1/ T = coefficient of thermal expansion [1/K] By inserting the Grashof number into E quation 4-16, the convection coefficient is: L k f L T T g hf s L(Pr) 4 ) ( 3 42 / 1 4 / 1 2 3 (5-18) Thus, the convection transfer coefficient decreases with decreasing density, i.e. pressure. The convection coefficient of a gas at a pressure of 0.6 kPa is 7.75 % of the convection coefficient of a gas at 100 kPa for laminar free vertical c onvection at the same temperature:

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70 ) 100 ( 0775 0 ) 100 ( ) 100 / 6 0 ( ) 6 0 (2 / 1kPa h kPa h kPa hL L L (5-19) It should be noted, that the convection coe fficient also depends on gravity. Thus it would be further reduced by 61.3% on Mars, wh ere the gravitational constant is only 3.69 m/s. ) m/s 81 9 ( 613 0 ) m/s 81 9 ( ) 81 9 / 69 3 ( ) m/s 69 3 (2 2 2 / 1 2 L L Lh h h (5-20) External free convection for a sphere The following correlation is recommended for spheres exposed to external free convection flow: 7 0 Pr 10 ] Pr) / 0469 0 ( 1 [ 589 0 211 9 / 4 16 / 9 4 / 1 D D f D DRa Ra k D h Nu (5-21) The Rayleigh number is defined as: f p s D Dk c D T T g Gr Ra 2 3) ( Pr (5-22) Combining Equation 5-21 and Equation 522 leads to the following convection coefficient: D k k c k c D T T g hf f p f p s D 9 / 4 16 / 9 4 / 1 2 3) /( 0469 0 1 ) ( 589 0 22 / 1 (5-23) Therefore, the convection transfer coeffi cient decreases with decreasing density, i.e. pressure. As the pressure variable in Equation 5-23 is implicit, a direct ratio of the convection coefficient at sta ndard pressure to the one at reduced pressure cannot be derived.

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71 Mass Transfer by Evaporation The diffusive flux depends on the mass diffu sivity coefficient. Assuming ideal gas behavior, the kinetic theory of gases predicts that the mass diffusivity is indirectly proportional to the pressure at a constant temperature. p T DAB 2 / 3~ (5-24) where: DAB = Mass diffusion coefficient [m/s] T = temperature [K] p = pressure [kPa] Thus, reducing the pressure to 20 kPa, w ould increase the mass diffusivity 5 times: ) 100 ( 5 ) 100 ( ) 20 / 100 ( ) 20 ( kPa D kPa D kPa DAB AB AB (5-25) Table 5-1 gives an overview of the effect of reduced pressu re on the convective heat transfer coefficient and the mass diffusi vity. Convection reduces considerably in the low pressure Mars greenhouse dome. In the vacu um chamber, convection is considered to be negligible, the major mode of heat transfer between the dome and the chamber is radiation. Mass diffusivity and therefore ev aporation rates increase significantly at low pressures. Table 5-1. Effect of reduced pressure on convective heat transfer coefficient and mass diffusion coefficient. Greenhouse Dome Vacuum Chamber CONVECTION h(20 kPa)/ h(100 kPa) h(0.6 kPa)/ h(100 kPa) Forced Convection – Horizontal Plate 44.7% (laminar) 27.6% (turbulent) Free Convection – Vertical Plate 7.75% (Earth) 7.75% x 61.3% (Mars)External Free Convection – Sphere See Equation 5-23 DIFFUSION D(20 kPa)/ D(100 kPa) Mass Diffusivity 500%

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72 Development of Low Pressure Psychromet rics for Non-Standard Atmospheres While most publications address the psyc hrometric relationships of water vapor and air for open systems, sea level pressure and Earth’s standard atmosphere composition (78.08% N2, 20.98% O2, 0.934% Ar, 0.0314% CO2, etc), there is nothi ng in the theory for developing the relationships that restricts them to these systems (Shallcross, 1997; ASHRAE, 2001). In the literature, very few publications are de dicated to altitude effects on psychrometrics, as barometric pressure decreases with alt itude (Haines, 1961; Hitchcock and Jacoby, 1980; Erickson and Ga rrett, 1981). Figure 5-1 shows the effect of reduced pressure on the saturation line of th e psychrometric chart. However, psychrometric charts that correct for altitude assume that the gas co mposition is equal to Earth’s. Compared to the Earth atmosphere, the atmos phere of the greenhouse differs significantly in terms of pressure and gas constituents. Furthermore, th e greenhouse dome is a closed system, whereas the classic psychrometric re lations were developed for open systems. Figure 5-1. Effect of pressu re on the saturation li ne of an open system with standard atmosphere composition

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73 The psychrometric relations are based on the following fundamental laws of physics: ideal gas equation of state, cons ervation of energy, c onservation of mass, Dalton’s law of partial pre ssures and the Gibbs-Dalton la w for energy, enthalpy and entropy (Gatley, 2002). If the total pressure of the system differs significantly from the sea level pressure of 101.3 kPa or the dry gas composition differs from the standard Earth atmosphere, the calculations can be modified to reflect this. The psychrometric chart is a tool for dete rmining the properties of the moist air and for visualizing the changes of these prope rties as a consequen ce of psychrometric processes. The-dry bulb temper ature is shown on the abscissa of the chart and therefore the dry-bulb temperature isolin es are vertical. The second ps ychrometric chart coordinate (the ordinate) is the humidity ratio, which is defined as the ratio of the mass of water vapor to the mass of the dry air in a moist air sample. Consequently the humidity ratio isolines are horizontal. Genera lly, the properties isolines pl otted on a psychrometric chart are: dry-bulb temperature isolines, humidity ratio isolines, adiabatic saturation temperature isolines, relative humidity isolines, water vapor saturation curve, enthalpy isolines and specific volume isolines (Ga tley, 2002). The following section develops general psychrometric relations that can be used for closed low pressure systems and non-standard gas compositions. Gas Theory Equation of state The classic psychrometric relationships ar e based on the assumption that moist air is a mixture of independent perfect gases (i .e. dry air and water vapor), and each gas is assumed to obey the perfect gas equation of stat e, where the compressibility factor equals one. If a low pressure environment is chosen the perfect gas law applies even better,

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74 since the virial coefficients pl ay less role in low pressure gases as the interaction between molecules is less common. Therefore, the co mpressibility factor converges to 1 with decreasing pressure. ... ) ( ) ( ) ( 13 2 p D p C p B RT pv Z (5-26) where: Z = compressibility (Z=1 for perfect gas) p = pressure B’,C’,D’ = virial coefficients Dry gas mixture The dry gas mixture includes all gas com ponents that remain gaseous and do not condense in the chosen temperature range. The molecular mass as well as the specific heat are important parameters for the deve lopment of the psychrometric relationships. If the partial pressures of the dry gas components are known, the content by volume can be obtained: dry i dry i dryp p, (5-27) where: dry,i = dry air content of gas component i by volume pdry,i = partial pressure of gas component i pdry = total pressure of dry gas Furthermore, the molecular mass of th e dry gas mixture can be calculated: i dry i dry i dryM m, , (5-28) i dry i dry dryM m, (5-29) where: mdry,i = mass of gas component i Mdry,i = molecular mass of gas component i mdry = total mass of dry gas

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75 By calculating the composition of the dry ga s mix by mass, the specific heat of the dry gas mixture is obtained: total dry i dry i drym m, , (5-30) i dry p i dry i dry pC c, , , (5-31) i dry p i dry dry pC c, , (5-32) where: dry,i = dry air content of gas component i by mass cp,dry,i = specific heat of gas component i cp,dry = specific heat of dry gas The specific enthalpy of dry air is depende nt on the temperature of the gas mix: t c hdry p dry (5-33) where: hdry = specific enth alpy of dry air t = temperature of gas mix Water vapor component The molecular mass of water is 18.01528. The specific enthalpy of the saturated water vapor component is ) 805 1 2501 ( t hg (5-34) where: hg = specific enthal py of water vapor Construction of Modified Psychrometric Chart Saturation line The humidity ratio is defined as the ratio of the mass of water vapor to the mass of dry air contained in a sample. At saturation, air contains the maximum amount of water: ) ( ) ( 01528 18 T p T p m x x m m Wdry ws dry dry ws dry w s (5-35)

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76 where: Ws = humidity ratio at saturation xws =mole fraction of water vapor in saturated moist air xdry = mole fraction of dry air in moist air The total pressure of the moist air is the sum of the partial pressure of the dry air component and the water vapor. ) ( ) ( T p T p pw dry total (5-36) where: ptotal = total pressure (barometric pressure) pw = partial pressure of water vapor The classic psychrometric equations are fo r open systems where the partial pressure of the water vapor is small compared to the total pressure. The total pressure is assumed to be constant even when state change of wate r occurs, i.e. the partial pressure of dry air decreases when water vapor pressure increase s and vice versa. In the case of a closed system, the partial pressure of the dry air component depends on the temperature and the initial conditions, as no dry gas leaves or en ters the system boundaries and the volume is constant: T T p T pdry dry 0 0) ( (5-37) where: pdry 0 = initial pressure of dry air component T 0 = initial temperature of the gas mixture Thus, increasing temperature and evaporati on lead to an increasing total pressure, decreasing temperature and condensati on to a decreasing total pressure. The saturated water vapor pressure is a f unction of the dry-bulb temperature only: Saturation pressure over ice for the temp erature range of –100 to 0 is given by T C T C T C T C T C C T C pwsln / ln7 4 6 3 5 2 4 3 2 1 (5-38)

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77 where: C1 = -5.6745359E+03 C2 = 6.9325247E+00 C3 = 9.6778430E-03 C4 = 6.2215701E-07 C5 = 2.0747825E-09 C6 = -9.4840240E-13 C7 = 4.1635019E+00 Saturation pressure over liquid water for the te mperature range of 0 to 200 is given by T C T C T C T C C T C pwsln / ln13 3 12 2 11 10 9 8 (5-39) where: C8 = -5.8002206E+03 C9 = 1.3914993E+00 C10 =4.8640239E-02 C11 = 4.1764768E-05 C12 = -1.4452093E-08 C13 = 6.5459673E+00 In both Equations: ln = natural logarithm pws= saturation pressure [Pa] T = absolute temperature [K] Humidity isolines The relative humidity is the ratio of the mole fraction of water vapor in a given moist air sample to the mole fraction in an air sample saturated at the same temperature and pressure: p t ws w p t ws wp p x x, (5-40) where: = relative humidity

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78 The relative humidity isolines are constr ucted for a given relative humidity and varying dry-bulb temperatures: dry ws dry w dry w dry wp T p m m x x m m W ) ( (5-41) The degree of saturation e quals to the relative humidity for closed systems: p t ws w p t sp p W W, (5-42) where: = degree of saturation Specific enthalpy isolines The specific enthalpy is the sum of the dr y gas specific enthalpy plus the specific enthalpy of the water vapor: ) 805 1 2501 (,t W t c Wh h hdry p g dry (5-43) The lines of constant enthalpy are constr ucted for a given enthalpy and varying dry bulb temperatures: t t c h Wdry p805 1 2501 ) (, (5-44) Specific volume isolines The specific volume of a gas mixture is defined as the volume of the mixture per unit dry gas: drym V (5-45) where: v = specific volume of moist air in terms of unit mass of dry air V = total volume

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79 The gas volume as well as the mass of the dr y air of a closed system are constant. Therefore, the specific volume is also constant: .0 0const p m RT p m RTdry dry dry dry (5-46) Vapor pressure isolines The humidity ratio is related to the water va por pressure and the partial pressure of the dry air as follows: dry w dry wp p m m W (5-47) Adiabatic saturation temperature isolines The wet-bulb temperature is considered to be the temperature measured by a thermometer with the outside surface kept wet. As moist gas passes the thermometer, some of the liquid evaporates causing the temperature of the wet-bulb thermometer to drop. As wet-bulb temperature is dependent on the gas velocity in respect to the thermometer and the radiative heat transfer it is not possible to predict the wet-bulb temperature precisely. Consequently, adiabatic saturation temperature is considered in this document. Adiabatic saturation temperature tad is defined as the temperature at which water, by evaporating into moist air at a given dry-bulb temperature and absolute humidity can bring the air to saturation adiabatically at the same temperature tad (Shallcross, 1997). However, for the air-water system of this document the curves of adiabatic saturation temperature and wetbulb temperature coincide. The adiabatic saturation temperature is related to the humidity ratio by the following correlation: ad ad dry p wet adt t t t c W t W 186 4 805 1 2501 ) ( ) 381 2 2501 (, (5-48) where: tad = adiabatic saturation temperature

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80 Dew-point temperature isolines The dew-point temperature is related to the humidity ratio by the following equation: dry dew ws dry W sp T p m m W ) ( (5-49) where: Tdew = dew-point temperature Table 5-2 lists the psychr ometric parameters of the greenhouse dome atmosphere with the selected composition for the pl ant experiments. Figure 5-2 shows the psychrometric chart for the greenhouse dome atmo sphere. It can be utilized to determine the dew-point temperature at which condensat ion starts to occur on the greenhouse shell. One important difference from the classical psychrometric chart is that the dew-point temperature isolines are not horizontal, as the pressure of the dry air changes with temperature in a closed system. Table 5-2. Psychrometric parameters of a low pressure atmosphere (76% N2, 20% O2, 4% CO2) with initial conditions of 20 kP a dry air at 20C and a constant specific volume of 0.004138m/kg. Tdry [C] Humidity pWs [Pa] pW [Pa] pt [Pa] w [kg/kgda] tdew [C] h [kJ/kgda] tad [C] 5 100% 872.49 872.49 19849 0.0281 5.02 1 75.6 5.00 10 100% 1228.00 1228.0020546 0.0389 10.03 1 108.0 10.00 15 100% 1705.45 1705.4521364 0.0531 15.03 1 149.2 15.00 20 100% 2338.80 2338.8022339 0.0715 20.01 1 201.5 20.00 25 100% 3169.22 3169.2223510 0.0953 25.00 1 267.7 25.00 30 100% 4246.03 4246.0324928 0.1256 29.98 1 350.9 30.00 5 90% 872.49 785.24 19762 0.0253 3.51 0.9 68.5 3.79 10 90% 1228.00 1105.2020423 0.0350 8.47 0.9 98.2 8.68 15 90% 1705.45 1534.9021194 0.0478 13.40 0.9 135.8 13.58 20 90% 2338.80 2104.9222105 0.0644 18.33 0.9 183.4 18.48 25 90% 3169.22 2852.2923193 0.0858 23.25 0.9 243.4 23.39 30 90% 4246.03 3821.4324504 0.1130 28.17 0.9 318.8 28.30 5 80% 872.49 697.99 19675 0.0225 1.83 0.8 61.5 2.48 10 80% 1228.00 982.40 20300 0.0311 6.74 0.8 88.4 7.27 15 80% 1705.45 1364.3621023 0.0425 11.61 0.8 122.3 12.04 20 80% 2338.80 1871.0421871 0.0572 16.47 0.8 165.2 16.83 25 80% 3169.22 2535.3722876 0.0762 21.32 0.8 219.2 21.64 30 80% 4246.03 3396.8224079 0.1005 26.16 0.8 286.7 26.45

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81 Table 5-2 continued Tdry [C] Humidity pWs [Pa] pW [Pa] pt [Pa] w [kg/kgda] tdew [C] h [kJ/kgda] tad [C] 5 70% 872.49 610.74 19587 0.0197 -0.04 0.7 54.4 1.09 10 70% 1228.00 859.60 20177 0.0272 4.80 0.7 78.6 5.71 15 70% 1705.45 1193.81 20853 0.0371 9.61 0.7 108.9 10.37 20 70% 2338.80 1637.16 21637 0.0501 14.40 0.7 147.1 15.03 25 70% 3169.22 2218.45 22560 0.0667 19.17 0.7 194.9 19.71 30 70% 4246.03 2972.22 23654 0.0879 23.93 0.7 254.7 24.42 5 60% 872.49 523.49 19500 0.0169 -2.18 0.6 47.4 -0.42 10 60% 1228.00 736.80 20055 0.0233 2.60 0.6 68.8 4.04 15 60% 1705.45 1023.27 20682 0.0318 7.33 0.6 95.5 8.53 20 60% 2338.80 1403.28 21403 0.0429 12.04 0.6 128.9 13.05 25 60% 3169.22 1901.53 22243 0.0572 16.72 0.6 170.6 17.59 30 60% 4246.03 2547.62 23230 0.0754 21.40 0.6 222.6 22.16 5 50% 872.49 436.24 19413 0.0141 -4.67 0.5 40.3 -2.05 10 50% 1228.00 614.00 19932 0.0194 0.03 0.5 59.0 2.20 15 50% 1705.45 852.72 20512 0.0265 4.69 0.5 82.1 6.50 20 50% 2338.80 1169.40 21169 0.0358 9.30 0.5 110.8 10.84 25 50% 3169.22 1584.61 21926 0.0477 13.89 0.5 146.4 15.21 30 50% 4246.03 2123.02 22805 0.0628 18.47 0.5 190.5 19.61 5 40% 872.49 348.99 19326 0.0112 -7.67 0.4 33.2 -3.83 10 40% 1228.00 491.20 19809 0.0156 -3.05 0.4 49.2 0.17 15 40% 1705.45 682.18 20341 0.0212 1.51 0.4 68.7 4.23 20 40% 2338.80 935.52 20936 0.0286 6.03 0.4 92.6 8.33 25 40% 3169.22 1267.69 21609 0.0381 10.51 0.4 122.1 12.48 30 40% 4246.03 1698.41 22381 0.0502 14.96 0.4 158.4 16.67 5 30% 872.49 261.75 19238 0.0084 -11.48 0.3 26.2 -5.79 10 30% 1228.00 368.40 19686 0.0117 -6.95 0.3 39.4 -2.09 15 30% 1705.45 511.63 20171 0.0159 -2.49 0.3 55.3 1.65 20 30% 2338.80 701.64 20702 0.0215 1.91 0.3 74.5 5.45 25 30% 3169.22 950.76 21292 0.0286 6.26 0.3 97.8 9.31 30 30% 4246.03 1273.81 21956 0.0377 10.58 0.3 126.3 13.22 5 20% 872.49 174.50 19151 0.0056 -16.75 0.2 19.1 -7.97 10 20% 1228.00 245.60 19563 0.0078 -12.32 0.2 29.6 -4.66 15 20% 1705.45 341.09 20000 0.0106 -7.98 0.2 41.9 -1.32 20 20% 2338.80 467.76 20468 0.0143 -3.72 0.2 56.3 2.06 24 20% 2985.13 597.03 20870 0.0180 -0.36 0.2 69.9 4.81 30 20% 4246.03 849.21 21531 0.0251 4.63 0.2 94.2 9.01 5 10% 872.49 87.25 19064 0.0028 -25.59 0.1 12.1 -10.40 10 10% 1228.00 122.80 19441 0.0039 -21.25 0.1 19.8 -7.61 15 10% 1705.45 170.54 19829 0.0053 -17.04 0.1 28.4 -4.84 20 10% 2338.80 233.88 20234 0.0072 -12.95 0.1 38.2 -2.06 25 10% 3169.22 316.92 20658 0.0095 -8.96 0.1 49.3 0.75 30 10% 4246.03 424.60 21107 0.0126 -5.03 0.1 62.1 3.61

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82 0.00 0.02 0.04 0.06 0.08 0.10 0.12 051015202530 Dry Bulb Temperature tdry [C]Humidity Ratio w [kgmoisture/kgdryair] 225 200 125 75 50 25 5 C 10C tdew = 25C tdew = 20C tdew = 15C tdew = 10C tdew = 5C tdew = 0C 15C 20C 175 150 100 h = 250 kJ/kgdry tad(=twet) = 25C 0C Figure 5-2. Psychrometric chart of low pressure atmosphere (76% N2, 20% O2, 4% CO2) with initial conditions of 20 kPa dry air at 20C and a constant specific volume of 0.004138m/kg.

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83 One–dimensional Steady State Heat Transfer Model of the Greenhouse Dome Overall Thermal Resistance Model A one-dimensional steady state analysis was selected as heat transfer model. The heat inside of the greenhouse produced by th e absorbed growth light radiation and the heating system is transferred to the outside in the following steps. First convection heat transfer takes place between the air and th e greenhouse inner shell, then heat is transferred through the greenhouse dome by conduction. Heat transfer between the greenhouse surface and the inner chamber wall o ccurs mainly due to radiation. Natural convection of the outside dome and the interi or chamber walls is negligible as the convection coefficient is reduced significantl y by the low pressure of 0.6 kPa (see Table 5-1). The effect of low pressure on conv ective heat transfer has been discussed extensively at the beginning of this Chapte r. Heat transfer through the vacuum chamber occurs by conduction. Finally, heat is re moved from the vacuum chamber wall by convection. At the same time, heat is also transferred out of the greenhouse through the dome base. Thick foam insulation had been in stalled under the base to minimize the heat loss through the floor. The equivalent thermal circuit concept is a useful tool for the development of a one-dimensional steady state heat transfer model. The thermal resistance is defined as the ratio of the temperature difference (the dr iving potential) to the corresponding heat transfer rate. Figure 5-3 depict s the modes of heat transfer and states the equivalent thermal resistance circuit.

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84 Figure 5-3. Heat transfer of greenhouse dome and thermal resistance circuit. Individual Thermal Resistance s and Thermal Coefficients The total heat flux out of the greenhouse dom e is the sum of the absorbed light plus the heat added by the heating coil. The heat fl ux is the ratio of the temperature difference to the total resistance: total Light Heater totalR T T Q Q Q9 3 (5-50)

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85 In analog to the electric circ uit the total resistance is determined by the seriesparallel configuration of th e individual resistances: 5 9 8 7 6 4 3 2 11 1 1 R R R R R R R R R Rtotal (5-51) The conduction resistance R7 is very large compared to the other resistances as the dome base is very well insulated. Thus, the total resistance reduces to: 5 4 3 2 1R R R R R Rtotal (5-52) where: 2 1 1 2 3 12 1 r h Q T T Rtotal = Convection heat transfer 2 1 25 5 2 21 1 2 1 r r k Q T T Rtotal= Conduction heat transfer Chamber s totalA r r T T T T Q T T R2 2 6 6 5 2 2 2 6 2 5 6 5 6 5 32 1 1 2 ) )( ( 1 = Radiation heat transfer Chamber totalA k S Q T T R67 7 6 4 = Conduction heat transfer Chamber totalA h Q T T R7 9 7 51 = Convection heat transfer r1 = inner dome radius [m] r2 = outer dome radius [m] h1 = convection coefficient dome inside [W m-2 K-1] k25 = conduction coe fficient dome [W m-1 K-1] s = Stefan-Boltzmann constant [5.670 10-8 W m-2 K-4] s = emissivity of greenhouse dome outside [-] 6 = emissivity of chamber inside [-] S = thickness of chamber [m]

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86 k67 = conduction coefficient chamber [W m-1 K-1] Achamber = Area of chamber [m] h7 = convection coefficient chamber outside [W m-2 K-1] The thermal resistances and coefficients, defined above, can be solved straightforward by inserting the steady state temperatures data of the Galactic lettuce experiment and the dimensions of the dome and chamber. Table 5-3 lists the temperature data at the selected locations. Table 5-4 gives an overvie w of the calculated thermal resistances and heat transfer coefficients. It can be observed that the data are different for the case when the light is switched on, compared to the light being switched off. This results from the temperature differences for both cases. The temp eratures of the surfaces are higher when the light is switched on, because part of the radiation is absorbed by the dome shell and chamber wall. The radiation coefficients 5 and 6 depend on each other and the equation cannot be solved without knowing one of them (see Figures 5-4 and 5-5). As the polycarbonate dome is very transparent a high emissivity of 0.9 was chosen, resulting in an emissivity value of the chamber of 0.55 for the light turned off and 0.48, wh en the light is turned on. Table 5-3. Steady state temper ature data of the long-term experiment involving Galactic lettuce plants. Freezer Temp. [C] Light Heating Power [W] Air T3 [C] Fan T4 [C] Shell Inside T2 [C] Shell Outside T5 [C] Inside Wall T6 [C] Outside Wall Middle T7 [C] Outside Wall Bottom T8 [C] Chamber Air T9 [C] -20 off 119 19.68 24.42 13.81 3.47 -16.73 -18.83 -19.51 -20.01 -20 on 40 20.12 22.16 15.61 8.35 -11.99 -16.04 -19.16 -19.96

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87 Table 5-4. Thermal resistances and coeffici ents based on the data obtained of the longterm experiment involving Galactic lettuce plants. Unit Light off Light on R1 Convection K/W 0.0494 0.0379 h1 Convection W/(Km) 11.3306 14.7518 R2 Conduction K/W 0.0869 0.0610 k25 Conduction W/(Km) 0.0404 0.0576 R3 Radiation K/W 0.1697 0.1709 5 Radiation 0.90 0.90 6 Radiation0.55 0.48 R4 Conduction K/W 0.0176 0.0340 k67 Conduction W/(Km) 0.1139 0.0591 R5 -Convection K/W 0.0099 0.0329 h7 Convection W/(Km) 16.7858 5.0598 R-total K/W 0.3336 0.3368 0 0.2 0.4 0.6 0.8 1 00.20.40.60.815(Dome)6(Chamber) 0.55 0.9 Figure 5-4. Emissivities of th e polycarbonate dome and the st ainless steel chamber (light off).

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88 0 0.2 0.4 0.6 0.8 1 00.20.40.60.815(Dome)6(Chamber) 0.48 0.9 Figure 5-5. Emissivities of th e polycarbonate dome and the st ainless steel chamber (light on). The thermal coefficients of Table 5-4 and the dimensions of the dome and the chamber are entered into a simulation module programmed in LabView. As the radiation resistance varies with the temperature of the dome and the chamber, a direct determination of the steady-state temperatures is not possible. A loop recalculates the temperatures beginning from the initial conditio ns until steady state is reached. Table 5-5 lists the simulated temperatures at the selected locations.

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89 Table 5-5. Simulated temp eratures based on the thermal resistance model. Freezer Temp. [C] Lights (0=off, 1=on) Heating Power [W] Air/ Plant T3 [C] Shell Inside T2 [C] Shell Outside T5 [C] Inside Wall T6 [C] Outside Wall T7 [C] Chamber Air T9 [C] 0 0 26 8.28 7.00 4.74 0.72 0.26 0.00 0 0 51 16.03 13.51 9.08 1.41 0.51 0.00 0 0 77 23.89 20.09 13.40 2.12 0.76 0.00 0 0 103 31.57 26.48 17.54 2.84 1.02 0.00 -10 0 26 -1.26 -2.54 -4.80 -9.28 -9.74 -10.00 -10 0 51 6.88 4.36 -0.07 -8.59 -9.49 -10.00 -10 0 77 15.10 11.30 4.61 -7.88 -9.24 -10.00 -10 0 103 23.10 18.02 9.07 -7.16 -8.98 -10.00 -20 0 51 -2.15 -4.67 -9.10 -18.59 -19.49 -20.00 -20 0 77 6.48 2.67 -4.02 -17.88 -19.24 -20.00 -20 0 103 14.83 9.75 0.80 -17.16 -18.98 -20.00 -20 0 128 22.64 16.32 5.21 -16.47 -18.73 -20.00 -10 1 0 16.14 13.14 8.33 -4.71 -7.40 -10.00 -10 1 26 24.08 20.10 13.70 -2.97 -6.54 -10.00 -10 1 51 31.47 26.54 18.62 -1.30 -5.72 -10.00 -10 1 77 38.93 33.01 23.51 0.44 -4.86 -10.00 -20 1 0 7.55 4.55 -0.26 -14.71 -17.40 -20.00 -20 1 26 15.82 11.84 -5.44 -12.97 -16.54 -20.00 -20 1 51 23.49 18.56 10.64 -11.30 -15.72 -20.00 -20 1 77 31.21 25.29 15.79 -9.56 -14.86 -20.00 -20 1 103 38.69 31.79 20.69 -7.82 -14.01 -20.00 Table 5-6 compares the temperature values obtained through the simulation to the temperatures measured during the initial heat transfer experiments. The model works well for high heating power. Furthermore, the errors are smaller when the light is turned on compared to the light being turned off. Th e main contribution to the difference between the measured and simulated values is the assumption that the heat transfer is only occurring in one direction. T hus, the vertical temperature distribution of the greenhouse air and therefore the greenhouse shell is not accounted for.

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90 Table 5-6. Comparison of measured and simulated temperature values. Freezer Temp. [C] Lights (0=off, 1=on) Heating Power [W] Measured Air/Plant Temp. T3 [C] Simulated Air/Plant Temp. T3 [C] Error Temp T3 [K] Measured Wall Temp. T7 [C] Simulated Wall Temp. T7 [C] Error Temp T7 [K] 0 0 26 12.74 8.28 4.46 0.01 0.26 -0.25 0 0 51 19.17 16.03 3.14 0.34 0.51 -0.17 0 0 77 24.06 23.89 0.17 0.49 0.76 -0.27 0 0 103 30.25 31.57 -1.32 0.11 1.02 -0.91 -10 0 26 5.29 -1.26 6.55 -9.63 -9.74 0.11 -10 0 51 10.76 6.88 3.88 -9.94 -9.49 -0.45 -10 0 77 18.44 15.10 3.34 -9.44 -9.24 -0.20 -10 0 103 24.01 23.10 0.91 -9.38 -8.98 -0.40 -20 0 51 3.38 -2.15 5.53 -19.13 -19.49 0.36 -20 0 77 9.06 6.48 2.58 -19.31 -19.24 -0.07 -20 0 103 15.51 14.83 0.68 -18.88 -18.98 0.10 -20 0 128 21.34 22.64 -1.30 -18.63 -18.73 0.10 -10 1 0 16.76 16.14 0.62 -6.22 -7.40 1.18 -10 1 26 25.74 24.08 1.66 -6.74 -6.54 -0.20 -10 1 51 32.17 31.47 0.70 -6.66 -5.72 -0.94 -10 1 77 38.27 38.93 -0.66 -6.31 -4.86 -1.45 -20 1 0 5.60 7.55 -1.95 -15.38 -17.40 2.02 -20 1 26 17.52 15.82 1.70 -14.38 -16.54 2.16 -20 1 51 23.39 23.49 -0.10 -14.13 -15.72 1.59 -20 1 77 32.73 31.21 1.52 -13.85 -14.86 1.01 -20 1 103 38.98 38.69 0.29 -13.20 -14.01 0.81 Total Thermal Resistance Figures 5-6 and 5-7 depict the heating power versus the temperature difference between the dome air and the freezer base d on the initial heat and mass transfer experiments without plants. The slope of the regression line is the value of the thermal resistance. The absorbed radiation of the growth light contribu tes to approximately 76-83 Watts of the total heat flux according to the linear regression equations in Figure 5-7. The total thermal resistance is higher fo r lower air temperatures and higher when the light is switched on. The total thermal resistance for the simula tion model (based on the Galactic lettuce experiment data) was determined to be 0. 3336 K/W when the light is switched off and

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91 0.3368 K/W when the light is being turned on. Those data points f it well into the total resistance range determined in Figures 5-6 and 5-7. T = 0.3517*QhR = 0.9954 T = 0.3349*QhR2 = 0.9993 T = 0.3194*QhR2 = 0.9996 25 30 35 40 45 50 7090110130150 Qheating [W] T (Tair-Tfreezer) [K] T Air = 15 C T Air = 20 C T Air = 25 C Figure 5-6. Required heating pow er versus temperature differe nce of the dome air to the freezer. Slope of linear regression is the total thermal resistance (light off). T = 0.3211*(Qh + 83.02024) R2 = 0.9962 T = 0.3425*(Qh + 77.45635) R2 = 0.9967 T = 0.3640*(Qh + 76.2841) R2 = 0.9971 25 30 35 40 45 50 0102030405060 Qheating [W] T (Tair-Tfreezer) [K] T Air = 15 C T Air = 20 C T Air = 25 C Figure 5-7. Required heating pow er versus temperature differe nce of the dome air to the freezer. Slope of linear regression is the total thermal resistance (light on).

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92 Comparison of Radiation and Convectio n in the Chamber at Mars Pressure One assumption of the thermal resistance model was that inside the vacuum chamber, at a low pressure of 0.6 kPa, c onvection is much smalle r than radiation and therefore convection was neglec ted. By comparing the heat flux through radiation to the heat flux through convection, it can be ve rified if the assumption was correct. In order to calculate the convective heat loss of the dome sphere and the chamber wall, the flow condition has to be analyzed first, by determining the Rayleigh number (see Equation 5-22). The Rayleigh number is below the critical Rayleigh number for convection of the dome as well as for the cham ber, therefore the flow is laminar in both cases. The convection coefficient of the dome is calculated with Equation 5-23 and the coefficient of the chamber wall with Equation 5-18. The convection heat loss is 3.9 W for the dome and 12.2 W for the chamber wall. Co mpared to the radiation heat loss of 119 W, the convection heat loss is only 3. 3% for the dome and 10.3% for the chamber wall. Thus, the assumption that convective heat tr ansfer can be neglecte d is correct, if the radiation heat loss is relativel y high. If the power of the h eating system decreases and the difference between the chamber wall and dome te mperatures is much smaller, convective heat loss plays a bigger role. This is the majo r reason, why in Table 5-6 the difference of the simulated and the measured values incr eases for low heating power. Table 5-7 lists the calculated values for the comparison of the convective heat transfer inside of the vacuum chamber to the radiation heat transfer.

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93 Table 5-7. Comparison of conv ection heat transfer to radiation heat transfer in the chamber at a pressure of 0.6 kPa. Shell Outside T5 [C] Air Chamber T [C] Inside Wall T6 [C] Light on 8.35 -5.995 -11.99 Light off 3.47 -8.365 -16.73 Convection Dome Ra Racrit Flow hconv Qconv Qrad Qconv/Qrad Light on 6.30E+04 1011 laminar 0.2072 3.8577 119 3.25% Light off 6.37E+04 1011 laminar 0.2077 3.8393 119 3.26% Convection Chamber Wall Ra Racrit Flow hconv Qconv Qrad Qconv/Qrad Light on 5.06E+04 109 laminar 0.1897 12.1868 119 10.28% Light off 5.15E+04 109 laminar 0.1905 12.1578 119 10.31% Transient Heat Transfer Model for G reenhouse Temperature Simulation For the transient heat transfer model, the overall system is split up into the greenhouse atmosphere, the greenhouse dome, the vacuum chamber and the greenhouse base plate. Four differential equations (5 -53 to 5-56) are set up based on the energy balance of the four sub-systems. The change of the internal energy is equal to the sum of the heat fluxes into and out of the system due to energy conservation. )] ( ) ( [ ) (1 3 1 25 3 1 3 1 3 n n base n n dome h rad n n atm pT T A h T T A h Q Q t T T V c (5-53) where: T3 n +1 = temperature of greenhouse atmos phere at next time step [K] T3 n = temperature of greenhouse atmos phere at current time step [K] t = time step [s] cp,atm = specific heat of greenhouse atmosphere [J/kg K] atm = density of greenhouse atmosphere at 20 kPa [kg/m] Vatm = volume of greenhouse atmosphere [m] Qrad = heat gain from radiation [W] Qh = heat gain from heating system [W]

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94 ) ( ) ( ) (67 25 25 3 1 25 1 25 n n rad rad n n dome n n dome pT T A h T T A h t T T V c (5-54) where: T25 n +1 = temperature of dome she ll at next time step [K] T25 n = temperature of dome shell at current time step [K] cp,dome = specific heat of polycarbonate dome shell [J/kg K] dome = density of polycarbonate dome shell [kg/m] Vdome = volume of polycarbonate dome shell [m] ) ( ) ( ) (67 7 67 25 67 1 67 n freeezer n chamber n n rad rad n n chamber pT T A h T T A h t T T V c (5-55) where: T67 n +1 = temperature of vacuum chamber at next time step [K] T67 n = temperature of vacuum cham ber at current time step [K] cp,chamber = specific heat of stainless steel vacuum chamber [J/kg K] chamber = density of stainless st eel vacuum chamber [kg/m] Vchamber = volume of stainless st eel vacuum chamber [m] ) ( ) (1 3 1 1 1 1 n n base n n base pT T A h t T T V c (5-56) where: T1 n +1 = temperature of base at next time step [K] T1 n = temperature of base at current time step [K] cp,base = specific heat of aluminum dome base [J/kg K] base = density of aluminum dome base [kg/m] Vbase = volume of aluminum dome base [m]

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95 The equations above are based on the assu mption that the conduc tion resistance of the dome, the vacuum chamber and the base pl ate are very small and therefore the inside and outside temperatures are lumped into one equivalent temperature, T25, T67 and T1 respectively. Furthermore, the dome base plate is considered to be perfectly insulated as it was assumed for the steady state heat transfer model. The four differential equations contai n the four unknown temperature variables T3 n+1 T25 n+1, T67 n+1and T1 n+1. With the initial conditions of the four temperature variables, the system can be solved. Figure 5-8, Figure 5-9 and Figure 5-10 compare the simulation data to the experimental data fo r three different hea ting power conditions. In all three cases the temperat ure rise of the simulation is much slower than in the experiment, i.e. it takes longer for the air and dome temperature to reach steady state. Consequently, the thermal inertia is higher for the simulation compared to the experimental data. Furthermore, it can be obs erved that the air temperature experiences a sudden rise at the beginning of the simulati on as the difference be tween the energy gain by heating and the energy loss by convecti on is relatively hi gh. The steady-state temperatures of the simulation are lower th an the steady-state temperatures of the experiment. The same phenomenon was also se en in the thermal resistance model results. The transient heat transfer model is a good first approach to simulate the transient temperature variations of the experiment. In combination with the psychrometric model, the state of the greenhouse ai r can be assessed and occurren ce of condensation can be predicted. Figure 5-11 shows the LabView Front Panel for the overall model. A condensation warning appears if the greenhouse shell temperature is below the dew point temperature.

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96 -15 -10 -5 0 5 10 15 20 050100150200 Time [min]Temperature [C] TairExperiment Tair Simulation Tdome-Experiment Tdome Simulation Tchamber Experiment Tchamber Simulation Figure 5-8. Simulation of greenhouse atmosphere, dome and vacuum chamber temperatures (light off, 51W heatin g power, -10 C freezer temperature). -15 -10 -5 0 5 10 15 20 050100150200250300 Time [min]Temperature [C] Tair Experiment Tair Simulation Tdome Experiment Tdome Simulation Tchamber Experiment Tchamber Simulation Figure 5-9. Simulation of greenhouse atmosphere, dome and vacuum chamber temperatures (light off, 77 W heatin g power, -10 C freezer temperature).

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97 -15 -10 -5 0 5 10 15 20 25 050100150200250300350400 Time [min]Temperature [C] Tair Experiment Tair Simulation Tdome Experiment Tdome Simulation Tchamber Experiment Tchamber Simulation Figure 5-10. Simulation of greenhouse atmosphere, dome and vacuum chamber temperatures (light off, 103 W heati ng power, -10 C freezer temperature). Figure 5-11. LabView front panel of overall model for simulation.

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98 CHAPTER 6 RESULTS AND CONCLUSION An understanding of the heat and mass transf er of a Mars greenhouse is essential to develop the environmental control system The environmental control system is responsible for keeping the atmosphere para meters in a range wh ere plant growth is productive. In this research, a Mars chamber was developed simulating the environment on Mars. A small scale Mars gree nhouse was exposed to the si mulated Mars environment. Tests included experiments on the heat and mass transfer without and with plants. The data obtained through the thermal experiments w ithout plants were used to refine the gas composition and temperature control algorithm. Furthermore, the temperature distribution data within the greenhouse and the chamber were utilized in the model development. Two sets of plant experiments were successfully conducted. The mid-term experiment involved eight buttercrunch lettu ce plants that were exposed to the low pressure Mars greenhouse environment fo r 36 hours. Temperature, pressure and atmosphere composition of the greenhouse a nd the simulated Mars environment were controlled. Evapo-transpiration, relative humidity and light levels were measured continuously. One plant started to wilt as the water supply ceased. The long-term experiments involved Galactic le ttuce plants that were exposed to the low pressure Mars greenhouse environment for 7 days. After one da y of continuous exposure to the growth light, a day-night cycle of 12 hours was impl emented. The temperature of the greenhouse shell decreased significantly during the night cycle, resulting in the formation of

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99 condensation and frost, especia lly in the lower colder part of the greenhouse. Relative humidity also decreased during the night cycle as more wate r condensed than evaporated. The plants showed no significant visible dama ge after seven days, only minor wilting was observed as the water supply was depleted. Data from the experiments were analyzed to develop a thermal resistance model that can be used to predict steady-stat e greenhouse temperatures for various Mars environment conditions. The analytical da ta of the model fitted well with the experimental data for low freezer temperat ures, i.e., high temperature differences between the Mars environment and the greenhou se temperature, as the thermal resistance model was based on the assumption that at low pressures convec tion is insignificant compared to radiation heat transfer. The tran sient heat transfer model was utilized to simulate the transient temperature variations of the equipment over time. Low pressure psychrometric relations were developed for closed systems at various gas compositions other than the standard at mosphere. The psychrometric model can be used to predict the state of the moist air. Knowledge of the psychr ometric parameters is especially important for the predicti on of the occurrence of condensation.

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100 CHAPTER 7 FUTURE WORK The results of this study show that ther e is a vertical temperature and humidity stratification of the greenhouse dome atmosphere. The installati on of a heater on the cold greenhouse aluminum base and improved insulation would lead to a more uniform atmosphere, preventing the build-up of conde nsate and ice in the lower part of the greenhouse (see Figure 7-1). If a passive humidity cont rol system is selected, th e water should condense on the greenhouse shell above the gravity-driven recollection funnel. At the same time, condensate should not collect above the plant level as it would interfere with the radiation required for plant growth. Anot her option of condensing the wa ter out of the atmosphere would be to pipe air out of the greenhouse to a heat exchange r with the Mars environment and to feed back the water and the dried air separately into the dome. Temperature of the condensation surface should be monitored caref ully as the temperature should be below the dew point but above the freezing point. Gravity driven wate r collection systems should be applied where possible as they work in the low-gravity Mars environment and avoid the installation of pumps. The duration of the experiments was limite d by the decreasing water supply to the plants. An efficient water recycling system, that collects the condens ate and feeds it back to the plants would minimize the required res upply of water from the outside and increase the length of the experiment.

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101 Future research should also include full grow th cycles of the plants from seeds to maturity as small plants are much more vulnerable to environmental changes. A simulated day-night cycle with gradual intensity increase of the growth light could be implemented, as it would replicate th e Mars environment more accurately. A) B) Figure 7-1. Ice building up on th e bottom part of the greenhous e shell. A) Overview. B) Detailed view of the ice-crystals.

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102 APPENDIX A STRUCTURAL ANALYSIS OF DOME SH ELL, BASE PLATE AND CYLINDRICAL CALIBRATION CHAMBER Structural Analysis of th e Spherical Greenhouse Dome Most Mars greenhouse experiments utilize enclosures that are under compression, because they incorporate standard atmosphere on the outside and low pressure inside of the vessel. In this case, a structural analys is should be performe d to avoid a stability failure under compression. Whereas, the greenhouse dome (operated at 20-25 kPa pressure) in this project is placed in a vac uum chamber operated at the low Mars pressure of 0.6 kPa. Therefore, the structural analys is should be performed for a semi-sphere under tension: The yield stress of the hemisphere is defined as: t r Pcritmax (A-1) where: Pcrit = critical pressure [3.67 psi = 0.25 atm.] r = radius of sphere [21 in (0.53 m)] t = wall thickness [0.25 in (0.635 cm)] The yield stress of the sphere of 308.28 ps i (2126 kPa) is well below the maximum yield stress of 1000 psi (6895 kPa). Theref ore, the safety factor is 3.24. Assuming a safety factor of 1.5 leads to the conclusion, that the greenhouse dome should not be operated at a pressure differe nce of more than 7.9 psi or 0.5 atm.

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103 Structural Analysis of Base Plate for Greenhouse Dome A inch aluminum plate serves as the base of the greenhouse dome. It is reenforced with aluminum tubes welded to the bottom of the plate. Figure A-1 shows the bottom view of the dome base plate. Figure A-1. Bottom view of greenhouse dome base. For the structural analysis the dome base is split up into four uniformly circular sectors with 90 degree angles (see Figure A-2). First the structural analysis is performed of a plate with the main two bracings consider ed as beams. A second analysis also takes the additional square bracing into account. The structural analyses of this section are based upon the equations found in Ameri can Aluminum Association (1981).

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104 Structural Analysis of the Base Plate without Additional Bracings The first analysis assumes a triangular lo ad over the full beam depicted in Figure A-2. Figure A-2. Triangular load over full beam. The total load on the sector, i.e., beam, is the area of the triangle and can be calculated by multiplying the pressure difference by the wedge area: 4 22 maxqL L w W (A-2) where: W = total load [lb]

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105 wmax = maximum distributed loading [lb/in] L = length of beam [m] q = pressure differential [psi] Therefore, the maximum loading of the beam is: 2max qL w (A-3) The reactions R1 and R2 at the supports are: 61wL R (A-4) 32wL R (A-5) The bending moment varies with the location x on the beam: L x L x w x L L Wx x M 6 ) ( ) ( 3 ) (2 2 max 2 2 2 L x 0 (A-6) The maximum bending moment is encountered at 0.55774 L: 4 1283 0 1283 0 ) 5774 0 (3 maxqL WL L x M (A-7) The deflection varies with the location x on the beam: ) 7 10 3 ( 180 ) (4 2 2 2 2L x L x EIL Wx x def L x 0 (A-8) The maximum deflection is encountered at 0.5193 L: EI qL EI WL L x def 4 01304 0 01304 0 ) 5193 0 (5 3 max (A-9)

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106 Structural Analysis of the Base Plate with Additional Bracings The second structural analysis also considers the additiona l bracing in the form of a square. Similar to the first analysis the plat e is split up into four sectors and the main bracing is considered as a beam (see Figure A-3). Figure A-3. Trapezoidal load over part of the beam.

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107 The load inside of the additional bracing (for x < a) is taken by the interior bracings, therefore only the dist ributed load outside the add itional bracing (for x>a) is considered. This leads to a trapezoidal lo ad distribution as shown in Figure A-3. In this case also Equation A-2 applies, leading to a maximum load of the beam, similarly to the triangular load distribution (see Equation A-3): 2maxqL w (A-10) The trapezoidal load on the beam can be calculated by super positioning a uniform load (see Figure A-4) and a triangular load (see Figure A-5) for x>a. Figure A-4. First part of super position: uniform load for x>a. The uniform load w* is related to the maximum trapezoidal load wmax (defined in Equation A-10) as follows: max* w L a w (A-11) The reactions R1 and R2 at the supports are: L w a L R 2 ) (2 1 (A-12) L w a L R 2 ) (2 2 2 (A-13)

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108 The bending moment M1 for xa is: 2 ) ( ) ( ) (2 2 2w x L L x R x M L x a (A-16) max 2 2 2 2] 2 ) ( 2 ) )( ( [ ) ( w L a x L L x L a L x M L x a (A-17) 4 ] ) ( ) )( ( [ ) (2 2 2 2aq x L L x L a L x M L x a (A-18) The second part of the superposition is a triangular load on the beam for x>a as shown in Figure A-5. Figure A-5. Second part of superposition: tria ngular load for x>a. The maximum triangular load w** is relate d to the maximum load of the trapezoid wmax (defined in Equation A-10) as follows: max1 * w L a w (A-19)

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109 The reactions R1 and R2 at the supports are: L w a L R 6 * ) (2 1 (A-20) ) 2 ( 6 * ) ( 6 * ) ( 2 * ) (2 2a L L w a L L w a L w a L R (A-21) The bending moment M1 for x
a is: *) ) ( * ( 3 * ) ( * 2 ) ( ) 2 *( ) ( 2 ) ( ) ( ) (2 2w a L a x w w a L a x w x L a x L w a L x L x L R x M L x a (A-25) 3 3 2 ) ( ) ( 2 ) ( ) )( 2 ( 6 ) ( * ) (2a x L x L a L x L x L a L L a L w x M L x a (A-26) 3 3 2 ) ( 2 ) ( 6 ) 2 )( )( ( * ) (2 2a x L a L x L L a L x L a L w x M L x a (A-27) ) 3 2 ( ) ( ) 2 )( ( ) ( 12 ) (2 2 2a x L x L L a L x L a L q x M L x a (A-28)

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110 The bending moments M1 and M2 of the trapezoidal load are calculated by superposition, i.e. summing up the bending mome nts of the uniform and of the triangular load: x L a q a L x L aq a L x M 1 12 ) ( 4 ) ( ) (2 2 1 a x 0 (A-29) x L q a L a L x M 12 ) 2 ( ) ( ) (2 1 a x 0 (A-30) ) 3 2 )( ( ) 2 ( ) ( 3 )] ( ) ( [ 12 ) ( ) (2 2 2 2a x L x L L a L a L a x L L a L q x L x M L x a (A-31) Figure A-6 shows the bending moments of the beam under a load in form of a trapezoid. The bending moments are decreasing for increasi ng distance a of the bracing from the center of the plate. Figure A-6. Bending moments of beam for trapez oidal load varies wi th the distance a of the additional bracing.

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111 The section modulus Sbeam of a 3 x 2 x 1/8 aluminum bar is 0.978 in3 (16.03 cm3) and the moment of inertia Ix about the x-axis is 1.467 in4 (61.06 cm4) (American Aluminum Association, 1981). Th e total moment of inertia of the beam and the plate is calculated as follows: 2 2beam beam beam plate Plate plate totald A I d A I I (A-32) where: Itotal = total inertia [3.23 in4 (134.44 cm4)] Iplate = inertia of plate section [ 4 300781 0 12 25 0 6 in (0.3251 cm4)] Aplate = area of plate section [1.5 in2 (9.68 cm2)] dplate=distance to plate centroid[ in A A A Aplate tube plate tube91 0 25 1 125 3 5 1 (2.3cm)] Ibeam = inertia of beam [1.467 in4 (61.06 cm4)] Abeam = area of plate section [1.1875 in2 (7.66 cm2)] dbeam = distance to beam centroid [0.47 in (1.19 cm)] With the moment of inertia, the section modulus Stotal of the plate and the beam is defined as: c I Stotal total (A-33) where: Stotal = section modulus of plate and beam[1.34 in3] c = distance centroid to base [ in A A A Aplate tube plate tube41 2 125 3 5 1 (6.12 cm)] The stress is defined as ratio of the be nding moment M to the section modulus S: S M (A-34)

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112 The maximum stress for tension and compression is 16000 psi (110316 kPa). Applying a safety factor of 1.65, results in a maximum stress of 9700 psi (33879 kPa). The maximum stress allowed near a weld ing is 6500 psi (44816 kPa) (American Aluminum Association, 1981). Tabl e A-1 lists the properties of the stress analysis for the base plate without and with the additional brac ings (at a = 7 in (17. 8 cm). Calculations are done for the beam and for the combination of the beam and the plate. The calculated stress for the plate without the additional bracings is higher then for the plate with the bracings. In all cases the stress was belo w 4000 psi (27579 kPa), i.e. below the maximum allowed stress of 6500 psi (44816 kPa) near weldings. Table A-1. Structural an alysis of base plate without and with additional bracings. Base plate without bracings ( load in form of triangle over full beam) L q E Mmax I S def [in] [psi] [psi] [in-lb][in4][in3][in] [psi] 21 4 1.05E+073732.81.47 0.9781.08E-02 3816.77 21 4 1.05E+073732.83.23 1.344.94E-03 2783.39 Base plate with bracings (load in form of a trapezoid over part of the beam) L a q E Mmax I S def [in] [in] [psi] [psi] [in-lb][in4][in3][in] [psi] 21 7 4 1.05E+073429 1.47 0.9783506.13 21 7 4 1.05E+073429 3.23 1.342556.86 Structural Analysis of Cylinder used as Sensor Calibration Chamber The stability behavior of cylin drical shells loaded by external pressure varies with length, shell thickness and wall curvature. Thei r behavior ranges from that of a pure long cylinder to behavior approachi ng that of flat plates for s hort cylinders (Galambos, 1998). Maximum Allowable Pressure Calculation of the maximum allowable pressure is the first step to determine structural failure of a cylinder including ax ial buckling and wall material yielding. In

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113 order to evaluate the maximum allowable pressu re, the cylinder has to be classified into one of the three following categories: short, intermediate or long cylinder. Short cylinder behavior The criterion for a cylinder to be classified as a short cylinder is: t D D L t D 5 5 1 1 (A-35) where: L = length of cylinder [12 in (30.5 cm)] D = diameter of cylinder [8 in (20.32 cm)] t = wall thickness [0.25 in (0.635 cm)] As the length to diameter ratio is 1.5, the cylinder cannot be cl assified as a short cylinder, defined by a length to radius ratio between 0.2 and 1.0. Intermediate cylinder behavior The criterion for a cylinder to be classified as an intermediate cylinder is: t D D L t D 55 0 5 5 (A-36) As the length to diameter ratio is 1.5, the cylinder can be classified as an intermediate cylinder, defi ned by a length to radius ratio between 1.0 and 3.1. At the same time, the parameter should be between 10 and 32 (=D/t) for an intermediate cylinder. is calculated at 15.4 by utili zing the following equation: t D D L 818 1 (A-37) The critical external pressure of an intermediate cylinder is defined as: 5 26 2 t D D L E Pcrit (A-38)

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114 Therefore, the critical pressure equals 134.7 psi (equivalent to 9.2 atmospheres). Utilizing a safety factor of 1.5 leads to the co nclusion, that the external pressure should not exceed 89.9 psi (equivalent to 6.4 atmospheres). Long cylinder behavior The criterion for a cylinder to be classified as a long cylinder is: t D D L 1 2 (A-39) As the length to diameter ratio is 1.5, the cylinder cannot be classified as a long cylinder, defined by a length to radius ratio above 11.9. Axial Buckling After the cylinder has been classified as an intermediate cylinder and the critical external pressure was dete rmined to be 134.4 psi (927 kPa), the cylinder should be checked for axial buckling. A safety factor of at least 10 should be applied. The wall stress should be calculate d at the critical pressure: t D Pcrit axial4 (A-40) The critical wall stress is defined as: D Etcrit21 1. (A-41) where: E = modulus of elasticity of wa ll material [450000 psi (3102641 kPa)] The ratio of the critical wall stress (17015.6 psi (117318 kPa)) to the actual wall stress (1077.2 psi (7427 kPa) at critical pressure) equals 15.8 fulfilling our design criterion of a safety factor of 10.

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115 Wall Yielding The cylinder should be checked for wall yieldi ng at the critical external pressure calculated at 124.4 psi (858 kPa). A safety factor of at leas t 1.6 is required For an intermediate cylinder the circumferential stress is defined by: t D Pcrit ntial circumfere4. (A-42) The ratio of the critical circumferential st ress (2154.5 psi (14855 kPa)) to the actual wall stress (1077.2 psi (7427 kPa) at critical pressure) is de termined to be 2.0 fulfilling our design criterion of a safety factor of 2 for wall yielding.

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116 APPENDIX B SENSOR CALIBRATION Pressure The two pressure sensors (ASCX15AN, Se nsym ICT) were calibrated against a portable precision pressure ga uge (Digiquartz 760 Series, Pa roscientific Inc.). Both sensors were calibrated by linear regression an alysis. Sensor #1 was calibrated for a range from 0 kPa to 75 kPa, as it was used in the greenhouse dome. Sensor #2 was calibrated for a range from 0 kPa to 28 kPa, as it was used in the vacuum chamber: Pr1[kPa] = 22.7546*Vout-5.1814 (B-1) Pr2[kPa] = 22.7386*Vout -5.8444 (B-2) Pressure sensor calibration data is shown in Figures B-1 and B-2. P1 = 22.7546*V 5.1814 R2 = 1.0000 0 10 20 30 40 50 60 70 80 00.511.522.533.54 Voltage [V]Pressure (Sensor #1) [kPa] Figure B-1. Pressure se nsor #1 calibration.

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117 y = 22.7386x 5.8444 R2 = 1.0000 0 5 10 15 20 25 30 00.20.40.60.811.21.41.6 Sensor Output [V]Pressure (Sensor #2) [kPa] Figure B-2. Pressure se nsor #2 calibration. Temperature The digital temperature sensors (DS18B20, Dallas Semiconductor) were exposed to a variety of pressure and gas composition co mbinations. The sensor readings were not affected by pressure or gas mixture. Relative Humidity Relative humidity (RH) measurement is affected by pressure and gas composition changes. However, the capacitance RH sens ors output differed by less than 3% when compared to the hygrometer standard (HMP 237, Vaisala) as described in Chapter 4 of this dissertation. Therefore, the factory calib ration was used for the four RH sensors: RH1[%]=(Vout-0.894)/0.0315 (B-3) RH2[%]=(Vout-0.875)/0.0313 (B-4) RH3[%]=(Vout-0.894)/0.0315 (B-5) RH4[%]=(Vout-0.855)/0.0319 (B-6)

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118 Carbon Dioxide Concentration The carbon dioxide sensor (GMP 221, Vais ala) was calibrated under different gas composition and pressures with th e method described in Mu (2005): CO2 [%] = Slope(P)*Vout + Inte rcept(P) (B-7) where: Slope(P) = 0.0267*P2 1.9901*P + 41.991 Intercept(P) = -0.0031*P2 + 0.2598*P 7.179 In contrast to Mu (2005), a pa rabolic regression fit was chosen for the slope and intercept equations, because the error was significantl y less compared to a linear regression. Figures B-3 and B-4 depict the calib ration of the carbon dioxide sensor. CO2%(50kPa) = 3.4609*V(50kPa) 1.3977 R2 = 0.9941 CO2%(40kPa) = 4.8602*V(40kPa) 1.7557 R2 = 0.9917 CO2%(30kPa)= 7.2743*V(30kPa) 2.3438 R2 = 0.9881 CO2%(20kPa) = 11.962*V(20kPa) 3.0986 R2 = 0.9891 CO2%(10kPa) = 25.071*V(10kPa) 4.9404 R2 = 0.96450 0.5 1 1.5 2 2.5 3 3.5 00.511.5Sensor Output [V]Carbon Dioxide Concentration [%] 50 kPa 40 kPa 30kPa 20kPa 10kPa Figure B-3. Carbon dioxid e sensor calibration.

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119 Intercept = -0.0031*P2 + 0.2598*P 7.179 R2 = 0.9926 Slope = 0.0267*P2 1.9901*P + 41.991 R2 = 0.9922 -10 -5 0 5 10 15 20 25 30 01020304050 Pressure [kPa]Slope/Intercept Slope Intercept Figure B-4. Carbon dioxid e sensor calibration. Oxygen Concentration The two oxygen sensors (Max250, Maxtec) ware calibrated under different gas composition and pressures with the same method as the carbon dioxide sensor (Mu, 2005): O2 [%]= Slope(P)*mVout + Intercept(P) (B-8) where: Slope1(P) = 0.023*P2 1.6411*P+ 33.25 Intercept1(P) = -0.0069*P2 + 0.5047*P 8.1629 Slope2(P) = 0.0479*P2 3.4467*P + 70.061 Intercept2(P) = -0.0315*P2 + 2.300*P 45.376 A parabolic regression fit was chosen for th e slope and intercept equations, because the error was significantly less compared to a li near regression. Figures B-5 and B-6 depict the calibration of the oxygen sensor #1; Figures B-7 and B-8 depict the calibration of the oxygen sensor #2.

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120 O2%(50kPa) = 3.2682*mV(50kPa)+ 1.3388 R2 = 0.9988 O2%(40kPa)= 4.1253*mV(50kPa) + 1.0695 R2 = 0.9987 O2%(30kPa)= 5.5565*mV(30kPa) + 0.6438 R2 = 0.9988 O2%(20kPa) = 8.7876*mV(20kPa) 0.6745 R2 = 0.9994 O2%(10kPa) = 19.419*mV(10kPa) 3.8516 R2 = 0.9988 0 5 10 15 20 25 30 35 0246810 Sensor Output [mV]Oxygen Concentration (Sensor #1) [%] 50 kPa 40 kPa 30kPa 20kPa 10kPa Figure B-5. Oxygen sensor #1 calibration. Slope1 = 0.023*P2 1.6411*P+ 33.25 R2 = 0.9891 Intercept1 = -0.0069*P2 + 0.5047*P 8.1629 R2 = 0.9969 -10 -5 0 5 10 15 20 25 01020304050 Pressure [kPa]Slope1/Intercept1 Slope Intercept Figure B-6. Oxygen sensor #1 calibration.

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121 O2%(50kPa) = 6.4224*mV(50kPa) 2.151 R2 = 0.9985 O2%(40kPa) = 8.3241*mV(40kPa) 3.5136 R2 = 0.9986 O2%(30kPa) = 11.479*mV(30kPa) 5.7532 R2 = 0.999 O2%(20kPa) = 18.619*mV(20kPa) 11.001 R2 = 0.9998 O2%(10kPa)= 40.947*mV(10kPa) 25.859 R2 = 0.9989 0 5 10 15 20 25 30 35 0123456 Sensor Output [mV]Oxygen Concentration (Sensor #2) [%] 50 kPa 40 kPa 30kPa 20kPa 10kPa Figure B-7. Oxygen sensor #2 calibration. Slope2 = 0.0479*P2 3.4467*P + 70.061 R2 = 0.9903 Intercept2 = -0.0315*P2 + 2.300*P 45.376 R2 = 0.9928 -30 -20 -10 0 10 20 30 40 50 01020304050Pressure [kPa]Slope2/Intercept2 Slope Intercept Figure B-8. Oxygen sensor #2 calibration. Load Cells The load cells of the scales were calibr ated against standard weights by linear regression analysis:

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122 massScale1 [g] = 188.84 mVout1 – 682.7 (B-9) massScale2 [g] = 207.64 mVout2 1259 (B-10) massScale3 [g] = 189.9 mVout3 – 624.67 (B-11) massScale4 [g] = 119.11 mVout4 – 1222.6 (B-12) massScale5 [g] = 215.86 mVout5 – 670.27 (B-13) The load cell calibration is shown in Figure B-9. m1 = 188.84*V1 682.7 R2 = 0.9999 m2 = 207.64*V2 1259 R2 = 0.9994 m3 = 189.9*V3 624.67 R2 = 1 m4 = 191.11*V4 1222.6 R2 = 1 m5 = 215.86*V5 670.27 R2 = 0.9996 0 100 200 300 400 500 600 700 800 900 1000 246810 Sensor Output [mV]mass [g] Scale 1 Scale 2 Scale 3 Scale 4 Scale 5 Figure B-9. Load cell calibration. Radiation The light sensor (LI-190SA, LI-Cor Inc.) wa s exposed to a variety of pressure and gas composition combinations. The sensor readin gs were not affected by pressure or gas mixture. Therefore, the factory calibration was used: Rad[ mol/(ms)]=mVout*1000/4.83 (B-14)

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123 Amplification of Lo w Voltage Sensors The sensors with an output in the mili volt range, such as the oxygen sensor, the light sensor and the scales had to be am plified in order be read correctly. Signal amplification was achieved by utilizing Burr-Brown’s Low Power Instrumentation Amplifier. The amplifica tion was set to 106.38 (50k /470 ). The amplification circuit is shown in Figure B-10. Figure B-10. Amplifier circuit.

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124 LIST OF REFERENCES Albright, L. D.; Gates, R.D. ; Arvanitis, K.G. and Drysdale, A. E. 2001. Plants on Earth and in Space. IEEE Control Systems Magazine 21(5): 28-41. American Aluminum Association. 1981. Engineering data for al uminum structures. Construction Manual Series. Section 3. Washington, DC. Andre, M. and Massimino, D. 1992. Growth of plants at reduced pressures. Experiments in wheat: technological adva ntages and constraints. Advances in Space Research 12(5): 97-106. Andre, M. and Richaud, C. 1986. Can plants grow in quasi-vacuum? In: CELSS 1985 Workshop. Ames Research Center. NASA Publication TM 88215: 395-404. American Society of Heating, Refrigerat ion and Air-Conditioning Engineers (ASHRAE). 2001. Handbook: Fundamentals SI Edition. Atlanta, GA: ASHRAE. Boardman, N.K. 1977. Comparative photos ynthesis of sun and shade plants. Annual Reviews of Plant Physiology 28: 355-377. Brown, D. and Lacey, R.E. 2002. A distributed control system for low pressure plant growth chambers. 2002 ASAE Annual International Meeting Paper No 02-3078. American Society of Agricultural Engineers. Chicago, IL. Bucklin, R.A.; Fowler, P.A.; Rygalov, V.Y.; Wheeler, R.M.; Mu, Y.; Hublitz, I. and Wilkerson, E.G. 2004. Greenhouse design for the Mars environment: Development of a prototype, deployable dome. Acta Horticulturae 659: 127-134. Carr, M. H. 1981. The surface of Mars. Yale University Press. New Haven, CT. Clawson, J. M.; Hoehn, A.; Stodiek, L. S. and Todd, P. 1999. AG-Pod The integration of existing technologies for efficient, affordable space flight agriculture. 29th International Conference of Environmental Systems. SAE Technical Paper Series, 1999-01-2176. Denver, CO. Corey, K. A.; Barta, D. J.; Edeen, M.A. and Henninger, D. L. 1997a. Atmospheric leakage and method for measurement of ga s exchange rates of a crop stand at reduced pressure. Advances in Space Research 20(10): 1861-1867.

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125 Corey, K. A.; Barta, D. J. and Henninger, D. L. 1997b. Photosynthesis and respiration of a wheat stand at reduced atmosphe ric pressure and reduced oxygen. Advances in Space Research 20(10): 1869-1877. Corey, K. A.; Barta, J.D. and Wheeler, R. M. 2002. Toward Martian agriculture: Responses of plants to hypobaria. Life Support & Biosphere Science 8: 103-114. Corey, K. A.; Bates, M.E. and Adams. S.L. 1996. Carbon dioxide exchange of lettuce plants under hypobaric conditions. Advances in Space Research 18 (4/5): 265-272. Daunicht, H. J. and Brinkjans, H. J. 1996. Plant responses to reduced air pressure: Advanced techniques and results. Advances in Space Research 18 (4/5): 273-281. Downs, R.J. and Hellmers, H.1975. Environment and the experimental control of plant growth. Academic Press Inc. Ltd. London, UK. Duffield, B. E. 2003. Advanced life support requirements document. JSC-38571, Revision C, National Aeronautics and Space Administration, Lyndon B. Johnson Space Center. Houston, TX. Eckart, P. 1996. Spaceflight life support and biospherics. Space Technology Library, Microcosm Press. Torrance, CA. Erickson, L.R. and Garrett, R.E. 1981. Atmo spheric pressure effect on vapor pressure deficit and potential moisture loss for horticultural commodities. Transactions of the ASAE 24: 252-254. Ferl, R.J.; Schuerger, A.C.; Paul, A.-L.; Gurley, W.B.; Corey, K and Bucklin, R.A. 2002. Plant adaptation to low atmospheric pressures: potential molecular responses. Life Support and Biosphere Science 8: 93-101. Fowler, P.A.; Bucklin, R.A.; Wheeler, R.M. and Rygalov, V.Y. 2002. Monitoring and control for artificial climate design. International Conference on Environmental Systems. Paper 02ICES-2286. Society of Automo tive Engineers. San Antonio, TX. Galambos, T.V. 1998. Guide to stability criteria for metal structures 5th Edition. John Wiley and Sons. New York, NY. Gatley, D. P. 2002. Understanding psychrometrics. American Society of Heating, Refrigeration and Air-Conditioning E ngineers (ASHRAE). Atlanta, GA. Gertner, B. 1999. Mars greenhouse study: Natural vs. artificial lighting. Lockheed Martin Space Mission Systems & Services Science, Engineering, Analysis, and Test. HDID-2G42-1167. Houston, TX. Goto, E.; Arai, Y. and Omasa, K. 2002. Grow th and development of higher plants under hypobaric conditions. International Conference on Environmental Systems. Tech Paper No. 2002-01-2439. Society of Auto motive Engineers. San Antonio, TX.

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126 Goto, E.; Ohta, H.; Iwabuchi, K. and Takakura, T. 1996. Measurement of net photosynthetic and transpira tion rates of spinach and maize plants under hypobaric condition. Journal of Agricu ltural Meteorology 52(2): 117-123. Haines, R. W. 1961. How to construct high-altitude psychrometric charts. Heating, Piping, and Air Conditioning 33(10): 144. Hanford, A.J. 2004. Advanced life support baseline va lues and assumptions document. NASA Technical Memorandum 208941. He, C.; Davies, F.T.; Lacey, R.E.; Drew, M.C. and Brown, D.L. 2003. Effect of hypobaric conditions on ethylene evoluti on and growth of lettuce and wheat. Plant Physiology 160: 1341-1350. Hitchcock, A. and Jacoby, G.C. 1980. Measurement of relative humidity in museums at high altitude. Studies in Conservation 25: 78-86. Hublitz, I. 2000. Engineering concepts for inflat able Mars surface greenhouses. MS thesis. Division of Astronautics, Techni sche Universitt Mnchen, Germany. Incropera, F.P. and DeWitt, D.P. 2002. Fundamentals of heat and mass transfer. 5th Edition. John Wiley and Sons. New York, NY. Iwabuchi, K.; Goto, E. and Takakura, T. 1996. Germination and growth of spinach under hypobaric conditions. Environmental Control in Biology 34(3): 169-178. Iwabuchi, K. and Kurata, K. 2003. Short-term and long-term effects of low total pressure on gas exchange rates of spinach. Advances in Space Research 31: 241-244. Kaplan, D. 1988. Environment of Mars, 1988. NASA Technical Memorandum 100470, NASA Johnson Space Center, Houston, TX. Kaplan, D.; Baird, R. S.; Flynn, H.F.; Ratli ff, J.E.; Baraona, C.R.; Jenkins, P.P.; Landis G.A.; Scheimann, D.A.; Johnson K.R.; and Karlmann, P.B. 2001. The 2001 Mars in-situ-propellant-produc tion precursor (MIP) flight demonstration: Project objectives and qualification test results. Space 2000 Conference and Exposition. AIAA-2000-5145. Long Beach, CA. Kennedy, K. J. 1999. Inflatable habita ts & greenhouse design: Technology & development for Mars implementation. In : R.M. Wheeler and C. Martin-Brennan (eds.) Mars greenhouses: Concep ts and challenges. NASA Technical Memorandum 208577. NASA Kenn edy Space Center, FL. Lacey, R.; Drew, M.; and Spanarkel, R. 2000. Low pressure systems for plant growth. In: R.M. Wheeler and C. Martin-Brennan (eds.) Mars greenhouses: Concepts and challenges. NASA Technical Memorandum 208577. NASA Kennedy Space Center, FL.

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127 Langhans, R.W. and Tibbitts, T.W. 1997. Plant growth chamber handbook. North Central Regional Research Publication No. 340. Iowa Agriculture and Home Economics Experimental Stati on Special Report No. 99. Mu, Y. 2005. A distributed control system for lo w pressure plant growth chambers. Ph.D. Dissertation. University of Florida. Musgrave M.E.; Gerth W.A.; Scheld H. W. and Strain B.R. 1988. Growth and mitochondrial respira tion of mungbeans ( Phaseolus aureus Roxb.) germinated at low pressure. Plant Physiology 86: 19-22. National Aeronautics and Space Administration (NASA). 2002. Advanced life support project plan. JSC-39168 (CTSD-ADV-348, Revision C). National Aeronautics and Space Administration, Lyndon B. Johns on Space Center, Houston, TX. National Aeronautics and Space Administration (NASA). 2004. Mars fact sheet. Accessed online 22 January 2005: http://nssdc.gsfc.nasa.gov/planetary/factsheet/marsfact.html Quebedeaux, B. and Hardy, R.W.F. 1973. Oxygen as a new factor controlling reproductive growth. Nature 243: 477–479. Rettberg, P.; Rabbow, E; Panitz, C. and Ho rneck, G. 2004. Biological space experiments for the simulation of Martia n conditions: UV radiation a nd Martian soil analogues. Advances in Space Research 33: 1294–1301. Rygalov, V.Y.; Bucklin, R.A.; Fowler, P.A. and Wheeler, R.M. 2000. Preliminary estimates of possibilities for deployable greenhouse for a planetary surface (Mars). In: R.M. Wheeler and C. Martin-Brennan (eds.) Mars greenhouses: Concepts and challenges. NASA Technical Memorandum 208577. NASA Kennedy Space Center, FL. Rygalov, V.Y.; Fowler, P.A.; Metz, J.M.; Wheeler, R.M. and Bucklin, R.A. 2002. Water cycles in closed ecological systems: Effects of atmospheric pressure. Life Support & Biosphere Sciences 8(3/4): 125-135. Shallcross, D.C. 1997. Handbook of psychrometric charts Humidity diagrams for engineers. Black Academic and Professional. London, UK. Schwartzkopf, S.H. and Mancinelli, R.L. 1991, Germination and growth of wheat in simulated Martian atmospheres. Acta Astronautica 25: 245-247. Spanarkel, R. and Drew, M.C. 2002. Germination and growth of lettuce (Lactuca sativa) at low atmospheric pressure. Physiologia Plantarum 116: 468-477. Tibbitts, T. W. 1979. Humidity and plants. BioScience 29(6): 358-363.

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128 Wheeler, R.M. 2000. Can CO2 be used as a pressurizing gas for Mars greenhouses? In: R.M. Wheeler and C. Martin-Brennan (eds.) Mars greenhouses: Concepts and challenges. NASA Technical Memorandum 208577. NASA Kennedy Space Center, FL. Wheeler, R.M.; G.W. Stutte; G.V. Subbarao and N.C. Yorio. 2001. Plant growth and human life support for space travel. In: M. Pessarakli (ed.) Handbook of plant and crop physiology 2nd Edition: 925-941. Wilkerson, E.G. 2005. Plant evapotranspiration in a greenhouse on Mars. Ph.D. Dissertation. University of Florida.

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129 BIOGRAPHICAL SKETCH Inka Hublitz was born on August 2nd, 1975, in Bavaria’s Capital “Mnchen” (Munich), Germany. In 1994 she enrolled in mechanical engineeri ng at the Technical University of Munich (TUM). While studying in Munich she participated in the LunarSat Project, the ambitious plan to send a micro orbiter, built by various universities, to the Moon. As Inka was always interested in other cultures and languages she studied two semesters as an exchange student at th e University of Crdoba, Argentina. Inka did the research for her master’s thesis on “Engineering Concepts for Inflatable Mars Surface Greenhouses” during a six month stay at NASA’s Johnson Space Center in Houston, Texas. During her resear ch she met her Ph.D. advisor, Prof. Ray A. Bucklin. In 2000 she graduated with a “Diplo m Ingenieur” degree (equivalent to US bachelor and master’s Degree) in mechanical engineering. After her graduation, Inka accepted a pos ition at the Brazilian Space Research Institute INPE in So Paulo, Brazil, where she worked in the thermal division of the satellite integration and test laboratory. In 2001 she decided to venture back to th e United States and to pursue a Ph.D. degree in Agricultural and Biological Engineer ing at the University of Florida. During her Ph.D. program she was the leader of Univ ersity of Florida’s team participating in NASA’s MarsPort engineering competition. He r team won an award for being one of six finalists in the nationwide competition.

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130 In 2004 she was awarded a scholarship by the German and European Space Agency to participate at the Summer Session Program of the Internationa l Space University in Adelaide, Australia. After the completion of her Ph.D. degr ee, Inka is looking forward to new adventures and challenges, hopefully addi ng numerous countries and new fields of interest to her long list.


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HEAT AND MASS TRANSFER OF A LOW PRESSURE MARS GREENHOUSE:
SIMULATION AND EXPERIMENTAL ANALYSIS

















By

INKA HUBLITZ


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


2006

































Copyright 2006

by

Inka Hublitz

































I dedicate this dissertation to my parents, Melitta and Bruno Hublitz, who have always
supported my adventures and endeavors. Their love and guidance encouraged me to
follow my dreams and to reach innumerable goals.















ACKNOWLEDGMENTS

First and foremost, I would like to express my deepest gratitude to my major

advisor, Dr. Ray Bucklin, for giving me the unique opportunity to complete my Ph.D.

program under his guidance. Furthermore, I am thankful that Dr. Bucklin encouraged me

to participate in various conferences and international events, such as the International

Space University's Summer Session Program in Australia. With his help I have

constantly increased my network of colleagues working in relevant fields. Dr. Bucklin's

help in realizing my stay at NASA's Kennedy Space Center was also highly appreciated.

I also acknowledge the members of my supervisory committee for their huge

amount of support and advice. I especially would like to thank

* Dr. Jim Leary for his positive attitude that helped me enrich my people skills.

* Dr. Khe Chau for providing me with lab space.

* Dr. Raymond Wheeler for introducing me to Dr. Bucklin during my master's thesis
research and for helping to organize my stay at NASA's Kennedy Space Center.

* Dr. David Hahn for his quick responses to all my questions and for being much
more involved in the project than an external committee member generally is.

I am grateful to Dr. Sencer Yeralan for sharing his great expertise in the field of

microcontrollers. At NASA's Kennedy Space Center I thank Dr. Vadim Rygalov, Dr.

Phil Fowler and Dr. John Sager for their support. I am thankful to Dr. Hartwell Allen for

teaching me how to grow plants and providing me with the right equipment. Bob

Tonkinson's, Billy Duckworth's and Steve Feagle's hard work was always greatly

appreciated.









My family and my husband, Sharath Cugati, deserve special thanks for their

emotional and technical support. My gratitude also extends to my friends Dr. Peter Eckart

and Dr. Kristian Pauly, for introducing me to the field of space life support systems and

biospherics.
















TABLE OF CONTENTS



A C K N O W L E D G M E N T S ................................................................................................. iv

LIST OF TA BLE S ........ ............................................... .......... .... ...... ....... ix

LIST OF FIGURES ......... ......................... ...... ........ ............ xi

A B S T R A C T .......................................... ..................................................x v

CHAPTER

1 IN TR OD U CTION ............................................... .. ......................... ..

Low Pressure M ars G reenhouses............................................ ........... ...............
Structure of the D issertation ........................................................................... .... ... 3

2 LITER A TU R E REV IEW ............................................................. ....................... 4

A advanced L ife Support.................................................................. ...................... 4
Mars Environment ...................... ............................ .....................6
Plant Requirements and Environment Control.....................................................10
T em p eratu re ............................................................................... 1 1
Tem perature effect .............................................. ..... .................... 11
Temperature control ..................................................... ...... ........... 12
R elative H um idity ..................................................... .. .. ...... .......... 12
R elative hum idity effect .................................... .... ..................................... 12
R elative hum idity control ................................... .............................. ...... 13
Atmospheric Pressure and Composition ........................................ .........13
C arbon dioxide effect ........................................................ ............. 13
C arbon dioxide control ........................................... ................................ 14
Oxygen effect .................................... .......................... .. ........14
O oxygen control ................................................................ ............... 15
V apor pressure effect and control ..................................... ............... ..15
Pressurizing gas .................. ........................... .... .. .. ............... 15
V e n tila tio n .................................................................. .................................1 5
R a d ia tio n ..............................................................................................................1 6
Radiation effects.............. .... ...................... .. ......16
Radiation control .......................................... ............. ... .......... 17
G row th A rea .................................................................... ......... 19









Low Pressure Plant G row th Studies ............................ ............................. ........... 19

3 OBJECTIVES OF THIS STUDY ........................................ ......................... 23

4 EXPERIM EN TAL W ORK ............................................... ............................. 24

System D description ........... ............ ............................ .. .. .. ...... ........... 24
Instrum entation and Sensor Calibration .......................................... ............... 28
L eak ag e T estin g ..................................................... ................ 32
Leakage of Vacuum Chamber....................................................................... 32
Leakage of Greenhouse D om e ........................................ ........................ 34
D ata Acquisition and Control System ............................................. ............... 36
Greenhouse Dome Environmental Control ..................................... ...............37
Gas Composition and Total Pressure Control Algorithm.............................. 37
A ir Tem perature Control A lgorithm ........................................ .....................39
Heat and Mass Transfer Experiments without Plants ...........................................41
Heat and Mass Transfer Experiments with Plants .............................................50
Medium-term Plant Experiment involving Buttercrunch Lettuce.....................50
Long-term Plant Experiment involving Galactic Lettuce ..................................56

5 MATHEMATICAL MODEL DEVELOPMENT ............................................... 65

Effect of Low Pressure on Heat and Mass Transfer.................................... 65
C onvection H eat Transfer............................................ ............................ 65
Laminar flow over a horizontal plate ................................. ............... 67
Turbulent flow over a horizontal plate................................. ... ..................68
Laminar free convection on a vertical plate.............................................. 69
External free convection for a sphere................................... ... ..................70
Mass Transfer by Evaporation.................... ........... ................71
Development of Low Pressure Psychrometrics for Non-Standard Atmospheres .......72
G as T h eory ........................................................................73
E quation of state ........................................... ........ .. .. .. .. ............ 73
D ry gas m ixture .................. .......................... .................... .. 74
W ater vapor com ponent .................................... ....... ................... 75
Construction of Modified Psychrometric Chart ...............................................75
S atu ration lin e ............................................................7 5
H um idity isolines ..................... .......... ............... .... ..... .. 77
Specific enthalpy isolines....................................... .......................... 78
Specific volum e isolines......................................... .......................... 78
V apor pressure isolines .......................................... .......................... 79
Adiabatic saturation temperature isolines .......................................... 79
D ew -point tem perature isolines ............................... ..... .................. .... 80
One-dimensional Steady State Heat Transfer Model of the Greenhouse Dome........83
O overall Therm al R resistance M odel ........................................... ............... .... 83
Individual Thermal Resistances and Thermal Coefficients ................................. 84
Total Thermal Resistance .................... ......... .. ..... ...................90
Comparison of Radiation and Convection in the Chamber at Mars Pressure .....92









Transient Heat Transfer Model for Greenhouse Temperature Simulation ...............93

6 RESULTS AND CONCLUSION...................... ..... ........................... 98

7 FU TU R E W O R K ................................................................................. ........ 100

APPENDIX

A STRUCTURAL ANALYSIS OF DOME SHELL, BASE PLATE AND
CYLINDRICAL CALIBRATION CHAMBER ............................................... 102

Structural Analysis of the Spherical Greenhouse Dome .........................................102
Structural Analysis of Base Plate for Greenhouse Dome................... ..............103
Structural Analysis of the Base Plate without Additional Bracings................ 104
Structural Analysis of the Base Plate with Additional Bracings.......................106
Structural Analysis of Cylinder used as Sensor Calibration Chamber.....................112
M aximum Allowable Pressure ....................................................................... 112
Short cylinder behavior .................................... ............................. ....... 113
Interm ediate cylinder behavior................. ...............................................113
Long cylinder behavior ................................................... ....... ........ 114
A x ial B u ck lin g .................................................................................. 1 14
W all Yielding .................................... .......................... ............115

B SEN SOR CA LIBR A TION ................................................................................. 116

P re ssu re ............................................................................... 1 16
T em perature ................................................................................................... ....... 117
R elative H um idity ......................................................... ................ 117
Carbon D ioxide Concentration .......................................................... ............... 118
O oxygen C concentration ................................................................... ... .................. 119
L o ad C ells .........................................................................12 1
R radiation ................................................................................................... ..... 122
Amplification of Low Voltage Sensors ...........................................................123

L IST O F R E FE R E N C E S ........................................................................ ................... 124

BIOGRAPHICAL SKETCH ............................................................. ............... 129
















LIST OF TABLES


Table page

2-1 Human metabolism values per crew member and per day (CM-d) for average
a ctiv ity lev e l. ..............................................................................................................5

2-2 Environm ent properties. ............................................................ ........................ 8

2-3 Atm osphere com position by volum e...................................... ........................ 8

2-4 Plant environm ent require ents..................................... ............................ ........ 10

2-5 Advanced life support crop growth conditions. ...................................................11

4-1 Sensors used to measure environmental parameters, the sensor ranges and
accuracies. ...........................................................................29

4-2 Steady state temperature distribution under different freezer temperature, light
and heating pow er conditions ...................................................................... ...... 44

4-3 Buttercrunch lettuce environmental conditions and their control ..........................53

4-4 Evaporation rates per scale with scales 2-5 containing two lettuce plants each. .....55

4-5 Galactic lettuce environmental conditions and their control............................... 57

5-1 Effect of reduced pressure on convective heat transfer coefficient and mass
diffusion coefficient. ........................... ................ ................... .. .....71

5-2 Psychrometric parameters of a low pressure atmosphere (76% N2, 20% 02, 4%
CO2) with initial conditions of 20 kPa dry air at 200C and a constant specific
volume of 0.004138m3/kg. ............................ ............... 80

5-3 Steady state temperature data of the long-term experiment involving Galactic
lettuce plants.................... ...... .... .... ................. ........... ............ 86

5-4 Thermal resistances and coefficients based on the data obtained of the long-term
experiment involving Galactic lettuce plants. ................... ........................ 87

5-5 Simulated temperatures based on the thermal resistance model............................89

5-6 Comparison of measured and simulated temperature values............................. 90









5-7 Comparison of convection heat transfer to radiation heat transfer in the chamber
at a pressure of 0.6 kPa............................................ .. ......93

A-1 Structural analysis of base plate without and with additional bracings ...............12
















LIST OF FIGURES


Figure p

1-1 "Astronaut" approaching University of Florida's Mars Greenhouse Dome. .............2

2-1 Martian spectral irradiance (Ls=250, 15S, noon) vs. terrestrial spectral
irradiance ........... .................................................... .. .................... 9

2-2 Average solar irradiance of Mars compared to Earth............... ..... .............. 10

2-3 P hotosynthetic efficiency ........................................... ........................................ 16

4-1 Dome used to protect plants from the simulated low pressure, low temperature
Mars environment. A) Empty dome. B) Dome with sensors, scales and flasks
in stalled .......................................................... ................ 2 5

4-2 Vacuum chamber used to simulate the low pressure Mars environment (less than
1% of Earth's atmosphere). .............. ..... ......... .... ............... 26

4-3 Industrial walk-in freezer ensures low temperature of the vacuum chamber
(sim ulated M ars environm ent). ........................................ .......................... 26

4-4 Schematic of experimental setup.................................................... 28

4-5 Cylinder used for calibration of pressure-sensitive sensors and for initial gas
mixing control algorithm development. ........................................ ............... 30

4-6 Comparison of Honeywell capacitance RH sensors to the HMP 237 reference
RH sensor for pressures of 0 to 25 kPa. ........................................ ............... 31

4-7 Forces on chamber window. A) Vacuum chamber at 0.6 kPa with top window
bulging in. B) Gasket drawn into the chamber due to pressure difference .............33

4-8 Dome and chamber leakage with gas resupply and vacuum pumps turned off at a
tem perature of-10 C. ................................................... .... ... ......... 35

4-9 Comparison of vacuum chamber and greenhouse dome leak rates to values of
other low pressure plant growth studies (leak rate is presented in logarithmic
sc ale) ...................................................... .... ................. 3 5

4-10 Gas mixing of dome greenhouse atmosphere without plants (oxygen set point at
4.0 kPa and carbon dioxide set point at 0.5 kPa). ............. ....................... ......... 38









4-11 Pressure control of vacuum chamber (set point 0.6 kPa) and greenhouse dome
(set points 20 kP a). ......................................................................39

4-12 Air temperature control of greenhouse dome (set point at 20 oC) .........................40

4-13 Sensor locations for heat and mass transfer experiments without plants.................41

4-14 Preparation of the steady state experiments. A) Bottom of dome base with foam
insulation. B) Side view of greenhouse dome with the sensors and scales
installed. C) Top view of greenhouse dome without shell. D) Installation of
greenhouse dome into the vacuum chamber. ................................ ..................42

4-15 Temperature readings until steady state is achieved. (0 C freezer temperature,
26 W heating power and light switched off). ................................ ..................43

4-16 Steady state temperatures versus power of heater at seven different locations
(T1-T7). Freezer temperature is 0 C and the growth light is switched off...............44

4-17 Steady state temperatures versus power of heater at seven different locations
(T1-T7). Freezer temperature is -10 C and the growth light is switched off. ..........45

4-18 Steady state temperatures versus power of heater at seven different locations
(T1-Ty). Freezer temperature is -20 C and the growth light is switched off. ..........45

4-19 Steady state temperatures versus power of heater at seven different locations
(T1-T7). Freezer temperature is -10 C and the growth light is switched on............46

4-20 Steady state temperatures versus power of heater at seven different locations
(T1-T7). Freezer temperature is -20 C and the growth light is switched on............46

4-21 Steady state air temperatures (T3) versus power of heater for freezer
temperatures of 0 oC, -10 C and -20 C (growth light switched off).....................47

4-22 Freezer temperature versus power of heater for steady state air temperatures (T3)
of 15 C 20 C and 25 C ................... .............................................................. 48

4-23 Condensation inside of greenhouse shell with a greenhouse air temperature of 20
C. A) Freezer temperature at 0 C. B) Freezer temperature at -20 "C...................50

4-24 Buttercrunch lettuce in Ehrlenmeyer flask. A) The average height of the shoot
zone is 15 cm. B) Putty and a stopper prevent evaporation of the hydroponic
solution as they separate the root from the shoot zone. .........................................51

4-25 Installation of flasks containing the lettuce plants onto the scales...........................52

4-26 Constant temperature distribution and varying relative humidity during the
buttercrunch lettuce experim ent. ........................................ ......................... 53









4-27 Plant evapo-transpiration rates of plants from 5 to 10 hours after the beginning
of the experim ent .................. ............. ........ ..... ............... .... 55

4-28 Lettuce plants after an exposure of 36 hours to the controlled Mars greenhouse
environment. Healthy plant without any visible physical damage on the left side,
wilted plant with roots that do not reach water and nutrient supply on the right
sid e ................................................................................ 5 6

4-29 Galactic lettuce plant for long-term experiments with an average height of 8 cm. .57

4-30 Sensor locations for the long-term experiments with galactic lettuce plants...........58

4-31 Temperature variations during the long-term galactic lettuce experiment. .............59

4-32 Comparison of steady state temperature distribution of the day cycle to the night
cycle during the long-term plant experiments.................. ................ ............... 60

4-33 Relative humidity variation during the day and night cycle. ..................................61

4-34 Gas composition control of the greenhouse atmosphere. Set points are 20 kPa
for total pressure, 4 kPa for oxygen partial pressure and 0.8 kPa for carbon
dioxide partial pressure. ................................................ ............................... 62

4-35 Water evaporation measured on scale 2 and 3 during the galactic lettuce plant
ex p erim e n t ........................................................................ 6 3

4-36 Galactic lettuce plants after exposure of seven days to the low pressure Mars
greenhouse environm ent. ............................................... .............................. 63

4-37 Visible damages of the plants. A) and B) Wilting/drying of the plant leaves..........64

5-1 Effect of pressure on the saturation line of an open system with standard
atm osphere composition.............................. ............................... 72

5-2 Psychrometric chart of low pressure atmosphere (76% N2, 20% 02, 4% CO2)
with initial conditions of 20 kPa dry air at 200C and a constant specific volume
of 0.00413 8m3/kg. .............. ......... ....... .... ........... ............. 82

5-3 Heat transfer of greenhouse dome and thermal resistance circuit .........................84

5-4 Emissivities of the polycarbonate dome and the stainless steel chamber (light
o ff) ........ ........ ........................................................................8 7

5-5 Emissivities of the polycarbonate dome and the stainless steel chamber (light
on ).............. ..................... .................................... ......... ...... 8 8

5-6 Required heating power versus temperature difference of the dome air to the
freezer. Slope of linear regression is the total thermal resistance (light off). ..........91









5-7 Required heating power versus temperature difference of the dome air to the
freezer. Slope of linear regression is the total thermal resistance (light on). ...........91

5-8 Simulation of greenhouse atmosphere, dome and vacuum chamber temperatures
(light off, 51W heating power, -10 C freezer temperature) ..................................96

5-9 Simulation of greenhouse atmosphere, dome and vacuum chamber temperatures
(light off, 77 W heating power, -10 C freezer temperature). ........................... 96

5-10 Simulation of greenhouse atmosphere, dome and vacuum chamber temperatures
(light off, 103 W heating power, -10 C freezer temperature) ...........................97

5-11 LabView front panel of overall model for simulation .........................................97

7-1 Ice building up on the bottom part of the greenhouse shell. A) Overview. B)
Detailed view of the ice-crystals. .................... .......................... ............... 101

A-i Bottom view of greenhouse dome base.......................................................103

A-2 Triangular load over full beam.......................... ............................... 104

A-3 Trapezoidal load over part of the beam................................ ...............106

A-4 First part of superposition: uniform load for x>a............................107

A-5 Second part of superposition: triangular load for x>a.................. .. ..................108

A-6 Bending moments of beam for trapezoidal load varies with the distance a of the
additional bracing. ............................................... ............. .. ........ .. 110

B -l Pressure sensor #1 calibration. ................................................................... ....... 16

B -2 Pressure sensor #2 calibration. ...................................................................... ....117

B-3 Carbon dioxide sensor calibration ....................................................................... 118

B-4 Carbon dioxide sensor calibration ............... ............. ....................... 119

B -5 O xygen sensor #1 calibration ......... ........................................................ ....... 120

B-6 Oxygen sensor #1 calibration ............... .. ................. ..... .......... 120

B -7 O xygen sensor #2 calibration .................................................................... ....... 121

B -8 O xygen sensor #2 calibration .................................................................... ....... 121

B -9 L oad cell calibration ......... .......................................................... ............... 122

B -10 A m plifier circuit. ...................... ...... ................ .. .. .... ..................123















Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

HEAT AND MASS TRANSFER OF A LOW PRESSURE MARS GREENHOUSE:
SIMULATION AND EXPERIMENTAL ANALYSIS
By

Inka Hublitz

May 2006

Chair: Ray A. Bucklin
Major Department: Agricultural and Biological Engineering

Biological life support systems based on plant growth offer the advantage of

producing fresh food for the crew during a long surface stay on Mars. Greenhouses on

Mars are also used for air and water regeneration and waste treatment. A major challenge

in developing a Mars greenhouse is its interaction with the thin and cold Mars

environment. Operating a Mars greenhouse at low interior pressure reduces the pressure

differential across the structure and therefore saves structural mass as well as reduces

leakage.

Experiments were conducted to analyze the heating requirements as well as the

temperature and humidity distribution within a small-scale greenhouse that was placed in

a chamber simulating the temperatures, pressure and light conditions on Mars. Lettuce

plants were successfully grown inside of the Mars greenhouse for up to seven days. The

greenhouse atmosphere parameters, including temperature, total pressure, oxygen and









carbon dioxide concentration were controlled tightly; radiation level, relative humidity

and plant evapo-transpiration rates were measured.

A vertical stratification of temperature and humidity across the greenhouse

atmosphere was observed. Condensation formed on the inside of the greenhouse when

the shell temperature dropped below the dew-point. During the night cycles frost built up

on the greenhouse base plate and the lower part of the shell. Heat loss increased

significantly during the night cycle. Due to the placement of the heating system and the

fan blowing warm air directly on the upper greenhouse shell, condensation above the

plants was avoided and therefore the photosynthetically active radiation at plant level was

kept constant. Plant growth was not affected by the temperature stratification due to the

tight temperature control of the warmer upper section of the greenhouse, where the

lettuce plants were placed.

A steady state and a transient heat transfer model of the low pressure greenhouse

were developed for the day and the night cycle. Furthermore, low pressure psychrometric

relations for closed systems and modified atmospheres were generated to calculate the

properties of the moist air in order to predict condensate formation. The results of this

study improve the design of the environmental control system leading to an optimization

of plant growth conditions.














CHAPTER 1
INTRODUCTION

Low Pressure Mars Greenhouses

Mars greenhouses are important components of the human Mars mission

infrastructure as plant-based life support systems offer self-sufficiency and possibly cost

reduction. Resupply is prohibitive for long duration Mars missions as it increases the

launch mass and consequently the launch costs. Relying on frequent resupply from Earth

also increases risk to the astronauts. Greenhouses produce edible biomass as well as

regenerate the air and water through photosynthesis.

The atmospheric surface pressure on Mars is on average 0.61 kPa, i.e., below 1% of

Earth's standard atmospheric pressure (NASA, 2004). Operating a greenhouse at low

interior pressure reduces the pressure differential across the structure and therefore saves

structural mass as well as reduces leakage. Studies have shown that plant growth is

feasible at pressures as low as 20 kPa; plants even survive short-term exposure to

pressures as low as 10 kPa (Andre and Richaud, 1986; Fowler et al., 2002). Inflatable

greenhouse structures are being studied as they offer the advantage of a high volume to

mass ratio, and can be packed efficiently for the transit, reducing the number of launches

(Clawson et al., 1999; Kennedy, 1999; Hublitz, 2000).

A major challenge in developing a Mars greenhouse is its interaction with the thin

and cold Mars environment. The environmental conditions inside the greenhouse have to

be controlled within the ranges where plants are highly productive. Transparent structures

capture day-time solar radiation that is required for photosynthesis and heating of the









greenhouse, whereas during the night they have to be covered with multi-layered

insulation to avoid heat loss (Hublitz, 2000).

Most experimental Mars greenhouse studies have focused on the ability of plants to

grow at reduced pressures with non-standard atmosphere compositions, but little research

has been done on the thermal interactions of the greenhouse with the Mars environment.

The heat and mass transfer analysis is an important step in the design of the thermal

control system that provides the climatic environment essential for plant growth.


Figure 1-1. "Astronaut" approaching University of Florida's Mars Greenhouse Dome.









Structure of the Dissertation

Chapter 1 introduces the importance of research on the heat and mass transfer of

low pressure Mars greenhouses and gives an outline of this dissertation. Chapter 2 states

the objectives of advanced life support systems, summarizes the fundamental knowledge

of the Mars environment and reviews the literature on low pressure plant growth studies.

The objectives of this dissertation are discussed in Chapter 3. Chapter 4 describes the

setup of the experimental work, the data acquisition and the control system. Data of the

heat and mass transfer experiments with and without plants are presented. The

mathematical model development and simulation results are discussed in Chapter 5.

Chapter 6 gives results and conclusions; Chapter 7 states recommendations for future

studies. The structural analyses of the greenhouse dome and sensor calibration cylinder as

well as the sensor calibration are included in the appendices.














CHAPTER 2
LITERATURE REVIEW

Advanced Life Support

The goal of NASA's Advanced Life Support (ALS) Project (National Aeronautics

and Space Administration (NASA), 2002), is to "provide life support self-sufficiency for

human beings to carry out research and exploration productively in space for benefits on

Earth and to open the door for extended on-orbit stays and planetary exploration."

For long-duration missions open loop life support systems have to be replaced by

closed loop life support systems, in order to avoid the high costs associated with the

launch and storage of consumables and high risk of relying on frequent resupply

missions. Advanced life support systems should not only provide a high degree of closure

of the air and water loop, but also begin to close the food loop (Eckart, 1996).

In contrast to the life support systems for the current short-duration missions,

biological processes, in addition to physico-chemical processes, such as food production

utilizing higher plants will be implemented for long-duration missions (Duffield, 2003).

Valuable chemicals will be recovered by processing solid waste. In-situ resources, where

available, may also be used to replenish life support consumables. Consumables for

human space missions amount to approximately 31 kg of oxygen, water and food per

astronaut and per day as listed in Table 2-1. Simultaneously, the same amount of waste is

created. Physico-chemical life support systems can provide oxygen, reduce carbon

dioxide and recycle water, whereas biological life support systems can fulfill all these

functions and additionally produce food (Eckart, 1996).









Table 2-1. Human metabolism values per crew member and per day (CM-d) for average
activity level.
Consumable Units Needs Effluents
Air
Carbon Dioxide Load kg/CM-d 1.00
Oxygen Consumed kg/CM-d 0.84
Food
Mass of Consumed Food (dry basis) kg/CM-d 0.62
Energy of Consumed Food MJ/CM-d 11.82
Potable Water Consumed (incl. water in food) kg/CM-d 3.91
Thermal
Sensible Metabolic Heat Load MJ/CM-d 6.31
Latent Metabolic Heat Load MJ/CM-d 5.51
Waste
Fecal Solid Waste (dry basis) kg/CM-d 0.03
Perspiration Solid Waste (dry basis) kg/CM-d 0.02
Urine Solid Waste (dry basis) kg/CM-d 0.06
Water
Fecal Water kg/CM-d 0.09
Respiration and Perspiration Water kg/CM-d 2.28
Urine Water kg/CM-d 1.89
Hygiene Water
Hygiene Water (Flush, Hand Wash, Shower, kg/C d
4 \kg/CM-d 25.58
Laundry, Dish Wash)
Greywater kg/CM-d 25.58
Total Mass kg/CM-d 30.95 30.95
Total Energy MJ/CM-d 11.82 11.82
Source: Hanford, 2004.

The objectives of ALS systems based on plant growth are to (NASA, 2002)

* Produce food that meets human requirements for nutrition, sensory acceptability
and food safety.

* Provide the environmental and cultural requirements to produce crops, including
efficient environmental control (temperature, relative humidity, gas composition),
the lighting intensity and spectral composition, the growth area, and nutrient
delivery system.

* Provide post-harvest processing, materials handling and storage of harvested
products.

* Utilize resources recovered from other life support systems, including carbon
dioxide, waste water and solid wastes.

* Provide non-food products to other life support systems for utilization, further
processing or disposal, including oxygen, transpired water, heat and inedible
biomass.









* Minimize required involvement of the crew in life support operations.

* Minimize the impact of life support on planetary environments.

For the development of bioregenerative life support systems for Mars, it is critical

to develop models to predict system behavior in the planetary environment and to

evaluate the performance through experiments in a simulated Mars environment.

Mars Environment

The Mars environment differs from that on Earth in several significant ways

including lower gravity, very low density atmosphere rich in carbon dioxide, reduced

light levels and very cold ambient temperatures.

The Mars atmosphere is highly variable on a daily, seasonal and annual basis. The

thinness of the atmosphere and the lower solar constant (which is 43% of the terrestrial

value) guarantee a large daily temperature range at the surface under clear conditions. On

an annual basis, the atmospheric pressure at the surface changed from 0.69 to 0.9 kPa at

the Viking 1 lander site due to condensation and sublimation of CO2 (NASA, 2004). The

mean atmospheric pressure is estimated at 0.64 kPa.

Although Mars has no liquid water and its atmospheric pressure is approximately

1.0 percent that of Earth, many of its meteorological features are similar to the terrestrial

ones. Water ice clouds, fronts with wind shifts and associated temperature changes

similar in nature to those on Earth can be found. The main differences between the Earth

and the Mars atmosphere are that the Mars atmosphere does not transfer as much heat by

conduction and convection as the Earth atmosphere and it cools much faster by radiation.

Mars' diurnal temperature cycle is larger than Earth's: 184 to 242 K during the summer

but stabilized near 150 K (CO2 frost point) during the winter (Kaplan, 1988; NASA,

2004). Water ice clouds occur due to many different causes just as on Earth. Nighttime









radiation cooling produces fogs; afternoon heating causes drafts which cool the air and

cause condensation; flow over topography causes gravity clouds; and cooling in the

winter polar regions causes clouds (Kaplan, 1988).

Mars has local dust storms of at least a few hundred kilometers in extent. The

duration and extent of Martian dust storms vary greatly. Dust storms of planetary scale

may occur each Martian year with a velocity of up to 30 m/s. Unfortunately, neither Earth

based nor spacecraft observations have been systematic enough to quantify the frequency

of dust storm occurrence or even the true extent of many individual storms. There is no

reliable method for prediction of great dust storms. They mainly occur during southern

spring and summer. Local dust storms have been observed on Mars during all seasons,

but they are most likely to occur during the same periods as the great dust storms. The

physical grain size of the drifting material is estimated to be 0.1 to 10 im. It has the

characteristics of very fine grained, porous materials with low cohesion (Kaplan, 1988).

The dust raised into the atmosphere by dust storms and the ordinary atmospheric

dust always present in the atmosphere settle out of the atmosphere onto any horizontal

surface. Measurements made by the Pathfinder Mission showed a 0.3% loss of solar array

performance per day due to dust obscuration (Kaplan et al., 2000). This dust deposition

could be a significant problem for a greenhouse operated with solar light for long

duration missions, unless a technique is developed to remove the dust periodically or

prevent settled dust from coating the greenhouse surface.

The Mars atmosphere consists mainly of carbon dioxide (95.3%). Photosynthesis

requires carbon dioxide which could be taken out of the planet's carbon dioxide rich










atmosphere, in case of an autonomous greenhouse that is pre-deployed before the first

humans arrive.

In Table 2-2 the Mars environment properties are summarized. Table 2-3 describes

the composition of the atmosphere of Mars in terms of the gases present by volume.

Table 2-2. Environment properties.


Property


Value Mars


Orbit period
Rotation period (day length)
Gravity
Surface Pressure



Surface density
Average temperature
Diurnal temperature range

Wind speeds

Solar irradiance in orbit


687 days
24.62 hours
3.69 m/s2
~ 0.64 kPa (variable, depending on
season and location)
0.69 to 0.9 kPa at Viking 1 lander site
(22 N lat.)
-0.020 kg/m3
-210K
184 to 242 K (summer)
150 K (winter)
2 to 7 m/s (summer)
5 to 10 m/s (fall)
589 W/m2


Value Earth
365 days
23.93 hours
9.81 m/s2
101.4 kPa
(at sea level)


1.217 kg/m3
288 K
283 to 293 K

0 to 100 m/s

1368 W/m2


Drifting material
Size 0.1 to
Cohesion 1.6+1
Source: Carr, 1981; Kaplan, 1988; NASA, 2004.


Table 2-3. Atmosphere composition by volume.
Gas Value Mars
Carbon Dioxide (COz) 95.32 %
Nitrogen (N2) 2.7 %
Argon (Ar) 1.6 %
Oxygen (02) 0.13%
Carbon Monoxide (CO) 0.08%
Water (H20) 210 ppm


Nitrogen Oxide(NO)
Neon (Ne)
Hydrogen-Deuterium-Oxygen (HDO)
Krypton (Kr)
Xenon (Xe)
Helium (He)
CH4
Hydrogen (H2)
Source: NASA, 2004.


100 ppm
2.5 ppm
0.85 ppm
0.3 ppm
0.08 ppm


Value Earth
0.035 %
78.084%
0.93%
20.946%

Highly variable
(typically 1%)

18.18 ppm

1.14 ppm

5.24 ppm
1.7 ppm
0.55 ppm


10 gm
.2 kPa


I










The solar irradiance varies as a function of season, latitude, time of day and optical

depth of the atmosphere. The solar irradiance incident on the surface of Mars consists of

two components: the direct beam and the fuse component. The fuse component

comprises the scattering by small particles in the atmosphere and the diffuse skylight.

The solar radiation on Mars varies according to the eccentricity of the Mars orbit. The

mean solar radiation in Mars orbit is 589 W/m2. The ultraviolet radiation that reaches the

Mars surface is much greater than on Earth, because the Martian atmosphere is more

tenuous and there is very little ozone. The ultraviolet radiation is mainly absorbed by

carbon dioxide; all ultraviolet radiation with a wavelength less than 200 nm is absorbed

by the atmosphere (Kaplan, 1988). The available photosynthetically active radiation

(PAR) changes throughout the Mars season. The average PAR is estimated to be 20.8

mol/(m2 day) (Gertner, 1999).

Figure 2-1 depicts the spectrum of the solar radiation on Mars. Dust affects both the

intensity and the spectral content of the sunlight. The solar irradiance on the surface of

Mars during a global dust storm is comparable to the one of a cloudy day on Earth (see

Figure 2-2).


10o .. ,-
100
Martian "sl a / 1r
irradiance 2
E 10-'
o r ( terrestrial
S 10.n 2 ( Irradiance




104-


10--
200 250 300 350 400
wavelength I nm
Figure 2-1. Martian spectral irradiance (L,=250, 15'S, noon) vs. terrestrial spectral
irradiance (Rettberg et al., 2004)











N' 1600
E 100%
S1400

w 1200

.2 1000
"a
56.6%
L 800
l 43%
m 600

400
5.7% 13% 6.5%
200

0
Earth Orbit Earth Earth Mars Orbit Mars Mars Mars
Surface Surface Surface Surface Surface
(Clear) (Cloudy) (Clear) (Cloudy (Cloudy -
Local Global
Storm) Storm)
Figure 2-2. Average solar irradiance of Mars compared to Earth (Clawson et al., 1999).

Plant Requirements and Environment Control

High yields in plant growth chambers can be achieved by controlling temperature,

relative humidity, atmosphere pressure and composition, ventilation, light intensity and

spectral quality, water and nutrient delivery. Table 2-4 lists the minimum, maximum and

optimum environmental parameters. The optimal growth conditions depend on the type

of crop. A list of crops identified for ALS application and the required environmental

condition is shown in Table 2-5.

Table 2-4. Plant environment requirements.
Parameter Unit Low Value High Value Optimal Value
Temperature C +5.0 +35 +20 to +27
Atmospheric kPa 10.0 (?) 100 100
Pressure
Photosynthetically W/m2 50 500 150 to 200
active radiation
Partial Pressure CO2 kPa 0.03 3.0 to 5.0 0.1 to 0.2
Partial Pressure 02 kPa 5.0 27 to 30 10(?) to 22
Relative Humidity % 55 100 70 to 85
Source: Rygalov et al., 2000.










Table 2-5. Advanced life support crop growth conditions.
Photo- Growth
synthetic Diurnal Period Air Air
Photon Flux Photoperiod [days after Temperature Temperature
Crop [mol/m2-d] [h/d] planting] Day [oC] Night [oC]
Cabbage 17 85 >25
Carrot 17 75 16-18
Chard 17 16 45 23 23
Celery 17 75
Dry Bean 24 18 85 28 24
Green Onion 17 50
Lettuce 17 16 28 23 23
Onion 17 50
Pea 24 75
Peanut 27 12 104 26 22
Pepper 27 85
Radish 17 16 25 23 23
Red Beet 17 16 38 23 23
Rice 33 12 85 28 24
Snap Bean 24 85 28 24
Soybean 28 12 97 26 22
Spinach 17 16 30 23 23
Strawberry 22 12 85 20 16
Sweet Potato 28 12 85 26 22
Tomato 27 12 85 24 24
Wheat 115 20-24 79 20 20
White Potato 28 12 132 20 16
Source: Hanford, 2004.

Temperature

Temperature effect

Temperature is an important physical parameter for controlling plant growth. It has

a direct effect on biochemical reaction rates in the various metabolic processes and can

indirectly contribute to water stress by enhancing transpiration (Downs and Hellmers,

1975). The various biochemical reactions have different minimum, maximum and

optimum temperatures. Up to 30 C temperature affects plant growth positively by more

rapid leaf expansion and increased root initiation (Albright et al., 2001). In general, most

plants grow well at a temperature from 10 to 30 C. Excessive temperatures result in heat

damage; temperatures below this range lead to chilling and/or freeze damage. The









severity of the damage increases with increasing temperature difference and the time the

plant spends in this unfavorable condition.

Temperature control

In order to control the air temperature of a Mars greenhouse, it is essential to

analyze the heat and mass balance of the greenhouse and its environment. Heat received

by the greenhouse through solar radiation or waste heat of internal electric equipment

may lead to a rise of the temperature. Convective, conductive and radiative heat loss of

the greenhouse to the environment may result in a decreasing internal greenhouse

temperature. Furthermore, the addition and removal of latent heat by evaporation and

condensation of water directly affect the plant as well as the greenhouse temperature.

Air temperature can be increased by addition of heat to the greenhouse such as by

turning on the heating system. Temperature is decreased by removing heat from the

greenhouse such as by utilization of cooling coils or maximizing heat emission of the

greenhouse structure to the Mars environment. Temperature uniformity within a

greenhouse is achieved by vertical ventilation.

Relative Humidity

Relative humidity effect

Relative humidity is an indicator of potential water loss from the plants as it is a

function of the water vapor pressure. Transpiration rates of plants increase as the vapor

pressure deficit between the cells of the leaf and the atmosphere increases. At a given

temperature, the vapor pressure deficit increases rapidly with decreasing humidity. The

balance and dynamics of water loss by transpiration and gain by root absorption

determine the plant water status. Water stress and possibly wilting can be caused by a

high transpiration rate and vapor pressure deficit.









Humidity also reduces the incident radiation on plants through absorption of

infrared radiation leading to a higher specific heat of the air. Condensation and

evaporation affect the energy balance and therefore the air temperature.

70-85% relative humidity is considered to be the optimal range for plant growth

(Tibbitts, 1979). Low relative humidity levels cause wilting of the plants; high relative

humidity levels lead to development of fungus and mold.

Relative humidity control

In a closed environment, humidity is increased by evaporation of open water

sources or evapo-transpiration of the plants. Humidity levels are reduced by

condensation. Humidity control can be achieved by studying the underlying

psychrometric relationships which are explained in detail in the psychrometrics section at

the end of Chapter 5.

Atmospheric Pressure and Composition

The greenhouse atmosphere is composed of essential gases required for plant

growth (such as carbon dioxide, oxygen and water vapor) and some non-essential gases

(such as nitrogen) for pressurizing the greenhouse structure. The total pressure of the

greenhouse atmosphere is the sum of the partial pressures of the gases.

Carbon dioxide effect

Apart from light and water, carbon dioxide is required for photosynthesis and

therefore plant growth. Plant response to increased/decreased carbon dioxide levels

depends on plant species, development stage, irradiance, temperature and mineral

nutrition (Langhans and Tibbitts, 1997). Slightly elevated carbon dioxide during the day

may lead to increased biomass production, whereas highly elevated carbon dioxide levels

can be toxic for plants. As net photosynthesis increases with elevated carbon dioxide









concentration (up to 0.5 kPa), transpiration may decrease due to stomatal closure and leaf

temperatures could rise (Wheeler, 2000). Thus, benefits from elevated carbon dioxide

concentrations can be reduced by higher leaf temperatures. On the other hand, studies

showed that at super-elevated levels of carbon dioxide concentration (0.5-1.0kPa) leaf

transpiration and plant water use increased significantly for some species (Wheeler,

2000). Plant photosynthesis and hence growth responses to carbon dioxide generally

show near linear increases at the low concentrations (up to 0.15 kPa), after which rates

either saturate or eventually taper off. Carbon dioxide concentration below terrestrial

ambient levels (370 ppm) decreases photosynthesis and plant growth (Langhans and

Tibbitts, 1997).

Carbon dioxide control

If carbon dioxide is not controlled in a plant growth chamber, it will decrease

during the day when it is used for photosynthesis. During the night the amount of carbon

dioxide increases due to plant respiration. Carbon dioxide that is taken up by the plants

for photosynthesis has to be replenished to the greenhouse atmosphere. In case of an

autonomous greenhouse, pre-deployed before human arrival, carbon dioxide is not

available as a byproduct of the human metabolism and should be taken out of the carbon

dioxide rich Mars atmosphere.

Oxygen effect

Oxygen is important for respiration, especially at night when there is no

photosynthetically generated oxygen. Probably at least 5 kPa of oxygen is needed to

sustain plant growth (Quebedeaux and Hardy, 1973). Partial pressure of oxygen is

especially critical for the root-zone respiration. The upper limit of oxygen partial pressure









can be set at 23.5%, because above this there are safety concerns related to fire risks

(Lacey et al., 2000).

Oxygen control

Photosynthesis produces oxygen and therefore the oxygen levels will build up in a

greenhouse over time. Thus, oxygen has to be scrubbed out of the atmosphere or used by

humans in order to keep the oxygen level constant.

Vapor pressure effect and control

The effect and control of relative humidity have been described above. Under Earth

atmospheric pressure in an open system, the change in vapor pressure has minimal effect

on total pressure, but in a totally closed system at low pressure, fluctuations in vapor

pressure will significantly influence total pressure (Bucklin et al., 2004). This effect is

explained in detail in the psychrometrics section in Chapter 5.

Pressurizing gas

Nitrogen and argon are two inert gases that may be used as pressurizing gases. In

case of a Mars greenhouse both of the gases could be used, as they are available in the

Mars atmosphere, so they could be extracted locally. Nitrogen and argon are biologically

inert. They would be used as make-up gases in order to increase the total pressure

required for the inflatable structure.

Ventilation

The ventilation system ensures a homogenous gas mix in terms of gas composition,

temperature and humidity inside of the greenhouse. Furthermore, ventilation provides a

minimum air velocity over the plants to facilitate gas exchange required for

photosynthesis. On the other hand, excessive air movement through the crop canopy

leads to increased transpiration and potential water stress (Albright et al., 2001).









Radiation

Radiation effects

Electromagnetic radiation is the energy source for plant growth. Radiation controls

photosynthesis not only through the intensity but also through the spectral distribution

and photoperiod.

For photosynthesis, plants require photosynthetically active radiation in the

wavelengths between 400 and 700 nm. Photosynthetic efficiency decreases in the region

of 500 to 600 nm where radiation is not absorbed well by the chlorophyll, giving the

plants their characteristic green appearance (see Figure 2-3).


IWO -4a Red


C U R /..,/, ," b,
Ial a ]i lb







9,4 0-5 0.6
TOWl CUan




Wwk ,- Iim1


Figure 2-3. Photosynthetic efficiency (Eckart, 1996).

The radiation intensity required to saturate C-3 plants is around 300 [mol/m2-s for

a daily photoperiod of 16 hours; C-4 plants require at least 500 [mol/m2-s for a daily

photoperiod of 16 hours (Langhans and Tibbitts, 1997).

Shade leaves tend to be larger, thinner, and contain more chlorophyll per unit

weight than do sun, i.e., bright light-grown leaves (Boardman, 1977). But sun leaves have

higher photosynthetic capacities. As a consequence, low levels of photosynthetically

active radiation result in bigger leaves, elongation of internodes and less dry weight,









whereas high light levels lead to stimulation of auxiliary branch growth and possibly to

photodestruction of chlorophyll. Excess radiation may cause heating of the leaves and

desiccation due to water loss (Langhans and Tibbitts, 1997).

Radiation control

Shading can lower radiation intensity and filters can change the spectrum. On Mars

the low levels of solar radiation may have to be supplemented by light collection systems

or by electric light. Options for electric lights suitable for plant growth are: Incandescent

lamps, fluorescent lamps, high-intensity discharge lamps (e.g. metal halide lamps, high

pressure sodium lamps), xenon lamps and light emitting diodes.

Incandescent light is blackbody radiation as it is created by a heated body. The

spectrum depends on the temperature of the heated element. Most of the energy from

incandescent lights is in the infrared-region. The infra-red radiation is not useful for

photosynthesis and must be dissipated from the growth chamber. The spectrum can be

shifted by changing the voltage to the lamp; the higher the voltage the lower the ratio of

infra-red to visible radiation. Another method of altering the spectrum is the use of filters.

Wavelengths not useful for photosynthesis can be filtered out. The disadvantage of this

method is that the overall radiation is reduced. Incandescent lamps have a very low

efficiency, not more than 10% of the output radiation is within the visible wavelengths

(Langhans and Tibbitts, 1997).

Fluorescent Lamps have many advantages over incandescent lamps. The radiation

output is continuous, generally uniform and the photosynthetically active radiation is

high. Their optimal operation temperature is only about 380 C. In order to alter the

spectrum of the fluorescent lamps the inner wall of the tubes, which emits the radiation,

can be coated with different phosphors. Most fluorescent plant growth lamps are coated









with a special phosphor mix to provide an enhanced blue and red spectrum. Cool white

lamps are the most efficient fluorescent lamps, with efficiencies of around 20%. Output

of very high output lamps decreases to 70% after the lamps have been operated for 1

year, 16 hours per day (Langhans and Tibbitts, 1997; Schwarzkopf, 1990).

High-intensity discharge lamps excite elements in the arc in order to emit

characteristic wavelengths. Their spectrum is uniform but not continuous. Irradiances are

higher than those of incandescent and fluorescent lamps. Two commonly used high-

intensity discharge lamps are metal halide and high-pressure sodium lights. In contrast to

fluorescent lamps the output radiation of metal halide lamps is not affected by the

ambient temperature. Most of the radiation output is in the 400-700 nm but output can

shift with lamp age. The efficiency of metal halide lamps is around 22%. The radiation

output of high pressure sodium lamps is concentrated in the 550-650 nm range, and very

scarce in the 400-550 nm range. High pressure sodium lights are useful in combination

with alternative lighting options such as metal halide, blue phosphor and cool-white

fluorescent lamps. High pressure sodium lights are very efficient with efficiencies of 25%

(Langhans and Tibbitts, 1997; Schwarzkopf, 1990).

Xenon lamps are rarely used for plant growth chambers even though they have a

spectrum similar to the solar spectrum. Their disadvantages include the high cost and

their emission of ultraviolet radiation, which leads to development of ozone.

Furthermore, the high infra-red radiation increases the cooling load of the plant growth

chamber (Langhans and Tibbitts, 1997).

Light emitting diodes (LEDs) are very useful for plant growth as certain LEDs have

specific outputs required for photosynthesis. Moreover, they are solid state devices and









have a long operating life. Blue and red LEDs can be combined to fulfill the plant needs

(Langhans and Tibbitts, 1997).

Growth Area

The size of the Mars greenhouse depends on the number of astronauts and the

desired amount of food grown locally vs. shipped from Earth. The required plant-growth

area per person can be estimated at 50 m2 to fulfill 100% of the food requirements

(Wheeler et al., 2001). Food, if grown on-site, can regenerate some or all of the crew's

air and water. If more than about 25% of the food, by dry mass, is produced locally, all

the required water can be regenerated by the same process. If approximately 50% or more

of the food, by dry mass, is produced on site, all the required air can be regenerated by

the same process depending on the crop and growth conditions (Wheeler et al., 2001;

Hanford, 2004).

Low Pressure Plant Growth Studies

Operating a greenhouse on Mars at low internal pressure reduces the pressure

differential across the structure and therefore saves structural mass as well as reduces

leakage. The literature contains a variety of studies on the plant responses to low

pressure. The lower limits of oxygen, carbon dioxide, water vapor and inert gases that

plants can tolerate and thrive in are a key in the development of hypobaric Mars

greenhouses.

Studies on plant responses to low pressure date back to the 1960s, when NASA

first considered the implementation of biological life support systems. These studies

include research at Brooks Air Force Base where the plant environment pressure was

dropped to 51 and 93 kPa and other research Wright-Patterson Air Force Base with an









even lower pressure of 1/3 atmosphere. No adverse effects on plant growth due to low

pressure were observed (Corey et al., 2002).

Further studies focused on the effect of the different atmosphere components on the

seed germination, seedling development and plant growth. Andre and Richaud (1986)

and Andre and Massimino (1992) evaluated if an inert gas such as nitrogen is necessary

for plant growth by studying barley at 7 kPa. They concluded that nitrogen is not

necessary for plant growth. An increased transpiration rate was observed at this low

pressure. Furthermore, these studies demonstrated that growth of wheat is possible at a

total pressure as low as 10 kPa. Wheat growth at 20 kPa was greater than at 10 kPa and

even greater than at atmospheric pressure levels.

Musgrave at al. (1988) found enhanced growth of mungbean at 21-24 kPa total

pressure atmospheres with a low oxygen level of 5kPa. A study by Schwartzkopf and

Mancinelli (1991) confirmed that an oxygen partial pressure of at least 5 kPa is necessary

for seed germination and initial plant growth, as seeds failed to germinate at atmospheres

with a partial pressure of oxygen lower than 5 kPa. With a total pressure of 6 kPa and

therefore an oxygen concentration of 83%, this study was well above the oxygen level of

23.5% that is the upper limit considered to be safe regarding fire hazards (Lacey et al.,

2000). Although others have operated systems at high oxygen concentration, e.g. Goto et

al. (2002) operated the growth chamber at a high level of 91% oxygen (21 kPa partial

oxygen pressure, 23 kPa total pressure).

Spanarkel and Drew (2002) reported that lettuce grown at 70 kPa total pressure was

normal in appearance, and that photosynthesis was unaffected compared to plant growth









at ambient pressure. Oxygen levels were maintained at 21 kPa and carbon dioxide at

66.5-73.5 Pa during both ambient and hypobaric conditions.

Research by Daunicht and Brinkjans (1996) compared plant growth at 100 kPa to

70 kPa and 40 kPa total pressure with equal carbon dioxide concentration. Photosynthetic

rate increased at 70 kPa compared to 100 kPa and was similar at 40 kPa and 100 kPa.

Furthermore, plant morphology was affected by the reduced pressures.

Experiments conducted in the variable pressure growth chambers at different

NASA centers tested wheat under 70 kPa and lettuce under a progressive reduction of

pressure down to 20 kPa (Corey et al., 1996; Corey et al., 1997b, Corey et al., 2002).

Lettuce, as well as the wheat experienced increased transpiration at reduced total

pressures. An effect of the oxygen partial pressure on the photosynthesis was also

observed. Photosynthesis increased with decreasing oxygen partial pressure and

decreased if oxygen was injected into the chamber.

Studies at Texas A&M also tested the performance of wheat and lettuce at low

pressures ranging from 30 to 101 kPa (He et al., 2003). Low pressure increased plant

growth and did not alter germination rate. Low oxygen concentration inhibited ethylene

production of lettuce. Low total pressure inhibited ethylene production of wheat, whereas

oxygen reduction did not have an influence on ethylene production for wheat.

The University of Tokyo performed a series of studies on spinach and maize in a

reduced pressure plant growth chamber (Goto et al., 1996; Iwabuchi et al., 1996;

Iwabuchi and Kurata, 2003). Similar to the other studies described above, they observed

increased photosynthesis and transpiration rates at reduced pressures. Furthermore,

stomatal size and aperture of leaves were significantly smaller at reduced total pressures.









Ferl et al. (2002) describes the adaptation and plant responses to low pressure

environments. Plant stress includes hypoxic stress, drought stress and heat shock that may

alter plant morphology. For this research genes were analyzed to understand the

fundamental processes that involve gene responses to environmental signals. Genetic

engineering will lead to plants that can tolerate and thrive in extreme environments.

In a study by Wilkerson (2005) evapo-transpiration rates of radishes increased

significantly at a low atmospheric pressure of 12 kPa and a carbon dioxide partial

pressure of 40 Pa. Furthermore, this research concluded that increasing the carbon

dioxide partial pressure from 40 Pa to 150 Pa is an effective countermeasure to wilting of

the plants at low atmospheric pressures because the stomata close at higher carbon

dioxide concentrations and therefore transpiration rates decrease.

The studies described above indicate that plant growth is possible under low

atmospheric pressure. Nevertheless, more detailed research is necessary on the response

of plants to the environment properties especially for more than one life cycle.

Additionally, studies on plant growth chambers exposed to the Martian environmental

conditions are necessary in case of transparent greenhouse structures, as the local climate

has a huge effect on the plant growth conditions. Operating a greenhouse in the Mars

environment may lead to stratification of temperature and humidity, condensation

resulting in lower light levels, as well as degradation of transparent greenhouse materials

leading to a change of the spectrum of the photosynthetically active radiation. Last but

not least, genetic engineering will play an important role in the selection of the crop

suited for advanced life support.















CHAPTER 3
OBJECTIVES OF THIS STUDY

This study can be divided into the theoretical (mathematical) simulation and the

experimental work.

The objectives of the experimental part were

* Design of simulated Mars environment and low pressure greenhouse for plant
growth.

* Development of control-algorithm to maintain total pressure and temperature of
vacuum chamber (simulated Mars environment).

* Development of control-algorithm to maintain total pressure, temperature and gas
composition (C02, 02 and N2 concentration) of greenhouse dome.

* Monitoring of stratification of temperature and relative humidity in greenhouse
dome.

* Monitoring of condensation pattern on interior of greenhouse dome and its effect
on light reduction.

* Monitoring of plant evapo-transpiration in low pressure greenhouse that is exposed
to low temperature environment.

The objectives of the simulation were

* Development of low pressure psychrometric relationships for closed systems and
non-standard atmospheres.

* Prediction of temperatures of greenhouse atmosphere, greenhouse floor, interior
and exterior greenhouse shell by creating a mathematical model to simulate the heat
and mass transfer.

* Prediction of occurrence of condensation on interior of greenhouse dome.

* Comparison of theoretical and experimental results to deduce conclusions.














CHAPTER 4
EXPERIMENTAL WORK

System Description

A careful selection of equipment for the set-up of the experimental work was

required in order to fulfill the objectives listed in Chapter 3. A polycarbonate

hemispherical dome with a diameter of 1 meter served as the Mars greenhouse (see

Figure 4-1). The dome was clamped to a re-inforced aluminum base with the help of a

silicon rubber gasket to ensure the enclosure of the system. A 10 centimeter thick layer of

polyurethane foam was fixed to the bottom of the aluminum dome base for insulation.

Feed-throughs in the dome base were used for data transfer, power and gas supply. The

maximum pressure differential that the dome structure could withstand without failure

was estimated to be +50 kPa. The structural analysis of the dome and its base plate is

presented in Appendix A.

A dome similar to the one that was utilized as a greenhouse model for this study

had been used at NASA's Kennedy Space Center as an autonomous low pressure growth

chamber. In a preliminary test lettuce was grown at a pressure of 25 kPa for 45 days

(Fowler et al., 2002; Bucklin et al., 2004). However, during this lettuce growth

experiment at NASA the dome was not exposed to simulated Mars conditions as in the

experiments described in this document.

A large stainless steel vacuum chamber was used to simulate the Mars atmosphere

of 0.6 kPa. Its interior volume was comprised by an area of 1.2 meter by 1.2 meter with a









height of 1 meter. The chamber was custom-made by Chicago Wilcox based on the

following requirements:

* The vessel should be able to hold a pressure of 0.1 kPa with no significant leakage.
* It should be big enough for the greenhouse dome (0.5 m radius) to fit in.
* It should have a window on top to allow growth light to penetrate into the chamber.
* It should have 12 ports on the side for data transfer, power and gas supply.
* It should have a door to move equipment in and out.

The stainless steel chamber was braced on the bottom and on all sides (except for

door) to avoid deflection of the walls because of the huge pressure difference. A 1.27 cm

thick polycarbonate sheet served as a window pane. A grid of steel bars supported the

polycarbonate window (see Figure 4-2).

An industrial freezer shown in Figure 4-3 ensured the low temperature of the

vacuum chamber (simulated Mars environment). The interior temperature of the freezer

could be dropped down to as low as -34 C. Initially, jacketing the vacuum chamber with

a heat exchanger was discussed as an option to reduce the temperature inside of the

chamber, but putting the entire vacuum chamber in a freezer had the advantage that the

temperature distribution was more uniform, especially at the chamber window.


A) B)
Figure 4-1. Dome used to protect plants from the simulated low pressure, low
temperature Mars environment. A) Empty dome. B) Dome with sensors,
scales and flasks installed.


































Figure 4-2. Vacuum chamber used to simulate the low pressure Mars environment (less
than 1% of Earth's atmosphere).


Figure 4-3. Industrial walk-in freezer ensures low temperature of the vacuum chamber
(simulated Mars environment).









Two vacuum pumps were installed outside the freezer. A powerful two-stage rotary

vane vacuum pump (DUO 10, Pfeiffer Vacuum) with a volumetric flow rate of

10 m3/hour was connected to the vacuum chamber; a two-stage vacuum pump (DV-85N,

J/B Industries) with a volumetric displacement of 5 m3/hour was connected to the

greenhouse dome. During the experiments the pumps were always turned on and the air

flow was controlled by two solenoid valves that were installed between the pumps and

the chamber/dome. Three mass flow controllers ensured the correct gas mixture that was

fed into the greenhouse dome. The mass flow controllers were connected to bottles of

nitrogen, oxygen and carbon dioxide.

Scale 1 was located on the bottom of the greenhouse. It measured the amount of

water that ran off the greenhouse shell and the recollection funnel. Four scales (Scale 2 to

Scale 5) were installed in the upper part of the dome. They measured the amount of water

that the plants evaporated and transpired. Two flasks, each containing one lettuce plant,

were placed on each of these four scales, leading to a total number of 8 flasks. A

512W/110V cooking range coil was placed in the center of the greenhouse dome and

served as the heater. A 24V fan ensured mixing of the air and minimized temperature, gas

composition and relative humidity stratification.

A high pressure sodium growth light (1000W HPS, Hortilux) was installed above

the vacuum chamber. Two I/O boards, one for data acquisition and one for control, were

connected to the sensors and actuators. They were connected to the computer for

programming and as user interface. Figure 4-4 gives an overview of the experimental

setup.

































Figure 4-4. Schematic of experimental setup.

Instrumentation and Sensor Calibration

Most commercially available sensors for the measurement of environmental

parameters contain a data sheet with calibration information under standard atmospheric

conditions. However, in this project, the pressure and gas composition of the environment

that the sensors were exposed to differed significantly from the standard atmosphere.

Therefore, the sensors were carefully selected according to the environmental conditions

and a re-calibration of the sensors was performed against a standard sensor that was not

affected by pressure or gas composition.

DS18B20 (Dallas Semiconductor) digital thermometers were selected for

temperature measurements. They were shielded to avoid measurement errors caused by

direct radiation onto the sensors. Relative humidity (RH) was monitored by HIH-3602-L

(Honeywell) capacitance type sensors capable of measuring RH in the range of 0-100%










(non-condensing). LI-COR's LI-190 SA quantum sensor monitored the level of

photosynthetically active radiation inside the greenhouse dome. The carbon dioxide

concentration was measured by Vaisala's infrared GMP 221 sensor, oxygen

concentration by Maxtec's Max 250 galvanic cell type sensor. The mass of the

recollected water and the masses of the individual plants were measured by Vishay

Celetron's LPS-2 kg load cells. Table 4-1 lists the environmental parameters that were

monitored and their corresponding sensors.

Table 4-1. Sensors used to measure environmental parameters, the sensor ranges and
accuracies.
Parameter Type Range Accuracy

Temperature DS18B20 digital thermometer -. t + O 0
Temperature -55 to +125 C + 0.5 C


Relative Humidity


Light


Pressure


Carbon Dioxide


Oxygen


Water / Plant Mass


UDallas SemiconuucLorl

HIH-3602-L capacitance type RH sensor
(Honeywell)

LI-190SA quantum sensor
(LI-COR Inc.)

ASCX15AN
(Sensym ICT)

GMP 221
(VAISALA)

Max 250
(MaxTec)

LPS-2 kg Load Cell
(Vishay Celtron)


0 to 100%

0to 10,000
gmol/m2/s

Oto 15 psi


Oto 10 %


2%


5%


+0.5%


0.02%


Oto 100% + 1.0 %


0 to 2 kg


+ 0.1 g


A transparent acrylic cylinder with an aluminum base served as calibration

chamber for the sensors. It had an interior diameter of 20.32 cm, a wall thickness of

0.64 cm and a height of 30.48 cm. The cylinder was supported by an aluminum base

containing feed-throughs for data transfer, power and gas supply. An O-ring minimized









leakage of air into the cylinder. The structural analysis of the cylinder is presented in

Appendix A. The calibration data of all sensors is found in Appendix B.






















Figure 4-5. Cylinder used for calibration of pressure-sensitive sensors and for initial gas
mixing control algorithm development.

The performance of the temperature sensors, light sensor and load cells was

unaffected by changes in total pressure. The sensors affected by low pressure, including

relative humidity (RH), carbon dioxide concentration and oxygen concentration, had to

be calibrated for low pressures. Carbon dioxide and oxygen were calibrated by a method

similar to the one described by Mu (2005).

Rygalov et al. (2002) compared various types of RH sensors under low

atmospheric pressure to RH readings from a chilled mirror/dew point hygrometer that is

unaffected by pressure changes. This study concluded that the dry-bulb/wet-bulb method

was not adequate for low pressures as not enough air mass moves over the sensor. In










contrast to this, the readings of the capacitance type RH sensor did not change

significantly at different pressures.

As the accuracy of the relative humidity measurements was of major importance to

the study described in this dissertation, further experiments were conducted to confirm

the independence of the output of the capacitance type RH sensor at different pressures.

The RH values of the capacitance sensors were compared to the output of Vaisala's

HMP 237 by exposing the sensors to a wide range of humidities and pressures. The

HMP 237 is also a capacitance RH sensor, but especially designed to measure RH and

temperature in both pressurized as well as vacuum chambers. The difference in RH of the

Honeywell sensors from Vaisala's low pressure RH sensor never exceeded 3%. Thus, the

RH values obtained by the Honeywell RH sensors were not corrected for pressure.

88 ----+---_--1
8 RH1

RH2 +. +
RH3 + :
87 RH4 / + -
+ RH5 +i- +
-- Target /+ +: +-H-.
G 86 RH conf+3% -+ + + +
S- RH conf-3% + +
con 3% a "-- + i +-+ + +

I 85 / +
8I 4 + + +
S0 + +
:t= A+ +





82
S++ + /

81 -


81 82 83 84 85 86 87 88

Reference Relative Humidity (HMP 237) [%]
Figure 4-6. Comparison of Honeywell capacitance RH sensors to the HMP 237 reference
RH sensor for pressures of 0 to 25 kPa.









Leakage Testing

In low pressure plant growth chambers, involving the measurement of gas

exchange rates and evapo-transpiration, it is important to minimize the leakage and to

account for the occurring leakage by making the necessary corrections (Corey, 1997a).

Leakage is defined as

1440
L O 100 x 44 (4-1)
P, t

where: L = leak rate [% vol/day]

P, = end pressure [kPa]

Po = initial pressure [kPa]

t = time interval [min]

Leakage of Vacuum Chamber

Initial leak tests of the freshly shipped vacuum chamber, showed very high leak

rates of 2.5 kPa/hour. Due to the high leak rate it was not possible to pump the chamber

down to a pressure lower than 4 kPa. Changing the plastic tubing to copper tubing,

attaching C-clamps to the chamber door, sealing ports additionally with Loctite glue,

utilizing high vacuum rated Swaglok valves and installing a powerful new two-stage

rotary vane vacuum pump (DUO 10, Pfeiffer Vacuum) with a volumetric flow rate of

10 m3/hour, led to a reduction of the leakage to 1.65 kPa/hour. Even at this lower leakage

the target Mars equivalent pressure of 0.6 kPa could not be reached in the chamber.

Further leak tests utilizing helium gas and a helium gas detector revealed that the gas was

mainly leaking through the chamber window. Therefore, the window was taken off and a

second layer of gasket was cut out and installed, so that the polycarbonate window would









be sandwiched in between the two gaskets. Thus, the window could deflect more, without

causing gaps for the gas to leak in.

Figure 4-7 depicts the strong forces that act upon the window when the chamber is

at low pressure: Photo A depicts the bulging of the polycarbonate window at low

pressures; in Photo B the window gasket is drawn inside by the large pressure difference.

Additionally, vacuum grease was applied to the window and the door. Finding the right

amount of vacuum grease is the key to success: enough to fill the gaps and reduce the gas

leakage but not so much, that lack of friction causes the gasket to dislocate. Finally, a

pressure of 0.07 kPa was achieved, well below the required pressure of 0.6 kPa.


A)
Figure 4-7. Forces on chamber window. A) Vacuum chamber at 0.6 kPa with top window
bulging in. B) Gasket drawn into the chamber due to pressure difference.





































B)
Figure 4-7. continued

Leakage of Greenhouse Dome

The greenhouse dome was installed in the 0.6 kPa vacuum chamber. Therefore, gas

leaked from the dome into the vacuum chamber, causing the dome pressure to drop. This

leakage was minimized by applying vacuum grease on the dome gasket, tightening the

36 screws of the dome and sealing the feed-throughs with additional glue.

Figure 4-8 presents the data of a combined leak test of the vacuum chamber and the

greenhouse dome. The dome leakage was found to be -0.375 kPa/hour (45 vol%/day) at

20 kPa; the chamber leakage 0.243kPa/hour (972 vol%/day) at 0.6 kPa. Figure 4-4

compares the leak rates of the vacuum chamber/greenhouse dome to other low pressure










plant growth systems. This comparison shows that the leak rates of this large system

compared relatively well with the much smaller bell jar or tube systems.


20
19.9
19.8
19.7
19.6
19.5
19.4
19.3
19.2
19.1
19


Time [min]
Figure 4-8. Dome and chamber leakage with gas resupply and vacuum pumps turned off
at a temperature of -10 oC.


0.01


- Greenhouse Dome Pressure [kPa]
- Mars Chamber Pressure [kPa]
I I I


SA A







Chamber / Dome
Mu (2005)
A Wilkerson (2005)
Brown & Lacey (2002)


Pressure [kPa]


Figure 4-9. Comparison of vacuum chamber and greenhouse dome leak rates to values of
other low pressure plant growth studies (leak rate is presented in logarithmic
scale).









Data Acquisition and Control System

The distributed control system for this project was developed by Rigel Corporation,

especially for low pressure plant growth experiments, with the aims of maximizing the

inputs and outputs while being very flexible yet low cost. This control system, described

in detail in Mu (2005), was modified and adapted after it had been used for previous plant

growth studies. Two control boards were utilized: one for data acquisition and a second

one to execute the control signals. The two boards combined had a large number of

analog and digital inputs/outputs

* 16 digital inputs for temperature sensors
* 16 analog inputs especially for thermocouples
* 32 single ended (16 differential) analog inputs
* 32 digital outputs for operating the relays
* 16 analog outputs for the control of the actuators (such as mass flow controllers)
* 8 digital outputs designed for pulse width modulation (e.g. utilized for the control
of the heating system)

The data board and the control board were both connected to the PC via the serial

port. The data acquisition and control software was separated into two parts: The low-

level programming of the microcontrollers was done by Rigel Corporation utilizing

Assembly and C language. These low-level programs, loaded onto the microcontrollers,

received the data from the sensors and sent out control commands to the actuators. For

the high-level programming LabView was chosen as it provides an excellent user-

interface and is comprised of many built-in functions. As LabView is a graphic

programming language it also facilitated multi-users to work with the same program and

to understand it quickly. The LabView programs communicated with the

microcontrollers, contained the control logic and managed the data.









Greenhouse Dome Environmental Control

Gas Composition and Total Pressure Control Algorithm

The dry atmosphere of the greenhouse was comprised of three gases: oxygen,

carbon dioxide and nitrogen. Oxygen and carbon dioxide are the essential gases required

for photosynthesis and therefore plant growth. Nitrogen was used to fill up the

atmosphere to the desired total pressure as total pressure is defined as the sum of the

partial pressures of all gases. The oxygen and carbon dioxide concentration of the

greenhouse dome were directly measured by sensors. Nitrogen was calculated by

measuring the total pressure and subtracting the partial pressures of oxygen and carbon

dioxide. Three mass flow controllers were utilized to control the resupply of oxygen,

carbon dioxide and nitrogen separately. Resupply of the individual gas was shut off if the

partial pressure of the gas was higher than the set point partial pressure. If the measured

partial pressure of the gas was lower than the set point, gas was resupplied. The required

mass flow of each gas was calculated by determining the mass of the gas to be resupplied

into the greenhouse dome, resulting in the following gas control algorithm:

Flo as, t) Mass (gas) Mass ct,,l (gas, t)
Flow(gas, t) = (4-2)
p(gas) At

where: Flow(gas, t) = gas flow rate [m3/s]


Masset (gas) = M(gas) Ppse, (gas) Vdome = mass of gas required [kg]
RTar


Massactal (gas, t) = M(gas) =pactua (gast) dome actual mass of gas [kg]
R Ta,

M(gas) = Molecular mass of gas [kg/mol]

Ppset(gas) = partial pressure of gas at setpoint [Pa]










Ppactua(gas) = actual partial pressure of gas [Pa]

Vdome = volume of dome [m3]

R = universal gas constant [8.3144J/(mol K)]

Tar = air temperature [K]

p(gas)= gas density [kg/m3]

At = length of control cycle [s]

Total pressure of the greenhouse dome was maintained constant by controlling

oxygen, carbon dioxide and nitrogen pressures separately as described above. Total

pressure of the vacuum chamber was kept constant by controlling a solenoid valve that

was connected to the vacuum pump. If the vacuum chamber pressure was above the

setpoint, gas was pumped out. If it was below the setpoint the pump was stopped.

Figure 4-10 depicts the oxygen and carbon dioxide partial pressures during a test of

the gas mixing control system that lasted 1 hour. Figure 4-11 shows the total pressures of

the vacuum chamber and the greenhouse dome.

5
4.5 1.4
4.5
4 IA-t ..J A-" NVV" 1.2 n
3.5
1
S3
0.8
S2.5 0
S2 0.6 X
0
S1.5 5
0.4
1 o
x Oxygen [kPa]2
0O- 0.2 m
00.5 Carbon Dioxide [kPa] 0
0 1 0
0 15 30 45 60
Time [min]
Figure 4-10. Gas mixing of dome greenhouse atmosphere without plants (oxygen set
point at 4.0 kPa and carbon dioxide set point at 0.5 kPa).










5 25
4.5 Mars Chamber Pressure [kPa] 24
S4 Dome Greenhouse Pressure [kPa] 23
CC
S3.5 22 (
3 3 21 2
I 2.5 ^ 20 |n
2 19o-
E 1.5 18 E
C 0
5 1 17
0.5 n'Tr-" r r I n 16
0 15
0 15 30 45 60
Time [min]

Figure 4-11. Pressure control of vacuum chamber (set point 0.6 kPa) and greenhouse
dome (set points 20 kPa).

Air Temperature Control Algorithm

Maintaining the air temperature in a range where the plants are productive is

essential in the cold Mars environment. Air temperature was kept constant by the heating

coil that was installed in the center of the greenhouse dome at plant level. The heater was

controlled by pulse width modulation with duty cycles of 0%-100%. At 100% the

maximum power output was calculated to be 512.7 W:

V2 (ll0V)2
Pmax = 3 512.7W (4-3)
ax R 23.60

where: Pmax = heating power [W]

V= voltage [V]

R = resistance [Q]


To maintain the air temperature T3 at a certain set point, the required power of the

heating system was calculated by adding the required steady state power (determined in










the following section: see equations 4-5 & 4-6) to a proportional control term with a gain

of 1/ T3air,set:


Preq (t) P,, (Tf,,,, T3 arse, Light) + T3 T3 r T(t)) (4-4)
air,set

where: Preq(t)= required heating power [W]

Pss(Tfreezer, T3airset, Light) = steady state heating power [W]

T3air,set = air set point temperature [C]

T3ar(t) = actual air temperature T3 [oC]

Figure 4-12 gives an example of how the temperature control algorithm regulated

the air temperature. A constant air temperature of 20 C was maintained by varying the

heating power. When the light was turned on the required heating power was much less

than when the light was turned off.


25 300
25 Light off Light on I Light off

2050
20

.I I 200 .
15 I I
I-I
I I 150 0C
10 -I
100
I-I
5 50

0 0

0 60 120 181
Time [min]


Figure 4-12. Air temperature control of greenhouse dome (set point at 20 oC).









Heat and Mass Transfer Experiments without Plants

The first step of modeling the heat and mass transfer of this Mars greenhouse was

to analyze the heat transfer without the plants. Figure 4-13 shows the location of the

sensors for measuring the environmental parameters. The CO2, 02 and light sensors were

installed at the plant level. Temperature was measured at seven locations

* T1 at the aluminum dome base
* T2 at the water collection slope
* T3 is the air temperature at the plant level
* T4 is the temperature of the exhaust air of the fan and heater.
* T5 is the temperature of the exterior of the transparent greenhouse shell
* T6 is the temperature of the vacuum chamber window
* T7 is the temperature of the vacuum chamber wall

Relative humidity sensors were installed at the location of T3 and T4. Furthermore,

total pressure was measured in the dome and in the vacuum chamber.


I ________I Vacuum Chamber Walk-n Freeer
Figure 4-13. Sensor locations for heat and mass transfer experiments without plants.


I HPS Growth Light (1000 W)


000000


Window


T,


Te






































C) D)
Figure 4-14. Preparation of the steady state experiments. A) Bottom of dome base with
foam insulation. B) Side view of greenhouse dome with the sensors and scales
installed. C) Top view of greenhouse dome without shell. D) Installation of
greenhouse dome into the vacuum chamber.

An exact understanding of the temperature distribution at the different locations

illustrated in Figure 4-13 was important to calculate the thermal resistances in Chapter 5.

The greenhouse dome was subjected to a combination of different freezer temperatures,

heating power levels and growth light states:

* Freezer temperatures at 0 oC, -10 oC and -20 C.
* Heating power levels at 0 W, 26 W, 51 W, 77 W and 103 W.
* Growth light switched on/off

Useless combinations such as a heating power of OW and the growth light switched

off were left out, as well as combinations that resulted in very high dome temperatures


4JE




~i~- :
L i;ii~r~- l1;










(e.g. 0 oC freezer temperature, 103 W heating power and growth light switched on).

Figure 4-15 depicts the trend of the seven different temperatures for a freezer temperature

of 0 oC, a heating power of 26 W and the growth light switched off. Temperature T6 at

the window and temperature T7 at the chamber wall oscillated as the freezer temperature

was controlled at 0 oC within a band of+l1 C and -1 oC. The time required to achieve

steady-state temperatures was always at least 10 to 12 hours. The steady state

temperatures at the seven locations for the different combination of freezer temperatures,

heating power levels and growth light state are given in table 4-2. Each experiment was

conducted two times to minimize errors. Figures 4-16 to 4-20 depict the temperature

distributions. It can be observed that the temperatures inside the dome increase linearly

with the increased in heating power. The chamber window (T6) and wall (T7)

temperatures increased only slightly with increasing heating power. On the other hand, T6

and T7 increased significantly when the growth light was turned on.


16
-T1 Base
14 T2 Slope
T3 Air/Plant
12 T4 Fan Exhaust
T5 Outside Shell
T6- Window
8 T7 Wall
C.
E 6
1-
4




0 100 200 300 400 500 600
Time [min]

Figure 4-15. Temperature readings until steady state is achieved. (0 oC freezer
temperature, 26 W heating power and light switched off).










Table 4-2. Steady state temperature distribution under different freezer temperature, light
and heating power conditions.
Freezer Lights Heating Base Slope Air/ Fan Shell Window Wall
Temp. (0=off, Power T1 T2 Plant Exhaust Outside Outside Outside
[C] l=on) [W] [oC] [oC] T3 T4 [C] T5 [oC] T6 [C] T7 [C]
locl
0 0 26 4.34 10.35 12.74 13.72 10.43 0.90 0.01
0 0 51 5.96 15.29 19.17 20.75 15.68 1.83 0.34
0 0 77 6.98 18.93 24.06 26.11 19.69 2.28 0.49
0 0 103 8.56 24.09 30.25 32.60 24.49 2.39 0.11
-10 0 26 -3.44 2.68 5.29 6.38 2.81 -7.56 -9.63
-10 0 51 -3.06 6.61 10.76 12.40 7.17 -8.00 -9.94
-10 0 77 0.34 12.95 18.44 20.59 13.51 -7.00 -9.44
-10 0 103 2.84 17.73 24.01 26.61 17.96 -6.44 -9.38
-20 0 51 -10.81 -0.94 3.38 4.94 -0.03 -17.25 -19.13
-20 0 77 -10.31 3.44 9.06 11.12 4.29 -17.06 -19.31
-20 0 103 -7.19 9.32 15.51 17.96 9.60 -15.94 -18.88
-20 0 128 -4.13 14.39 21.34 24.32 14.14 -15.00 -18.63
-10 1 0 9.47 18.74 16.76 18.96 19.88 8.74 -6.22
-10 1 26 10.12 23.66 25.74 27.08 25.22 9.28 -6.74
-10 1 51 10.61 28.59 32.17 34.15 30.62 9.81 -6.66
-10 1 77 11.96 32.50 38.27 39.56 34.63 10.56 -6.31
-20 1 0 -5.06 6.13 5.60 6.09 7.73 -5.56 -15.38
-20 1 26 1.75 15.37 17.52 18.18 16.76 -5.25 -14.38
-20 1 51 5.09 19.88 23.39 24.48 20.88 -5.06 -14.13
-20 1 77 9.81 27.22 32.73 34.95 29.17 -3.08 -13.85
-20 1 103 11.63 31.73 38.98 41.22 33.68 -3.88 -13.20


0 oC Freezer Temperature Light off


35

S30
e
- 25
"-
S20
E
S15

S10
5

Co


X i T1 Base
T2 Slope
X A T3 Air/Plant
XT4 Fan Exhaust
A 0 *T5 Outside Shell
E T6 Window
SA T7 -Wall




A, A

D 50 100 150 20
Heating Power [W]


Figure 4-16. Steady state temperatures versus power of heater at seven different locations
(Ti-T7). Freezer temperature is 0 C and the growth light is switched off











-10 OC Freezer Temperature Light off

X T1 Base
A *T2 Slope
SA T3 Air/Plant
T4 Fan Exhaust
X T5 Outside Shell
o T6 Window
SAT7 Wall
* *

* *
0 n 0 0


Heating Power [W]


Figure 4-17. Steady state temperatures versus power of heater at seven different locations
(Ti-T7). Freezer temperature is -10 C and the growth light is switched off


-20 OC Freezer Temperature Light off
30
e T1 Base
25 X T2 Slope
20 A AT3-Air/Plant
15 xT4- Fan Exhaust
0 *T5 Outside Shell
S10
~" T6 Window
5 AT7 Wall
o0
-5
1 -10
S-15 U ED
-20 A A
0 50 100 150 200
Heating Power [W]


Figure 4-18. Steady state temperatures versus power of heater at seven different locations
(Ti-T7). Freezer temperature is -20 C and the growth light is switched off







46



-10 OC Freezer Temperature Light on


o T1 Base
I T2 Slope
SAT3 Air/Plant
SxT4 Fan Exhaust
*T5 Outside Shell
O T6 Window
'- -IA T7 Wall




A A A

0 50 100 150 2C
Heating Power [W]


Figure 4-19. Steady state temperatures versus power of heater at seven different locations
(Ti-T7). Freezer temperature is -10 C and the growth light is switched on.



-20 OC Freezer Temperature Light on


50

U 40
U,
S30
"-
. 20
E
- 10

o 0
*-1
2 -10
C,


ST1 Base
*T2 Slope
SA T3 Air/Plant
xT4 Fan Exhaust
S*T5 Outside Shell
E T6-Window
SAT7 Wall





A A A A

3 50 100 150 2C
Heating Power [W]


Figure 4-20. Steady state temperatures versus power of heater at seven different locations
(Ti-T7). Freezer temperature is -20 C and the growth light is switched on.

Figure 4-21 depicts the steady state air temperature T3 of the greenhouse dome for

different heating power and freezer temperatures. The steady state air temperature









increases linearly with increasing heater power. The linear equations for the freezer

temperatures of 0 oC, -10 C and -20 C are shown in Figure 4-21. According to the

equations, the steady state air temperature is not equal to the freezer temperature when

the heating system is switched off. This difference results from the waste heat that is

introduced by running the fan continuously and the difference of freezer temperature and

wall temperature of the vacuum chamber T7 (see Table 4-2). Combining these three

equations into one, the power of the heater required to heat the air to temperature T3 with

a freezer temperature of Tfreezer can be calculated as follows:

T3 ,ai 0.831 x Tfreezer) + 7.741)
Pss = (4-5)
(-0.000598 X Tfreezer) + 0.23047

where: Pss = power of heater [W]

T3,ar = steady state temperature of air T3 [oC]

Tfreezer = temperature of freezer [C]


o 0 OC Freezer/ Light off
P 30 m -10 C Freezer /Light off
I-
5 25 A -20 OC Freezer/ Light off

20
S2 / T3ss(0 oC) = 0.2240*W + 7.2000
I 15 R2 = 0.9975

S10 T3ss(-10 OC) = 0.2490*W 1.3350
/ R2 = 0.9954
5
"A T3ss(-20 OC) = 0.2353*W 8.7930
0 Q R2 = 0.9994
0 50 100 150
Heating Power[W]

Figure 4-21. Steady state air temperatures (T3) versus power of heater for freezer
temperatures of 0 oC, -10 C and -20 C (growth light switched off).










When the light is switched on, the power of the heater required to heat the air to

temperature T3 with a freezer temperature of Tfreezer can be calculated as following:

T3,ar (0.951x Treeer) + 26.271
Pss = (4-6)
(-0.00526 x Tfreezer) + 0.2146


Figure 4-22 depicts the heating power requirement depending on the freezer

temperature for steady state air temperatures T3 of 15 C, 20 C and 25 C. When the

growth light was switched off and if the freezer temperature was -20 C, e.g., the required

heater power was 95.5 W, 116.2 W and 136.8 W to achieve a steady state air temperature

of 15 C, 20 C and 25 C respectively. If the growth light was switched on, the required

heating power was reduced significantly. At a freezer temperature of -20 C and an air

temperature of 20 C, the heating power was reduced by 79.8 W, with the light switched

on.

350


300


250


200



100



50


0


-40 -35 -30 -25 -20 -15 -10 -5 0
Freezer Temperature [OC]
Figure 4-22. Freezer temperature versus power of heater for steady state air temperatures
(T3) of 15 C, 20 C and 25 C.


--Air Temperature = 150C / light on
- Air Temperature = 200C / light on
- Air Temperature = 250C / light on
- Air Temperature = 150C / light off
- Air Temperature = 200C / light off
- Air Temperature = 250C / light off







. f,,,,,..AP(200C)=
9.8 W

-









If the interior temperature of the greenhouse dome shell decreased below the dew

point of the air temperature, condensation could occur. Figure 4-23 shows two photos of

condensation on the inside of the greenhouse dome. High condensation occurred for low

freezer temperatures (Photo B) as those low temperatures resulted in a lower greenhouse

shell temperature. These photos also clearly show a stratification of temperature within

the greenhouse dome. The top of the dome was warmed by radiation of the growth light

and the air from the heating system that the fan blew across the inside shell. As the

greenhouse shell was colder close to the water recollection funnel (black surface)

condensation was more likely to occur there. The bottom of the greenhouse dome near

the aluminum base showed less condensation, because the relative humidity was less in

the lower part of the dome as the flasks were installed in the upper level. The curvature of

the dome shell and the slope of the recollection funnel led to runoff of the water to the

collection container located on scale 1 (see Figure 4-13). Under certain conditions, ice

crystals had been observed on the aluminum base as temperatures may have dropped

below 0C, even though the dome base was well insulated.

During the long-term experiments involving lettuce plants (see next section) water

evaporated from the collection container and the relative humidity in the bottom part of

the greenhouse increased. Condensate and frost formed on the lower part of the

greenhouse shell and the dome base plate due to the low temperatures. This can be clearly

observed in the two photos shown in Figure 7-1, which were taken after the vacuum

chamber was opened at the end of the 7 day experiment.




























A)



















B)
Figure 4-23. Condensation inside of greenhouse shell with a greenhouse air temperature
of 20 C. A) Freezer temperature at 0 oC. B) Freezer temperature at -20 oC.

Heat and Mass Transfer Experiments with Plants

Medium-term Plant Experiment involving Buttercrunch Lettuce

Selection criteria for the plants involved in the Mars greenhouse experiments were

a short growth period, high evapo-transpiration rate, tolerance to cold temperatures, low









light requirements, suitability for hydroponic growth in 150 ml Ehrlenmeyer flasks and

dome height constraints. Buttercrunch lettuce (Lactuca Sativa cv. Buttercrunch) was

selected as lettuce is one of NASA's baseline crops (see Chapter 2) and it fulfills the

criteria mentioned above. Six weeks old lettuce plants grown in soil under atmospheric

conditions were transplanted into flasks filled with 50% water and 50% nutrient solution.

The flasks were wrapped in aluminum foil to avoid growth of algae caused by direct

radiation onto the nutrient solution. One hole of the stopper was cut open from the side

and the plant was carefully inserted. Evaporation of the hydroponic solution was avoided

by sealing the gap between the plant and the stopper with putty as shown in Figure 4-24.

Eight flasks were placed into the greenhouse dome; two on each scale (see Figure 4-25).





















A) B)

Figure 4-24. Buttercrunch lettuce in Ehrlenmeyer flask. A) The average height of the
shoot zone is 15 cm. B) Putty and a stopper prevent evaporation of the
hydroponic solution as they separate the root from the shoot zone.































Figure 4-25. Installation of flasks containing the lettuce plants onto the scales.

The plants were exposed to a controlled environment inside the greenhouse dome

for 36 hours. The environment conditions and their control methods are summarized in

Table 4-3. The air temperature and the gas composition were tightly controlled by

actuators. A total pressure of 25 kPa was selected as plants still were to be productive at

this low pressure level. The partial pressure of oxygen was set to 4 kPa, resulting in an

oxygen level of 16%, lower than on Earth because oxygen is a very precious resource

during a space mission on Mars: it must be shipped from Earth as it is barely available in

the Mars atmosphere and will be mainly used for human breathing. The partial pressure

of carbon dioxide was set to a high level of 0.8 kPa, as carbon dioxide can easily be

extracted from the Mars atmosphere. High levels of carbon dioxide are known to enhance

plant growth.

The greenhouse humidity was passively controlled by the equilibrium between

evaporation of the water from the plants and the open water surfaces versus the










condensation of water on the cold surfaces. The variation of the humidity in the time

range of 5 to 10 hours after the experiment had been started can be observed in Figure

4-26. The light was switched on during the complete experiment and the radiation level

was measured to be at a constant value of 684 pmol/(m2s) at plant level. Therefore, no

condensation occurred on the greenhouse surface directly below the growth light.

Table 4-3. Buttercrunch lettuce environmental conditions and their control.
Parameter Value Controlled by
Greenhouse Dome 20 heating coil
20 0C
Air/Plant Temperature [ freezer temperature
Greenhouse Domev e plant evaporation (passive control)
Relative Humidity v condensation on cold surface (passive control)
Greenhouse Dome 25 kPa N2, 02 and CO2 mass flow controllers
Total Pressure [ vacuum pump (& passively by leakage)
Greenhouse Dome Oxygen 4 kPa 02 mass flow controller
Partial Pressure [ vacuum pump (& passively by leakage)
Greenhouse Dome Carbon 0.8 kPa CO2 mass flow controller
Dioxide Partial Pressure vacuum pump (& passively by leakage)
Greenhouse Dome 684 / growth light on
Radiation Level 6 molm) growth light off (& passively by condensation)
Vacuum Chamber 0.6 kPa leakage (passive control)
Total Pressure vacuum pump
t thermostat on freezer
Freezer Temperature -20 C ( 1C) thermostat on freezer
thermostat on freezer

60
60 T~3 Air/Plant
50 ".....- .. T4 Fan Exhaust
-. ,40 T6 -Window
0, --T7 -Wall
e- 30 Relative Humidity

20
S20

10
0 0

-10
-10 -------------------------------
-20
300 350 400 450 500 550 600

Time [min]
Figure 4-26. Constant temperature distribution and varying relative humidity during the
buttercrunch lettuce experiment.









Figure 4-27 depicts the rates of plant evapo-transpiration from the scales 2-5.

Scale 1 measured the water in the recollection container. It had been filled with

245 grams of water before the experiment in order to keep the humidity high at the

beginning of the experiment. The change of the mass value of scale 1 is the difference

between water evaporating from the open water surface and recollected water dripping

into the container. A positive slope indicates more water was recollected than evaporated,

a negative slope leads to the conclusion that more water was evaporated than re-collected.

Surprisingly, in this experiment the slope of scale 1 had a negative value of-0.0661.

Thus, the recollection system proved to be inefficient as less water was recollected than

had evaporated. This resulted in higher humidities in the lower greenhouse part and

therefore water condensation on the cold dome aluminum base. The plant evapo-

transpiration can be calculated by dividing the water evaporation rate of the scale by the

plant leaf area per scale.

In order to calculate the plant leaf area, the leaves were cut off the plants at the end

of the experiment and the silhouettes were drawn on a white sheet of paper. The

silhouettes were scanned together with a calibration square. The pictures were converted

to black and white images and the silhouettes were filled with black ink. The pictures

were read into matlab and an image processing code determined the ratio of white to

black pixels. The resulting values of the plant leaf areas per scale are given in Table 4-4.

Plant evapo-transpiration varied from 1.6 g/(min m2) to 2.87 g/(min m2). Evapo-

transpiration rates for lettuce under atmospheric conditions are given as 1.23 g/(min m2)

in NASA's Baseline Values and Assumptions Document (Hanford, 2004). Low pressure

increases evaporation rates and therefore the evapo-transpiration values calculated in the










research described in this document seem reasonable. It should be noted that evapo-

transpiration rates are further affected by other factors, including relative humidity, air

temperature, leaf temperature, radiation level and lettuce cultivar, making it difficult to

compare the values of different experiments.


--- Scale 1
380 -- Scale 2

360 Scale 3

340 --i- Scale 4

320 --- Scale 5

300 ml = -0.0661*t + 249.99
S8 R2 = 0.8428
280 m2 = -0.1382*t + 379.57
R2 = 0.9692
260
m3 = -0.1308*t + 370.65
240 __R2 = 0.9279
m4 = -0.1187*t + 392.48
220R2 = 0.8827
200 m m5 = -0.1052*t + 348.2
300 350 400 450 500 550 600 R2 = 0.9003
Time [min]

Figure 4-27. Plant evapo-transpiration rates of plants from 5 to 10 hours after the
beginning of the experiment.

Table 4-4. Evaporation rates per scale with scales 2-5 containing two lettuce plants each.
Scale 1 Scale 2 Scale 3 Scale 4 Scale 5
Evaporation/Time [g/min] 0.0661 0.1382 0.1308 0.1187 0.1052
LeafArea Plant 1 [m] 0.042335 0.0234 0.039542 0.032599
LeafArea Plant 2 [m] 0.033219 0.02215 0.023296 0.033002
Total Leaf Area [m2] 0.075554 0.045549 0.062838 0.065601
Evapo-transpiration Rate[g/min/m2] 1.83 2.87 1.89 1.60

At the end of the experiment, seven out of the eight plants appeared to be healthy

and without visible damage. One plant started wilting after the water level inside the flask


Ann _









decreased to a point where the roots could not reach the remaining water and nutrient

solution (see Figure 4-28).






















Figure 4-28. Lettuce plants after an exposure of 36 hours to the controlled Mars
greenhouse environment. Healthy plant without any visible physical damage
on the left side, wilted plant with roots that do not reach water and nutrient
supply on the right side.


Long-term Plant Experiment involving Galactic Lettuce

For the long-term plant experiments Galactic lettuce plants (Lactuca Sativa cv.

Galactic) were selected (see Figure 4-29). The plants were grown from seeds in the

departmental environment-controlled growth chamber under atmospheric conditions with

a day-night cycle of 12 hours. After four weeks, measuring an average height of 8 cm, the

lettuce plants were transplanted into the flasks filled with the hydroponic nutrient

solution. Similar to the previous experiment, eight plants were installed into the

greenhouse dome, two per scale. Table 4-5 lists the environmental conditions the plants

were exposed to and their control. All environmental parameters except of the total dome









pressure were kept the same as in the buttercrunch lettuce experiments. The greenhouse

dome total pressure was lowered to 20 kPa.


Figure 4-29. Galactic lettuce plant for long-term experiments with an average height of
8 cm.

Table 4-5. Galactic lettuce environmental conditions and their control.
Parameter Value Controlled by
Greenhouse Dome 2 heating coil
20 0C
Air/Plant Temperature { freezer temperature
Greenhouse Dome variable plant evaporation (passive control)
Relative Humidity v condensation on cold surfaces (passive control)
Greenhouse Dome 20 kPa N2, 02 and CO2 mass flow controllers
Total Pressure [ vacuum pump (& passively by leakage)
Greenhouse Dome 4 kPa 02 mass flow controller
Oxygen Partial Pressure [ vacuum pump (& passively by leakage)
Greenhouse Dome Carbon 0.8 kPa CO2 mass flow controller
Dioxide Partial Pressure vacuum pump (& passively by leakage)
Greenhouse Dome 0 or 684 I growth light on
Radiation Level pmol/(m2s) 1 growth light off (& passively by condensation)
Vacuum Chamber 0.6 kPa leakage (passive control)
Total Pressure vacuum pump
t thermostat on freezer
Freezer Temperature -20 C ( 1C) thermostat on freezer
{ thermostat on freezer










Figure 4-30 shows the locations of the sensors for the second set of plant

experiments. Various temperature sensors were added or moved from their previous

position: T2 was moved from the recollection funnel to the inside of the greenhouse dome

shell, T5 was moved to the side of the exterior greenhouse shell, T6 was fixed to the

inside of the vacuum chamber wall, T7 on the outside of the chamber wall at medium

height, T8 at the bottom of the chamber wall and T9 measured the freezer air temperature.


HPS Growth Light (1000 W)

00000000



r- WIdow -,


Vacuum Chamber


T7


7/ TS


Figure 4-30. Sensor locations for the long-term experiments with galactic lettuce plants.


Plants were exposed to the low pressure controlled greenhouse environment for

7 days. Initially they were exposed to the growth light for 24 hours until steady state of

all parameters was reached, the following days the day-night cycle was set to 12 hours.

Figure 4-31 illustrates the temperature changes over time during the experiment. The air


E








temperature at plant level was controlled at 20 oC, the freezer temperature was controlled

at -20 oC (+ 10C). Figure 4-32 depicts the steady state temperatures during the day and

night cycle, when the growth light was switched on/off, respectively. A heating power of

40 Watts was required to maintain an air temperature of 20 C at the plant level during

the day cycle, a heater power of 119 Watts during the night cycle. The temperature of the

fan exhaust was higher for the night cycle as more heating was required, all other

temperatures were lower when the growth light was switched off compared to when the

growth light was switched on.


r


ri


ESE E i
Light Light Light Light Light Light Light Light Light Light Light LightLigh
ON OFF ON OFF ON OFF ON OFF ON OFF ON OFF ON
0 24 48 72 96 120 144 168
Time [hours]


-T3 Air/Plant

-T4 Fan
Exhaust
-T2 Inside
Shell
-T5 Outside
Shell
-T6 Chamber
Wall Inside
--T7- Chamber
Wall Outside
Middle
- T9 -Air
Freezer
- T8 Chamber
Wall Outside
Bottom


Figure 4-31. Temperature variations during the long-term galactic lettuce experiment.


w c~ d-1
pi rcl
r ~Y ~C1


P~r






60



25
20 0 / Light off (119 W Heating)
2 15 A Light on (40 W Heating)
2 10 A
5 A
e0 5
I! -5 ------------------------------------
E
0
0
S-5
C,
>, -10
-15 I



C 0-20 E -
o o
3 1 ------------- -------<-----


co x E ~E.- a) w r E EE
LL U, 0 --


Figure 4-32. Comparison of steady state temperature distribution of the day cycle to the
night cycle during the long-term plant experiments.


Figure 4-33 shows the variation of the relative humidity during the day and night

cycle. Before the experiment started, when the greenhouse dome was closed but the

freezer not switched on yet, the relative humidity rose to 70%. This high humidity was

due to addition of water vapor to the atmosphere by plant evapo-transpiration and the

lack of water vapor removal by condensation as the temperatures of the all surfaces of the

greenhouse were at temperatures above 20 C and therefore above the dew-point.

Relative humidity decreased to 35% during the first 24 hours when the growth light was

switched on. During the following day-night cycles the relative humidity varied between

a maximum of 35% when the growth light was switched on and a minimum of 28% when

the growth light was switched off Relative humidity was low during the night cycle as

more condensation occurred due to the lower temperatures of the greenhouse surfaces.










Relative humidity was high during the day due to less condensation and more evapo-

transpiration of the plants.


80

70

60

50

40

30

20

10

0


Light Light Light Light Light Light Light Light Light Light Light
OFF ON OFF ON OFF ON OFF ON OFF ON OFF

4 48 72 96 120 144
Time [hours]


Figure 4-33. Relative humidity variation during the day and night cycle.



Figure 4-34 shows the effectiveness of the gas composition control, resulting in a

constant gas composition even when all other environmental parameters were subject to

great variations. Changes in temperature, relative humidity and radiation level did not

affect the gas composition of 20 kPa total pressure, 4 kPa oxygen partial pressure and 0.8

kPa carbon dioxide partial pressure.










16

14
--N2
S12 _-02
c 12
2C02
S10

c. 8

u6
aW
: 8 -----------------.. .---- --.------. .. ..--------. . ..-----------_---...-"--..
E




0
0 24 48 72 96 120 144 168
Time [hours]

Figure 4-34. Gas composition control of the greenhouse atmosphere. Set points are
20 kPa for total pressure, 4 kPa for oxygen partial pressure and 0.8 kPa for
carbon dioxide partial pressure.


Figure 4-35 shows the mass values of the scales that were measured from 5 to 10 hours

after the galactic lettuce plant experiment had started. For this experiment only two out of

the five scales were connected to the data acquisition system due to the limited amount of

available channels because of the added temperature sensors. The evapo-transpiration

rates of the plants were determined with the same leaf area calculation method described

earlier in this Chapter. The evapo-transpiration rates were found to be 3.71 g/min/m2 for

scale 2 and 4.84 g/min/m2 for scale 3. These evaporation rates are slightly higher than the

ones in the Buttercrunch lettuce experiments. One possible reason is that the pressure was

reduced from 25 kPa to 20 kPa, leading to an increase in mass diffusivity and therefore

higher evaporation rates.











290
280
270
260
250
240
230
220
210
200


-)- Scale2

-- Scale3





m3 = -0.1132*t + 314.83
R2 = 0.9801

m2 = -0.1128*t + 303.16
R2 = 0.9572


300 360 420 480 540 600
Time [min]

Figure 4-35. Water evaporation measured on scale 2 and 3 during the galactic lettuce
plant experiment.


Figure 4-36 shows the galactic lettuce plants after they were exposed to the low

pressure Mars greenhouse environment for 7 days. They showed only slight visible

physical damage such as minor signs of water stress (see Figure 4-37 A and B).


Figure 4-36. Galactic lettuce plants after exposure of seven days to the low pressure Mars
greenhouse environment.
















































SB)
Figure 4-37. Visible damages of the plants. A) and B) Wilting/drying of the plant leaves.














CHAPTER 5
MATHEMATICAL MODEL DEVELOPMENT

Effect of Low Pressure on Heat and Mass Transfer

Operating the greenhouse dome at a reduced pressure in the low pressure Mars

environment has a huge influence on the heat and mass transfer. Of the three heat transfer

modes conduction, convection and radiation, convective heat transfer is the one that is

most dependent on the total pressure. Regarding the mass transfer, evaporation rates have

to be analyzed for pressure dependency. Furthermore, the effect of the low pressure on

psychrometric relations should be studied, in order to be able to determine the state of the

moist air.

Convection Heat Transfer

Convection is defined as heat transfer between a surface and a fluid moving over

the surface. Convective heat transfer at low pressures is analyzed based on the equations

given in Incropera and DeWitt (2002). The convection heat transfer depends on the

convection coefficient and on the temperature difference of the moving fluid and the

surface:

q = h(T, T) (5-1)

where: q" = heat flux [W/m2]

h = convection coefficient [W/(m2 K)]

T = surface temperature [K]

T = fluid temperature [K]









If there is a temperature difference between the fluid stream and the surface a

thermal boundary layer develops. The local heat flux may be obtained by applying

Fourier's Law to the heat flux at the surface where y = 0. As there is no fluid motion at

the surface, energy transfer occurs only by conduction:

q T
q =-k fT (5-2)
f = y=0


Combining both equations leads to the following convection coefficient:

kT
-k T
h = f ly=0
h=

In order to find out if the boundary layer is laminar or turbulent the Reynolds

number has to be calculated:

n u L


(5-3)


Re, (5.

where: ReL = Reynolds number [-]

p = density [kg/m3]

um = velocity [m/s]

/ = absolute viscosity [N s/m2]

L = characteristic length [m]

The critical Reynolds number for which transition from laminar to turbulent flow

occurs is 5x105.

A parameter that provides a measure of the convection heat transfer is the

dimensionless temperature gradient, the Nusselt Number:

hL BT *
Nu= + = f(x,ReL,Pr) (5.
kf a y* =O


-4)


-5)









T-T
where: T*= T-T, = dimensionless temperature


y* Y = dimensionless variable

The average Nusselt number represents the average heat transfer independent of

location:

hL
NUL f(Re,,Pr) (5-6)
k,

The Prandtl number is the ratio of the properties v/a:


Pr= Cp/ (5-7)
a kf

where: v= dynamic viscosity [m2/s]

a = thermal diffusivity [m2/s]

c = specific heat [kJ/(kg K)]

kf= conduction coefficient [W/(m K)]

Laminar flow over a horizontal plate

For laminar flow, the Reynolds number has to be below the critical Reynolds

number of 5x105:


ReL,ol p ujL 5x 10 (5-8)


For laminar flow the Nusselt number may be obtained from:


NuL = 0.664ReL Pr3 Pr > 0.6 (5-9)


Inserting Equations 5-4 and 5-7 into Equation 5-9, results into the following convection

coefficient:









1/2 (kf)2/3
S= 0.664( (Cp)1/3 Pr > 0.6 (5-10)
(//)1/6 1/2
Therefore, convective heat transfer depends on the following parameters: High

density, specific heat and thermal conductivity increase heat transfer. Low absolute

viscosity increases heat transfer.

Specific heat as well as absolute viscosity are independent of density, i.e., pressure.

They are only dependent on temperature. Thermal conductivity is also independent of the

air pressure. Thus, the convection transfer coefficient decreases with the square root of

density/pressure.

hL ~ (pressure)1 /2 for density ~ pressure (T = const) (5-11)

Thus, the convection coefficient of a gas at a pressure of 20 kPa is 44.7 % of the

convection coefficient of gas at a pressure of 100 kPa for laminar fluid flow with same

velocity and temperature:

I20_1/2
hL(20kPa) =- x hL (100kPa)= 0.447 hL(100kPa) (5-12)

Turbulent flow over a horizontal plate

For turbulent flow, the Reynolds number has to be above the critical Reynolds

number of 5x105. For turbulent flow the Nusselt number may be obtained from:

hLL 4/5 1/3
NuL h- L 0.037ReL Pr (5-13)

Inserting the Reynolds and the Prandtl number into Equation 5-13:


hL = 0.037 (pu)4/5 ( 3 (kL2/3 (5-14)
(k)7/15 (Cp)









Thus, the convection transfer coefficient decreases with decreasing density, i.e.

pressure. The convection coefficient of a gas at a pressure of 20 kPa is 27.6 % of the

convection coefficient of a gas at 100 kPa for turbulent fluid flow with the same velocity

and temperature:

h (20kPa) = (20/100)4/5 x h (100kPa) = 0.276hL (100kPa) (5-15)

Laminar free convection on a vertical plate

For laminar free convection on a vertical plate, the Nusselt number is defined as:

1/4
NuL 4kf 4- L f(Pr) (5-16)


0.75Pr1/2
where: f(Pr) =0.75
(0.0609 +1.221Pr2 + 1.238 Pr)1/4

The Grashof number is the ratio of the buoyancy to the viscous force:

gP(T T,)L
GrL = (5-17)



where: g = gravitational constant [m/s2]

l = 1/Th = coefficient of thermal expansion [1/K]

By inserting the Grashof number into Equation 4-16, the convection coefficient is:

4 14/
4(gfl(Ts -T)L ,12 kf
hL 2 f (Pr) (5-18)
3 4p L

Thus, the convection transfer coefficient decreases with decreasing density, i.e.

pressure. The convection coefficient of a gas at a pressure of 0.6 kPa is 7.75 % of the

convection coefficient of a gas at 100 kPa for laminar free vertical convection at the same

temperature:









h,(0.6kPa) = (0.6/100)1 2 xh (1OOkPa) = 0.0775hL (lOOkPa) (5-19)

It should be noted, that the convection coefficient also depends on gravity. Thus it

would be further reduced by 61.3% on Mars, where the gravitational constant is only 3.69

m/s2.

h (3.69m/s2) = (3.69/9.81)1/2 x h (9.81m/s2) = 0.613 hL (9.81m/s2) (5-20)

External free convection for a sphere

The following correlation is recommended for spheres exposed to external free

convection flow:

1/4
hDD + 0.589RaD 11
ND kf+ (0. 9 /164/9 RaD <10 Pr > 0.7 (5-21)
ky [1+(0.0469/Pr)9/16

The Rayleigh number is defined as:

g8(T, -T.)D3 c, p
RaD = GrD Pr = (TO (5-22)

Sk

Combining Equation 5-21 and Equation 5-22 leads to the following convection

coefficient:



0.589 gP(Ts -T.)D3 Cp 1/41/2
/P2 kf kf


1+ 0.0469/(cPf-)
k-f

Therefore, the convection transfer coefficient decreases with decreasing density,

i.e. pressure. As the pressure variable in Equation 5-23 is implicit, a direct ratio of the

convection coefficient at standard pressure to the one at reduced pressure cannot be

derived.









Mass Transfer by Evaporation

The diffusive flux depends on the mass diffusivity coefficient. Assuming ideal gas

behavior, the kinetic theory of gases predicts that the mass diffusivity is indirectly

proportional to the pressure at a constant temperature.

T3/2
DAB (5-24)
P

where: DAB = Mass diffusion coefficient [m2/s]

T= temperature [K]

p = pressure [kPa]

Thus, reducing the pressure to 20 kPa, would increase the mass diffusivity 5 times:

DAB (20kPa) = (100 / 20) x DAB (100kPa) = 5 x DAB (100kPa) (5-25)

Table 5-1 gives an overview of the effect of reduced pressure on the convective

heat transfer coefficient and the mass diffusivity. Convection reduces considerably in the

low pressure Mars greenhouse dome. In the vacuum chamber, convection is considered to

be negligible, the major mode of heat transfer between the dome and the chamber is

radiation. Mass diffusivity and therefore evaporation rates increase significantly at low

pressures.

Table 5-1. Effect of reduced pressure on convective heat transfer coefficient and mass
diffusion coefficient.
Greenhouse Dome Vacuum Chamber
CONVECTION h(20 kPa)/ h(0.6 kPa)/
h(100 kPa) h(100 kPa)
Forced Convection Horizontal Plate 44.7% laminarr)
27.6% (turbulent)
Free Convection Vertical Plate 7.75% (Earth)
7.75% x 61.3% (Mars)
External Free Convection Sphere See Equation 5-23
DIFFUSION D(20 kPa)/ D(100 kPa)
Mass Diffusivity 500%








Development of Low Pressure Psychrometrics for Non-Standard Atmospheres

While most publications address the psychrometric relationships of water vapor

and air for open systems, sea level pressure and Earth's standard atmosphere composition

(78.08% N2, 20.98% 02, 0.934% Ar, 0.0314% CO2, etc), there is nothing in the theory for

developing the relationships that restricts them to these systems (Shallcross, 1997;

ASHRAE, 2001). In the literature, very few publications are dedicated to altitude effects

on psychrometrics, as barometric pressure decreases with altitude (Haines, 1961;

Hitchcock and Jacoby, 1980; Erickson and Garrett, 1981). Figure 5-1 shows the effect of

reduced pressure on the saturation line of the psychrometric chart. However, psychro-

metric charts that correct for altitude assume that the gas composition is equal to Earth's.

Compared to the Earth atmosphere, the atmosphere of the greenhouse differs significantly

in terms of pressure and gas constituents. Furthermore, the greenhouse dome is a closed

system, whereas the classic psychrometric relations were developed for open systems.

0.25
-+- 20% patm (20.3kPa)
i' -e- 40% patm (40.5kPa)
"0 -+- 60% patm (60.8kPa)
0.2 80% patm (81.0kPa)
S-4- 100% patm (101.3kPa)

SEarth Standard Gas Composition
o 0.15 (78.08% N2, 20.948% 02, 0. 934% Ar,
0.0314% C02, etc)

*I 0.1
^ ,


-5 0 5 10 15 20 25 30 35
Temperature [C]
Figure 5-1. Effect of pressure on the saturation line of an open system with standard
atmosphere composition









The psychrometric relations are based on the following fundamental laws of

physics: ideal gas equation of state, conservation of energy, conservation of mass,

Dalton's law of partial pressures and the Gibbs-Dalton law for energy, enthalpy and

entropy (Gatley, 2002). If the total pressure of the system differs significantly from the

sea level pressure of 101.3 kPa or the dry gas composition differs from the standard Earth

atmosphere, the calculations can be modified to reflect this.

The psychrometric chart is a tool for determining the properties of the moist air and

for visualizing the changes of these properties as a consequence of psychrometric

processes. The-dry bulb temperature is shown on the abscissa of the chart and therefore

the dry-bulb temperature isolines are vertical. The second psychrometric chart coordinate

(the ordinate) is the humidity ratio, which is defined as the ratio of the mass of water

vapor to the mass of the dry air in a moist air sample. Consequently, the humidity ratio

isolines are horizontal. Generally, the properties isolines plotted on a psychrometric chart

are: dry-bulb temperature isolines, humidity ratio isolines, adiabatic saturation

temperature isolines, relative humidity isolines, water vapor saturation curve, enthalpy

isolines and specific volume isolines (Gatley, 2002). The following section develops

general psychrometric relations that can be used for closed low pressure systems and

non-standard gas compositions.

Gas Theory

Equation of state

The classic psychrometric relationships are based on the assumption that moist air

is a mixture of independent perfect gases (i.e. dry air and water vapor), and each gas is

assumed to obey the perfect gas equation of state, where the compressibility factor equals

one. If a low pressure environment is chosen, the perfect gas law applies even better,









since the virial coefficients play less role in low pressure gases as the interaction between

molecules is less common. Therefore, the compressibility factor converges to 1 with

decreasing pressure.


Z-= = 1+(B'p)+(C'p2)+(D'p3)+... (5-26)
RT
where: Z= compressibility (Z=1 for perfect gas)

p = pressure

B', C ',D'= virial coefficients

Dry gas mixture

The dry gas mixture includes all gas components that remain gaseous and do not

condense in the chosen temperature range. The molecular mass as well as the specific

heat are important parameters for the development of the psychrometric relationships.

If the partial pressures of the dry gas components are known, the content by volume

can be obtained:


Vdy,, dry, (5-27)
Pdry

where: ydry,, = dry air content of gas component i by volume

pdry,z = partial pressure of gas component i

pdry = total pressure of dry gas

Furthermore, the molecular mass of the dry gas mixture can be calculated:

mdr, = Vdy,2Mdy,z (5-28)

md =I Vdc/d,rMdy, (5-29)

where: mdry, = mass of gas component i

Mdry,, = molecular mass of gas component i

mdry = total mass of dry gas









By calculating the composition of the dry gas mix by mass, the specific heat of the

dry gas mixture is obtained:

m
dry, (5-30)
mdry,total

cp,dry,l dry,, p,dry, (5-31)

cp,dry dry,, p,dry,, (5-32)

where: (dry,t = dry air content of gas component i by mass

Cp,dry,1 = specific heat of gas component i

Cp,dry = specific heat of dry gas

The specific enthalpy of dry air is dependent on the temperature of the gas mix:

hdry = Cp,dry 1 (5-33)

where: hdry = specific enthalpy of dry air

t = temperature of gas mix

Water vapor component

The molecular mass of water is 18.01528. The specific enthalpy of the saturated

water vapor component is

hg = (2501+1.805t) (5-34)

where: hg = specific enthalpy of water vapor

Construction of Modified Psychrometric Chart

Saturation line

The humidity ratio is defined as the ratio of the mass of water vapor to the mass of

dry air contained in a sample. At saturation, air contains the maximum amount of water:

mW xW, 18.01528 pw,(T)
W, m x Pd ((5-35)
mdry Xdry mdy Pdy (T)









where: W, = humidity ratio at saturation

Xw, =mole fraction of water vapor in saturated moist air

Xdry = mole fraction of dry air in moist air

The total pressure of the moist air is the sum of the partial pressure of the dry air

component and the water vapor.

Ptotl = Pd (T) + p (T) (5-36)

where: otal = total pressure (barometric pressure)

pw = partial pressure of water vapor

The classic psychrometric equations are for open systems where the partial pressure

of the water vapor is small compared to the total pressure. The total pressure is assumed

to be constant even when state change of water occurs, i.e. the partial pressure of dry air

decreases when water vapor pressure increases and vice versa. In the case of a closed

system, the partial pressure of the dry air component depends on the temperature and the

initial conditions, as no dry gas leaves or enters the system boundaries and the volume is

constant:


Pdy (T) = T (5-37)

where: pdry = initial pressure of dry air component

To= initial temperature of the gas mixture

Thus, increasing temperature and evaporation lead to an increasing total pressure,

decreasing temperature and condensation to a decreasing total pressure.

The saturated water vapor pressure is a function of the dry-bulb temperature only:

Saturation pressure over ice for the temperature range of -100 to 00 is given by

In p = C / T + C2 + CT + C4T2 + CT3 + C6T4 + C7 InT (5-38)









where: C1 = -5.6745359E+03
C2= 6.9325247E+00
C3= 9.6778430E-03
C4= 6.2215701E-07
C5= 2.0747825E-09
C6= -9.4840240E-13
C7= 4.1635019E+00
Saturation pressure over liquid water for the temperature range of 0 to 2000 is given by

In pw = C, /T + C9 + CoT + C1,T2 + C,2T3 + C3 In T (5-39)

where: C8= -5.8002206E+03
C9= 1.3914993E+00
Clo=- 4.8640239E-02
C1 = 4.1764768E-05
C12= -1.4452093E-08
C13= 6.5459673E+00
In both Equations:
In = natural logarithm

pws= saturation pressure [Pa]
T = absolute temperature [K]

Humidity isolines

The relative humidity is the ratio of the mole fraction of water vapor in a given

moist air sample to the mole fraction in an air sample saturated at the same temperature

and pressure:



St rws(5-4 t0)


where: O= relative humidity









The relative humidity isolines are constructed for a given relative humidity and

varying dry-bulb temperatures:


W W x m Op(T) (5-41)
mdry Xdry mdry Pdry

The degree of saturation equals to the relative humidity for closed systems:


w -0 w (5-42)
s t,p PWS tp

where: p = degree of saturation

Specific enthalpy isolines

The specific enthalpy is the sum of the dry gas specific enthalpy plus the specific

enthalpy of the water vapor:

h = hdy+ Wh = p,dryt + W(2501 +1.805t) (5-43)

The lines of constant enthalpy are constructed for a given enthalpy and varying dry

bulb temperatures:

h (c,d, t)
W = (5-44)
2501+1.805t

Specific volume isolines

The specific volume of a gas mixture is defined as the volume of the mixture per

unit dry gas:

v =- (5-45)
mdry

where: v = specific volume of moist air in terms of unit mass of dry air

V= total volume









The gas volume as well as the mass of the dry air of a closed system are constant.

Therefore, the specific volume is also constant:

RT RT
v = o= const. (5-46)
mdryPdry mdry dy

Vapor pressure isolines

The humidity ratio is related to the water vapor pressure and the partial pressure of

the dry air as follows:


W = m p. (5-47)
mdry Pdy

Adiabatic saturation temperature isolines

The wet-bulb temperature is considered to be the temperature measured by a

thermometer with the outside surface kept wet. As moist gas passes the thermometer,

some of the liquid evaporates causing the temperature of the wet-bulb thermometer to

drop. As wet-bulb temperature is dependent on the gas velocity in respect to the

thermometer and the radiative heat transfer, it is not possible to predict the wet-bulb

temperature precisely. Consequently, adiabatic saturation temperature is considered in

this document. Adiabatic saturation temperature tad is defined as the temperature at which

water, by evaporating into moist air at a given dry-bulb temperature and absolute

humidity can bring the air to saturation adiabatically at the same temperature tad

(Shallcross, 1997). However, for the air-water system of this document the curves of

adiabatic saturation temperature and wet-bulb temperature coincide. The adiabatic

saturation temperature is related to the humidity ratio by the following correlation:

(2501 -2.381 td)Wvet -cp,dry(t- td)
2501= (5-48)
2501+1.805t 4.186tad


where: tad = adiabatic saturation temperature










Dew-point temperature isolines

The dew-point temperature is related to the humidity ratio by the following

equation:


m, p,(Tdw)


(5-49)


where: Tdew = dew-point temperature

Table 5-2 lists the psychrometric parameters of the greenhouse dome atmosphere

with the selected composition for the plant experiments. Figure 5-2 shows the

psychrometric chart for the greenhouse dome atmosphere. It can be utilized to determine

the dew-point temperature at which condensation starts to occur on the greenhouse shell.

One important difference from the classical psychrometric chart is that the dew-point

temperature isolines are not horizontal, as the pressure of the dry air changes with

temperature in a closed system.

Table 5-2. Psychrometric parameters of a low pressure atmosphere (76% N2, 20% 02,
4% C02) with initial conditions of 20 kPa dry air at 200C and a constant
specific volume of 0.004138m3/kg.
Tdry Humidity Pws Pw Pt w tdew J h tad
[C] 0 [Pa] [Pa] [Pa] [kg/kgda] [oC] [kJ/kgda] [C]
5 100% 872.49 872.49 19849 0.0281 5.02 1 75.6 5.00
10 100% 1228.00 1228.00 20546 0.0389 10.03 1 108.0 10.00
15 100% 1705.45 1705.45 21364 0.0531 15.03 1 149.2 15.00
20 100% 2338.80 2338.80 22339 0.0715 20.01 1 201.5 20.00
25 100% 3169.22 3169.22 23510 0.0953 25.00 1 267.7 25.00
30 100% 4246.03 4246.03 24928 0.1256 29.98 1 350.9 30.00
5 90% 872.49 785.24 19762 0.0253 3.51 0.9 68.5 3.79
10 90% 1228.00 1105.20 20423 0.0350 8.47 0.9 98.2 8.68
15 90% 1705.45 1534.90 21194 0.0478 13.40 0.9 135.8 13.58
20 90% 2338.80 2104.92 22105 0.0644 18.33 0.9 183.4 18.48
25 90% 3169.22 2852.29 23193 0.0858 23.25 0.9 243.4 23.39
30 90% 4246.03 3821.43 24504 0.1130 28.17 0.9 318.8 28.30
5 80% 872.49 697.99 19675 0.0225 1.83 0.8 61.5 2.48
10 80% 1228.00 982.40 20300 0.0311 6.74 0.8 88.4 7.27
15 80% 1705.45 1364.36 21023 0.0425 11.61 0.8 122.3 12.04
20 80% 2338.80 1871.04 21871 0.0572 16.47 0.8 165.2 16.83
25 80% 3169.22 2535.37 22876 0.0762 21.32 0.8 219.2 21.64
30 80% 4246.03 3396.82 24079 0.1005 26.16 0.8 286.7 26.45





Pw Pt W tdew 9 h tad


Table 5-2 continued
Tdry Humidity Pws
[C] 0 [Pa]
5 70% 872.4
10 70% 1228.(
15 70% 1705.z
20 70% 2338.
25 70% 3169.:
30 70% 4246.(
5 60% 872.4
10 60% 1228.(
15 60% 1705.z
20 60% 2338.
25 60% 3169.:
30 60% 4246.
5 50% 872.4
10 50% 1228.(
15 50% 1705.z
20 50% 2338.
25 50% 3169.:
30 50% 4246.
5 40% 872.4
10 40% 1228.
15 40% 1705.z
20 40% 2338.
25 40% 3169.:
30 40% 4246.
5 30% 872.4
10 30% 1228.
15 30% 1705.z
20 30% 2338.
25 30% 3169.:
30 30% 4246.(
5 20% 872.4
10 20% 1228.
15 20% 1705.z
20 20% 2338.
24 20% 2985.
30 20% 4246.(
5 10% 872.4
10 10% 1228.(
15 10% 1705.z
20 10% 2338.
25 10% 3169.:
30 10% 4246.(


[Pa]
9 610.74
)0 859.60
15 1193.81
80 1637.16
22 2218.45
)3 2972.22
9 523.49
)0 736.80
15 1023.27
80 1403.28
22 1901.53
)3 2547.62
9 436.24
)0 614.00
15 852.72
80 1169.40
22 1584.61
)3 2123.02
9 348.99
)0 491.20
15 682.18
80 935.52
22 1267.69
)3 1698.41
9 261.75
)0 368.40
15 511.63
80 701.64
22 950.76
)3 1273.81
9 174.50
)0 245.60
15 341.09
80 467.76
13 597.03
)3 849.21
9 87.25
)0 122.80
15 170.54
80 233.88
22 316.92
)3 424.60


lC] [kJ/kgda] [oC]


[Pa] [kg/kgda]
19587 0.0197
20177 0.0272
20853 0.0371
21637 0.0501
22560 0.0667
23654 0.0879
19500 0.0169
20055 0.0233
20682 0.0318
21403 0.0429
22243 0.0572
23230 0.0754
19413 0.0141
19932 0.0194
20512 0.0265
21169 0.0358
21926 0.0477
22805 0.0628
19326 0.0112
19809 0.0156
20341 0.0212
20936 0.0286
21609 0.0381
22381 0.0502
19238 0.0084
19686 0.0117
20171 0.0159
20702 0.0215
21292 0.0286
21956 0.0377
19151 0.0056
19563 0.0078
20000 0.0106
20468 0.0143
20870 0.0180
21531 0.0251
19064 0.0028
19441 0.0039
19829 0.0053
20234 0.0072
20658 0.0095
21107 0.0126


-0.04 0.7
4.80 0.7
9.61 0.7
14.40 0.7
19.17 0.7
23.93 0.7
-2.18 0.6
2.60 0.6
7.33 0.6
12.04 0.6
16.72 0.6
21.40 0.6
-4.67 0.5
0.03 0.5
4.69 0.5
9.30 0.5
13.89 0.5
18.47 0.5
-7.67 0.4
-3.05 0.4
1.51 0.4
6.03 0.4
10.51 0.4
14.96 0.4
-11.48 0.3
-6.95 0.3
-2.49 0.3
1.91 0.3
6.26 0.3
10.58 0.3
-16.75 0.2
-12.32 0.2
-7.98 0.2
-3.72 0.2
-0.36 0.2
4.63 0.2
-25.59 0.1
-21.25 0.1
-17.04 0.1
-12.95 0.1
-8.96 0.1
-5.03 0.1


54.4
78.6
108.9
147.1
194.9
254.7
47.4
68.8
95.5
128.9
170.6
222.6
40.3
59.0
82.1
110.8
146.4
190.5
33.2
49.2
68.7
92.6
122.1
158.4
26.2
39.4
55.3
74.5
97.8
126.3
19.1
29.6
41.9
56.3
69.9
94.2
12.1
19.8
28.4
38.2
49.3
62.1


1.09
5.71
10.37
15.03
19.71
24.42
-0.42
4.04
8.53
13.05
17.59
22.16
-2.05
2.20
6.50
10.84
15.21
19.61
-3.83
0.17
4.23
8.33
12.48
16.67
-5.79
-2.09
1.65
5.45
9.31
13.22
-7.97
-4.66
-1.32
2.06
4.81
9.01
-10.40
-7.61
-4.84
-2.06
0.75
3.61













0.12




0.10 =~50 Lkd tad(=twet)= 250C
2tdew = 250C


Etw200
0.06
200C
2 175
tdew = 200C


150w=150C



0.04 .100 __
.. tdew 1 00C

tdew = 50C
0.02 tdew = 10C
75


tdew = 500C




0.00
0 5 10 15 20 25 30
Dry Bulb Temperature tdry [oC]
Figure 5-2. Psychrometric chart of low pressure atmosphere (76% N2, 20% 02, 4% CO2) with initial conditions of 20 kPa dry air at
200C and a constant specific volume of 0.004138m3/kg.









One-dimensional Steady State Heat Transfer Model of the Greenhouse Dome

Overall Thermal Resistance Model

A one-dimensional steady state analysis was selected as heat transfer model. The

heat inside of the greenhouse produced by the absorbed growth light radiation and the

heating system is transferred to the outside in the following steps. First convection heat

transfer takes place between the air and the greenhouse inner shell, then heat is

transferred through the greenhouse dome by conduction. Heat transfer between the

greenhouse surface and the inner chamber wall occurs mainly due to radiation. Natural

convection of the outside dome and the interior chamber walls is negligible as the

convection coefficient is reduced significantly by the low pressure of 0.6 kPa (see Table

5-1). The effect of low pressure on convective heat transfer has been discussed

extensively at the beginning of this Chapter. Heat transfer through the vacuum chamber

occurs by conduction. Finally, heat is removed from the vacuum chamber wall by

convection. At the same time, heat is also transferred out of the greenhouse through the

dome base. Thick foam insulation had been installed under the base to minimize the heat

loss through the floor.

The equivalent thermal circuit concept is a useful tool for the development of a

one-dimensional steady state heat transfer model. The thermal resistance is defined as the

ratio of the temperature difference (the driving potential) to the corresponding heat

transfer rate. Figure 5-3 depicts the modes of heat transfer and states the equivalent

thermal resistance circuit.












hchamber

'T7 TO


T7,

T9


RI RZ R3 R4

Conv, -(T2)- Cond. -( Ts)- Rad. -(To)-Cond. R5



Conv. T, )- Cond- T- TrJ- Rad. (Ti-- Cond.

R6 R- Ra Rs
Figure 5-3. Heat transfer of greenhouse dome and thermal resistance circuit.

Individual Thermal Resistances and Thermal Coefficients

The total heat flux out of the greenhouse dome is the sum of the absorbed light plus

the heat added by the heating coil. The heat flux is the ratio of the temperature difference

to the total resistance:

T,-,5
Total = Heater + Lght -- (5-50)
Rtotal