xml version 1.0 encoding UTF-8
REPORT xmlns http:www.fcla.edudlsmddaitss xmlns:xsi http:www.w3.org2001XMLSchema-instance xsi:schemaLocation http:www.fcla.edudlsmddaitssdaitssReport.xsd
INGEST IEID EDWLOLB4U_QDBN20 INGEST_TIME 2014-10-03T21:28:16Z PACKAGE UFE0046435_00001
AGREEMENT_INFO ACCOUNT UF PROJECT UFDC
1 CONTROL OF CHARGED LUNAR DUST USING ELECTROSTATIC TECHNOLOGIES By NIMA AFSHAR MOHAJER A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE O F DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2014
2 2014 Nima Afshar Mohajer
3 To my loving Mom and Dad
4 ACKNOWLEDGMENTS I first would like to thank my advisor, Professor Chang Yu Wu. Without his guidance during my study, this PhD would not have been possible. Especially, I am thanking him for his patience and helping me to realize my dream of studying PhD in US. Dr. Wu was more than a PhD advisor for me and inspired me a lot on how to deal with scientific problems from a raw idea to the final conclusion. I would also like to thank my committee members: Drs. Ben Koopman, Jennifer Curtis, Robert Moore, and Nicoleta Sorloaica Hickman. They have been very helpful with improving the quality of the study and givi ng me advice throughout my PhD. Their insightful comments contributed a lot in my interesting multidisciplinary research. My research could not have been accomplished without my lab mates who helped me with training, technical questions, and everyday tasks I would like to extend my appreciation to all my lab mates at the University of Florida past and present, but especially: Dr. Brian Damit, Dr. Jun Wang, Dr. Min Zhong, Dr. Myung Heui Woo, Dr. Hsing Wang Li, Dr. Hailong Li and Yunseok Im. I would like to express my gratitude to Dr. Brent Gila, Dr. Kevin Powers and Mr. Ken Reed for helping me in the experimental phase of the work, and Yatit Thakker for working with me as a mentee. I am very grateful to the Space Research Initiative (SRI) at the state Florid a for funding me within the last four years. Finally, I want to thank my parents for their love, encouragement and support during these past four years. I appreciate my mom for being available online for me whenever I needed in spite of the time difference Her positive attitude helped me to complete my research. I appreciate my dad for his support and being an inspiration throughout of my life.
5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 8 LIST OF FIGURES ................................ ................................ ................................ .......... 9 ABSTRACT ................................ ................................ ................................ ................... 12 CHAPTERS 1 INTRODUCTION ................................ ................................ ................................ .... 14 Lunar Dust Levitation ................................ ................................ .............................. 14 Previously Examined Lunar Dust Mitigation Technologies ................................ ..... 15 Mechanical Removal of Lunar Dust ................................ ................................ .. 15 Gas and Liquid Dust Removal Sprays ................................ .............................. 16 Surface Modification and Passive Methods ................................ ...................... 16 Electrodynamic Dust Removal Methods ................................ ........................... 17 Lunar Dust Properties ................................ ................................ ............................. 18 Size, Density and Shape of Lunar Dust ................................ ............................ 18 Charge of Particles ................................ ................................ ........................... 19 Kinematic of the Levitated Lunar Dust Motion ................................ .................. 20 Electrostatic Control of Particles ................................ ................................ ............. 21 Research Hypothesis ................................ ................................ .............................. 22 Electrostatic Lunar Dust Collector (ELDC) Operation ................................ ............. 23 Research Objectives ................................ ................................ ............................... 24 2 EULERIAN BASED ANALYTICAL MODEL TO PREDICT ELDC EFFICIENCY ..... 29 Objective ................................ ................................ ................................ ................. 29 Methods ................................ ................................ ................................ .................. 29 Model Development ................................ ................................ ......................... 29 Assumption s ................................ ................................ .............................. 29 Derivation of the ELDC Efficiency Equation ................................ ............... 30 Dimensionless Ratios ................................ ................................ ................ 33 Results and Discussion ................................ ................................ ........................... 34 3 LAGRANGIAN BASED NUMERICAL 3 D MODEL FOR ELDC EFFICIENCY ....... 42 Objective ................................ ................................ ................................ ................. 42 Methods ................................ ................................ ................................ .................. 42 Discrete Element Method (DEM) ................................ ................................ ...... 42 Non Uniform Charge Distribution on ELD C Plates ................................ ........... 44 Simulated Conditions ................................ ................................ ....................... 47
6 Results and Discussion ................................ ................................ ........................... 48 Ef fect of Electrical Particle Particle Interactions ................................ ............... 48 Effect of Non Uniform Charge Distribution on ELDC Plates ............................. 51 Effect of ELDC Dimensions and Particle Concentrations ................................ 53 4 INFLUENCE OF BACK ELECTROSTATIC FIELD ON ELDC COLLECTION EFFICIENCY ................................ ................................ ................................ .......... 62 Objective ................................ ................................ ................................ ................. 62 Methods ................................ ................................ ................................ .................. 62 Model Configuration ................................ ................................ ......................... 62 Rescaling the ELDC Dimensions ................................ ................................ ..... 63 Analysis of Particle Trajectories ................................ ................................ ....... 65 Results and Discussion ................................ ................................ ........................... 66 Qualitative Observation of Particle Trajectories ................................ ................ 66 Effect of Back Electrostatic Field on Particle Fate ................................ ............ 67 ELDC Collection Effic iency as a Function of Time ................................ ........... 69 Estimating ELDC Power Consumption ................................ ............................. 71 5 EXPERIMENTAL ELECTROSTATIC COLLECTION OF TRIBOCHARGED LUNAR DUST SIMULANTS ................................ ................................ ................... 78 Objective ................................ ................................ ................................ ................. 78 Materials and Methods ................................ ................................ ............................ 78 Experime ntal Protocol ................................ ................................ ...................... 78 Properties of the Lunar Dust Simulants ................................ ............................ 79 Sample Preparation ................................ ................................ .......................... 80 Remotely Controlled Particle Tribocharger ................................ ....................... 81 Charge Measurement and Electrostatic Particle Collection .............................. 84 Result s and Discussions ................................ ................................ ......................... 85 Tribocharging Properties of JSC 1A and Chenobi Simulants ........................... 85 Collection Efficiency of the ELDC at Low Vacuum Condition ........................... 87 Effect of Plate Conductivity on Particle Collection at Low Vacuum Condition .. 92 6 DESIGN OF AN ELECTROSTATIC LUNAR DU ST REPELLER FOR MITIGATING DUST DEPOSITION ................................ ................................ ......... 97 Objective ................................ ................................ ................................ ................. 97 Electrostatic Lunar Dust Repeller (ELDR) ................................ ............................... 97 Methods ................................ ................................ ................................ .................. 97 Model Configuration ................................ ................................ ......................... 98 Charge Distribution on Needle Shaped Electrodes ................................ .......... 98 Discrete Element Modeling ................................ ................................ ............. 100 Analysis of Particle Trajectories ................................ ................................ ..... 101 Configuration of the Final Model ................................ ................................ ..... 102 Results and Discussion ................................ ................................ ......................... 104 Charge Distribution on the Single Electrode ELDR ................................ ........ 104
7 Removal Efficiency of the Single Electrode ELDR ................................ ......... 105 Arrangement of Ensemble Electrodes ................................ ............................ 106 Comparison between Single Electrode and Ensemble Electrode ELDRs ...... 109 7 CONCLUSIONS ................................ ................................ ................................ ... 115 APPENDICES A: MATLAB SOURCE CODE FOR CALC ULATING THE CHARGE DISTRIBUTION ON THE ELDC PLATES S AT DIFFERENT APPLIED VOLTAGES PRESENTED IN CHAPTERS 3 AND 4 ................................ ............ 121 B: VBA SOURCE CODE FOR EVALUATING PARTICLE TRAJECTORIES AND CALCULATING THE FRACTION OF REPELLED PARTICLES AT DIFFERENT APPLIED VOLTAGES PRESENTED IN CHAPTERS 3 AND 4 ............................ 123 C: MATLAB SOURCE CODE FOR CALCULATING THE CHARGE DISTRIBUTION ON NEEDLE SHAPED ELECTRODES OF THE ELDR AT DIFFERENT APPLIED VOLTAGES PRESENTED IN CHAPTER 6 ..................... 129 D: VBA SOURCE CODE FOR EVALUATING PARTICLE TRAJECTORIES AND CALCULATING THE FRACTION OF REPELLED PARTICLES AT DIFFERENT APPLIED VOLTAGES PRESENTED IN CHAPTER 6 ................................ .......... 131 LIST OF REFERENCES ................................ ................................ ............................. 139 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 145
8 LIST OF TABLES Table page 1 1 Comparing previously developed lunar dust mitigation technologies ................. 26 3 1 Collection efficiency as a function of provided voltages for three studied models ................................ ................................ ................................ ................ 55 4 1 Correction factors of different key parameters after ELDC resizing .................... 73
9 LIST OF FIGURES Figure page 1 1 Schematic of the ELDC configuration and arrangement of plates to protect lunar installed surfaces ................................ ................................ ....................... 27 1 2 Finite element analysis (FEA) results of the electrostatic field streamlines and electric potential distribution in an assumed spherical neighborhood around a pair of ELDC plates (the electric potential difference between ELDC plates is V = 100 V) ................................ ................................ ................................ ........ 28 2 1 Schematic of the ELDC configuration with an angle between initial particle velocity vector and gravitational force direction ................................ .................. 38 2 2 ELDC collection efficiency as a function of particle size at different voltages ( s = 100 V, L = 10 cm and D = 5 cm) ................................ ................................ 38 2 3 ELDC collection efficiency of horizontal orientation as a function of surface potential at different voltages for several particle sizes ( L = 10 cm and D = 5 cm) ................................ ................................ ................................ ..................... 39 2 4 Collection efficiency of the vertical E LDC as a function of surface potential at different voltages for several particles sizes ( L = 10 cm and D = 5 cm) .............. 40 2 5 ELDC collection efficiency as a function of tilting angle ( ) for several particle sizes at different voltages ................................ ................................ ................... 41 3 1 Schematic of the modeled ELDC configuration to protect optical/photovoltaic surface at the worst case s cenario ................................ ................................ ..... 56 3 2 The ELDC geometry and particle placement in sections 1 and 2 (100 lunar dust particles at the middle, initially forming a line inside the particle factory; L = W = 10 cm and D = 5 cm) ................................ ................................ ................ 56 3 3 Sensitivity analysis on electrical screening distance around the particles (one hundred 20 m sized particles at uniform electrostatic field; L = W = 10 cm, D = 5 cm and = 100 V) ................................ ................................ .................. 57 3 4 Collection efficiency as a function of provided voltage via 3 different models: Lagrangian based approach with a uniform e field, Lagrangian based approach with a non unifor m e field, and Eulerian based approach. In all 3 models: d p = 20 m, s = 100 V, L = W = 10 cm and D = 5 cm) ......................... 58 3 5 Effect of particle number concentration on collection efficiency of the ELDC ( d p = 20 m, s = 100 V, = 100 V, L = W = 10 cm and D = 5 cm) .................. 59
10 3 6 The ELDC capacitance at different number of subsections ( L = W = 10 cm and D = 5 cm at = 100 V) ................................ ................................ .............. 60 3 7 Distribution of surface charge on ELDC plates at 4 different provided voltages in pC ................................ ................................ ................................ ..... 60 3 8 DEM results for two different sizes of the ELDC a nd comparison with Eulerian based model ................................ ................................ ......................... 61 4 1 Schematic of the ELDC plates arrangement to protect lunar installed surfaces ................................ ................................ ................................ .............. 74 4 2 Trajectories of the falling lunar dust ................................ ................................ ... 75 4 3 Fate of incoming particles by category and applied volt age ............................... 76 4 4 Collection efficiency drop as a function of time for the described ELDC when incoming particles fall continuously ................................ ................................ .... 77 5 1 Schematic of the experi mental set up ................................ ................................ 93 5 2 Components of the designed particle tribocharger/dropper ................................ 93 5 3 Total charge/mass ratio of lunar dust simul ants at different tribocharging time and air p ressures ................................ ................................ ................................ 94 5 4 ELDC collection efficiency for JSC 1A simulants as a function of applied voltage at low vacuum condition ................................ ................................ ......... 94 5 5 Collected JSC 1A particles on the positively charged collection plate ................ 95 5 6 Collected JSC 1A particles on ELDC collection plate at V = 33 V ................... 95 5 7 Comparing collection efficiencies of steel made and aluminum made ELDC plates for JSC 1A simulants as a function of applied volta ge at the low vacuum ................................ ................................ ................................ .............. 96 6 1 Schematic of the ELDR ................................ ................................ .................... 111 6 2 Sensitivity analysis on the number of segments modeled on a single electrode ELDR and normalized c harge distribution over the electrode length ( L = 5 cm and D = 1 mm) at = 100 V ................................ ........................... 111 6 3 Particle trajectories of 100 falling lunar particles influenced by a single electrode ELDR (shown by the dark rod in the center, L = 5 cm, D = 1 mm) at = 4 kV ................................ ................................ ................................ .......... 112
11 6 4 Removal efficiency of the single electrode ELDR ( L = 5 cm and D = 1 mm) over a 5 cm 5 cm surface area as a function of ap plied voltage and particle number concentration ................................ ................................ ....................... 112 6 5 Removal efficiency of the single electrode ELDR as a function of applied voltage for two electrode lengths ................................ ................................ ...... 113 6 6 Plan view of different arrangements of electrodes over the 30 cm x 30 cm exposed surface investigated in this study (black circles indicate electrode cross section, small arrows display the directions of the elect ric field vector of each electrode on the x y plane, and large arrows indicate the direction of the resultant e field streamlines) ................................ ................................ ............. 113 6 7 Sample 3 D electric potential distribution for the 9 electrode ELDR at V = 2.2 kV ................................ ................................ ................................ ............... 114 6 8 Electric field streamlines of the x shaped nine electrode ensemble ELDR ....... 114
12 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 CONTROL OF CHARGED LUNAR DUST USING ELECTROSTATIC TECHNOLOGIES By Nima Afshar Mohajer Ma y 2014 Chair: Chang Yu Wu Major: Environmental Engineerin g Sciences Protecting sensitive surfaces from dust deposition in the limiting condition of the lunar atmosphere is imperative for future space exploration. An electrostatic lunar dust collector (ELDC) was developed to prevent lunar dust deposition o n the exposed surface equipment efficiently. First Eulerian based analytical equations were derived to interrelate key parameters. Application of electrostatic field strength of 20 kV/m was found to be the Lagrangian based discrete element method (DEM) was used to track particle trajectories individually. Inclusion of electrical particle particle interactions and non uniformity of the e field provided a more accurate efficiency determination resulting i n an e field strength of 3.5 kV/m for 100% collection of 20 How back electrostatic field due to charge build up on the collection plates affect performance of an ELDC was then studied using a modified DEM model. The maximum time ELDC can run without significant loss in collection efficiency was estimated to be 3 times per month Finally, the collection efficiency of the ELDC was investigated experimentally inside a vacuum chamber. The results indicated better tribochargeability of JSC 1A
13 parti cles than Chenobi particles. The pattern of the obtained collection efficiencies were consistent with the theoretical models confirming linear relationship with the applied voltage and non uniform charge distribution over the collection plate. An electrost atic lunar dust repeller (ELDR) was developed to repel approaching like charged lunar dust as an alternative approach This study demonstrated that x shaped electrode pattern is the most effective electrodes arrangement due to the absence of dead zones in between like charged electrodes. Modeling results showed that 2.2 kV and 1.4 kV were the minimum needed voltages applied to electrode lengths of 5 and 10 cm, respectively to achieve 100% removal efficiency. The novel techno logies introduced in this study o ffer advantages over previously studied technologies by preventing dust deposition at the first place using low electric power. This study serves as the first step for surface protection of equipment on asteroids and Mars, and paves the road for developmen t of electrostatic shields to protect solar panels and PV cells in arid terrestrial areas to secure consistent power generation.
14 CHAPTER 1 INTRODUCTION Lunar Dust Levitation Dusty environment of the lunar surface was troublesome in previous NASA explorat ions. A cloud of levitated lunar grains with high affinity of adhering to the nearby surfaces, which hampered the lunar surface operations, was observed during the entire Apollo program (from 1969 to 1973) (Abbas et al., 2007; Colwell et al., 2009; Renno & Kok, 2008; Stubbs et al., 2006) Observations from the Apollo missions revealed that the hard vacuum lunar environment is suffused with electrically charged fine particles. Having ultrahigh vacuum in the lunar environment (10 13 to 10 14 Torr) (Heiken et al., 1991) leaves the lunar surface unshielded from intense solar radiation (UV, x ray and cosmic rays) and solar winds (high velocity charged particles and electrons). While photoemissive radiations (e.g., UV and x ray) on lunar dayside accumulate positiv e charges, impingement of electrons on lunar nightside leads to negative charge accumulation on lunar grains (Halekas et al., 2008; Halekas et al., 2002; Walch et al., 1995) The like charged particles create a local electric field near the surface, overco ming gravitational and cohesive forces (Stubbs et al., 2006) Eventually, the process of charge accumulation inside the created sheath region leads to lifting the like charged particles from the lunar surface because of interparticle repelling forces (Colw ell et al., 2009; Stubbs et al., 2006) The resulting electric field on the lunar surface forms a sheath region with non uniform thickness (from less than 10 cm to several tens of meters) around the moon (Sternovsky et al., 2008) Relatively smaller and li ghter lunar particles are forced up outside the region to the point where the electric field is screened out and no longer acts on the particles. Thus, the majority of levitated
15 particles fall back toward the lunar surface (Colwell et al., 2009) The conse quent deposition of lunar dust on the exposed equipment surfaces deteriorates performance of the solar panels (Sims et al., 2003) obscures optical surfaces (Calle et al., 2011) degrades thermal radiators (Gaier et al., 2011) creates false responses from the measuring devices, interferes with the operation of Extra Vehicular Activity (EV A) systems (Gaier & Creel, 2005) and requires frequent replacement of the costly devices. ation (NAS A) has established dust mitigation programs to study all the possible lunar and Martian dust control technologies for future exploratory space missions. Previously Examined Lunar Dust Mitigation Technologies Inspired from terrestrial applications a wide variety of passive and active methods have been proposed to mitigate the effects of lunar dust. However, there are a variety of limitations associated with each method, making them either inefficient or infeasible in hard vacuum lunar environment as summarized below: Mechanical Removal of Lunar Dust Application of a dust wiper proposed by Fernndez et al. (2007) and brushes proposed by Gaier et al. (2011) are two examples of the mechanical methods for removing the deposited lunar dust. The lunar du st wiper was made from teflon, titanium and kapton. This robotic technology provided a wiper lever rotating up to 150 o with 93% materials (nylon, PTFE and Thunderon) ope rating at the constant stroke speed and run time over thermal surfaces of AZ93, AlFEP and AgFEP. The results of their study indicated that Thunderon bristle brush was not effective, and nylon bristle and PTFE bristle brushes showed 90% and 80% removal effi ciency, respectively, on the AZ93
16 surface. The Thunderon brush was the best for AlFEP surface though the highest removal efficiency of which was about 66%. As for the brush shape, they concluded that both fan brush and round brush designs were more effecti ve than strip brushes. Longer bristles were found to be more effective at removing dust shorter bristles though the effect seemed to be less important than the brush material. Although these methods are efficient and light, they are abrasive and only appro priate for removing large particles 2 ). Additionally, the methods require complex robotic technology and frequent brush cleaning. Gas and Liquid Dust Removal Sprays Since the mechanical methods are abrasive and may degrade the surface finish, application of gas, liquid, foams and gels for dust removal purposes have been investigated. The main idea is to break surface attraction forces with strong puff of gas, liquid, foam and gel (Wood, 1991) Ho wever, implementation of any gas, liquid, foam or gel spray in the hard vacuum lunar environment is almost inapplicable due to the impracticality of directing the materials toward the contaminated surfaces. Moreover, these systems require strong pumps and blowers with difficulty of spatial shipment and power provision in addition to the chance of having chemical residues left over the surface. Surface Modification and Passive Methods Instead of exerting an external force to remove deposited particles, the p rotected surfaces have been treated to reduce the adhesive force between depositing particles and the surface. Since these techniques rely upon surface modification, they are hat rely on external power. Dove et al. (2011) applied a proprietary ion beam process to
17 selectively extract positive ions from the plasma and accelerate them toward the surface. Then, by effectively choosing the precursor gas, vacuum level, ion energy, io n current and the distance between substrate and ion source, the surface energy of three different surfaces (black Kapton, Silicon and Quartz) were reduced. The surface modification of this study resulted in averagely 4 times reduction in contact charging. However, the main drawbacks of these methods include the high cost of surface modification and a small group of appropriate materials. Similarly, Gaier et al. (2011) studied another group of three surfaces (AZ 93, AgFEP and AlFEP) with application in ther mal surfaces. The surface chemistry and surface texture were modified using an oxygen ion beam to etch away part of the surfaces. The experiments were conducted inside a high vacuum bell jar vacuum chamber with JSC 1A lunar dust simulants. The resultant su rface textures were observed at different elapsed times of oxygen ion exposure. However, the research showed that none of the three treatments significantly improved the removal of dust against a certain puff of passing nitrogen gas. Electrodynamic Dust R emoval Methods He et al. (2011) reviewed a number of suggested self cleaning methods for the solar panels and concluded that electrodynamic based approaches are the best strategies for dust removal. The best characterized technology in this category is the electrodynamic dust shield (EDS), introduced by researchers at NASA Kennedy Space Center (KSC) (Calle et al., 2008; Sims et al., 2003) using the electric curtain concept developed by Tatom et al. (1967) at NASA and Masuda and Matsumoto (1973) at the Unive connected to an AC source inside a transparent insulator film installed on the solar cell surfaces, lifts and transports deposited particles with generated standing and travelling
18 wa ves (Calle, et al., 2011) been reported in various studies (Atten et al., 2009; Calle et al., 2011; Calle et al., 2004; Liu & Marshall, 2010) operation of an EDS with AC current may expend energy significantly faster than the energy capture rate of the solar panel (Qian et al., 2012) Clark et al. (2010) introduced another electrostatic based tool called Space Plasma Alleviation of Regolith Concentrations in the Lunar Environment (SPARCLE). The SP ARCLE consists of an electron gun and a surrounding collection circular plate to charge particles to deposit on an assumed surface. After adequate bombardment of the dust layer with a low energy beam of electrons, repelling Coulomb forces between the parti cles overcome gravitational force and surface forces over the particles to lift the particles up for collection on the oppositely charged surfaces around the device. Although SAPRCLE is portable and operates at low power, it requires either robotic arms or cumbersome. Lunar Dust Properties Size, Density and Shape of Lunar Dust Unlike terrestrial dust, lunar dust is exposed to meteorite impacts. These hypervelocity impacts result in shap e irregularity and fragmentation of lunar grains in a wide range of size distribution (from nanometer to centimeter) (Abbas et al., 2007; Wood, 1991) Between 10 to 20% of lunar grains by number are smaller than 20 m, but the median size ranges from 40 to 130 m (Heiken et al., 1991) Over 95% and over 50% are finer than 1 mm and 60 m, respectively (Taylor et al., 2005) The average value for median size has been reported as 70 m (Walton, 2007) Lunar dust density ranges from 2300 to 3100 kg/m 3 (Walton, 2007)
19 However, the size of the particles liberated from the regolith has not yet been well characterized. Using images taken by the Surveyor 7 Lander, Renno and Kok (2008) estimated 10 m as the representative size of levitated lunar dust with a concentr ation of about 50 #/cm 3 Charge of Particles The simplest equation for estimating the charge on a dust grain is given by writing the charge as the product of the grain capacitance, C and surface potential, s (Hornyi, 1996) : (1 1 ) The following approximation for the capacitance was suggested by Goertz (1989): (1 2 ) where 0 and d are vacuum space permittivity (8.854 10 12 F/m) and Deb and d p the distance beyond which a charge becomes screened by the ionized particles of the lunar environment. When the particle diameter is much less than d ( d p << d ), Eq. (1 2 ) can be reduced to: (1 3 ) As the lunar surface potential depends on lunar Debye length and solar plasma flow over the lunar grains, it is sensitive ly variable. The reported values obtained from Lunar Prospector Electron Reflectometer (LPER) measurements were 10 to 100 V for near terminator solar wind (Freeman & Ibrahim, 1975) and 0 to 1 kV for different regions on the moon (Halekas, et al., 2008) Th e results from different modeling studies are also
20 greatly dissimilar. For example, a numerical particle in cell model developed by Wang et al. ( 2008) of ions and electrons in lun ar atmosphere, indicated the range of 30 to +5 V, whereas an analytical model by Manka (1973) estimated values of a few volts on lunar dayside and a few tens of volts on lunar nightside. Kinematic of the Levitated Lunar Dust Motion Stubbs et al. (2006) ha ve developed an equation for the lunar dust motion. They assumed photoemission as the only contributor for charging the particles and the gravitational force being the only acting force on the particles after exiting the Debye sheath. From this model, the maximum height, Z max above the lunar surface that a particle can travel was determined as shown in Eq. (1 4 ) Sickafoose et al. (2001) performed laboratory experiments for dust levitation in low density plasma and their results were consistent with the theoretical formula that Stubbs et al. (2006) obtained years later: (1 4 ) where p is the density of particle and g l is the lunar gravitational acceleration. After reaching Z max the particle falls back to the lunar surface following a b allistic trajectory. The final particle velocity upon reaching the lunar surface given constant acceleration, g l estimated by Eq. (1 5 ) : (1 5 )
21 This is a high end approximation for the initial velocity at the device entrance. Therefore, the value of the later obtained collection efficiency will be a conservative estimate. Electrostatic Control of Particles Electrostatic precipitation is a well developed and widely applied control technology for removing fine particles from the flue gases produced in industrial processes, aerosol sampling and air cleaning. An electrostatic Precipitator (ESP) first charges particles and then collects the charged particles using an external electrostatic field created between conducting parallel plates. Particles are usually charged by field charging mechanism using a corona discharge, and the generated field and ion concentration are such that the particles get their highest possible total charge, literally instantly (Hinds, 2012) In terrestrial ESPs, charged particles migrate to the plate under the influence of the electric field, where the gravitational force is negligible compared to the electrostatic force. However, there is a terminal velocity beyond which particles migrating toward the plate cannot be accelerated further. This velocity is the consequence of the balance between the electrostatic force and the drag force on the particle moving through the surrounding gas (Schnelle & Brown, 2001) In the lunar environment, particles experience no drag force. The Deutsch Anderson equation shown below further assumes perfect radial mixing due to turbulence in the ESP (Cooper & Alley, 2011) while there is no mixing in the vacuum environment: (1 6 ) where is drift terminal velocity, is dynamic viscosity, Q is flow rate, D is the distance between each two plates, A is the total surface area of one plate (double sided) and Cc
22 is Cunningham correction factor. In the hard vacuum of lunar environment, neither flow rate ( Q ) nor drift velocity ( ) exists. Therefore, the terrestrial ESP equation is not applicable to the lunar syst em. The proposed dust control technology in this study is inspired from the collection method and configuration of ESPs. Similar to an ESP, there will be parallel electrically conducting plates; the electrical potential difference between each pair gives r ises to an electric field to attract oppositely charged particles. However, as this study targets collection of falling naturally charged particles in lunar atmosphere, there will be three major differences with terrestrial ESPs: 1) the targeted particles in this study are naturally charged with no need of high voltage to initially charge particles, 2) the hard vacuum condition of lunar environment makes Deutsch Anderson equation invalid as there is no resistive forces to slow incoming particles and no radi al mixing of particles within the device, and 3) the operational voltage of our proposing technology is a couple of hundred times smaller In average, this is about 200 times lower than the operating range of voltage of a conventional ESP. Research Hypoth esis It is hypothesized that application of electrostatic based technologies can serve as an effective way of protecting hardware surfaces from the deposition of naturally charged lunar particles in limiting conditions of the lunar environment either by a ttracting the dust to an alternative surface or by repelling the dust away from the control volume Additional advantages include relatively low electrical power requirement, low cost, negligible blockage of sunlight and low frequency for collection plate cleaning.
23 Electrostatic Lunar Dust Collector (ELDC) Operation The principal is to provide an electric potential between electrically conducting parallel plates to create an electrostatic field. Inspired by Electrostatic Precipitators (ESPs), the Electrost atic Lunar Dust Collector (ELDC) is proposed for collecting already charged lunar particles by migrating charged particles toward the oppositely charged plate. The ELDC consists of a grid layer of rectangular and parallel thin plates in front of the surfac e to be protected. The ELDC plates are conducting, oppositely charged and hard vacuum condition between the plates acts as an insulator to p ractically form a capacitor ( Figure 1 1 ). Providing electrical potential difference between each pair of plates connected to an electric power supply (i.e., solar panel), an electrostatic field is created (the electric field streamlines extend from the positively charged plate to th e negatively charged plate) ( Figur e 1 2 ) to collect falling dust particles before surface impact Since the solar panels can store energy in the lunar day for all the equipment, the provision of the required voltage between the plates can be easily maintained However, the collection plates attract incoming particles continuously and as time goes by, a layer of deposited particles carrying the opposite charge builds up on the plate. Collected fine particles stay on the plates due to strong surface forces as we ll as electrostatic attraction between the particles and the collection plate. The process of particle deposition on the collection plates forms a back electrostatic field which strengthens with time (Zukeran et al., 1999) and influences proper collection of the l ater approaching particles. Reduction in collection efficiency as a function of time is the measure for determining the frequency of plate cleaning.
24 Research Objectives In this dissertation, two electrostatic based lunar dust control technologies (ELDC and ELDR) were developed and evaluated for protecting exposed equipment surfaces on lunar surface to address the limitations of current technologies. The use of electrostatic fields for control of naturally charged lunar dust particles offers signif icant advantages and can help improve strategies for dust control in any low vacuum medium. The main goal of this study is to investigate the proficiency of the ELDC in lunar dust control and to identify its advantages and disadvantages for case scenarios through both theoretical (analytical and numerical) and experimental approaches. Additionally, the needed frequency of cleaning the collection plate was determined. The possibility of using an electrostatic lunar dust repeller (ELDR) was explored. Overall, five objectives were completed to fully study the application of electrostatic based technologies in lunar dust control: 1 Development of an Eulerian based analytical model: To estimate ELDC collection efficiency using a predictive analytical model, to iden tify relationships between the key parameters (i.e., applied voltage, ELDC dimensions and particle properties), to derive dimensionless ratios for future design of the experimental set up, to identify the most conservative case scenario, and to clarify the significance of each parameter on the resultant collection efficiency. 2 Development of a Lagrangian based numerical model: To track particle trajectories one by one using a discrete element method ( DEM ) focusing on the previously identified most conservati ve configuration, to develop a more accurate model with inclusion of electrical particle particle interactions and non uniform distribution of the charges on the ELDC plates inside the model, and to study the effect of ELDC dimensions on collection efficie ncy. 3 Approximation of the frequency of ELDC plate cleaning: To investigate the Influence of the built up layer of previously collected particles on collection of newly incoming like charged particles using a modified Lagrangian based DEM model. 4 Verificati on of the theoretical findings with experiments: To develop an experimental set up to examine the proficiency of a customized ELDC for
25 collection of 20 sized lunar dust simulants, to compare tribochargeability of the lunar dust simulants (JSC 1A and Che nobi), and to evaluate the effect of vacuum level in tribochargeability of the particles and ELDC collection efficiency. 5 Possibility of using an ELDR: To assess the proficiency of an alternative method of electrostatic lunar dust repelling using DEM and fi nite element analysis (FE A) methods in lunar dust particles removal, to develop a model for single electrode ELDR, to identify the most beneficial arrangement of electrodes for protecting larger surfaces to develop the optimum ensemble electrode ELDR for p rotection of larger surfaces, and to compare the obtained results with the ELDC responsible for protecting the same surface area.
26 Table 1 1 Comparing previously developed lunar dust mitigation technologies Control Technology A dvantages Disadvantages References Brush 1) Removal of both charged and uncharged particles 2) Applicable on all types of surfaces 1) No prevention. Removal of already deposited particles 2) Abrasion of surfaces 3) Complication of robotic technologies f or the brush levers 4) Need for brush cleaning 5) Not effective for fine particles (Gaier et al., 2011) Dust Wiper 1) Removal of both charged and uncharged particles 2) Applicable on all types of surfaces 1) Abrasion of surfaces 2) Complication of roboti c technologies for the brush levers 3) Need for wiper replacement 4) Only good for coarse particles (Fernndez et al., 2007) Surface Modification 1) Operation with no external forces 2) No surface blockage 1) No prevention. Removal of already deposited pa rticles 2) Not applicable for all types of materials 3) Very costly to treat the entire surface area of the surfaces (Dove et al., 2011) (Gaier et al., 2011) SPARCLE 1) Removal of both charged and uncharged deposited dust 1) No prevention. Removal of alr eady deposited particles 2) Relatively high electrical power consumption as charging electrode moves line by line over a wide surface 3) Cleaning process is very time consuming 4) Involvement of complicated robotic levers (Clark et al., 2010) Electrodyna mic Dust Shield (EDS) 1) Removal of both charged and uncharged deposited dust 2) Negligible surface blockage 1) No prevention. Removal of already deposited particles 2) Relatively high electrical power consumption due to need for converting DC to AC curren t 3) High cost of covering all surfaces with thin film of ITO (Calle et al., 2011) (Sims et al., 2003)
27 Figure 1 1 Schematic of the ELDC configuration and arrangement of plates to protect lunar installed surfaces
28 Figur e 1 2 Finite element analysis (FE A) results of the electrostatic field streamlines and electric potential distribution in an assumed spherical neighborhood around a pair of ELDC plates (the electric potential difference between ELDC plates is V = 100 V)
29 CHAPTER 2 EULERIAN BASED ANALYTICAL MODEL TO PREDICT ELDC EFFICIENCY Objective The main objective of the study in this chapter was to develop a predictive 2 D analytical model to evaluate the effectiveness of ELDC. To investigate the importance of key parameters on collection efficiency, sensitivity analyses were conducted. The most conservative case scenario was identified, which would serve to be the focus in follow up numerical modeling. Dimensionless analysis provided insight into relationsh ips between key parameters and correction factors to relate subsequent experimental results to theoretical results. Methods Model Development Assumptions In order to derive an analytical model, a number of assumptions have been made. The physics of electr ostatic collection can be complicated, as demonstrated by the terrestrial ESP theory. The following assumptions allowed a simplified equation to be obtained provided insight into the most important parameters in ELDC design and a handy tool to estimate col lection efficiency. The assumptions which are common with collection efficiency derivations of ESP were as below: 1 Particles are assumed to be point charges of finite diameter and mass. 2 Charged particles do not exert any force on each other. The electrostat ic force by the plates is sufficiently higher than the Coulomb force between particles. Furthermore, particles do not perturb the electric field generated by the ELDC plates due to their charge or the electric permittivity which they induce. 3 The electrosta tic field is uniform between the plates. There are no edge effects of the field caused by plates of finite size. Consequently, there is no dielectrophoresis force acting on the particles due to non uniformity in the field.
30 4 Particles enter the ELDC with ide ntical size, density, shape, charge, and they are distributed uniformly at the entrance of the ELDC. 5 The initial velocity vector of the incoming particle is parallel to the ELDC plates to make the most conservative situation. 6 The electric field strength re mains the same regardless of dust accumulation. 7 Re entrainment and bouncing of the collected particles are negligible. The following assumptions were exclusively needed for the ELDC model: 1 There is neither air flow nor drag force acting on the particles. 2 T he derivation is envisaged for 2 D schematic, meaning the widths of the ELDC plates are infinite. Derivation of the ELDC Efficiency Equation Since the ELDC can have different orientations with respect to the lunar surface for its protective task, the angle between the gravitational force (which is always normal towards the lunar surface) and electrostatic force (which is always normal towards the pertinent ELDC plate) can change. As the electrical polarity (positive or negative) of incoming particles is kno wn on each side of the moon, the electrical polarity of ELDC plates should also be determined wisely to make the gravitational force effective in assisting particle collection. In other words, the ELDC plates alternate between positive and negative to util ize the gravitational force for enhanced collection. Therefore, several scenarios can be envisaged for the ELDC configuration with respect to the equipment to be protected. Figure 2 1 shows the ELDC configuration, the equipment to be protected and the relationship between the forces in the general case for collecting positively charged particles. Then, the electrostatic force ( F e ) acting on a particle with charge ( q p ) entering the electric field ( E ) generated by the ELDC plates is described by Eq. (2 1 ). (2 1 )
31 The electric field vector can be defined as the gradient of the electric potential. The magnitude of electrostatic field acting on a particle possessing charge q p can be then obtained by Eq. (2 2 ): (2 2 ) where V is the potential difference between the plates and D is the distance between the plates. When the device to be protected is inclined rel ative to the fixed system of x and y directions, the gravitational force, which is in the direction, has one component in each x and y direction. Hereafter the angle between the initial velocity vector ( v 0p ) and gravitational force ( F g ) will be labeled The resulting force balance equations on the particle can be written as: (2 3 ) (2 4 ) where m p g l is the lunar gravitational constant. Assuming the particles are spheres of diameter d p with density p the acceleration in the y direction can be written as: (2 5 ) This simplification allows the collection efficiency equation to be written as a function of particle size and provided voltage. As depicted in Figure 2 1 a x is only due to F g component in the x direction. Using the kinematic equation of motion for constant
32 acceleration in each direction one may obtain the velocity ( x y ) and position ( x y ) components as a function of time. For this purpose, initial condi tions must be taken into account to remove constants of integration. (2 6 ) (2 7 ) (2 8 ) (2 9 ) Thereby, the position of the particle in the y direction can be related to the x direction by substituting Eq. (2 8 ) into Eq. (2 9 ) to obtain: (2 10 ) In calculating the collection efficiency, the particle is ass umed to attach to the plate if it reaches the ELDC plate before exiting the ELDC. Considering a particle with a displacement r in the y direction that will reach the ELDC plate after it travels precisely a distance L of one plate length in the x direction ( Figure 2 1 ), particles with a displacement smaller than r will then be collected while those larger than r will penetrate. Assuming a uniform distribution of particles at the entrance line, the collection efficien cy for a given v 0p is simply defined as the ratio r / D as: (2 11 )
33 Equation (2 11 ) is the most general case for the collection efficiency of the lunar ELDC given an arbitrary orientation. There are two special orientations of interest: ELDC plates parallel or perpendicular to the lunar surface. For horizontal configuration, the electrostatic force is in the same direction as gravitational force. This situation could activities ( = 90). This r esults in an undefined value for the efficiency in Eq. (2 11 ) as the cosine term in the denominator is zero. This singularity can be resolved by applying Eq. (2 12 ): (2 12 ) When the gravitational force acts perpendicularly to the electrostatic force so that = 0 as in a vertical configuration, Eq (2 11 ) reduces to Eq. (2 13 ): (2 13 ) Dime nsionless Ratios Dimensionless analysis provides insight into the key parameters and allows exploration of new interactions not considered in the initial planning. Dimensionless ratios were investigated for the two special orientations. For the horizontal ELDC ( = 90), the collection efficiency equation can be rearranged into two dimensionless ratios as follows: (2 14 ) The first term corresponds to the summatio n of electrical energy and potential energy over the kinetic energy whereas the second ratio has to do with the ELDC
34 geometry. Consequently, parameters of each ratio can be manipulated to adjust collection efficiency. For example, if the ELDC length is sho rtened, the plate distance also needs to be reduced in order to maintain the same efficiency. As another example, if the incipient velocity is larger than expected, a higher voltage is needed to maintain the same efficiency via Eq. (2 14 ). Moreover, ratios may compensate each other. As an example, a change in initial velocity of incoming particles to twice a given value requires a change of the plate distance to half of its primary value. For the vertical ELDC ( = 0), parameters in Eq. (2 13 ) can be rearranged to form three dimensionless ratios as follows: (2 15 ) The first term shows the ratio of electrical to gravitational potential energy of the particle. The second term is again an energy ratio, expressing the ratio of kinetic energy to gravitational potential energy. Fin ally, as with the horizontal case, the third term is the squared ratio of the ELDC length to the distance between the plates. Equation (2 15 ) demonstrates that by changing the angle between electrostatic force and gravitational force, from 90 to 0, kinetic energy is no longer in the denominator and potential energy is no longer in the numerator. This is simply due to changing the prevailing role of gravitational force from collecting the particles to accelerati ng them pass the plate. Results and Discussion Sensitivity analysis was performed to assess the effects of four important parameters on ELDC performance: 1) particle size, 2) electric potential difference, 3) electric surface potential and 4) orientation a ngle. The charges of particles were
35 estimated by equations (1 1 ), (1 2 ) and (1 3 ) while initial velocities of particles were estim ated by equations (1 4 ) and (1 5 ). Lunar gravitational acceleration ( g l ) of 1.62 m/s 2 lunar particle density of 3100 kg/m 3 and ELDC dimensions of 5 cm as the distance bet ween ELDC plates and 10 cm as the length of plates (based on the common size of modules on solar panels) were assumed. The results of sensitivity analyses are displayed as in Figure 2 2 to Figure 2 5 Figure 2 2 a shows the relationship between efficiency and particle size for various applied voltages when ELDC plates are positioned horizontally with respect to lunar surface. As shown larger particles are collected more easily than smaller particles collected. This minimum size required for 100% collection efficiency reduces as voltage increases. When a pplying 100 V to the system, particles of all sizes are collected. Collection efficiency is insensitive to particle size for values smaller than a few microns. The interesting conclusion to be drawn from the graphs of Figure 2 3 for the horizontal ELDC is that there is a decrease in collection efficiency when s increases. electrostatic force linearly, incipient velocity also increases lin early. As the collection efficiency is inversely proportional to 0p 2 the increase in incipient velocity is more influential, and eventually collection efficiency would be decreased. One may compensate for this by increasing the applied voltage from 10 to 150 V, which shifts the graphs to the top and right, enhancing collection efficiency. Finally, it was found that >80
36 The sensitivity analysis regarding the surface potential for a vertical orientation is shown in Figure 2 4 is not large enough to be attracted to the pertinent ELDC plate and efficiency is almost zero. For charge increase linearly for particles of a fixed size. Therefore, the electrical energy in the numerator of the first ratio in Eq. (2 15 ) also increases linearly, whereas the denominator is fixed for all surface potentials. As the third ratio is always fixed, the kinetic energy in the numerator of the second energy ratio is the only term responsible for the observed peaks in the graphs, which are brought about due to intrinsic characteristic of quadratic equations. It is distinctly clear from the figure that for each applied voltage there is a maximum collection efficiency. For relatively smaller particles the foregoing maximum collection efficiency may correspond to 100% as the gravitational force is not effective enough for accelerating them. As can be expected, increasing the applied voltage facilitates improved collection efficiency for larger particles. For instance, when the applied voltage collected with 100% efficiency. When the voltage is raised to 250 V, all the particles cted. The collection efficiency as a function of orientation angle for several voltages and fixed surface potential ( s = 100 V) is displayed in Figure 2 5 All the graphs are similar in the sense that the efficien cy increases when the angle increases to 90 o (horizontal ELDC), wherein the gravitational force collaborates with electrostatic force for collecting particles. It can be seen that the efficiency is not a strong function of for particles
37 applied voltage, the numerator of Eq. (2 11 ) increases more than the denominator. Thus, the fraction becomes big ger, and as the change in the particle velocity is also growing faster for larger particle sizes of interest, the constancy of collection efficiency no longer persists. Although collection efficiency for all sizes of particles increases as the provided vol tage increases, the ratio of electrostatic force to gravitational force for relatively small particles grows faster than that of large particles. Hence, there would be a larger range of angles in which smaller particles would have better collection efficie ncy. The above analysis is helpful for simplifying design procedures. Based on shown graphs as in Figure 2 2 to Figure 2 5 we can find the minimal voltage needed to reach 100% collection efficiency regardless of ELDC orientation. As was mentioned in our discussion of Figure 2 2 conceivable angles, electric potential of 250 V is needed for this sizing of the ELDC.
38 Figure 2 1 Schematic of the ELDC configuration with an angle between initial pa rticle velocity vector and gravitational force direction Figure 2 2 ELDC collection efficiency as a function of particle size at different voltages ( s = 100 V, L = 10 cm and D = 5 cm) A) Horizontal orientation. B) V ertical ori entation
39 Figure 2 3 ELDC collection efficiency of horizontal orientation as a function of surface potential at different voltages for several particle sizes ( L = 10 cm and D = 5 cm)
40 Figure 2 4 Colle ction efficiency of the vertical ELDC as a function of surface potential at different voltages for several particles sizes ( L = 10 cm and D = 5 cm)
41 Figure 2 5 ELDC collection efficiency as a function of tilting angle ( ) for several particle sizes at different voltages
42 CHAPTER 3 LAGRANGIAN BASED NUMERICAL 3 D MODEL FOR ELDC EFFICIENCY Objective The main objective of this study was to develop a 3 D model for determining ELDC collection efficiency at the worst case sce nario. A Lagrangian based DEM model was developed to track all particle trajectories within the geometry. Inclusion of electrical particle particle interactions and non uniformity of distributed charges on the ELDC plates realized a more accurate estimatio n regarding the ELDC collection efficiency. Methods Discrete Element Method (DEM) To address the mechanical contacts and electrical interactions of the falling particles, a Lagrangian approach is required to track particles individually at each time step. In this study, the Discrete Element Method (DEM) which has been widely used in particulate systems, was implemented for tracking the particles. The basic idea of DEM modeling is placement of the initial set of particles followed by consideration of all the equation conclude updated positions of the particles for the next time step (Hogue et al., 2008) EDEM 2.3.1 developed by DEM Solutions, Inc. which has incorporated electro static forces into DEM computations, was adopted for this study. Flexibility in creating different geometries, ease of conducting sensitivity analyses and capability of designing more complicated particle characteristics are other advantages of the softwar e.
43 Contact detection is the most time consuming part in DEM modeling of a particulate system (for a system made of n particles, on the order of n 2 detection checks are required at each time step) (Hogue et al., 2008) Moreover, there are electrostatic part icle particle interactions among the charged particles. The EDEM uses a Cartesian grid on the computational domain to limit particle contact detection to the number of particles located in the same or adjacent grid cells. A soft contact force model (Hertz Mindlin with no particle slip) was used for the mechanical contacts. This model is based on frictional elasticity of a spherical particle in contact with wall or other particles (Hertz model for the normal direction, and Mindlin model for the tangential di rection ) ( Di Renzo et al., 2004) As for electrostatic interactions, a screening radius around all particles is defined. For any target particle, only those particles inside its screening distance are involved in calculations of electrical interactions. T he electrostatic screening distance in EDEM is practically the Debye length of the particles, Dp The following equation is the suggested Debye length in vacuum (Hogue et al., 2008) : (3 1 ) where q e is unit charge of an electron (1.60210 19 C), K B (1.3810 23 J/K), T is temperature in Kelvin, n i is number of i type particles of charge z i Thus, the model considers a circle around each particle with Dp as radius and calculates the electrostatic potential ( U e ) between the cen tered particle and each particle inside the circle: (3 2 )
44 where q i is charge of particle i inside the screening distance and r pi is distance between the center particle and particle i. The resultant Coulomb force from all the included particles is derived from electrostatic potential as shown in Eq. (3 3 ): (3 3 ) Time step is the last factor influencing the accuracy and total run time of simulations. The adopted time step is the largest time in which all the above mentioned calculations can be performed accurately. The EDEM guideline suggests 40 to 60% of the Rayleigh time step to be taken as the time step of calculations. The Rayleigh time step (t R ) is the time taken for a shear wave to propa gate through a solid particle, and it is defined as in ( EDEM Guideline, 2010) : (3 4 ) where G p and p Lunar dust is mostly composed of glassy materials (Loftus et al. 201 0) So, these values for lunar dust were assumed to be analogous to glass, and 40% of the calculated t R was considered as the time step. Non Uniform Charge Distribution on ELDC Plates The assumption of uniformity of the created electrostatic field is valid for the case if the spacing between the plates ( D ) is fairly small compared to the length or width of the plates ( L or W) (Nishiyama & Nakamura, 1994) Providing a high L/D ratio in ELDC geometry may block optical or photovoltaic surfaces from the sun lig ht. If the solar panel is not maintained normal to the sun by a tracking mechanism, extra spacing must be provided between the ELDC plates, so as to not shade portions of the active solar cells
45 from oblique radiation. Such shading is of great concern in so lar panels, since the performance deteriorates significantly with a small reduction in the absorbed sun beams. The limited ratio of L/D = 2 assumed in the Eulerian based analytical model is smaller than the recommended value for uniform electrostatic field validity in parallel plate capacitors (Bueno Barrachina et al., 2009) So, the second section of DEM modeling was designed to study the influence of the non uniform charge distribution on ELDC plates and influence of charge accumulation at the edges (so c alled fringe effect) on the generated electrostatic field and collection efficiency of the ELDC. The charge distribution on the ELDC plates is denser at the edges. To create an accurate non uniform electrostatic field between the plates, charge distributio n on the ELDC plates was calculated. Each ELDC plate was divided equally into n pieces of squared subsections. The electrical potential of each subsection was derived from the is constant within each subsection, and electrical potential on all the subsections of a plate is equal and is a constant (Reitan, 1959; Reitan & Higgins, 1951) : (3 5 ) V i (electrical potential of i th subsection) is equal to /2 ( to be the provided electrical potential between the ELDC p V i is equal to /2. Vector r is position vector between any two points on the ELDC plates, s is surface charge density and s refers to area of each plate. Since each plate was discretized into n subsections, Eq. (3 5 ) was estimated using Eq. (3 6 ) where electrical
46 potential on i th subsection is the product of charge interactions with the other subsections o n the same plate and subsections on the opposite plate: (3 6 ) (3 7 ) where j is the surface charge density of the j th subsection, i is the area of i th subsection, R ij is the distance between i th subsection and j th subsection and A ij is a 2n 2n matrix defined for the sake of convenience. As the subsections are squar ed, d x = d y = l So, the matrix A ij (3 8 ) (3 9 ) Equations (3 5 ) to (3 9 ) relate electrical potential of a subsection ( V i = /2) to its surface charge. This set of equations was solved numerically us ing MATLAB 7.10.0 i and total charge on the plate ( Q ). The capacitance ( C ) of the ELDC which is defined as ratio of total charge on a plate over the provided electrical potential was used to determin e the appropriate number of subsections. So, the capacitance of the ELDC was plotted as a function of the number of subsections, and since the graph shows an asymptote with an increase in n, the minimum number of subsections providing the observed asymptot e was opted as n in computations.
47 Simulated Conditions The numerical simulations were divided into three sections. In section 1, the ELDC geometry was adopted based on the dimensions of commercial photovoltaic cells on solar panel surfaces (i.e., 10 cm 1 0 cm squared plates which were 5 cm away from each other). It was also assumed the electrostatic field between the parallel plates is constant with time and eve rywhere between the plates ( Figure 3 2 ). In section 2, the ELDC geometry was kept the same but the effect of non uniformity in charge distribution on the plates (so called fringe effect) on ELDC collection efficiency, was addressed. Finally in the third section, a half size ELDC geometry (halving L W and D s o the same L / D and W / D ratios) was examined to survey the influence of ELDC dimensions combined with the fringe effect on the collection efficiency. Initially, 100 spherical particles ( d p p = 3100 kg/m 3 and s = 100 V) uniformly positioned at the entrance of ELDC (at y = 0) to cover the spacing between plates were modeled (i.e., the distance between two particles was 0.495 mm in sections 1 and 2, and it was 0.2475 mm in section 3 of the simulations as all dimensions were halved). Charge and initia l velocity of the particles were assigned according to Eq. (1 1 ) and Eq. (1 5 ) Before starting the main sets of simulations, a pre simulation was conducted to validate the model with one single falling down particle with aforementioned characteristics (when there is no particle particle interaction) at different initial positions at the ELDC entrance. The final position of the particle at each simulation was compared with t he predicted result from formerly derived results of an Eulerian model. The identical results from both methods verified the validity of the DEM model for the three sectioned simulations of this study. All the simulations were surveyed at = 25, 50, 75 and 100 V.
48 Then the ELDC plates in the DEM model were divided into subsections and the calculated surface charges were assigned as point charges at the center of each subsection. The DEM simulations were restarted at this non uniform electr ostatic field. Since the surface charge distribution on ELDC plates was no longer uniform, the line of 100 particles at the ELDC entrance was located at 5 different positions in the y direction ( y = 4, 2, 0, +2, +4 cm) to cover the entire 10 cm width. So falling particles were exposed to different areas of the ELDC plates with different surface charges. Then, the obtained collection efficiencies at different y values were averaged to get the representative collection efficiency. Results and Discussion Ef fect of Electrical Particle Particle Interactions In the first set of simulations, charge distribution on ELDC plates was assumed ideally uniform. This means horizontal acceleration due to the external electrostatic field on falling particle, is a constant value (as well as vertical acceleration which is simply gravitational acceleration). The Coulomb forces among 100 like charged particles complicate the model. Since the main focus of these simulations was electrostatic interactions, the cell grid size for mechanical contacts was not limiting. The effect of cell grid size on 100 incoming particles was surveyed and no mechanical contact was recorded for this number of particles in the applied geometry (the cell grid size was fixed to 50 d p in the main simulat ions). The particle concentration and electrical screening distance around the particles are two key parameters in setting up the DEM model. Referring to Eq. (3 4 ), the required electrical screening distance for 2 0 m sized particles is a few meters which is larger than the ELDC geometry. As the screening distance significantly influences the
49 displayed in Figure 3 3 obtained collection efficiencies at Dp greater than 2.5 mm are fairly constant. This means at this concentration of particles taking any value larger than 2.5 mm as the screening distance does not matter. On the other hand, the electrical particle particle interaction is dependent on the to tal number of initially falling particles within the screening distance. Since the DEM simulations were conducted with initially 10, 25, 50, 75, 100 and 120 particles, Dp = 12.5 mm was chosen as the screening distance of particles to ensure even at the lo west particle concentration (n = 10), at least two particles were located inside the screening distance of any target particle. Figure 3 4 includes the effect of electrical particle particle interactions, as it com pares the obtained results from Lagrangian based approach with formerly developed Eulerian based approach in the absence of electrical interactions (using Eq. (3 10 )). (3 10 ) In the absence of electrical particle particle interaction, pro viding about 110 V between ELDC plates is adequate to get 10 0% collection efficiency for 20 lunar dust Apparently from Figure 3 4 estimated collection efficiency from the DEM model (dashed line for Lagrangian based approach with uniform e field) at this applied voltage is lower than that determined by the analytical model (Eulerian based approach). Figure 3 4 indicates for obtaining any collection efficiency greater tha n about 46%, the Lagrangian based model is more conservative, asking for higher required voltage and vice versa.
50 The observed behavior is due to the repelling forces among the like charged particles. After starting a simulation, the 50 particles originall y located in the closer side of the centerline with respect to the collecting plate repel the other 50 particles originally located in the further side of the centerline. Consequently, these particles at the closer side accelerate toward the collecting pla te faster than what would be expected. On the other hand, the other 50 particles at the further side are repelled away from the collecting plate. Later on, the repelling effect on these particles fades away and these particles start to move toward the coll ecting plate with a small delay. In other words, initially the further side particles sacrifice themselves to expedite collecting process of the other 50 particles. This is also the reason for observing the intersection between the models close to 50% coll ection efficiency. Using the Eulerian based model as explained in the previous chapter, the expected value for the collection efficiency at = 100 V is 91%. The result of sensitivity analysis on particle number concentration at this certain applied voltage is shown in Figure 3 5 This figure indicates the collection efficiency decreases with an incre ase in the initial number of falling particles. Since the initial distances among the particles at higher number concentration is shorter, the observed effect of electrical particle particle interactions at higher particle concentration is greater. Figure 3 4 displays the extra electrostatic field required due to the electrical particle particle interactions. On this basis, about 29% more electrostatic field should be provided to ensure 100% collection efficiency of one hundred 20 m sized lunar dust particles. At = 120 V, the total required electrostatic field strength would be 2760 V/m ( dash ed line in Figure 3 4 ). Furthermore, the lowest value of collection efficiency is
51 not zero which is distinct at low provided voltages ( = 2.5, 5 and 10 V). Therefore, it can be concluded that even without providing an electrostatic field, electrical particle particle interactions help to collect a small fraction of particles. Effect of Non Uniform Charge Distribution on ELDC Plates Before starting the DEM simulations on a non uniform electrostatic field, capacitance of the ELDC with the above mentioned geometry at different numbers of subsections was calculated. Obviously, a higher nu mber of subsections results in more accurate results for the capacitance and charge distribution of subsections. The relationship between the ELDC capacitance and the number of subsections on the ELDC plates was investigated by numerical computations as sh own in Figure 3 6 This figure indicates the capacitance of the above mentioned ELDC geometry has an asymptotic trend approaching C = 3.9 pF, and for any number greater than 10 (number of sub sections on side of th e plate), the difference is less than 2%. Hence, 100 subsections were opted for discretizing the ELDC plate. The results of non uniform charge distribution on ELDC plates have been tabulated as in Figure 3 7 Figure 3 4 also displays the obtained DEM results (dotted line) comparing with the previous simpler models. From the dotted plot in Figure 3 4 apparently the collection efficie ncy reduces due to the fringe effect. Surface charges tend to leave the plate center and approach the edges. Hence, wherever particles start to fall, they experience 3 different stages of electrostatic field. Initially the electrostatic field is relatively strong. So, in spite of the repelling forces from the 50% particles which are closer to the collecting plate on the 50% particles which are further away from the centerline, the stronger electrostatic field
52 dominates the initial repelling actions and more particles move toward the collecting plates. Thus, initially all the particles approach the collecting plate faster than the case of a uniform e field, and a fraction of closest particles would be collected quicker than the case of a uniform e field. When most particles have moved toward the collecting plate, the distances between the particles become shorter, and the electrical repelling interactions increase. The collecting electrostatic forces from point charges on the center of subsections and repellin g Coulomb forces from charged particles on any assumed particle are both proportional to particle distance squared, but the relatively stronger electrostatic field shortens the distances among approaching particles. Hence, for any particle there is a balan ce point inside the ELDC where these two sets of forces equalize and thereafter, repelling Coulomb forces dominate the particle motion. If this balance point for a particle is close enough to the collecting plate, the particles would be collected due to la ck of adequate number of repelling particles between the target particle and the collecting plate. On the contrary, if the balance point is relatively far away from the collecting plate, there would be enough number of like charged particles between the ta rget particle and the plate to repel the target particle away from the collecting plate. The above mentioned balance point for the majority of the particles occurs inside the central region of the ELDC possessing a weaker electrostatic field. When the move d away particles are in the bottom section of the ELDC, the attractive electrostatic field which is again symmetrically strong may not be adequate to collect them before they pass the ELDC. This expresses the reason for observing the intersection of Euleri an based model (solid line) and Lagrangian based model (dotted line) at about = 22.2%.
53 The ELDC collection efficiency with a non uniform e field strongly varies with location, and the particle collection ends up with a lower collection efficiency compare d to a uniform electrostatic field. However, the observed decrease in collection efficiency due to the fringe effect is not severe and does not influence the feasibility of the ELDC. According to Table 3 1 require d voltage for 100% collection efficiency with non uniform electrostatic field is 172.7 V which is equivalent to less than 3.5 kV/m e field strength for the opted ELDC geometry. Moreover, the electrostatic field close to the entrance of the ELDC bends out o f the ELDC, and this phenomenon reduces some lu nar dust entering the ELDC ( Figur e 1 2 ). Effect of ELDC Dimensions and Particle Concentrations The sensitivity of 3 D DEM simulations which deals with point charges a t the center of subsections on ELDC plates is different from the derived 2 D equation by Eulerian model. The final set of simulations was conducted to study the influence of ELDC dimensions on the collection efficiency. For this purpose, a half size ELDC ( L = W = 5 cm, D = 2.5 cm) was considered and all the other conditions were kept the same as the previous set of simulations. The obtained results from DEM modeling are displayed as dash ed line and dotted line in Figure 3 8 Results obtained from the 2 D Eulerian based model using Eq. (3 10 ) are also plotted as solid lines in Figure 3 8 The obtained collection efficiencies from the L agrangian based model for the half size ELDC are greater than those obtained from larger ELDC and those obtained from the Eulerian model. This is due to the 3 D nature of the ELDC plates in DEM modeling as halving the dimensions decreases the distances bet ween any falling particles and point charges at the center of the subsections on ELDC plates.
54 Although collection efficiency is not exactly proportional to L / D in the Eulerian based model, its predicted collection efficiencies for both ELDCs are very simil ar. The electrostatic force between any individual particle and point charges on the collecting plate increases proportionally to particle distance squared. Since the 2 D Eulerian based model only exerts uniform electrostatic field on the particles in a si ngle plane and the ELDC width and point charges on ELDC plates are both neglected, the Eulerian model gives similar collection efficiencies as long as L / D ratio is constant. As charged particles are denser at the ELDC entrance, the effect of electrical par ticle particle interactions in particle collection is enhanced even at very low electrostatic field strength. This is why obtained results of DEM modeling for both ELDC sizes in Figure 3 8 have similar slopes but t he y interception of a half size ELDC is significantly greater than the normal size ELDC. This means a higher concentration of falling lunar particles improves ELDC collection efficiency at relatively lower voltages.
55 Table 3 1 Collection efficiency as a function of provided voltages for three studied models Model Function R 2 Req. voltage at = 100% in volts Eulerian based Model = 0.915V 1 109 Lagrangian based Model (Uniform E Field) = 0.576V + 17.5 0.992 143 Lagrangian based Model (Non Uniform E Field) = 0.5295V + 8.57 0.999 173
56 Figure 3 1 Schematic of the modeled ELDC configuration to protect optical/photovoltaic surface at the worst case scenario Figure 3 2 The ELDC geometry and particle placement in sections 1 and 2 (100 lunar dust particles at the middle, initially forming a line inside the particle factory; L = W = 10 cm and D = 5 cm)
57 Figure 3 3 Sensitivity analysis on electrical screening distance around the particles (one hundred 20 m sized particles at uniform electrostatic field; L = W = 10 cm, D = 5 cm and = 100 V)
58 Figure 3 4 Collection efficiency as a function of provided voltage via 3 different models: Lagrangian based approach with a uniform e field, Lagrangian based approach with a non uniform e field, and Eulerian bas ed approach. In all 3 models: d p = 20 m, s = 100 V, L = W = 10 cm and D = 5 cm)
59 Figure 3 5 Effect of particle number concentration on collection efficiency of the ELDC ( d p = 20 m, s = 100 V, = 100 V, L = W = 10 cm a nd D = 5 cm)
60 Figure 3 6 The ELDC capacitance at different number of subsections ( L = W = 10 cm and D = 5 cm at = 100 V) Figure 3 7 Distribution of surface charge on ELDC plates at 4 diffe rent provided voltages in pC
61 Figure 3 8 DEM results for two different sizes of the ELDC and comparison with Eulerian based model
62 CHAPTER 4 INFLUENCE OF BACK ELECTROSTATIC FIELD ON ELDC COLLECTION EFFICIENCY Objective Th e main objective of this study was to investigate the significance of the back electrostatic field as a function of time and to optimize the ELDC operation accordingly, as cleaning the ELDC plates in the lunar environment with constraining resources is inc onvenient. Methods Obtaining the ELDC collection efficiency at any point of time requires Lagrangian based modeling to track particle trajectories individually. First, lunar particles were characterized using previously developed models. Then, ELDC dimensi charge distribution on the ELDC plates. Considering the acting forces on each particle, the trajectory of all the lunar particles were tracked and recorded at each time step by to be discussed DEM model. The fate of any individual particles was determined by analyzing the output logs using developed VBA code ( Appendix A) Finally, sensitivity analyses were conducted on the concentration of the incoming particles, the number of the pre collected particles and the applied voltage (electrostatic field). Model Configuration Figure 4 1 shows a pair of square and parallel plates which represents the ELDC within the provided model. The dimensional ratio of L / D = 2 was maintained throughout the simulations, where D is the spacing between the plates and L is the plate height. Since the relationship between the collection efficiency and L / D ratio has been
63 discussed in former chapters, all later obtain ed results can be approximated for another L / D ratio using the derived analytical equation. Similar to the previous chapter, the most conservative case in which ELDC shows the lowest collection efficiency was considered, i.e., ELDC plates were aligned nor mally to the lunar surface (in y z plane) and all falling particles were subjected to the lunar gravity in the z direction. Two sets of particles were created via particle factories befor e starting each simulation ( Figure 4 1 A) Parti particles carrying positive charges on the ELDC plates before simulations runs. Although fringe effect more favorably attracts particles closer to the edges of the collection plate, model limitation requires that Parti cle Factory 1 placed particles uniformly on the ELDC plates. The same numbers of particles were assumed in columns and rows to cover the entire D W area of the E LDC entrance as shown in Fig. 2B Pre collection of charged particles on the collection plate requires an assumption of a thin insulation film between the collection plate and particle factory 1 as will be discussed later. The role of Particle Factory 2 was to create falling particles. Concentration of the incoming particles and loading of the pre collected particles were addressed by taking different values for the number of rows and columns (m and n) wit hin the particle factories ( Figure 4 1 B) Rescaling the ELDC Dimensions The concentration of levitated lunar particles is not well documented. According to measured data by Surveyor 7 Lander, it has been approximated as 50 particles/cm 3 (Criswell, 1973) As mentioned earlier, the needed run time to detect particle interactions in DEM simulation for a system made of n particles is proportional to n 2 So, considering a smaller ELDC helps running simulations for the measured range of lunar
64 dust concentration in a reasonable time scale. Providing a comprehensive model to be applicable for any ELDC configuration is imperative, and requires finding reasonable relationships between all ELDC key parameters including ELDC dimensions, applied voltage, surface charges and collection efficiency. To do so, a new approach was taken using well known concepts of ELDC capacit ance and acting forces on lunar particles in this study. The ELDC capacitance ( C ) is defined as the ratio of the total charge on each plate ( Q ) over the provided electrical potential between the conducting parallel plates, V On the other hand, since ELDC capacitance is a function of ELDC dimensions ( L W D ) and the type of the insulating medium ( 0 ) it serves as a measure for ELDC scaling: (4 1 ) Three major force s act on falling lunar particles: gravitational force, electrostatic force due to the charges on ELDC plates, and interparticle electrostatic forces. Independent from ELDC sizing, the gravitational force (F G ) is a constant but the electrostatic force (F E ) is governed by Coulomb force as the following (Hinds, 2012) : (4 2 ) where K E is the electrical constant (9109 Nm 2 /C 2 ), is either a point charge on the ELDC plates or the charge of another lunar particle and R is the magnitude of the position vecto r connecting the assumed particle to the other point charge or charged particle. Resizing the ELDC dimensions times smaller changes interparticle distances and the distances between particles and point charges on the collection plate times
65 smaller. Thi s reduces R value in Equation (4 2 ) times, leading to 2 times increase in the pertinent electrostatic force. To obtain the same collection efficiency from ELDCs with different sizes, all acting forces on particl es with certain properties must be unchanged. Equation (4 2 ) concludes the way to maintain the same values for q p and by a correction factor of ( 1/ ). Then, Equation (4 1 ) obtains the corresponding applied voltage for the new ELDC dimensions with the corrected total surface charges. Table 4 1 summarizes how ELDC res izing requires correction factors for the key parameters inside the DEM model. As we have explained in our former studies, the ideal ELDC dimensions are L = W = 10 cm and D = 5 cm. However, in order to handle the reported value of lunar dust number concent ration and expedite the DEM simulations run time in this study, the ELDC dimensions were selected as L = W = 10 mm and D = 5 mm which are 10 times smaller than the values used in the former studies. Using the aforementioned correction method, our modeling results can be considered as for the real size ELDC ( L = W = 10 cm and D = 5 cm), since the total surface charge on the ELDC plates ( Q ) and particle charge ( q p ) were modified with the correction factor of 0.1 to cancel out ELDC resizing effect inside the D EM model. Analysis of Particle Trajectories The DEM model records positions of all the particles at each time step. Investigating the fate of the particles requires analysis of the obtained trajectories to determine if a particle is collected. The DEM mode l produces separate output logs for each direction ( x y or z ), separately. Visual Basic for Applications (Microsoft VBA 7.0) code was developed to identify particles and to sort each particle coordinate as ( x y z ).
66 Then, MATLAB 7.10.0 code displayed the 3 D graph of the particle trajectories to provide insight into defining 3 possible cases for the particles at the end of the simulation: collected, penetrated and suspended. VBA code also classified all the particles and calculated the fraction within eac h class. A number of assumptions were made for particle classification as below: 1 If a particle reaches the collection plate before leaving the ELDC within the simulation run time, it is considered as collected. 2 If a particle leaves ELDC before reaching th e collection plate within the simulation run time, it is considered as penetrated. 3 Particles may be repelled back after reaching the collection plate due to the back electrostatic field created by the pre collected particles. 4 Suspended particles are simply the fraction of particles which have neither been collected nor penetrated within the simulation run time. A fraction of particles leaves the ELDC through the y direction before passing the entire length of L in the z direction. This is also classified as suspended. 5 Pre collected particles (generated by Particle Factory 1) do not move throughout the simulation. Results and Discussion Qualitative Observation of Particle Trajectories The graphical feature of EDEM 2.4.2 provides a real time observatory tool t o track particle trajectories. For the same number of falling particles, the cross sectional snap shots in the x z plane were taken to observe the effect of the back electrostatic field at certain elapsed time of the simulation. Similar to re entrainment a nd back flow in conventional ESPs (Miller et al. 1998) the provided images illustrated how particles approaching the collection plate changed direction and got repelled back from the plate due to back e field eddies ( Figure 4 2 ). This effect is clearly strengthened at higher loadings of the pre collected particles with the same concentrations of the incoming
67 particles. However, at the same loading of the pre collected particles and point of time, an increase in p article concentration led to irregular suspension patterns instead of circular eddies. The reason is that falling particles are mobile in contrast to the pre collected particles. Thus, increasing the number of moving particles results in more chaos in the observed suspension pattern. Figure 4 2 presents the mentioned particle eddies in the vicinity of the collection plate at an intentionally high concentration of the incoming particles (3200 #/cm 3 ). Effect of Back E lectrostatic Field on Particle Fate The next step was processing all particle trajectories using the developed VBA code to evaluate the final fate of the particles. In contrast to the conventional particulate controlling devices considering particle fate a s either penetrated or collected, qualitative lunar dust unable to pass through the ELDC and not collected on the ELDC plate within the defined run time. On this basi s, the particle fraction from each category (i.e., collected, penetrated or suspended) was plotted separately for different concentrations of the incoming particles and loadings of t he pre collected particles ( Figure 4 3 ). For this particular ELDC dimension, the dust concentration ranged from 18 to 128 #/cm 3 to include the 50 #/cm 3 value reported by Surveyor 7 lander (Criswell, 1973) The upper limit for the number of the pre collected particles was taken as 900 #/c m 2 in that collection efficiency dropped to zero at this particle loading even at the highest applied voltage. In general, the ELDC collection efficiency starts dropping when the collection plate has accumulated a minimum number of particles. This threshol d for collection efficiency depends on the applied voltage. While particles immediately started to be
68 repelled for any number of pre collected particles at V = 50 V ( Figure 4 3 A) a relatively stronger e field at V = 100 V made the ELDC more resistive to the back electrostatic field effect and no change in collection efficiency was detected for the number of pre collected particles lower than 220 #/cm 2 ( Figure 4 3 B) As th e number of collected particles rises, there would be a corresponding number of collected particles when lunar particles can no longer be collected. In other words, the generated back e field is sufficiently strong to completely disrupt the ELDC. For an EL DC with no pre collected particles, the collection efficiency of the one with a higher incoming particle concentration was lower. This confirms the results from our previous studies concluding that electrical particle particle interactions, which increases as particle concentration increases, tend to make ELDC collection efficiency closer to 50%. Sensitivity analysis on the concentration of the falling particles also reveals that the rate of collection efficiency reduction decreases with an increase in the concentration of falling particles at V = 50 V. The reason is that at a higher concentration of the falling particles through an ELDC, a greater e field resulting from stronger particle particle interactions better resists the back e field effect while these particles approach the collection plate. At V = 100 V, the stronger e field dominates the system leading to the similar rate of collection efficiency reduction for different concentrations of the incoming particles ( Figure 4 3 B) Inferring from Figure 4 3 C and Figure 4 3 D the percentage of particles penetrating the ELDC increases as the number of pre collected lunar dust particles increases. As time goes by, back e field enhancement leads to significant deceleration in particle motion. Then, the majority of the particles that are not collected become
69 suspended. Thereafter, similar to particle collection, particle penetration stops. However, particle penetration cont inues for a while after attaining 0% collection efficiency (between 400 to 625 #/cm 2 at V = 50 V, and between 625 to 900 #/cm 2 at V = 100 V). Back e field created by the build up layer of already collected particles on the ELDC plate prevents incoming pa rticles from both collection and penetration. In other words, the incoming particles are simultaneously under the influence of attraction forces from charges on ELDC plate, and the repelling forces from the like charged previously collected particles or ot her approaching particles. This forms a cloud of particles in front of the protected surface deteriorating the performance of the ELDC and the pertinent device. Presumably, increasing the applied voltage postpones the final suspension ( Figure 4 3 E vs. Figure 4 3 F ). The worst period of time in ELDC operation can be envisaged from two different perspectives. From surface protection point of view, the corresponding time for the highest possible particle penetration is when the ELDC becomes the least efficient. Although a decrease in particle penetration occurs thereafter, particle suspension strengthens at the same time which also lowers the performance of the protected surfaces if the surface function is to receive solar radiations (e.g., solar panels). ELDC Collection Efficiency as a Function of Time Estimating the frequency of the ELDC plate cleaning requires obtaining insight into how collection efficiency changes with time. Presenting a general analytical way to relate collection efficiency and elapsed time is not possible as it involves many complicating factors. For example, two ELDCs with the same applied electrostatic field but different sizes may start with the same col lection efficiency, but the larger ELDC has
70 the capacity to hold more particles before the back e field starts to affect the performance. Nevertheless, an example is presented here to demonstrate how ELDC collection efficiency changes over time for a given ELDC dimensions, operating conditions and particle characteristics. This requires the following simplifying assumptions: 1 In order to maintain the particle number concentration constant, the following set of incoming particles enters the ELDC volume only a fter the elapsed time of the previous set of particles. This assumption is justified because the longest possible time for a particle to stay inside an ELDC with clean plates is quite short (0.08 s for 20 m sized lunar dust to pass through 1 cm length of ELDC). 2 Cleaning is presumed when the collection efficiency drops below 90%. Figure 4 3 b demonstrates that for any number of incoming particles, the collection efficiency at a particle loading of 400 #/cm 2 on the EL DC collection plate is higher than 90%. Thus, a final DEM simulation was run for the same ELDC sizing ( L = W = 1 cm and D 100 V. Assuming the previously described time T = 0.16 s is adeq uate for either particle collection or penetration, the same number of incoming particles were fed from the Particle Factory 2 after each 0.16 s to keep the particle concentration at 50 #/cm 3 The simulation run time was long enough to ensure 400 particles had been collected on the ELDC collection plates. Approximately, such a particle loading on ELDC collection plate occurred between the releases of the 19th and the 20th sets of incoming particles ( Figure 4 4 ). The equivalent collection efficiency was 82.9% which is lower than the expected value of 90%. As shown in Figure 4 3 F suspension starts for particle loading greater than 200 #/cm 2 ; i.e. suspended particles accumulate d from the earlier released sets caused such a reduction in collection efficiency.
71 However, this assumption of continuous lunar dust influx through the ELDC plates is very conservative. The deposition rate of the lunar particles on surfaces has not been me asured meticulously during Apollo missions. The only relevant reported data has come from the studies on Surveyor 3 components after Apollo 12 mission. The lunar dust coverage on camera lens was roughly estimated as 25% of its surface area during 945 days of operation (0.8% per month) without human activities (Murphy et al. 2010) Accordingly, the number of 20 m sized particles deposited presumably as a single layer on the surface is estimated to be 1273 #/month for the ELDC geometry used in this study. T hus, considering 400 #/cm 2 on the ELDC collection plate as the criterion for plate cleaning, the ELDC plates should be cleaned almost every 10 terrestrial day. Estimating ELDC Power Consumption As discussed in chapter 3, assuming 1010 cm plates with a 5 c m distance in between, 200 pairs of ELDC plates with 175 V applied voltage between each pair of the plates are needed to cover 1 m 2 of the solar panel surface and to provide the previously mentioned 3.5 kV/m electric field which runs a clean ELDC with 100% collection efficiency. Duke et al. (2001) have estimated 65 W/m 2 as the provided electric power by a solar panel in lunar environment. Since the ELDC is practically a capacitor with vacuum as its insulator, the required power to run the ELDC can be approx imated using the following the equation (Ulaby et al., 2001) : (4 3 ) where N is the number of plate pairs and A is the plate area ( L W ). According to Eq. (4 3 ), 5.42 10 6 W/m 2 would be the required power for the E LDC described above,
72 which is a negligible fraction of the produced 65 W/m 2 estimated by Duke et al. (2001) This means the ELDC runs practically with no driving force in the limiting condition of the lunar environment. One should notice that ideally ELDC only needs power supply connection initially to attain the maximum possible charges on its plate surfaces. Afterwards, ELDC becomes a capacitor and the distributed charges would be maintained in the absence of the power supply.
73 Table 4 1 Correction factors of different key parameters after ELDC resizing Resizing factor of the ELDC dimensions Particle charge ( q p ) Total charge on collection plate ( Q ) ELDC capacitance ( C ) Electrical potential between ELDC plates ( V ) 1/ 1/ 1
74 Figure 4 1 Schematic of the ELDC plates arrangement to protect lunar installed surfaces
75 Figure 4 2 Trajectories of the falling lunar dust A) I n absence of pre collected particles B) In presence of pre collected particles
76 Figure 4 3 Fate of incoming particles by category and applied voltage: A) C ollected percentage at = 50 V. B) C ollected percentage at = 100 V. C) P enetrated percentage at = 50 V. D) P enetrated percentage at = 100 V. E) S uspended percentage at = 50 V. F) S uspended percentage at = 100 V.
77 Figure 4 4 Collecti on efficiency drop as a function of time for the described ELDC when incoming particles fall continuously
78 CHAPTER 5 EXPERIMENTAL ELECTROSTATIC COLLECTION OF TRIBOCHARGED LUNAR DUST SIMULANTS Objective The objective of this study was to evaluate the colle ction efficiency of an ELDC experimentally to complement prior modeling studies. First, tribocharging properties of two selected lunar dust simulants (JSC 1A and Chenobi) were investigated. Then, the collection efficiency of a customized ELDC was determine d, and the results at low vacuum were compared with the model predictions. Final experiments were aimed to investigate the importance of plate conductivity in particle collection by comparing stainless steel and aluminum. Materials and Methods Experimental Protocol The experimental set up consisted of a transparent cylindrical chamber enclosing a particle tribocharger/dropper, a particle collecto r (ELDC), and a Faraday Cup ( Figure 5 1 ). First, particle tribocharger rotating around its longitudinal axis charged particles for a certain period of time. Then, the charged particles were released down from the tribocharger. The exact elevation of the tribocharger inside the chamber was located to attain approximately the s ame particle velocity at the ELDC entrance as in the previous modeling efforts. Since the first set of experiments aimed to obtain charging properties of the lunar dust simulants as a function of time, the ELDC was turned off, and dropping particles direct ly enter the Faraday Cup (MONROE, diameter = 10 cm, depth = 15 cm). The total charge of the ensemble particles inside the Faraday Cup was measured using an electrometer (KEITHLEY, Model 6514).
79 To study the effect of air pressure on tribocharging, exp erimen ts were conducted at two different pressures: atmospheric and low vacuum. Provided by a 2 stage rotary vane vacuum pump, the low vacuum experiments were conducted at the vacuum level of about 10 1 Torr Surveying the influence of tribocharging duration on the created charge on particles was the main goal of the first set of experiments. In the second set of experiments, ELDC was turned on, and its collection efficiencies at different applied voltages and plate materials were determined. Properties of the Lu nar Dust Simulants Numerous lunar dust simulants made for different purposes are commercially available. In this study, two types of lunar dust simulants, JSC 1A and Chenobi, were tested. Developed by NASA Johnson Space Center, JSC 1A lunar dust simulant i s produced from a basaltic ash and sheet deposit located in San Francisco Volcanic Field of Arizona showing similar mechanical properties and characteristics of the lunar grains (McKay et al., 1994) On the other hand, Chenobi is a chemically enhanced vers ion of OB 1 and is produced from a mixture of anorthosite located in northern Ontario of Canada and smelter glass made of anorthosite itself (Rickman et al., 2012) Willman et al. (1995) determined the average particle density of JSC 1A lunar simulant to b e 2.91 g/cm 3 while Battler and Spray (Battler & Spray, 2009) measured particle density of Chenobi lunar dust simulant to be 2.76 g/cm 3 The most conservative particle size for the mentioned cycle of lunar dust levitation deposition was estimated to be d p ~ 20 m as discussed in previous chapters. For consistency with previous results obtained from analytical and numerical models, lunar dust simulants with the size ranging from 20 to 25 m were used in the experiments.
80 Particle velocity at the entrance of t he ELDC was controlled by changing the distance between the tribocharger exit and the ELDC entrance. Based on the developed dynamic fountain model for lunar dust levitation by Stubbs et al. (2006) the particle velocity ( 0p ) at the ELDC entrance can be es timated conservatively as in Eq. (1 5 ) In order to get the same initial particle velocity at the ELDC entrance ( 0p ) as in our previous studies (1.31 m/s for d p tribocha rger exit and the ELDC entrance was determined based on kinematic equations of motion to be 0p 2 /2 g Sample Preparation The standard test sieves (Gilson Inc.) conforming with ASTM E 11 specifications were used to classify lunar dust simulants with the size of interest. The sieves were mounted on a vibratory sieve shaker (Retsch AS200 control) running at amplitude of 1 mm for 1 hour. Preliminary sieving tests showed that continuing the particle sieving longer than 1 hour at the 1 mm amplitude does not affect the mass distribution of the accumulated particles on the sieves. For both types of lunar dust simulants, particles which passed through the sieve No. 500 (corresponding to the mesh size of 25 m) and collected on the sieve No. 635 (corresponding to the m esh size of 20 m) were selected for the experiments of this study. Due to the specific condition of the lunar environment, lunar grains are fully dry. To keep the particles away from the high relative humidity of the laboratory (RH = 95% in average), part icles were stored inside sealed glass containers with silica gel packets installed on the internal walls. Before starting each experiment, the weighed sample was kept inside an oven (Fisher Isotemp Oven, 100 Series, Model 106G) at 100 o C for an hour. A 5 gr am simulant sample was selected for each experiment using a high
81 replicated 5 times to increase statistical precision. Remotely Controlled Particle Tribocharger Tribocharin g of particles is a common technique for separating insulator particles in various industrial applications (e.g., treatment of ash from coal in power plants) (Zelmat et al. 2013 ) In this charging mechanism (also known as triboelectricity or contact elect rification), electrical charges are generated and exchanged when the particles contact the container wall as well as when they slide on other particles. Tribocharging of a sample of in contact particles is based on band theory and establishment of a therm odynamic equilibrium between the contacting particles or surfaces Electrons flow from the material with a lower work function ( 1 ) to the material with a higher work function ( 2 ) until equilibrium is reached (Sternovsky et al., 2002) In contrast to the conducting particles, there is no unified model for charge transfer between insulating materials. However, results by Castle (1997) showed that the total transferred charge is linearly proportional to the absolute difference between work functions of the c ontacting materials. The work function of Chenobi lunar dust simulants is still unknown, and there is only a handful of studies regarding the work function of JSC 1A lunar dust simulations. Sternovsky et al. (2002) conducted tribocharging experiments insid e a vacuum chamber on fine particles to infer the work function of JSC 1A by comparing the total measured charge of the JSC 1A sample compared to other particles made from known materials. The result of this study suggested 5.9 eV as the work function of J SC 1A lunar dust simulants (Walton, 2007) Trigwell et al. (2009) took a similar approach for determining the JSC 1A work function by adding inclined planes made of certain materials between
82 the dust dropper and a Faraday Cup for strengthening the electrif ication. This resultant JSC 1A work function was found to be 5.4 eV. Considering JSC 1A = 5.4 ~ 5.9 eV, in this study, the selected material to be in contact with the lunar dust simulants was aluminum with two advantages of having relatively greater | 2 1 | compared to other common materials ( Al = 4.28 eV), as well as being adequately light to be held horizontally while it is rotating to tribocharge. Different tribocharing devices are commonly used such as fluidized beds, vibrating feeders, static tribo chargers, tribo cyclones, tribo fans, and rotating tubes. Since the experimental set up was aimed to run at low pressures, choice of particle tribocharger type was limited to the ones not disturbing the air pressure inside the chamber. Both inclined plane tribocharger proposed by Captain et al. (2007) and rotary milling tube proposed by Sharma et al. (2008) are known to be effective tribocharging methods for the lunar dust simulants inside vacuum. In this study, a hybrid tribocharger utilizing the idea of b oth rotary tube and inclined plane was designed to obtain the highest possible surface charges via tribocharging. As shown in Figure 5 2 the aluminum connector attached the aluminum tube to the armature which was connected to a low voltage power supply. Due to centrifugal force acting on fine particles with negligible weights, particles may stick to the tube wall preventing them from the repeatedly effective contacts with the aluminum surfaces. This acting centrifu gal force depends on particle size, tube diameter and rotational speed of the tube. Yang et al. (2008) conducted sensitivity analysis on the rotational speed of a drum partially loaded with 3 mm sized particles through numerical simulations. This study ide ntified six regimes for the particles dynamics inside the rotating drum:
83 slumping, slumping rolling transition, rolling, cascading, cataracting and centrifuging. While movements of particles become more limited from slumping to centrifuging regime where al l particles are stuck to the tube wall, effective particle contacts occurs only at slumping and rolling regimes. Tribocharging of the particles requires repeatedly contacts between particles and aluminum wall surface. Thus, the rotational speed of the arma ture was controlled by limiting the applied voltage on the armature to 1 V in all experiments. Moreover, chains of 2 mm sized aluminum beads were glued to the aluminum connector to enhance particles friction with aluminum surfaces whil e they slid inside th e tube ( Figure 5 2 ). The dual functionality of the tribocharger (tribocharging and dropping) was achieved using a small lever connected to the remotely controlled armature to switch the particle tribocharger/droppe r orientation from horizontal (when it was tribocharging the particles) to vertical (when it was releasing the tribocharged particles down toward the Faraday Cup). When tribocharging was accomplished, the tribocharger/dropper rotated around the pivot to d rop the charged particles down toward the aluminum funnel. Part of the fallen particles slid on the funnel for further tribocharging improvement of the system. Geometry and rotational speed of the tribocharger determine the appropriate amount of sampled mi crometer particles to ensure effective tribocharging. Zelmat et al. (2013) performed an experimental study on different types of tribocharging devices to charge 1 mm sized PVC particles in atmospheric pressure. Their study revealed that charging efficienc y of the static tribocharger utilizing inclined surfaces to direct particles falling under gravity and rotating tubes are insensitive to the mass of particles inside the
84 tribocharger. However, not all of the tribocharged particles reached the ELDC entrance after the release, because a fraction of particles either stuck to the tribocharger wall, stayed on the funnel, or puffed out from the tribocharger while rotating. In order to get an adequate amount of released particles inside the Faraday Cup and possess ing enough charges to be detected by the electrometer, the weight of all sampled particles initially put inside the tribocharger were selected to be 5 g. Charge Measurement and Electrostatic Particle Collection A standard Faraday Cup, connected to a nano C oulomb meter electrometer (KEITHELY 6514, 0.1 pC reading precision) was implemented for the charge measurements. The ELDC was made of two squared shape conducting parallel plates mounted on a wooden insulating frame. Using alligator clips, the ELDC plates were connected to a low voltage DC power supply with capability of voltage provision up to 150 V. Due to insulating property of the vacuum medium existing between the plates, ELDC acted practically as a parallel plate capacitor with electrostatic field str eamlines from the positively charged plate toward the negatively charged plate. Similar to the examined ELDC in our previously developed numerical Lagrangian based model, dimensions of the plates and separation distance were (10 cm 10 cm) and 5 cm, respe ctively. Since aluminum made tribocharger produced negatively charged particles, the positively charged plate of the ELDC was the collection plate for the entire experiments. Two plate materials of stainless steel and aluminum were tested in this study.
85 R esults and Discussions Tribocharging Properties of JSC 1A and Chenobi Simulants The first set of experiments obtained insight into tribo chargeability of the lunar dust simulants. Tribocharging duration was increased at 5 min increments to investigate how total charge of the sample changes as a function of time. Figure 5 3 displays results on the time of tribocharing ( T t ) at both atmospheric and low vacuum air pressures. In the beginning of the tribocharging, partic les were free of charge. As a result, the gradient of electron transfer from the aluminum tube walls and stirring beads (with lower work function) to the lunar dust simulants (with higher work function) was the greatest. As time goes by, charged particles become more spread out due to possession of the same electrical polarity. However, a group of particles closer to the aluminum surfaces (both inner wall and beads) stick to the oppositely charged surfaces. Not only the attached particles are not effectivel y mobile over the aluminum surfaces, but also they block other particles from tribocharging surfaces resulting in a lower gradient of incoming electrons comes to the particles. In the presence of air molecules (atmospheric pressure), the maximum total char ge occurs at T t = 5 min as the interactions with air molecules hinder achievement of any greater values of the total charge. The tribo chargeability improved significantly (2 to 3 times) at the low vacuum condition due to the negligibility of air molecules interactions with the particles while charging. Hence, even after the mentioned reduction in the flow of the incoming electrons, charge build up on the particles continued, though the rate of increase was reducing with time. In all cases, the collected sa mples inside
86 the Faraday Cup were discharged rapidly, and no accumulated charge could be maintained longer than 1 min. The tribochargeability of the Chenobi particles was lower. However, smaller error bars at both applied pressures (as observed in Figure 5 3 B) imply more stability in charge accumulation for Chenobi lunar dust simulants. Higher cohesivity and surface energy related forces (e.g., Van der Waals force) of the Chenobi particles may be responsible for bot h observations as these particles apparently agglomerate inside the storing containers. Although cohesivity of the JSC 1A particles have been studied using a DEM model developed by Walton and Johnson (2010) and through shear stress test following ASTM 6773 standard by Ram et al. (2010) unfortunately, no studies have been conducted on Chenobi particles to compare the interparticle cohesion forces. According to Fig. 3a, the highest obtained total charge per mass ratio (|Q/m|) on JSC 1A samples in our study was almost 2.5 nC/g. This is about 12 times smaller than the |Q/m| ratio resulted from the study by Captain, et al. (2007) where tribocharging property of the JSC 1A was evaluated against aluminum inclined planes. The difference may stem from the fact that the particle size of their tested JSC 1A having larger size were run under the high vacuum level of 810 6 Torr. The average charge per particle (q p ) for the sieved particles of JSC 1A with d p = 17 C. For d p s = 100 V which was assumed in the previous models, by Goertz (1989) ( equations (1 1 ) to (1 3 ) ), the highest possible surface charge on a particle was about 1.1110 13 C, which is significantly larger than that obtained experimentally. This means the surface potential
87 of the JSC 1A simulant is much smaller than the assumed s = 100 V in our previously developed models. The surface potential of the lunar grains is a function of environmental factors such as vacuum level, temperature, density of the incoming solar particles and intensity of the solar radiations. Therefore, the di fferent method of charging (tribocharing) and environment make the surface potential of the lunar dust simulants smaller in the current experiments. One should notice that the tribocharging in Figure 5 3 A & B incre ased with time, and continuing the experiments for longer than 20 min will result in a higher amount of surface charge on the sample. However, the rate of tribocharged particles will reduce with time and extrapolating the plotted graph to obtain the highes t possible charge on particles is not possible. Moreover, the required tribocharging time to achieve saturated charge particles will be excessively long, making th e experiment infeasible. Using e quations (1 1 ) to (1 3 ) the average surface potentials of the JSC 1A and Chenobi particles inferred from this set of experiments at the low vacuum condition after 20 min of tribocharing were 0.035 V and 0.021 V, respectively. Collec tion Efficiency of the ELDC at Low Vacuum Condition Due to observation of relatively better tribocharging property for the JSC 1A simulants, collection efficiency evaluation of the ELDC was performed only on JSC 1A particles for low vacuum condition. Excep t having the ELDC turned on, similar experimental procedure as for the first set of experiments was followed for this set of experiments. The tribocharging time of T t = 20 min corresponding to the highest obtained surface charge on particles in the first s et of experiments, was chosen for this entire set of experiments. Since tribocharging makes lunar dust simulants negatively charged, the ELDC plate connected to the positive terminal of the power supply collects
88 a fraction of falling particles. Two mass ba sed and charge based ratios were considered as the ELDC collection efficiencies ( 1 and 2 ) as defined in: (5 1 ) (5 2 ) where m c is the mass of particles collected on the collection plate, m 1 and q 1 are the total mass and total charge of the particles inside the Faraday Cup, respectively, when ELDC is turned on at a ce rtain applied voltage, and m 2 and q 2 are the total mass and total charge of the particles inside the Faraday Cup when ELDC is turned off. Equation (5 1 ) is solely mass based requiring one run per data point. Howeve r, particle collection is because of the electric force attracting particles toward the plate. Equation (5 2 ) requires two experimental runs per data point: one in the presence and one in the absence of the electro static field. Although the particles were monodisperse with ideally identical properties, the created surface charge on particles were different from one another due to the randomness of their tribocharging contacts. Consequently, not only the probability of collection depends on its initial displacement with respect to the collection plate, but also is a function of the acquired surface charge on the target particle. This explains the importance of presenting ELDC collection efficiency based on the charged based Eq. (5 2 ) Figure 5 4 displays collection efficiency results at the low vacuum. The charge based collection efficiency is slightly higher than the mass based collect ion efficiency for the same applied voltage. If surface charge on each particle and initial displacement of falling particles at ELDC entrance could be uniformly distributed, the values for the
89 collection efficiencies obtained from Equations (5 1 ) and (5 2 ) should be the same for any tested monodisperse lunar dust simulants. Obtaining higher charge based collection efficiency concludes that the fraction of particles collecte d over the collection plate have acquired higher surface charge compared to the particles that penetrated through the ELDC and settled inside the Faraday Cup. However, the difference between these approaches is slim indicating qualitatively a small deviati on for the distributed charges over the tribocharged sample. Collection efficiency of the ELDC improves linearly with an increase in electric potential difference between the plates. This linear relationship is consistent with the derived 2 D equation and the numerically obtained graphs shown in previous chapters. The range of the selected potential difference was the same as our previous DEM model. However, experimentally obtained collection efficiencies are significantly lower than what are expected from analytical and numerical models. Equations (5 3 ) and (5 4 ) express dependency of the collection efficiency to the applied voltage, particle charge and gravitational acceler ation which are concluded from the 2 D analytical work in chapter 2. Based on these equations, several reasons justify the above mentioned difference regarding the ELDC collection efficiency. (5 3 ) ) (5 4 ) First, t he provided vacuum level inside the chamber is about ~2 10 1 Torr 13 to 10 14 Torr (Heiken h
90 Considering the obtained results of this study at two different air pressures and similar studies by Trigwell et al. (2009), Captain et al. (2007) and Sharma et al. (2008), vacuum level is the most important factor to achieve high surface charge on the particles, and consequently high collection efficiencies as predicted from the models. The limitation in air pressure simulation has two effects on the evaluation of ELDC collection efficiency. First, the highe r concentration of air molecules existing inside the chamber contradicts with the ideal theoretical assumption of not having drag force acting on the lunar dust. However even at the low provided vacuum level of this study (10 1 Torr), the drag force on par ticles must be fairly negligible. Second, higher concentration of air molecules and consequent higher interactions between the air molecules and charged particles shorten the time particles maintain the created surface charge. The latter effect is more imp ortant, and it was already concluded from the first stage of the current study. The accumulated charges on lunar grains and electric surface potential at low vacuum were significantly higher than what were obtained experimentally in this study. In fact, ac quisition of the adequate amount of charge is the prerequisite of lunar dust levitation in the first place. Surface potential of the theoretical works being 100 V was one of the assumptions in the formerly developed models. Inefficiency of tribo electrific ation at 10 1 Torr in creation of nearly saturated lunar simulants was concluded in the first stage of this study. Thus, insufficient charges on the particles was the main reason for underestimation of ELDC ability in particle collection. The six times dif ference between the lunar gravitational acceleration ( g l = 1.62 m/s 2 ) assumed in the models and terrestrial gravitational acceleration governed the
91 experiments ( g = 9.81 m/s 2 ), makes falling lunar dust accelerating faster than expected while penetrating th rough the ELDC. Consequently, the experimental ELDC in this study has a shorter time for lunar dust collection compared to the real case on the moon. Required applied voltage for 100% collection efficiency of 20 sized lunar dust from 2 D Eulerian based model and 3 D Lagrangian based model are 109 and 173 V, respectively. The highest experimentally obtained collection efficiency at low vacuum was about 1.05% (two orders of magnitude smaller than the models), and about 1000 times greater than what is obtai ned from Eq. (5 4 ) This difference is due to the 3 D nature of the experiments compared to 2 D analytical model and non uniformity of the distributed charges on falling particles. Similar to the effect of halving ELDC dimensions, the experimental results confirmed that the 2 D Eulerian based model underestimate the ELDC collection efficiency. This also emphasizes the importance of vacuum level in collection efficiency of the ELDC and necessity of performing experim ents at the higher vacuum level. Figure 5 5 illustrates how doubling the applied voltage from 33 V to 65 V increased the amount of collected particles. Figure 5 5 and later explained Figure 5 6 demonstrate that the density of the collected particles was higher near the corners of the collection plate. This observation is consistent with the non uniform electrostatic field observed in our previous study which is due to non uniformity of the distributed cha rge known as fringe effect ( Figure 3 7 ) (Reitan, 1959) However, most particles are collected particularly on the upper one third of the plat e. As discussed in chapter 3, the reason is that falling particles which are entering the ELDC closer to the collection plate are attracted with relatively stronger electrostatic field toward the upper one third of the
92 plate and have to pass relatively sho rter distances compared to other falling particles. Other particles which are entering the ELDC relatively further from the collection plate, need to move a longer path to reach the plate. The exertion of relatively weaker e field from the center and exert ion of relatively stronger e field from the lower one third might be too late to collect these particles before they exited the ELDC. Effect of Plate Conductivity on Particle Collection at Low Vacuum Condition The effect of electrical conductivity ( ) of t he ELDC plates on ELDC collection 6 S/m) with aluminum ( = 3.5 10 7 S/m). This is equivalent to 24 times increase in electron mobility of the collection plate. As shown in Figure 5 7 collection efficiency of the ELDC was improved using aluminum electrode though such a small increase was not obvio us on the collection plates ( Figure 5 6 ). Collection efficien cy improvement due to replacement of aluminum increased at the higher applied voltages. Similar to the case with stainless steel, the charge based collection efficiencies were higher than the mass based ones.
93 Figure 5 1 Sch ematic of the experimental set up Figure 5 2 Components of the designed particle tribocharger/dropper
94 Figure 5 3 Total charge/mass ratio of lunar dust simulants at different tribocharging time and air pressures A) JSC 1A B) Chenobi. Figure 5 4 ELDC collection efficiency for JSC 1A simulants as a function of applied voltage at low vacuum condition
95 Figure 5 5 Collected JSC 1A partic les on the positively charged collection plate A) A t V = 33 V B) A t V = 65 V. Figure 5 6 Collected JSC 1A particles on ELDC collection plate at V = 33 V A) O n stainless steel plate B) O n aluminum plate
96 Figure 5 7 Comparing collection efficiencies of steel made and aluminum made ELDC plates for JSC 1A simulants as a function of applied voltage at the low vacuum A) M ass based collection efficiencies. B) C harge based collection efficiency
97 CHAPTER 6 DESIGN OF AN ELECTROSTATIC LUNAR DUST REPELLER FOR MITIGATING DUST DEPOSITION Objective The objective of this study was to develop an electrostatic lunar dust repeller (ELDR) to address concerns associated with wide applications of ELDC: the w eight of the plates, probable partial blockage of the solar radiation and the need for occasional cleanin g Its electrical power requirement and arrangement of electrodes were optimized. Electrostatic Lunar Dust Repeller (ELDR) The ELDR consists of an arra y of needle shaped thin electrodes, all connected in parallel to the same terminal of the DC power supply. As the other terminal of the power field forms around the gro up of electrodes to direct falling particles away from the protected surface. Because the levitated lunar particles are ideally like charged on each side of the moon, the electrostatic field created by the electrode array will repel the falling lunar dust away before it approaches the protected surfaces. Methods Evaluating the removal efficiency of the ELDR involves calculation of non uniform charge distribution on the electrodes surface, individual follow up of the particle trajectories, and determination of electric field vectors and electric potential distributions for the system of electrodes, all around the protected area. Removal efficiency of a single electrode ELDR was studied initially with sensitivity analyses on the applied voltage and electrode l ength. The results give insight into proposing an electrode
98 ensemble ELDR operating not only more efficiently but also at a lower voltage. Inputting the lunar dust properties using the related literature (as explained earlier) was the first step of this st udy. To fulfill each of the abovementioned modeling tasks, an appropriate numerical modeling scheme was implemented. Model Configuration The ELDR consists of a set of thin rod shaped electrodes oriented perpendicular to the protected surface. All electrode s carry the same electrical charge and polarity as they are all connected to the same terminal of the DC power supply (in the lunar environment the power supply is practically the solar panel itself). As the falling lunar particles are ideally like charged either positive or negative on each side of the moon, the electrical sign of this terminal is selected to be the same as incoming particles to ensure the repelling action. The other terminal is connected to a grounded wire above and surrounding the entire protected area. The role of grounded wire is to direct the electrostatic field streamlines upward and away from the protected surface ( Figure 6 1 ). Charge Distribution on Needle Shaped Electrodes Since most of the spatial explorations are performed on the dayside of the moon, both the surface charges on incoming particles and the transferred charges on the ELDR electrodes from the power supply are assumed to be positive. Given the electrical potential ( V ) on each electrode, the charge distribution on the array of electrodes (Sadiku, 2001) : (6 1 )
99 where s is the surface charge density and vector r is the position vector between each point of space and the origin. The method of moments (MOM), a common numerical technique for solving integral equations, was used in this study. For the initial case, a single, thin, rod shaped electrode of diameter D a nd length L ( L >> D ), the electrode was discretized into a number of segments (n), each of length L As the electrical potential is constant over the entire electrode and equal for all segments, Eq. (6 1 ) was (6 2 ) : (6 2 ) where the indices i and j refer to i th electrode and j th segment, respectively, sj is the charge per unit length of the j th segment, and A ij indicates the inver se momentum of charge density sj of the i th segment. Using a Gaussian elimination technique, the following set of equations was substituted into Eq. (6 2 ) for A ij Then, MATLAB 7.10 code was developed to solve equ ations (6 2 ) to (6 4 ) at different applied voltages, numerically: (6 3 ) (6 4 ) Because the distributed charges at each applied electrical potential depend on n and L sensitivity analysis was conducted on the number of segments for the particular electrode geometry ( L = 5 or 10 cm and D = 1 mm) of this study. To consider the highest possible surface charge on the electrodes, the number of segments in which the
100 highest possible total charge on the ELDR elec trode could be achieved was used for the charge distribution calculations and electrostatic field inclusion into the DEM model (to be discussed next). For this purpose, the pertinent charge distribution at each applied voltage was computed and assigned to the discretized elements of the modeled geometry inside the DEM model. Discrete Element Modeling EDEM 2.4.4 developed by DEM Solutions, Inc., with a dedicated module for incorporating the electrostatic calculations into the DEM model was adopted. The first set of simulations was conducted to model a single electrode ELDR protecting an assumed 5 cm 5 cm area. Detecting particle collisions for each particle was limited to the grid cell the target particle has been positioned in and the adjacent cells. This means that refining the grid cell size promises to provide a better numerical convergence by inclusion of all potential particle collisions at each time step. Sensitivity analysis conducted on the grid cell size demonstrated that grid sizes finer than 1 mm do not influence the particle trajectories. Therefore, considering the electrode length, the entire domain of the model was discretized into one million cells for L = 5 cm or two million cells for L = 10 cm. As discussed in previous models, the electrical screening distance is the radius of an imaginary sphere around each centered particle in which the electrical interactions of the target particle with other charged elements of the model will be taken into account. An electrical screening distance of 36 m m the length of the diagonal connecting two opposite corners of the 3 D control volume was selected for this set of simulations to ensure inclusion of the entire model domain in all possible electrical interactions.
101 A rectangular planar particle factory wa s assigned on the top of the electrode to create 20 m sized particles with the charge and initial velocity calculated from Eq. (1 1 ) and Eq. (1 5 ) respectively. Initially the generated particles were uniformly distributed within the particle factory (the same number of particles within rows and columns of the particle factory). Gravitational force, Coulomb force from the ELDR electrodes, and electrical particle particle i nteractions were the acting forces. Forty percent of the Rayleigh time step (~ 2.1 10 7 s) was taken for the simulations of this study. More details about setting up the implemented DEM model have been explained in the previous chapters. All simulations were conducted on a Dell Precision T5500 Workstation with 8 Intel(R) Xenon(R) CPU E5620 cores with a processing speed of 2.4 GHz, and 8 GB DDR3 RAM. The simulation runtime is a function of the total number of particles, electrical screening distance, cell grid size and time step. The longest simulation runtime for the single electrode ELDR with 1600 particles was about 8 hr, and for the electrode ensemble ELDR was about 4 days. The simulations continued until all particles were either repelled out from the geometry or deposited on the surface. Analysis of Particle Trajectories Determining whether a particle is successfully removed or deposited on the assumed surface requires analysis of the trajectories obtained. The removal efficiency of the ELDR was define d as the percentage of particles repelled away from the protected surface before passing the entire length of the electrode. The DEM model produces separate output logs for x y and z components of each particle trajectory. Visual Basic for Applications (V B A) code was developed to identify each particle by
102 integrating its coordinates ( x y z ) as a function of time, and to calculate the fraction of particles repelled out of the space. Configuration of the Final Model The first set of simulations focused on a single electrode ELDR to estimate the total applied voltage needed to protect an exposed surface at a given size. The pattern of arranging the electrodes and number of applied electrodes at certain electrode length are the key parameters in optimizing th e ELDR operation over any protected surface. The entire modeling was then conducted for a double length electrode at the same diameter (i.e., L = 10 cm and D = 1 mm) to investigate how electrode sizing influences the removal efficiency. Then, more electrod es were added to protect larger surface areas at even lower applied electrical power. The charge distribution on each electrode is non uniform, and varies as a function of electrode location. Thus, before setting up the final simulation, the charge distrib ution of each electrode for two cases ( L = 5 cm and 10 cm) were estimated at a selected voltage. The electrode ensemble ELDR consisted of a certain number of electrodes to protect an assumed 30 cm 30 cm area. The electric field streamlines specified the best possible pattern of the electrode arrangement. For this purpose, a finite element analysis (FE A) solver package coupled with an electrostatics module, COMSOL Multiphysics 4.2, was implemented. After the most effective electrode arrangement was found, 3 D vectors of the electrostatic field were determined by solving the following set of equations using COMSOL 4.2: (6 5 )
103 (6 6 ) where n is the number of electrodes, m is the number of discretized segments on each electrode, vector r is the position vector of the observation point with respect to the origin and r ij is the position vector of segment j of electrode i with respect to the origi n. Sensitivity analysis on the voltage applied to the electrode ensemble ELDR to investigate its effect on the ELDR removal efficiency required a huge computational effort. Hence, to select the appropriate applied voltage to be applied to the electrodes o f the ensemble array, distribution of the electric potentials within the control volume of the single electrode ELDR was studied. For each electrode length, the single electrode model and its surrounding volume were analyzed using the FEA model at their ap plied voltage corresponding to 100% removal efficiency (4 kV for L = 5 cm and 1.5 kV for L = 10 cm). The geometry was finely meshed to solve Equations (6 5 ) and (6 6 ) numer ically to obtain the electric potential distribution inside the control volume. The output logs were processed to find the minimum value of the distributed electric potentials for each case. Because the applied voltages on each single electrode corresponde d to 100% removal efficiency, providing electric potentials greater than the obtained minimum values within the control volume of the single electrode ELDR for the electrode ensemble ELDR should be a proper scheme to estimate the voltage needed on the elec trodes in the final DEM models. Thus, different voltages were applied to the developed FEA model of the electrode ensemble ELDR to find the minimum applied voltage on the electrodes of this model ensuring the abovementioned minimum for the electric potenti al within the control volume. Then, the calculated charge distributions for
104 the selected applied voltages were imported into the DEM model for particle trajectory computations. Afterwards, 100 uniformly distributed lunar particles were generated inside the particle factory at t = 0 of the simulation. The 30 cm 30 cm protected surface was 5 cm beneath the lower ends of the electrodes. The gaps between diagonally arranged electrodes were 8.5 cm. The properties of aluminum, glass and vacuum were assigned to the electrodes, protected surface and surrounding volume, respectively. The final simulations were conducted on two different electrode lengths of 5 cm and 10 cm. Results and Discussion Charge Distribution on the Single Electrode ELDR As displayed in (6 2 ) the numerical scheme in Eq. (6 4 ) applied to resolve the singularity problem of zero denominator for Eq. (6 3 ) at i = n led to o bserving a maximum value for the total surface charges on the electrode. Considering a single segment on the electrode (uniform charge distribution), the total charge on the electrode ( L = 5 cm and D = 1 mm) was about 60.4 pC at V = 100 V. However, this value increased with increasing numbers of segments. The maximum possible total charge was about 66.4 pC (total increase of ~10%), which occurred when 18 segments were selected. Afterwards, increasing the number of segments result ed in a gradual drop in the total charge. Thus, 18 discretized units were used for the entire charge distribution calculations on the electrodes. The general pattern of charge distribution over the electrode normalized to uniform charge distribution is dep icted in Figure 6 2 b. As shown, the middle section of the electrode carries about 90% of the value corresponding to the uniform charge distribution (red line on the graph), whereas 15% of each end of the electrode length
105 carries significantly higher charges with respect to the uniform value, due to the fringe effect of the equipotential lines. Removal Efficiency of the Single Electrode ELDR Sensitivity analyses were then conducted on the particle number concentratio n and the applied voltage. Figure 6 3 illustrates the space charge expansion of particles, and displays how a charged 5 cm long single electrode operating at 4 kV altered the particle trajectories of one hundred 20 m particles falling, to avoid their deposition on the 5 cm 5 cm surface (the trajectories moving out of the control volume before hitting the imaginary protected surface at the bottom). The farther a particle is from the electrode, the shorter the late ral distance it needs to travel before hitting the protected surface. However, the repelling force from the electrode on a particle is inversely proportional to the distance squared, so particles further away from the electrode are under a smaller lateral force. As a result, there would be a critical distance from the electrode at which removing particles requires the greatest repelling force. Deriving an analytical relationship to determine such a distance is complicated due to the varying forces on each p article at each time step. However, the processed particle trajectories for the 5 cm electrode at V = 4 kV showed that the mentioned critical distance was 15 to 17.5 mm from the electrode. In contrast, particles falling along either x or y axes were repelled away more strongly than others (dashed r lateral distance to move out from the surface in the time unit. Figure 6 4 presents computed plots of removal efficiency as a function of applied voltage for a 5 cm long, single electrode ELDR. Voltages applied t o the electrode ranged from 0.5 kV to 4 kV, in increments of 0.5 kV, and the number of falling particles
106 at each side of the particle factory was selected to be 10, 20, 30 and 40. An increase in removal efficiency by increasing the applied voltage is trivi al but the results obtained imply an almost linear relationship between removal efficiency and applied voltage. Interestingly, increasing the number concentration of the particles slightly improves the removal efficiency due to interparticle repulsion of t he like charged particles. An electric potential of 4 kV applied to the single electrode ELDR ensured 100% removal efficiency of 20 m sized lunar dust over the 5 cm 5 cm surface. However, application of 4 kV electrical potential to protect a relatively small surface area of 25 cm 2 is not desirable. Before adding more electrodes into the system, we explored the effect of electrode length on the removal efficiency of the single electrode ELDR. As lowering the particle concentration resulted in a more conse rvative removal efficiency, only 100 (10 10) lunar particles were considered for all remaining simulations. Electric field enhancement in the vicinity of the single electrode ELDR may be achieved by increasing the aspect ratio of the electrode ( L / D ) at a certain applied voltage. Narrowing the electrode diameter to less than 1 mm may not be practical. To reduce the electrical power required, the electrode length was increased to 10 cm. Figure 6 5 expresses how ele ctrode elongation reduces the required applied voltage on the ELDR electrode. At the same electrode diameter, doubling the electrode length resulted in approximately 63% reduction in the required applied voltage (~ 1.5 kV) to achieve 100% removal efficienc y ( Figure 6 5 ). Arrangement of Ensemble Electrodes Any change in the arrangement of electrodes over the protected surface alters the charge distribution on each electrode, electric field vectors and electric potent ial
107 values at all points of the surrounding space, and consequently the ELDR removal efficiency. At first sight, the simplest solution to ensure all parts of the exposed surface are protected by the arranged electrodes seems to be uniform distribution of t h e electrodes over the area ( Figure 6 6 A) As all electrodes carry the same electrical charge polarity, any arrangement making closed areas with the positioned electrode (e.g., areas shown in Figure 6 6 A and B) is ineffective. The reason is that the repelling interactions between like charged electrodes make the electric field streamlines diverge inside the area bounded by the electrodes. Consequently, dead zone areas form b etween electrodes wherever the in plane repelling forces from the electrodes cancel each other, and the falling particles will be deposited on the surface in the absence of any effective lateral forces. To find the optimum electrode arrangement, four diffe rent scenarios with the same number of electrodes were considered ( Figure 6 6 ). The distances between each two successive electrodes on the same line were chosen to be 8.5 cm to guarantee negligible negating effect s due to repulsive forces in the vicinity of the neighbor electrodes. Thereby, each of the studied ensemble models included nine identical electrodes to cover the entire 30 cm 30 cm protected area. Electric field vectors for the discretized geometry of s everal electrode arrays were examined and the points with the lowest electric field coverage were recognized (corners of the squared plate and mid of the sides of the squared plate in Figure 6 6 c and Figure 6 6 d) via COMSOL 4.2 Multiphysics simulations. There is no dead zone in both + shaped and x shaped arrangements except the dotted lines connecting the m as in perpendicular rows ( Figure 6 6 c and Figure 6 6 d). However, the removal efficiency of
108 the x shaped arrangement at a certain voltage is higher than the + shaped arrangement. The reason is that particles falling toward the protected surfa ce around the mentioned critical points are the most difficult to repel because they are at the greatest distance from nearby electrodes compared to all other points within the space. For a certain number of electrodes, the distance between a critical poin ts and the nearest electrode for the x shaped arrangement is shorter than the + shaped arrangement. Hence, the x shaped arrangement requires shorter lateral distances for the falling particles to be repelled away before reaching the surface. This configura tion also displayed the highest electric field strength with no dead zones inside the control volume. Therefore, the x shaped arrangement of electrodes was adopted for further analyses. Figure 6 7 illustrates a sam ple 3 D electric potential distribution for the ensemble ELDR of this study at = 2.2 kV. Figure 6 8 displays the 3 D electrostatic field streamlines of the selected arrangement of electrodes. The plotted streamlines extending from the positively charged electrodes toward the grounded ring predict particle trajectories of the incoming lunar particles of the DEM model. When lunar particles are falling toward the exposed surface, the upward component of the electric field ( E z ) decelerates the particles while the planar electric field component s ( E x and E y ) shift them away from the surface edges. Processing the COMSOL output logs regarding the electric potential distribution in the vicinity of the single electrode 5 cm ELDR held at V = 4 kV (corresponding to = 100%) to protect a 5 cm 5 cm surface area, indicated that the minimum electric potential in the surrounding volume was 324 V. Similar calculation for the 10 cm single
109 electrode ELDR held at V = 1.5 kV (corresponding to = 100%) to protect the same surface area was 115 V. The minimum voltages assigned to each electrode of the nine electrode ensemble model ensuring the aforementioned minima of 324 V and 115 V at each point of the modeled volume were determined by sensitivi ty analysis on the applied voltage. Voltages of 2.2 kV and 1.4 kV were obtained as the voltage needed for L = 5 cm and L = 10 cm, respectively. The last two DEM simulations were run for the nine electrode ELDR model at L = 5 cm and L = 10 cm, over the 30 c m 30 cm surface area. The removal efficiency of the shorter ELDR was 92% at the applied voltage of 2.2 kV, and the 10 cm ELDR achieved 100% removal efficiency at V = 1.4 kV. Comparison between Single Electrode and Ensemble Electrode ELDRs The voltage r equired on each electrode of the ensemble electrode to obtain 100% removal efficiency is lower than for the single electrode ELDR. For instance, in the shorter ELDR design ( L = 5 cm), 92% removal efficiency is achieved by applying 2.2 kV on the x shaped ni ne electrode ELDR, much less than the 4 kV required for the single electrode ELDR to reach 100% removal efficiency. Similarly, in the longer design ( L = 10 cm) applying V = 1.4 kV on the x shaped nine electrode ELDR leads to 100% removal efficiency which is smaller than the 1.5 kV for the single electrode ELDR at 100% removal efficiency. In summary, the cooperation of the electrodes in the ensemble model decreases the vo ltage needed on each electrode. The evolution of the electrode ensemble ELDR from the single electrode basic case fulfills both goals of this study: full protection of a larger area and applying a lower voltage to each electrode. Adding only eight more ele ctrodes to form an x shaped ELDR enabled the protection of a 36 times greater area. The electric power consumption is
110 proportional to V 2 and the number of electrodes. Considering the observed reduction in the applied voltage on the ensemble electrodes, the electric power factor for an n electrode ensemble ELDR based on the single electrode ELDR is ( Ensemble / Single ) 2 n. As discusse d earlier, Ensemble is smaller than Single making ( Ensemble / Single ) 2 smaller than 1. This means the x shaped, nine electrode ELDR protects a 36 times larger area with the most conservative cost of only nine times more electric power consumption.
111 Figure 6 1 Schematic of the ELDR Figure 6 2 Sensitivity analysis on the number of segments mode led on a single electrode ELDR and n ormalized charge distribution over the electrode length ( L = 5 cm and D = 1 mm) at = 100 V
112 Figure 6 3 Particle trajectories of 100 falling lunar particles influenced by a single electrode ELDR (shown by the dark rod in the center, L = 5 cm, D = 1 mm) at = 4 kV Figure 6 4 Removal efficiency of the single electrode ELDR ( L = 5 cm and D = 1 mm) over a 5 cm 5 cm surface area as a function of applied voltage and particle number concentration
113 Figure 6 5 Removal efficiency of the single electr ode ELDR as a function of applied voltage for two electrode lengths Figure 6 6 Plan view of different arrangements of electrodes over the 30 cm x 30 cm exposed surface investigated in this study (black circles indicate elect rode cross section, small arrows display the directions of the electric field vector of each electrode
114 on the x y plane, and large arrows indicate the direction of the resultant e field streamlines) Figure 6 7 Sample 3 D elec tric potential distribution for the 9 electrode ELDR at V = 2.2 kV Figure 6 8 Electric field streamlines of the x shaped nine electrode ensemble ELDR
115 CHAPTER 7 CONCLUSIONS Control of lunar dust is one of the primary requirements for the future lunar explorations as a variety of problems associated with lunar dust have been documented from the Apollo missions. Considering limiting conditions of lunar environment, electrostatic lunar dust c ollector was proposed as an effective way of hindering dust deposition on the exposed surfac es. In the Eulerian based analytical model, sensitivity analyses showed that the ELDC was more effective for larger particles when it was closer to horizontal orientation due to the assistance of the gravitational force. The collection efficiency was very sensitive to surface potential, as it could change both incipient velocity and the charge of particles. For the horizontal ELDC, smaller surface potentials made greater collection efficiencies and the device needed about 10 times less voltage for the same efficiency as compared to the vertical ELDC. In contrast, for vertical ELDC there was a maximum in the efficiency graph which occurred when surface potential was between 30 and 120 V. The most critical case happened when large size particles were dealt wit h at the lowest surface potential (close to zero on some parts of the lunar dayside surface) and when ELDC plates were perpendicular to the lunar surface. Considering an average of 100 V for surface potential, 1 kV voltage for the selected ELDC dimensions ( E = 20 kV/m) was the Van der Waals force between particles settled on the surface, this value was about 4000 times less than the required electrostatic field for r epelling already settled particles (Wood, 1991)
116 In the Lagrangian based DEM model, the electrical particle particle interaction in the uniform electrostatic field was investigated, and the results demonstrated that achieving 100% collectio n efficiency for 20 m sized lunar particles required a 29% higher electrostatic field ( = 143 V for ELDC dimensions of L = W = 10 cm and D = 5 cm) than without electrical particle particle interaction. This was due to repelling effects of charged partic les that caused some particles to move relatively further away from the collection plates. Then, the effect of non uniformity of the electrostatic field on particle collection was studied by defining 100 subsections on the ELDC plates carrying different am ounts of surface charges. The results concluded that non uniformity of the electrostatic field also decreased the collection efficiency since subsections closer to the edges possessed more charges than those closer to the center ( = 173 V) for the same particle size. However, all the simulations were conducted for the most conservative case scenario and providing less than 3.5 kV/m electric field was more than enough for collecting this size of lunar particles. Maintaining the el ectric field at this upper limit is not difficult and does not cause electrical breakdown due to the hard vacuum condition. The results of the DEM modeling on a half size ELDC with a non uniform e field indicated higher collection efficiencies compared to the Eulerian based model. This observation was true for the entire range of applied voltages, as the 3 D Lagrangian based model considered the ELDC width and included all point charges on the ELDC plates in Coulomb force calculations. This conclude s the c onservative nature of Lagrangian based modeling at 100% collection efficiency compared to the Eulerian based model is not generally assured. In other words, d epending on the ELDC
117 dimensions and particle concentrations, DEM modeling with less simplifying as sumptions may indicate higher collection efficiency. The higher the concentration of incoming lunar dust, the higher the collection efficiency of the ELDC at lower provided e field. This means time consuming DEM simulations can be avoided by predicting a m ore conservative value using the Eulerian based model for lower range of voltages. In the Lagrangian based DEM model developed for studying the influence of back electrostatic field, the obtained results from tracking particle trajectories confirmed the fo rmation of eddies in proximity of the collection plate. The extracted plots from sensitivity analyses demonstrated that there were three stages in the operation of an ELDC. Initially, the clean ELDC was highly efficient in particle collection. The back e f ield then enhanced gradually as more particles got collected; thus, a fraction of supposedly collected particles penetrated the ELDC due to repulsion from the collection plate. Eventually, the generated back e field prevented all incoming particles from co llection and penetration by making them suspending inside the device. Such a suspension is undesirable in that it blocks the surface to be protected and it avoids any new incoming particles from collection. Increasing the applied voltage from 50 V to 100 V enabled the ELDC to run with 100% collection efficiency at particle loadings less than 220 #/cm 2 whereas the ELDC operated under a lower voltage experienced an immediate reduction in collection efficiency. Increasing the number concentration of incoming particles decreased the rate of reduction in collection efficiency as it counteracted the effect of back e field. T he ELDC collection efficiency was related to the elapsed time of ELDC operation. While presenting a general explicit model for such a relati onship is not feasible,
118 difference between an ELDC starting fresh and one with pre collected dust was found. After collecting 400 #/cm 2 compared to 90% of an ELDC with 400 #/cm 2 pre collected particl es. The suspended fraction was responsible for the difference. Using reported values from Surveyor 3 operation during Apollo 12, a rough estimation on how often the ELDC plate must be cleaned concluded 3 times per month as the required frequency of the pla te cleaning. E xperimental results from the tribocharg ing experiments on ~ 20 lunar dust simulants showed that tribochargeability of both simulants strongly depends on the air pressure as the total amount of created charge on the sample at low vacuum con dition of 0.3 Pa was 2 to 3 times higher than the case at the ambient pressure. The accumulated surface charge at the standard pressure increased with time initially but decreased later on due to the contacts of identical particles with the same work funct ion and the interactions with existing air molecules. At low vacuum, total charge increased with time though charging rate was decreasing due to the lower gradient of the attracted electrons. Tribochargeability of the JSC 1A particles was clearly better th an the Chenobi particles. The maximum surface charge on the JSC 1A particles after 20 min of tribocharging was about 2.5 nC/g, equivalent to the surface potential of s = 0.035 V, which is 10 4 times smaller than the assumed particle charge in our previous modeling studies; short time terrestrial tribocharing in low vacuum is less efficient than the long time lunar surface exposure to the solar based radiations in the hard vacuum. Next, experiments focused on the JSC 1A at low vacuum condition. Collection ef ficiency of a customized ELDC ( L = W = 10 cm, D = 5 cm) was examined for the
119 applied electric potentials of = 33, 65, 98 and 130 V. The charge based and mass based results of the ELDC collection efficiency confirmed the predicted linear relationship between the ELDC collection efficiency and the applied voltage. The observed pattern of particle collection ove r the collection plate was consistent with the numerical model in that the majority of the collected particles were located close to the plate corners (especially in the upper third). Although the resultant range of collection efficiencies (0.25 to 0.7% fo r the mass based definition and 0.35 to 1.05% for the charge based definition) were relatively low, the obtained ranges were justified with the previously developed predictive models. Studying the plate material indicated that application of aluminum plate s with 24 times higher conductivity compared to stainless steel plate, improves ELDC collection efficiency especially at the higher applied voltages. In investigation of appropriateness of the ELDR, the effect of space charge was found to be helpful in par ticle exclusion. Application of 4 kV to a 5 cm electrode was adequate to achieve 100% removal efficiency of falling particles with the most conservative properties over a 5 cm 5 cm surface. Doubling the electrode length resulted in 63% reduction in the t hreshold applied voltage (1.5 kV to protect the same are a ) An increase in the number concentration of the incoming particles was found to be a beneficial factor. The second stage of this part of study was to evaluate the use of the ELDR to protect a large r area, 30 cm 30 cm. Sensitivity analysis results on the electrode arrangement of the electrode ensemble ELDR demonstrated that any electrode arrangement forming closed shapes over the panel creates a dead zone that allows
120 particles to deposit on the pr otected surface. The x shaped pattern was found to be the most effective arrangement as its dead zones are only two perpendicular lines and its lateral distance to shift particles away is the shortest. Approximating the electric potentials in the vicinity of a single electrode at a certain applied voltage was the criterion to predict the appropriate applied voltage for a nine electrode ensemble ELDR of the adopted x shaped arrangement. Thereby, the minimum electric potentials of 324 V and 115 V were produce d within the control volume for electrode lengths of 5 cm and 10 cm, respectively, at applied voltages of 2.2 kV and 1.4 kV. Operating the x shaped electrode ensemble ELDR at the above mentioned applied voltage and electrode length led to removal efficien cies of 92% and 100%, respectively. This provided us with 100% protection of a 36 times larger area. Thanks to the lower required voltage on the electrodes, electric power consumption was only nine times more than the single electrode ELDR. In summary, b ot h ELDC and ELDR technologie s introduced in this study offer advantages over previously studied technologies by preventing the dust deposition at the first place using low electric power. These control technologies serve as an initial step for surface prote ction of equipment on asteroids and Mars as well. The obtained results of this study pave the road for development of electrostatic shields to protect solar panels and PV cells in arid terrestrial areas to secure consistent power generation from deposition of the windblown dust.
121 APPENDIX A MATLAB SOURCE CODE FOR CALCULATING THE CHARGE DISTRIBUTION ON THE ELDC PLATES S AT DIFFERENT APPLIED VOLTAGES PRESENTED IN CHAPTERS 3 AND 4 % This program uses the Method of Moment (MOM) % To determine charge distribut ion over the ELDC plates and % To estimate the total charge and capacitance of the ELDC % The parallel plate ELDC consists of two conducting plates % with certain dimensions of AA and BB separated by % distance of D, and maintained at applied voltages of % +50 VOLT AND 50 VOLT, for instance in here % One plate is located on the z=0 plane while the other % is located on the z=D plane % All dimensions are in SI units % N is the number of subsections into which each plate is divided % To specify the paramet ers ER = 1.0; EO = 8.8541e 12; AA = 0.010; BB = 0.010; D = 0.005; N = 400; NT = 2*N; M = sqrt(N); DX = AA/M; DY = BB/M; DL = DX; % To calculate the elements of the coefficient of Matrix A % To define coordinates and mid points of each segments K = 0; for K l=1:2 for K2=1:M for K3=1:M K = K + 1.0; X(K) = DX*(K2 0.5); Y(K) = DY*(K3 0.5); end end end for K1=1:N Z(K1) = 0.0; Z(K1+N) = D; end for I=1:NT for J=1:NT if (I==J) A(I,J) = DL*0.8814/(pi*EO); else R = sqrt( (X(I) X(J))^2 + (Y(I) Y(J) )^2 + ( Z(I) Z(J) )^2 ) ; A(I,J) = DL^2/(4.*pi*EO*R); end end end % Now determine the matrix of constant vector B
122 for K=1:N B(K) = 50.0; B(K+N) = 50.0; end % To invert A and calculate RHO, and to calculate the total charge, Q, and Capacitance, C F = inv( A) ; RHO = F*B' SUM = 0.0; for I=1:N SUM = SUM + RHO(I); end Q = SUM*(DL^2); VO = 100.0; C = abs(Q)/VO; [C]
123 APPENDIX B VBA SOURCE CODE FOR EVALUATING PARTICLE TRAJECTORIES AND CALCULATING THE FRACTION OF REPELLED PARTICLES AT DIFFERENT APPLIED VOLTAGES PRESENTED IN CHA PTERS 3 AND 4 Option Explicit Public particles As Single Public departicles As Single Sub masterformat() Call variables Windows("Book2.xlsm").Activate Call looknice Windows("Book3.xlsx").Activate Call looknice Windows("Book1.xlsm" ).Activate Call looknice Windows("Book3.xlsx").Activate Call moderate Windows("Book2.xlsm").Activate Call moderate Windows("Book1.xlsm").Activate Call moderate Windows("Book3.xlsx").Activate Call formattrans1 Windows ("Book2.xlsm").Activate Call formattrans1 Windows("Book1.xlsm").Activate Call formattrans1 Call Transinsert Call Transcopypasta Call Transhighlights Call Transdatasort Call Maxmin Call transfinalcoords Call transcoll ection Call transefficiency Call finalformat End Sub Sub Transinsert() Dim i As Single For i = 0 To particles Rows(7 + 3 i).Select Selection.Insert Shift:=xlDown, CopyOrigin:=xlFormatFromLeftOrAbove Selection.Insert Shift:=xlDown, CopyOrigin:=xlFormatFromLeftOrAbove Next i End Sub Sub Transcopypasta() 'pastes y and z values Dim i As Single
124 For i = 0 To particles Windows("Book2.xlsm").Activate Rows(6 + i).Select Selection.Copy Windows("Book1.xlsm").Activate Cells(7 + 3 i, 1).Select ActiveSheet.Paste Windows("Book3.xlsx").Activate Rows(6 + i).Select Selection.Copy Windows("Book1.xlsm").Activate Cells(8 + 3 i, 1).Select ActiveSheet.Paste Next i End Sub Sub formattrans1() Cells(1, 173).FormulaR1C1 = "max" Cells(1, 174).FormulaR1C1 = "min" Cells(1, 175).FormulaR1C1 = "final coords" Cells(1, 177).FormulaR1C1 = "status" Cells(1, 179).FormulaR 1C1 = "fraction suspended" Cells(1, 181).FormulaR1C1 = "fraction collected" Cells(1, 183).FormulaR1C1 = "fraction penetrated" Cells(1, 185).FormulaR1C1 = "# collec" Cells(1, 186).FormulaR1C1 = "total #" Cells(1, 187).FormulaR1C1 = "# su sp" Cells(1, 188).FormulaR1C1 = "i" End Sub Sub looknice() 'creates a user input line of code in the master macro for # particles and # deposited particles Dim i As Single Dim j As Single Range(Cells(1, 1), Cells(particles, 200)).Select Selec tion.Cut Destination:=Range(Cells(4, 1), Cells(particles + 3, 200)) Range("A1").Value = "# particles" Range("A2").Value = particles i = 0 For i = 0 To 100 Range(Cells(4, 2 + 2 i), Cells(particles + 3, 2 + 2 i)).Select 'loops rows 7 and 8 for # of time steps to organize and separate time numbers from particle coordinates Selection.Cut Destination:=Range(Cells(6, 1 + 2 i), Cells(particles + 5, 1 + 2 i)) Next i Range(Cells(4, 1), Cells (particles + 5, 200)).Select Selection.Cut Destination:=Range(Cells(4, 2), Cells(particles + 5, 201)) Range("A4").Select ActiveCell.FormulaR1C1 = "TIME" Range("B1").Select ActiveCell.FormulaR1C1 = "# DEPOSITED" Range("B2").Value = d eparticles
125 Rows("5:5").Select Selection.ClearContents Range("A5").Select ActiveCell.FormulaR1C1 = "PARTICLES" j = 0 For j = 0 To particles Cells(6 + j, 1).Value = j + 1 Next j End Sub Sub variables() particles = 0 dep articles = 0 On Error Resume Next Application.DisplayAlerts = False particles = InputBox(Prompt:="Please enter the total number of particles.", Title:="# PARTICLES") On Error GoTo 0 departicles = InputBox(Prompt:="Pl ease enter the total number of deposited particles.", Title:="# DEPOSITED") On Error GoTo 0 Application.DisplayAlerts = True End Sub Sub Transhighlights() Dim i As Single For i = 0 To particles Rows(6 + 3 i).Select With Selectio n.Font .ThemeColor = xlThemeColorAccent1 .TintAndShade = 0.249977111117893 End With Rows(7 + 3 i).Select With Selection.Font .ThemeColor = xlThemeColorAccent6 .TintAndShade = 0.249977111117893 End With Rows(8 + 3 i).Select With Selection.Font .ThemeColor = xlThemeColorAccent3 .TintAndShade = 0.249977111117893 End With Next i End Sub Sub Transdatasort() 'triggered when particle exits domain Dim i As Single Dim j As Single Dim k As Single Dim column As Single Dim x As Double Dim y As Double
126 Dim z As Double For i = 0 To particles For j = 0 To 85 x = Cells(6 + 3 i, 2 + 2 j).Value y = Cells(7 + 3 i, 2 + 2 j).Value z = Cells(8 + 3 i, 2 + 2 j).Value k = 0 Do While x < 4.5 Or x > 9.5 Or z < 10.5 Or z > 1 Or y > 9.5 Or y < 9.5 Cells(6 + 3 i, 2 + 2 j + 2 k).Select Selection.ClearContents Cells(7 + 3 i, 2 + 2 j + 2 k).Select Selection.ClearContents Cells(8 + 3 i, 2 + 2 j + 2 k).Select Selection.ClearContents k = k + 1 column = 2 + 2 j + 2 k If column > 200 Then Exit Do End If Loo p Next j Next i End Sub Sub Maxmin() Dim i As Single For i = 0 To 3 particles Cells(6 + i, 173).Value = "=MAX(RC[ 171]:RC[ 7])" Cells(6 + i, 174).Value = "=MIN(RC[ 171]:RC[ 7])" Next i End Sub Sub transfina lcoords() Dim i As Single Dim j As Single Dim a As Double Dim b As Double For j = 0 To 3 particles For i = 0 To 85 a = Cells(6 + j, 2 + 2 i).Value b = Cells(6 + j, 4 + 2 i).Value If b = 0 And a <> 0 Then 'combined, these two conditions prevent the final coordinate from being 0 Cells(6 + j, 175).Value = a i = 0 Exit For End If Next i Next j End Sub Sub transcollection() Dim i As Single
127 Dim xmax As Double Dim ymax As Double Dim zmax As Double Dim xmin As Double Dim ymin As Double Dim zmin As Double Dim xf As Double Dim yf As Double Dim zf As Double For i = 0 To particles xmin = Cells(6 + 3 i, 174).Value ymin = Cells(7 + 3 i, 174).Value zmin = Cells(8 + 3 i, 174).Value xmax = Cells(6 + 3 i, 173).Value ymax = Cells(7 + 3 i, 173).Value zmax = Cells(8 + 3 i, 173).Valu e xf = Cells(6 + 3 i, 175).Value yf = Cells(7 + 3 i, 175).Value zf = Cells(8 + 3 i, 175).Value If xmax > 4.85 And xmax < 5.15 And zmin > 10 Then 'by using xmax instead of xf, we take bouncing into accou nt and register particles that bounce off the collection plate as collected Cells(6 + 3 i, 177).Value = "collected" ElseIf xmax > 5.15 And xf > 4.85 And xf < 5.15 Then Cells(6 + 3 i, 177).Value = "collected" ElseIf xmax > 4.85 And xf <= xmax Then 'if particle is bounced out from the colelcting plate Cells(6 + 3 i, 177).Value = "collected" ElseIf zmin < 10 Then 'if particle es capes through the z direction, it will be labeled as "not collected" Cells(6 + 3 i, 177).Value = "penetrated" ElseIf xmax < 4.85 Or xmax > 5.15 Then 'suspension: particle has not had enough time to be collected or n ot collected, likely due to the intensity of particle particle interactions Cells(6 + 3 i, 177).Value = "suspended" Else : Cells(6 + 3 i, 177).Select 'gives any other unconsidered scenario a red background fill With Selection.Interior .Pattern = xlSolid .PatternColorIndex = xlAutomatic .Color = 255 .TintAndShade = 0 .PatternTintAndShade = 0 End With End If If xf = 0 Then 'eliminates the bug where non existent particles are registered as "not collected" Cells(6 + 3 i, 177).Select Selection.ClearContents End If If i < departicles Then 'eliminates the bug where initially deposited particles are being labeled as "collected" Cells(6 + 3 i, 177).Value = "deposited" End If
128 Next i End Sub Sub transeffi ciency() Dim i As Single Dim j As Single Dim k As Single Dim l As Single Dim m As Single j = 0 k = 0 l = 0 m = 0 For i = 0 To particles If Cells(6 + 3 i, 177).Value = "collected" Then j = j + 1 k = k + 1 ElseIf Ce lls(6 + 3 i, 177).Value = "penetrated" Then k = k + 1 ElseIf Cells(6 + 3 i, 177).Value = "suspended" Then l = l + 1 k = k + 1 Else : End If Next i Cells(3, 181).Value = j / k 'collection fraction Cells(3, 179).Value = l / k 'suspension fraction Cells(3, 183).Value = (k l j) / k 'penetration fraction Cells(3, 185).Value = j Cells(3, 186).Value = k Cells(3, 187).Value = l Cel ls(3, 188).Value = i End Sub Sub finalformat() Dim i As single particles = Workbooks("Book1.xlsm").Sheets("Sheet1").Cells(2, 169).Value For i = 0 To particles Rows(9 + 4 i).Select Selection.Insert Shift:=xlDown, CopyOrigin:=x lFormatFromLeftOrAbove Next i End Sub Sub moderate() Dim i As Integer Dim timestep As Double For i = 1 To 100 timestep = Cells(4, 2 i).Value 1000000 If timestep Mod 20 > 0 Then Columns(2 i).Select Selection.De lete Shift:=xlToLeft Selection.Delete Shift:=xlToLeft End If Next i End Sub
129 APPENDIX C MATLAB SOURCE CODE FOR CALCULATING THE CHARGE DISTRIBUTION ON NEEDLE SHAPED ELECTRODES OF THE ELDR AT DIFFERENT APPLIED VOLTAGES PRESENTED IN CHAPTE R 6 % This program obtains charge distribution on a thin rod shaped electrode % The electrode is thin and conductive with known radius and length % The electrode is connected to the power supply and it possess constant V % The charge distribution is not u niform, requiring numerical model % Moment method is used to perform such a computations clear all clc % Part 1) input data er = 1.0; % relative permitivitty of the space e0 = 8.8541e 12; % Permitivitty of the vacuum (F/m) L = 4.5; % electrode's length (cm) d = 1.0; % electrode's diameter (mm) V0 = 4000; % provided electrical potential on the electrode (V) n = 18; % # of segments (discretized elements) on the electrode % Part 2) forming matrix A elements r = (d / 2) 0.001; % radius of the electrode (m) delta_x = (L / n) 0.01; % length of each segments (m) I = 1 : n; % number of each segment x = delta_x (I 0.5); % distance between center of each segment and origin (m) for i = 1 : n for j = 1 : n if i ~= j A(i,j) = delta_x / abs(x(i) x(j)); else A(i,j) = log((delta_x/2+((delta_x/2)^2+r^2)^0.5)/(( 1)*delta_x/2+((delta_x/2)^2+r^2)^0.5)); %A(i,j) = 2.0 log(delta_x/r); end end end % Part 3) obtaining the line charge density (RHO) using: RHO = INV( A) *B B = 4 pi e0 V0 ones(n,1); RHO_l = inv( A) *B; % linear charge density (C/m) RHO_s = RHO_l / (2.0 pi r); % surface charge density (C/m2) Q = 0; for i = 1 : n Q = (Q + RHO_l(i) delta_x); RHO_EDEM(i) = RHO_l(i) delta_x; % Charge per geometry for EDEM simulations (C) RHO_EDEM(i); end % Part 4) displaying results as a plot delta_x / r Q*10^12 % total charge (pC)
130 for i = 1 : n RHO_ l(i)/(Q/(n delta_x)) end %plot(x 100,(RHO_l)/(Q/(n delta_x))) %grid on %xlabel('Distance from the origin of the electrode (cm)') %ylabel('Normalized charge distribution')
131 APPENDIX D VBA SOURCE CODE FOR EVALUATING PARTICLE TRAJECTORIES AND CALC ULATING THE FRACTION OF REPELLED PARTICLES AT DIFFERENT APPLIED VOLTAGES PRESENTED IN CHAPTER 6 Option Explicit Public particles As Single Public times As Single Sub Master() Call input_box Windows("Book1.xlsm").Activate Call looknice Windows("Book2.xlsm").Activate Call looknice Windows("Book3.xlsx").Activate Call looknice Windows("Book1.xlsm").Activate Call headlines Call insert_rows Call YZ_copypaste Call xyz_highlighter Call domain_exit_c hecker Call zero_deleter Call max_min Call problem_terminator_x Call problem_terminator_y Call final_coordinations Call removal_determination Call removal_efficiency End Sub Sub input_box() particles = 0 times = 0 On Error Resume Next Application.DisplayAlerts = False particles = inputbox(Prompt:="Please enter the total number of particles.", Title:="# PARTICLES") On Error GoTo 0 times = inputbox(Prompt:="Please enter the number of recorded times.", Title:="# TIMES") On Error GoTo 0 Application.DisplayAlerts = True End Sub Sub looknice() 'to create a user input line of code in the master macro for the # of incoming particles Dim i As Integer Dim j As Integer Range (Cells(1, 1), Cells(particles, 2 times)).Select Selection.Cut Destination:=Range(Cells(4, 1), Cells(particles + 3, 2 times)) Range("A1").Value = "# particles" Range("A2").Value = particles
132 i = 0 For i = 0 To times 'to m ake a loop on lines 7 and 8 for # of time steps to organize and separate time numbers from particle coordinates Range(Cells(4, 2 + 2 i), Cells(particles + 3, 2 + 2 i)).Select Selection.Cut Destination:=Range(Cells(6, 1 + 2 i), Cells(p articles + 5, 1 + 2 i)) Next i Range(Cells(4, 1), Cells(particles + 5, 2 times)).Select Selection.Cut Destination:=Range(Cells(4, 2), Cells(particles + 5, 2 times + 1)) Range("A4").Select ActiveCell.FormulaR1C1 = "TIME" R ange("B1").Select Rows("5:5").Select Selection.ClearContents Range("A5").Select ActiveCell.FormulaR1C1 = "PARTICLES" j = 0 For j = 0 To particles 1 Cells(6 + j, 1).Value = j + 1 Next j End Sub Sub headlines() 'th is program helps tabulating the final results Cells(1, 2 times + 4).FormulaR1C1 = "Min" Cells(1, 2 times + 5).FormulaR1C1 = "Max" Cells(1, 2 times + 6).FormulaR1C1 = "Initial Pos" Cells(1, 2 times + 7).FormulaR1C1 = "Final pos" Cells(1, 2 times + 9).FormulaR1C1 = "Status" Cells(1, 2 times + 11).FormulaR1C1 = "Removed #" Cells(1, 2 times + 12).FormulaR1C1 = "Total #" Cells(1, 2 times + 13).FormulaR1C1 = "Removed(%)" Cells(1, 2 times + 14).FormulaR1C1 = "P enetrated(%)" End Sub Sub insert_rows() Dim i As Integer For i = 0 To particles Rows(7 + 3 i).Select Selection.Insert Shift:=xlDown, CopyOrigin:=xlFormatFromLeftOrAbove Selection.Insert Shift:=xlDown, CopyOrigin:=xlFormatFromL eftOrAbove Next i End Sub Sub YZ_copypaste() 'to copy and paste y and z values respectively from Book 2 and Book 3 Dim i As Integer For i = 0 To particles Windows("Book2.xlsm").Activate Rows(6 + i).Select Selection.Copy Windows("Book1.xlsm").Activate Cells(7 + 3 i, 1).Select ActiveSheet.Paste
133 Windows("Book3.xlsx").Activate Rows(6 + i).Select Selection.Copy Windows("Book1.xlsm").Activate Cells(8 + 3 i, 1).Sele ct ActiveSheet.Paste Next i End Sub Sub xyz_highlighter() Dim i As Integer For i = 0 To particles Rows(6 + 3 i).Select With Selection.Font .ThemeColor = xlThemeColorAccent1 .TintAndShade = 0.249977111117893 End Wi th Rows(7 + 3 i).Select With Selection.Font .ThemeColor = xlThemeColorAccent6 .TintAndShade = 0.249977111117893 End With Rows(8 + 3 i).Select With Selection.Font .ThemeColor = xlThemeColorAccent3 .Ti ntAndShade = 0.249977111117893 End With Next i End Sub Sub domain_exit_checker() 'This part of codes prevent reproduction of particles after exitting from the domain Dim i As Integer Dim j As Integer Dim k As Integer Dim column As Inte ger Dim x As Double Dim y As Double Dim z As Double For i = 0 To particles For j = 0 To times x = Cells(6 + 3 i, 2 + 2 j).Value y = Cells(7 + 3 i, 2 + 2 j).Value z = C ells(8 + 3 i, 2 + 2 j).Value k = 0 Do While x < 30 Or x > 30 Or y < 30 Or y > 30 Cells(6 + 3 i, 2 + 2 j + 2 k).Select Selection.ClearContents Cells(7 + 3 i, 2 + 2 j + 2 k).Select Selection.ClearContents Cells(8 + 3 i, 2 + 2 j + 2 k).Select Selection.ClearContents k = k + 1 column = 2 + 2 j + 2 k If column > 2 times Then Exit Do End If
134 Loop Next j Next i End Sub Sub zero_deleter() Dim i As In teger Dim j As Integer For i = 1 To 3 particles + 5 For j = 1 To 2 times + 1 If Cells(i, j).Value = 0 Then Cells(i, j).Select Selection.ClearContents End If Next j Next i End Sub Sub max _min() Dim i As Integer For i = 0 To 3 particles 1 Cells(6 + i, 2 times + 4).Value = Application.Min(Range(Cells(6 + i, 2), Cells(6 + i, 2 times))) Cells(6 + i, 2 times + 5).Value = Application.Max(Range(Cells(6 + i, 2 ), Cells(6 + i, 2 times))) Next i End Sub Sub problem_terminator_x() Dim i As Integer Dim j As Integer Dim k As Integer For i = 0 To particles 1 If (Cells(6 + 3 i, 2 times + 5).Value Cells(6 + 3 i, 2 times + 4).Value < 0) And Cells(6 + 3 i, 2).Value < 0 Then Cells(6 + 3 i, 2 times + 9).Value = "Removed" For j = 2 To 2 times If Cells(6 + 3 i, j).Value > 0 Then Cells(6 + 3 i, j).ClearContents Cells(7 + 3 i, j).C learContents Cells(8 + 3 i, j).ClearContents Cells(6 + 3 i, 2 times + 4).Value = Application.Min(Range(Cells(6 + 3 i, 2), Cells(6 + 3 i, 2 times))) Cells(7 + 3 i, 2 times + 4).Value = Applicat ion.Min(Range(Cells(7 + 3 i, 2), Cells(7 + 3 i, 2 times))) Cells(8 + 3 i, 2 times + 4).Value = Application.Min(Range(Cells(8 + 3 i, 2), Cells(8 + 3 i, 2 times))) Cells(6 + 3 i, 2 times + 5).Value = Applic ation.Max(Range(Cells(6 + 3 i, 2), Cells(6 + 3 i, 2 times))) Cells(7 + 3 i, 2 times + 5).Value = Application.Max(Range(Cells(7 + 3 i, 2), Cells(7 + 3 i, 2 times))) Cells(8 + 3 i, 2 times + 5).Value = Appl ication.Max(Range(Cells(8 + 3 i, 2), Cells(8 + 3 i, 2 times))) End If Next j ElseIf (Cells(6 + 3 i, 2 times + 5).Value Cells(6 + 3 i, 2 times + 4).Value < 0) And Cells(6 + 3 i, 2).Value > 0 Then For k = 2 To 2 times If Cells(6 + 3 i, k).Value < 0 Then
135 Cells(6 + 3 i, k).ClearContents Cells(7 + 3 i, k).ClearContents Cells(8 + 3 i, k).ClearContents Cells(6 + 3 i, 2 tim es + 4).Value = Application.Min(Range(Cells(6 + 3 i, 2), Cells(6 + 3 i, 2 times))) Cells(7 + 3 i, 2 times + 4).Value = Application.Min(Range(Cells(7 + 3 i, 2), Cells(7 + 3 i, 2 times))) Cells(8 + 3 i, 2 t imes + 4).Value = Application.Min(Range(Cells(8 + 3 i, 2), Cells(8 + 3 i, 2 times))) Cells(6 + 3 i, 2 times + 5).Value = Application.Max(Range(Cells(6 + 3 i, 2), Cells(6 + 3 i, 2 times))) Cells(7 + 3 i, 2 times + 5).Value = Application.Max(Range(Cells(7 + 3 i, 2), Cells(7 + 3 i, 2 times))) Cells(8 + 3 i, 2 times + 5).Value = Application.Max(Range(Cells(8 + 3 i, 2), Cells(8 + 3 i, 2 times))) End If Next k End If Next i End Sub Sub problem_terminator_y() Dim i As Integer Dim j As Integer Dim k As Integer For i = 0 To particles 1 If (Cells(7 + 3 i, 2 times + 5).Value Cells(7 + 3 i, 2 times + 4).Value < 0) And Cells(7 + 3 i, 2).Value < 0 Then Cells(6 + 3 i, 2 times + 9).Value = "Removed" For j = 2 To 2 times If Cells(7 + 3 i, j).Value > 0 Then Cells(6 + 3 i, j).ClearContents Cells(7 + 3 i, j).ClearContents Cells(8 + 3 i, j).ClearContents Cells(6 + 3 i, 2 times + 4).Value = Application.Min(Range(Cells(6 + 3 i, 2), Cells(6 + 3 i, 2 times))) Cells(7 + 3 i, 2 times + 4).Value = Application.Min(Range(Cells( 7 + 3 i, 2), Cells(7 + 3 i, 2 times))) Cells(8 + 3 i, 2 times + 4).Value = Application.Min(Range(Cells(8 + 3 i, 2), Cells(8 + 3 i, 2 times))) Cells(6 + 3 i, 2 times + 5).Value = Application.Max(Range(Cell s(6 + 3 i, 2), Cells(6 + 3 i, 2 times))) Cells(7 + 3 i, 2 times + 5).Value = Application.Max(Range(Cells(7 + 3 i, 2), Cells(7 + 3 i, 2 times))) Cells(8 + 3 i, 2 times + 5).Value = Application.Max(Range(Ce lls(8 + 3 i, 2), Cells(8 + 3 i, 2 times))) End If Next j ElseIf (Cells(7 + 3 i, 2 times + 5).Value Cells(7 + 3 i, 2 times + 4).Value < 0) And Cells(7 + 3 i, 2).Value > 0 Then For k = 2 To 2 times If Cells(7 + 3 i, k).Value < 0 Then Cells(6 + 3 i, k).ClearContents Cells(7 + 3 i, k).ClearContents Cells(8 + 3 i, k).ClearContents Cells(6 + 3 i, 2 times + 4).Value = Appl ication.Min(Range(Cells(6 + 3 i, 2), Cells(6 + 3 i, 2 times)))
136 Cells(7 + 3 i, 2 times + 4).Value = Application.Min(Range(Cells(7 + 3 i, 2), Cells(7 + 3 i, 2 times))) Cells(8 + 3 i, 2 times + 4).Value = Ap plication.Min(Range(Cells(8 + 3 i, 2), Cells(8 + 3 i, 2 times))) Cells(6 + 3 i, 2 times + 5).Value = Application.Max(Range(Cells(6 + 3 i, 2), Cells(6 + 3 i, 2 times))) Cells(7 + 3 i, 2 times + 5).Value = Application.Max(Range(Cells(7 + 3 i, 2), Cells(7 + 3 i, 2 times))) Cells(8 + 3 i, 2 times + 5).Value = Application.Max(Range(Cells(8 + 3 i, 2), Cells(8 + 3 i, 2 times))) End If Next k End If Next i End Sub Sub final_coordinations() Dim i As Integer Dim j As Integer Dim a As Double Dim b As Double For i = 0 To 3 particles For j = 0 To times a = Cells(6 + i, 2 + 2 j).Value b = Cells(6 + i, 4 + 2 j).Value If b = 0 And a <> 0 Then 'combined, these two conditions prevent the final coordinate from being 0 Cells(6 + i, 2 times + 7).Value = a j = 0 Exit Fo r End If Next j Cells(6 + i, 2 times + 6).Value = Cells(6 + i, 2).Value Next i End Sub Sub removal_determination() Dim i As Integer Dim xmax As Double Dim ymax As Double Dim zmax As Double Dim xmin As Doubl e Dim ymin As Double Dim zmin As Double Dim xi As Double Dim yi As Double Dim zi As Double Dim xf As Double Dim yf As Double Dim zf As Double For i = 0 To particles 1 xmin = Cells(6 + 3 i, 2 times + 4).Value ymin = Cells(7 + 3 i 2 times + 4).Value zmin = Cells(8 + 3 i, 2 times + 4).Value xmax = Cells(6 + 3 i, 2 times + 5).Value ymax = Cells(7 + 3 i, 2 times + 5).Value zmax = Cells(8 + 3 i, 2 times + 5).Value xi = Cells(6 + 3 i, 2 times + 6).Value
137 yi = Cells(7 + 3 i, 2 times + 6).Value zi = Cells(8 + 3 i, 2 times + 6).Value xf = Cells(6 + 3 i, 2 times + 7).Value yf = Cells(7 + 3 i, 2 times + 7).Value zf = Cells(8 + 3 i, 2 times + 7).Value If xf < 24.5 And zf > 44.5 Then Cells(6 + 3 i, 2 times + 9).Value = "Removed" ElseIf zf > 0 Then Cells(6 + 3 i, 2 times + 9).Value = "Removed" ElseIf xf > 24 .5 And zf > 44.5 Then Cells(6 + 3 i, 2 times + 9).Value = "Removed" ElseIf yf < 24.5 And zf > 44.5 Then Cells(6 + 3 i, 2 times + 9).Value = "Removed" ElseIf yf > 24.5 And zf > 44.5 Then Cells(6 + 3 i, 2 times + 9).Value = "Removed" ElseIf xf xi < 0 And zf > 44.5 And (yf < 24.5 Or yf > 24.5) Then Cells(6 + 3 i, 2 times + 9).Value = "Removed" ElseIf yf yi < 0 And zf > 44.5 And (xf < 24.5 Or xf > 24.5) Then Cells(6 + 3 i, 2 times + 9).Value = "Removed" ElseIf ( 22.5 < xf And xf < 22.5) And ( 22.5 < yf And yf < 22.5) Then Cells(6 + 3 i, 2 times + 9).Value = "Penetrated" ElseIf zf < 44 .5 Then Cells(6 + 3 i, 2 times + 9).Value = "Penetrated" 'gives any other unconsidered scenario a red background fill Else : Cells(6 + 3 i, 2 times + 9).Select With Selection.Interior .Pattern = xlSolid .PatternColorIndex = xlAutomatic .Color = 255 .TintAndShade = 0 .PatternTintAndShade = 0 End With End If Next i End Sub Sub removal_effici ency() Dim i As Integer Dim j As Integer Dim k As Integer Dim l As Integer j = 0 k = 0 l = 0 For i = 0 To particles 1 If Cells(6 + 3 i, 2 times + 9).Value = "Removed" Then j = j + 1 k = k + 1 ElseIf Cells(6 + 3 i, 2 times + 9).Value = "Penetrated" Then l = l + 1 k = k + 1
138 Else : End If Next i Cells(3, 2 times + 11).Value = j '# of removed Cells(3, 2 times + 12).Value = k 'total # Cells(3, 2 times + 13).Value = (j / k) 100 'removed fraction Cells(3, 2 times + 14).Value = (l / k) 100 'penetrated fraction End Sub
139 LIST OF REFERENCES Abbas, M., Tankosic, D., Craven, P., Spann, J., LeClair, A., & West, E. (2007). Lunar dust charging by photoelectric emissions. Planetary and Space Science, 55 953 965. Atten, P., Pang, H.L., & Reboud, J. L. (2009). Study of dust removal by standing wave electric curtain for application to solar ce lls on mars. Industry Applications, IEEE Transactions on, 45 75 86. Battler, M.M., & Spray, J.G. (2009). The Shawmere anorthosite and OB 1 as lunar highland regolith simulants. Planetary and Space Science, 57 2128 2131. Bueno Barrachina, J. M., Caas Pe uelas, C. S., Catalan Izquierdo, S., & Cavall Ses, F. (2009). Capacitance evaluation on perpendicular plate capacitors by means of finite element analysis. In Proceedings of International Conference on Renewable Energies and Power Quality (ICREPQ09) (Edit ed Editor), Book Capacitance evaluation on perpendicular plate capacitors by means of finite element analysis City. Calle, C., Buhler, C., Johansen, M., Hogue, M., & Snyder, S. (2011). Active dust control and mitigation technology for lunar and Martian ex ploration. Acta Astronautica, 69 1082 1088. Calle, C., Buhler, C., Mantovani, J., Clements, S., Chen, A., Mazumder, M., Biris, A., & Nowicki, A. (2004). Electrodynamic dust shield for solar panels on Mars. NASA Tech. Rpt. 20040062533 Calle, C., McFall, J ., Buhler, C., Snyder, S., Arens, E., Chen, A., Ritz, M., Clements, J., Fortier, C., & Trigwell, S. (2008). Dust particle removal by electrostatic and dielectrophoretic forces with applications to NASA exploration missions. In Proceedings of the electrosta tics society of America Annual meeting, Minneapolis (Edited Editor), Book Dust particle removal by electrostatic and dielectrophoretic forces with applications to NASA exploration missions (pp. 17 19), City. Captain, J., Trigwell, S., Arens, E., Biris, A., Captain, J., Quinn, J., & Calle, C. (2007). Tribocharging lunar simulant in vacuum for electrostatic beneficiation. In AIP Conference Proceedings (Edited Editor), Book Tribocharging lunar simulant in vacuum for electrostatic beneficiation (Vol. 880, pp. 951 ), City. Castle, G. (1997). Contact charging between insulators. Journal of Electrostatics, 40 13 20. Clark, P., Curtis, S., Minetto, F., Marshall, J., Nuth, J., & Calle, C. (2010). SPARCLE: Electrostatic Dust Control Tool Proof of Concept. In AIP Confere nce Proceedings (Edited Editor), Book SPARCLE: Electrostatic Dust Control Tool Proof of Concept (Vol. 1208, pp. 549), City.
140 Colwell, J.E., Robertson, S.R., Hornyi, M., Wang, X., Poppe, A., & Wheeler, P. (2009). Lunar dust levitation. Journal of Aerospace E ngineering, 22 2 9. Cooper, C.D., & Alley, F.C. (2011). Air Pollution Control: A Design Approach Waveland Press, Incorporated. Criswell, D.R. (1973). Horizon glow and the motion of lunar dust. In Photon and Particle Interactions with Surfaces in Space Ph oton and Particle Interactions with Surfaces in Space (pp. 545 556). Springer, City. Di Renzo, A., & Di Maio, F.P. (2004). Comparison of contact force models for the simulation of collisions in DEM based granular flow codes. Chemical Engineering Science, 5 9 525 541. Dove, A., Devaud, G., Wang, X., Crowder, M., Lawitzke, A., & Haley, C. (2011). Mitigation of lunar dust adhesion by surface modification. Planetary and Space Science, 59 1784 1790. Duke, M.B., Ignatiev, A., Freundlich, A., Rosenberg, S.D., & M akel, D. (2001). Silicon PV cell production on the Moon as the basis for a new architecture for space exploration. In AIP Conference Proceedings (Edited Editor), Book Silicon PV cell production on the Moon as the basis for a new architecture for space explo ration (Vol. 552, pp. 19), City. Fernndez, D., Cabs, R., & Moreno, L. (2007). Dust Wiper Mechanism for Operation in Mars. In Proc. 12th European Space Mechanisms & Tribology Symposium (ESMATS), Liverpool, UK (Edited Editor), Book Dust Wiper Mechanism for Operation in Mars City. Freeman, J., & Ibrahim, M. (1975). Lunar electric fields, surface potential and associated plasma sheaths. Earth, Moon, and Planets, 14 103 114. Gaier, J.R., & Creel, R.A. (2005). The Effects of Lunar Dust on Advanced EVA Systems: Lessons from Apollo. Presentation Jan Gaier, J.R., Journey, K., Christopher, S., & Davis, S. (2011). Evaluation of Brushing as a Lunar Dust Mitigation Strategy for Thermal Control Surfaces National Aeronautics and Space Administration, Glenn Research Ce nter. Gaier, J.R., Waters, D.L., Misconin, R.M., Banks, B.A., & Crowder, M. (2011). Evaluation of Surface Modification as a Lunar Dust Mitigation Strategy for Thermal Control Surfaces National Aeronautics and Space Administration, Glenn Research Center. G oertz, C. (1989). Dusty plasmas in the solar system. Reviews of Geophysics, 27 271 292.
141 Halekas, J., Delory, G., Lin, R., Stubbs, T., & Farrell, W. (2008). Lunar Prospector observations of the electrostatic potential of the lunar surface and its response to incident currents. Journal of Geophysical Research, 113 A09102. Halekas, J., Mitchell, D., Lin, R., Hood, L., Acua, M., & Binder, A. (2002). Evidence for negative charging of the lunar surface in shadow. Geophysical research letters, 29 77 71 77 74. He, G., Zhou, C., & Li, Z. (2011). Review of Self Cleaning Method for Solar Cell Array. Procedia Engineering, 16 640 645. Heiken, G.H., Vaniman, D.T., & French, B.M. (1991). The Lunar sourcebook: A user's guide to the Moon CUP Archive. Hinds, W.C. (2012) Aerosol technology: properties, behavior, and measurement of airborne particles John Wiley & Sons. Hogue, M.D., Calle, C.I., Weitzman, P.S., & Curry, D.R. (2008). Calculating the trajectories of triboelectrically charged particles using Discrete Element Modeling (DEM). Journal of Electrostatics, 66 32 38. Hornyi, M. (1996). Charged dust dynamics in the solar system. Annual Review of Astronomy and Astrophysics, 34 383 418. Liu, G., & Marshall, J. (2010). Particle transport by standing waves on an elect ric curtain. Journal of Electrostatics, 68 289 298. Loftus, D., Rask, J., McCrossin, C., & Tranfield, E. (2010). The chemical reactivity of lunar dust: from toxicity to astrobiology. Earth, Moon, and Planets, 107 95 105. Manka, R.H. (1973). Plasma and po tential at the lunar surface. In Photon and particle interactions with surfaces in space Photon and particle interactions with surfaces in space (pp. 347 361). Springer, City. Masuda, S., & Matsumoto, Y. (1973). Theoretical characteristics of standing wave electric curtains. Electrical Engineering in Japan, 93 71 77. McKay, D.S., Carter, J.L., Boles, W.W., Allen, C.C., & Allton, J.H. (1994). JSC 1: A new lunar soil simulant. Engineering, Construction, and Operations in Space IV, 2 857 866. Miller, J. Hoferer, B., & Schwab, A. (1998). The impact of corona electrode configuration on electrostatic precipitator performance. Journal of Electrostatics, 44 67 75. Murphy Jr, T., Adelberger, E., Battat, J., Hoyle, C., McMillan, R., Michelsen, E., Samad, R., Stubbs, C., & Swanson, H. (2010). Long term degradation of optical devices on the Moon. Icarus, 208 31 35.
142 Nishiyama, H., & Nakamura, M. (1994). Form and capacitance of parallel plate capacitors. Components, Packaging, and Manufacturing Technology, Part A IEEE Transactions on, 17 477 484. Qian, D., Marshall, J., & Frolik, J. (2012). Control analysis for solar panel dust mitigation using an electric curtain. Renewable Energy, 41 134 144. Ram, E., Wilkinson, A., Elliot, A., & Young, C. (2010). Flowabilit y of lunar soil simulant JSC 1a. Granular Matter, 12 173 183. Reitan, D.K. (1959). Accurate Determination of the Capacitance of Rectangular Parallel Plate Capacitors. Journal of Applied Physics, 30 172 176. Reitan, D.K., & Higgins, T.J. (1951). Calculation of the electrical capacitance of a cube. Journal of applied physics, 22 223 226. Renno, N.O., & Kok, J.F. (2008). Electrical activity and dust li fting on Earth, Mars, and beyond. In Planetary Atmospheric Electricity Planetary Atmospheric Electricity (pp. 419 434). Springer, City. Rickman, D., Immer, C., Metzger, P., Dixon, E., Pendleton, M., & Edmunson, J. (2012). Particle shape in simulants of the lunar regolith. Journal of Sedimentary Research, 82 823 832. Sadiku, M.N. (2001). Elements of electromagnetics (Vol. 428). Oxford university press UK. Schnelle Jr, K.B., & Brown, C.A. (2001). Air pollution control technology handbook CRC press. Sharma, R., Clark, D.W., Srirama, P.K., & Mazumder, M.K. (2008). Tribocharging characteristics of the Mars dust simulant (JSC Mars 1). Industry Applications, IEEE Transactions on, 44 32 39. Sickafoose, A., Colwell, J., Hornyi, M., & Robertson, S. (2001). Experim ental investigations on photoelectric and triboelectric charging of dust. Journal of Geophysical Research: Space Physics (1978 2012), 106 8343 8356. Sims, R., Biris, A., Wilson, J., Yurteri, C., Mazumder, M., Calle, C., & Buhler, C. (2003). Development of a transparent self cleaning dust shield for solar panels. In Proceedings ESA IEEE joint meeting on electrostatics (Edited Editor), Book Development of a transparent self cleaning dust shield for solar panels (pp. 814 821), City. Solutions, D. (2010). EDEM 2.3 User Guide. DEM Solutions Ltd., Edinburgh, UK
143 Sternovsky, Z., Chamberlin, P., Horanyi, M., Robertson, S., & Wang, X. (2008). Variability of the lunar photoelectron sheath and dust mobility due to solar activity. Journal of Geophysical Research: Space Physics (1978 2012), 113 Sternovsky, Z., Robertson, S., Sickafoose, A., Colwell, J., & Hornyi, M. (2002). Contact charging of lunar and Martian dust simulants. Journal of Geophysical Research: Planets (1991 2012), 107 15 11 15 18. Stubbs, T.J., Vondrak, R.R., & Farrell, W.M. (2006). A dynamic fountain model for lunar dust. Advances in Space Research, 37 59 66. Tatom, F., Srepel, V., & Johnson, R. (1967). Lunar dust degradation effects and removal prevention concepts [R]. 280 Northrop: NASA George C Mars hall Space Flight Center. In (Edited Editor), Book Lunar dust degradation effects and removal prevention concepts [R]. 280 Northrop: NASA George C Marshall Space Flight Center TR 792 7 207A, City. Taylor, L.A., Schmitt, H.H., Carrier, W.D., & Nakagawa, M. (2005). The lunar dust problem: from liability to asset. AIAA, 1st Space Exploration Mission Trigwell, S., Captain, J.G., Arens, E.E., Quinn, J.W., & Calle, C.I. (2009). The use of tribocharging in the electrostatic beneficiation of lunar simulant. Indus try Applications, IEEE Transactions on, 45 1060 1067. Ulaby, F.T., Michielssen, E., & Ravaioli, U. (2001). Fundamentals of Applied Electromagnetics: XE AU Prentice Hall. Walch, B., Hornyi, M., & Robertson, S. (1995). Charging of dust grains in plasma wi th energetic electrons. Physical review letters, 75 838. Walton, O.R. (2007). Adhesion of lunar dust. National Aeronautics and Space Administration, NASA/CR 214685 Walton, O.R., & Johnson, S.M. (2010). DEM Simulations of the Effects of Particle Shape, In terparticle Cohesion, and Gravity on Rotating Drum Flows of Lunar Regolith. In Earth and Space 2010@ sEngineering, Science, Construction, and Operations in Challenging Environments (Edited Editor), Book DEM Simulations of the Effects of Particle Shape, Inte rparticle Cohesion, and Gravity on Rotating Drum Flows of Lunar Regolith (pp. 36 41). ASCE, City. Wang, J., He, X., & Cao, Y. (2008). Modeling electrostatic levitation of dust particles on lunar surface. Plasma Science, IEEE Transactions on, 36 2459 2466. Willman, B.M., Boles, W.W., McKay, D.S., & Allen, C.C. (1995). Properties of lunar soil simulant JSC 1. Journal of Aerospace Engineering, 8 77 87. Wood, K. (1991). Design of Equipment for Lunar Dust Removal. NASA Contractor Report, 190014
144 Yang, R., Yu, A., McElroy, L., & Bao, J. (2008). Numerical simulation of particle dynamics in different flow regimes in a rotating drum. Powder Technology, 188 170 177. Zelmat, M.E. M., Rizouga, M., Tilmatine, A., Medles, K., Miloudi, M., & Dascalescu, L. (2013). Exper imental Comparative Study of Different Tribocharging Devices for Triboelectric Separation of Insulating Particles. Industry Applications, IEEE Transactions on, 49 1113 1118. Zukeran, A., Looy, P.C., Chakrabarti, A., Berezin, A.A., Jayaram, S., Cross, J.D. Ito, T., & Chang, J. S. (1999). Collection efficiency of ultrafine particles by an electrostatic precipitator under DC and pulse operating modes. Industry Applications, IEEE Transactions on, 35 1184 1191.
145 BIOGRAPHICAL SKETCH Nima Afshar Mohajer was bor n in the last days of 1983 in Tehran, Iran. Nima received his B.S. and M.S. in Feb ruary 2006 and Jan uary 2009 respectively, from the most prestigious engineering university in Iran: Sharif University of Technology. In January 2010, he was admitted to the P hD program in the Department of Environmental Engineering Sciences at the University of Florida, and joined Aerosol and Particulate Research La boratory to work under Dr. Chang study, Nima focused on electrostatic collection of particles and air pollutant dispersion modeling, prepared 5 manuscripts for peer reviewed journals, mentored one undergraduate student a nd contributed as a teaching assistant of the course Air Pollution Control Devices, ENV 4121/6126, in Fall 2013. His hobbies and interests include running, playing badminton and traveling. Nima graduated with his PhD in May 2014.