Simulation of microscale particle interactions for optimization of an electrodynamic dust shield to clean desert dust from solar panels

Solar Energy 155 (2017) 1197–1207

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Simulation of microscale particle interactions for optimization of an electrodynamic dust shield to clean desert dust from solar panels Jennifer K.W. Chesnutt a,⇑, Husain Ashkanani b,1, Bing Guo c, Chang-Yu Wu a a

Department of Environmental Engineering Sciences, Engineering School of Sustainable Infrastructure and Environment, University of Florida, Gainesville, FL, USA Department of Chemical Engineering, University of Florida, Gainesville, FL, USA c Mechanical Engineering Program, Texas A&M University at Qatar, Doha, Qatar b

a r t i c l e

i n f o

Article history: Received 17 October 2016 Received in revised form 4 July 2017 Accepted 21 July 2017

Keywords: Dust mitigation Particulate flow Discrete element method Photovoltaic

a b s t r a c t A largely neglected aspect necessary to prevent energy losses of photovoltaic (PV) panels is efficient and cost-effective mitigation of dust soiling. A potential solution is an electrodynamic dust shield (EDS) to lift and transport dust off the PV panel via electrodynamic waves generated by electrodes on the panel surface. Accordingly, the objective of this research was to determine the effects of EDS parameters on the optimal cleaning efficiency of PV panels soiled by desert dust. A discrete element method was used to computationally simulate the transport, collision, and adhesion of charged particles, representative of dust in Doha, Qatar, subject to two-phase waves on an inclined EDS. Results showed that under given conditions, the optimal distance between electrodes (pitch) was 14 mm, which resulted from a balance between increasing pitch that aided dust transport and concomitant decreasing electric field strength that hindered transport. Optimal voltage was 2.8 kVp-p, while particles remained adhered to the surface at small voltages (0.7 kVp-p) but were repelled and attracted by the same electrode at high voltages (11.8 kVp-p). Dust transport distance per 10 cycles generally decreased as cycle frequency increased from 0.5 to 10 Hz; however, transport distance per time was largest with an intermediate frequency of 1 Hz. Our study revealed various ways in which individual dust particles were repelled and attracted by electrodes under different conditions that produced different transport patterns, which can be used to improve the efficiency of dust mitigation for PV panels. Ó 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction Over fifty percent of investments in the power industry worldwide are in clean energy systems, and the renewable energy industry continues to grow globally (National Renewable Energy Laboratory, 2013). From 2000 to 2010, the power produced globally by photovoltaic (PV) solar energy grew at rates between 40% and 90% annually (Tyagi et al., 2013). Although solar energy has benefited from substantial investment to assure feasibility and reliability of the technology, a largely neglected aspect is the efficient and cost-effective mitigation of dust soiling of PV panels (Sarver et al., 2013; Sayyah et al., 2014). Because solar power plants are often located in regions that receive plentiful sunlight, such as in arid and semi-arid zones, these plants also experience

⇑ Corresponding author at: University of Florida, Department of Environmental Engineering Sciences, P.O. Box 116450, Gainesville, FL 32611-6450, USA. E-mail address: [email protected] (J.K.W. Chesnutt). 1 Present address: Department of Chemical and Petroleum Engineering, University of Pittsburgh, Pittsburgh, PA, USA.

significant output power losses of up to 1% or more per day due to dust accumulation (Sayyah et al., 2014). Monthly soiling rates in dry and arid regions in California ranged from 1 to 12%, with soiling rates varying greatly across California (Caron and Littmann, 2013). Significant losses for PV panels, modules, cells, and systems due to dust were reported in a review by Sarver et al., for example, 66% reduction in efficiency after six months in Saudi Arabia and 17% reduction in efficiency after six days in Kuwait (Sarver et al., 2013). Currently employed dust mitigation strategies include highpressure fresh water jets, automated air jets, automated mechanical brushes, and surface coatings on panels. However, these strategies have disadvantages that include the scarcity of fresh water for solar plants in arid zones, damage to panels, degradation of surface coatings, disruption of light transmission, and the need for manual labor and mechanical maintenance. An electrodynamic dust shield (EDS) is a technology that has the potential to avoid problems of existing dust mitigation strategies through generation of electrodynamic waves that lift and transport dust away from the surface. Electrodynamic waves are generated by a series of parallel elec-

http://dx.doi.org/10.1016/j.solener.2017.07.064 0038-092X/Ó 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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trodes located on the surface of the PV panel, within a dielectric adhesive material and below a dielectric cover sheet (Fig. 1). The EDS can be powered by the PV panel and consumes a negligible amount of power produced by the panel (Kawamoto and Shibata, 2015; Mazumder et al., 2013; Sharma et al., 2009; Chesnutt et al., 2016). The amount of dust that an EDS can clean from a PV panel is affected by various factors, such as electrical operation of the EDS, electrode properties, dielectric material properties, dust properties, and environmental conditions. Through use of a small experimental EDS, Kawamoto and Shibata (2015) demonstrated effects of many of these factors on cleaning efficiency for different types of desert sand and found several conditions that produced cleaning efficiencies above 80% and up to 90%. As well, the EDS design was able to clean a large PV panel (Kawamoto and Shibata, 2015). In other studies, small experimental EDSs were utilized to examine many factors affecting cleaning efficiency for dust from the Beijing Daxing district in China and to identify conditions that produced cleaning efficiencies up to 99% (Wu et al., 2015, 2014). Mazumder et al. (2014) accounted for light blocked due to electrodes on an experimental flat solar mirror by measuring dust cleaning efficiency and loss in reflectivity and found the optimal width and spacing of electrodes, given a specific voltage and frequency of operation. In addition to experimental studies, modeling and computational studies have examined EDS electric fields and the transport and mitigation of dust by electrostatics under various conditions (Kawamoto and Shibata, 2015; Chesnutt et al., 2016; AfsharMohajer et al., 2014; Chesnutt and Marshall, 2013; Horenstein et al., 2013a, 2013b; Kawamoto et al., 2006, 2011; Liu et al., 2010; Liu and Marshall, 2010a, 2010b; Sun et al., 2012; Sayyah et al., 2015, 2016). Horenstein et al. (2013a, 2013b) numerically examined effects of several factors on the trajectory of a single particle subject to a traveling wave on a horizontal EDS. These studies found that particle trajectory depended on the initial particle location and that a particle with a smaller diameter traveled with the wave, while a particle with a larger diameter traveled with chaotic motion. Kawamoto et al. (2006) utilized computational simulations to determine effects of wave frequency on particle speed and modes of transport with a traveling wave on a horizontal EDS, finding that high frequencies prevented particles from traveling with the wave. Marshall and co-workers (Chesnutt and Marshall, 2013; Liu and Marshall, 2010a, 2010b) identified effects of collisions, electrostatic interactions, and adhesion on particle transport distance and modes of transport (e.g., hopping and rolling) by computational simulation of standing and traveling waves on horizontal and inclined EDS systems. EDS systems for mitigation and transport of particles have been investigated for specific types of particles and environments, such as lunar and Martian dust simulants in both vacuums and atmospheres (Sharma et al., 2009; Kawamoto et al., 2011; Kawamoto and Miwa, 2011; Mazumder et al., 2007), toner particles (e.g., iron oxide) on both horizontal and inclined surfaces (Chesnutt et al., 2016; Chesnutt and Marshall, 2013; Kawamoto et al., 2006; Liu and Marshall, 2010a, 2010b), outdoor natural dust in Beijing on horizontal surfaces (Wu et al., 2015, 2014), and different types of desert sand on inclined surfaces (Kawamoto and Shibata, 2015). Authors of the latter study (Kawamoto and Shibata, 2015) noted that cleaning efficiency varied with sand type and suggested that EDS systems must be designed and optimized for environmental conditions at the site of operation. Because solar power plants in arid regions experience significant power losses due to soiling (Sayyah et al., 2014) and because rates of soiling vary greatly across neighboring areas (Caron and Littmann, 2013), the focus of the current study was on EDS systems intended for the unique environment of Doha, Qatar. Though located in an arid region, Doha occasionally also experiences significant relative humidity,

Fig. 1. Cross-sectional schematic diagram of an array of two planar strip electrodes embedded within a dielectric material below the EDS top surface. D is electrode width, H is the distance from the EDS top surface to the electrode top surface, P is electrode pitch, and g is acceleration due to gravity. Electrodes have an infinite length in the z-direction and zero thickness.

which is correlated with soiling, as are airborne dust concentration and wind in Doha (Guo et al., 2015). Hence, the current study centered on important conditions at our specific location of interest, which were the properties and amount of dust particles accumulated on PV panels and PV panel inclination angle. The current study provided a basis for future studies that will incorporate additional environmental conditions of humidity and wind. As well, EDS design can benefit from discovery of the microscopic mechanisms of interactions of individual dust particles with each other and the electric field, which has been accomplished under specific conditions in some previous studies that examined individual particles by photographs of experiments or tracked particles through computational simulations (Chesnutt et al., 2016; Chesnutt and Marshall, 2013; Kawamoto et al., 2006, 2011; Liu and Marshall, 2010a, 2010b; Kawamoto and Miwa, 2011; Kawamoto, 2015). Kawamoto and Miwa (2011) examined particle motion in air and a vacuum through complementary computational simulations and experiments, and under conditions on the moon by computational simulations; however, the study did not report specifically on microscopic mechanisms of interactions of individual particles with each other and the electric field. Additionally, previous studies have not described the motion and interaction of individual particles under varying combinations of EDS design and operating parameters to optimize cleaning efficiency for inclined PV panels, to the best of our knowledge. Because tracking trajectories of individual dust particles is difficult experimentally, computational studies greatly strengthen our ability to examine particle behavior during EDS operation and achieve optimal EDS performance in a shorter timeframe. Accordingly, the objective of this research was to identify optimal EDS design and operating parameters by determining the effects of parameters on interactions of individual dust particles to improve cleaning efficiency of PV panels soiled by desert dust at a location of interest, Doha, Qatar. 2. Methods In this section, the first subsection presents computational models for simulation conditions in general, while the second subsection describes specific simulation conditions for a representative case. Because the computational models have been previously published, only brief details of the models are presented, and the reader is referred to previous works for full details (Liu et al., 2010; Liu and Marshall, 2010a; Marshall, 2009). 2.1. Computational models The electric field generated by the EDS was computed at the beginning of each simulation before the start of calculations of the dynamics of individual dust particles. During particle dynamics

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calculations, the pre-computed electric field was linearly interpolated onto centroids of particles to calculate electrostatic forces on particles. Details of the computational model to calculate the electric field and the computational model to calculate particle dynamics are as follows. 2.1.1. Computational model of electric field The computational geometry is illustrated in Fig. 1. The electric field was generated by a periodic array of parallel, planar strip electrodes that each had a width of D, a distance (i.e. pitch) of P between symmetry axes of neighboring electrodes, an infinite length in the z-direction, and zero thickness. Justification and implications of the assumption of infinite length are explained at the end of this subsection. Electrodes were embedded within a dielectric adhesive below a dielectric cover sheet (collectively called the dielectric material) at a distance H below the EDS top surface. The computational domain contained two electrodes, which were energized by a square wave with opposite voltages of ±½V. A boundary element method (Liu et al., 2010; Liu and Marshall, 2010a) was used to calculate the electric field for each half cycle of the square wave. Three periods in the x-direction on each side of the computational domain, each period being identical to the computational domain, were included during calculation of the electric field. Both electrodes were discretized by 200 evenly distributed line elements and the EDS surface was discretized by 1600 evenly distributed line elements. The electric field was computed on a uniform mesh that covered the computational domain with 9k/D and 66k/D mesh points in the x- and y-directions, respectively. Here, k = 2P is wavelength. Due to the assumption of infinite length of electrodes in the z-direction, the zcomponent of the electric field was zero, and the x- and ycomponents of the electric field were invariable in the z-direction.

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that were one to two orders of magnitude larger than the concentration in this current work, and for the same reasons, particle electrostatic images about the EDS surface were neglected. As well, the force between a given particle on the EDS surface and its own image charge can be shown to be an order of magnitude smaller than the force of gravity, such that image force can be neglected. Capillary force was neglected due to sufficiently low relative humidity in summer months of 36 ± 10% for our region of interest, Doha, Qatar (Javed et al., 2017). For particles on an EDS, Sayyah et al. (2016) developed an estimate of the threshold at which capillary force becomes important to be 40% relative humidity, while in other works this threshold was considered to be 50% (Mazumder et al., 2016) or 60% (Mazumder et al., 2013). The computational domain encompassed the EDS surface and the region above two electrodes, and had a length of k in the xdirection, height of 2k in the y-direction, and width of 0.027k in the z-direction. Particles were initially placed in a monolayer on the EDS surface in a lattice formation with approximately equal spacing in the x- and z-directions and then were given small random perturbations in location on the surface. Particle motion was assumed periodic in the x- and z-directions. For computational efficiency, the number of particles required for simulation was reduced by utilizing these periodic boundary conditions, which necessitated the assumption of infinite length of electrodes in the z-direction. Hence, rather than simulating an entire solar panel, which would be computationally infeasible, the necessary assumptions corresponded to a region near the center of the solar panel where edge effects had minimal significance. Also, inclusion of particle motion in the z-direction, rather than only the x- and ydirections, allowed for simulation of effects of particle-particle collisions on trajectories in all three coordinate directions. 2.2. Computational simulation conditions

2.1.2. Computational model of particle dynamics A discrete element method similar to Marshall and co-workers (Liu et al., 2010; Marshall, 2009) was utilized to model forces and torques on individual spherical dust particles due to van der Waals adhesion, particle-particle collisions, particle-surface collisions, electrodynamics, the fluid (air), and gravity. The motion of each particle was evolved in time using the second-order AdamsBashforth method to solve the linear and angular momentum equations, given by

m

dv ¼ FF þ FA þ FE þ mg; dt

I

dX ¼ MF þ MA dt

ð1Þ

where m is particle mass, I is particle moment of inertia, v is particle velocity, X is particle angular velocity, and g is gravitational acceleration. The fluid above the surface was stationary, and due to the differences in linear and angular velocities between particles and the fluid, particles experienced a fluid drag force with a modification for particle crowding, FF , and viscous torque, MF . The combined adhesion and collision force is FA , which included a normal collision force due to a combination of elastic repulsion, van der Waals adhesion, and viscous dissipation and included resistance to sliding with modifications to account for van der Waals adhesion. The combined adhesion and collision torque is MA , which included resistance to rolling of one particle over another particle or over the EDS surface and resistance to twisting of particles over each other or the surface with modifications to account for van der Waals adhesion. The Coulomb force induced by the electric field, E, is FE ¼ Q E, where Q is particle charge. Torque induced by the electric field (ME ¼ p  E) was zero because particles were assumed to lack a permanent dipole (p). For computational efficiency, particle-particle electrostatic interactions were neglected due to the low concentration of particles, as was assumed in a previous computational work (Kawamoto and Miwa, 2011) that utilized particle concentrations

To determine the effects of EDS design parameters, a baseline case (Table 1) was set up with design and operating parameters adopted from a previous work (Kawamoto and Shibata, 2015). All simulations utilized these parameters unless explicitly stated otherwise. Electrodes were located a distance H = 0.1 mm below the EDS top surface and each electrode had a width of D = 0.3 mm and a pitch of P = 7 mm (Fig. 1). The previous work (Kawamoto and Shibata, 2015) selected this same small electrode size and large electrode pitch to minimize the amount of light blocked by nontransparent electrodes that are less expensive than transparent electrodes such as indium tin oxide electrodes. The dielectric material of the baseline case was assumed to be polyethylene terephthalate (PET) and was compared with rayon and glass. Relative permittivities were 1.3, 3.3, and 10 for rayon (Kawamoto, 2008), PET (Beaty and Donald, 2013), and glass (Young et al., 2012), respectively. These dielectric materials were chosen because they have been used in experimental EDSs to remove or transport dust particles (Kawamoto and Shibata, 2015; Kawamoto et al., 2006; Kawamoto, 2008; Sayyah et al., 2017) and because they provided a wide range of relative permittivities for examination to ensure differences in results would be observed if present. For these reasons, the high end of the range of permittivities of glass, 10, was chosen. Density and viscosity of the air above the EDS were 1.225 kg m–3 and 1.79  105 kg m1 s1, respectively. Rather than simulating cylindrical copper electrodes embedded under a glass cover sheet as in the previous work (Kawamoto and Shibata, 2015), we simulated strip electrodes to correspond to electrodes that can be screen-printed, such as silver ink, onto PET for ease of portability and application to PV panels. Electrodes were energized by a square wave with peak-to-peak amplitude (V) of 5.6 kVp-p, a phase shift of 180° or p, and frequency (f) of 1 Hz, as in Kawamoto and Shibata (2015). That is, one elec-

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Table 1 Parameter values of baseline case. Parameter

Value or condition

Unit

Electrode width, D Electrode shape Electrode pitch, P Electrode depth (cover sheet thickness), H Relative permittivity of dielectric material Dielectric material composition Wavelength, k = 2P Wave or cycle frequency, f Peak-to-peak voltage, V Inclination angle of surface Particle diameter Particle density Charge per particle surface area Adhesion energy per particle surface area Particle mass loading Number of particles Fluid density Fluid viscosity Computational domain X  Y  Z

0.3 Planar strip 7 0.1 3.3 PET 14 1 5.6 22 20 2710 1.8  106 3.7  106 0.215 100 1.225 1.79  105 14  28  0.378

mm – mm mm – – mm Hz kVpp deg lm kg m3 C m2 J m2 g m2 – kg m3 kg m1 s1 mm3

trode was energized at +2.8 kV while the other electrode was energized at 2.8 kV. The inclination angle of the EDS was 22°, which is typically employed for PV panels at the location of interest, Doha, Qatar (Guo et al., 2015). Dust particle diameter was 20 mm. This diameter was chosen because it is the mode of particle size distribution for dust accumulated on PV panels at our location of interest (Javed et al., 2017). This diameter is also typical of the diameter with the highest deposition rate on solar tracking mirrors in another desert region, the Negev desert (Biryukov, 1996). Particles were assumed to be composed of calcite, the main component of dust that soils PV panels in Doha, Qatar (Javed et al., 2017), with a density of 2710 kg m–3. The charge per particle surface area was assumed to be constant with time with a value of 1.8  106 C m2, which is on the order of magnitude of the surface density charge acquired by dust particles subject to contact with a dielectric surface in an electrostatic field (Kawamoto et al., 2006, 2011). Charging of particles with time, such as by tribocharging and field-assisted charging, was assumed negligible due to the short timeframe of simulations, as assumed in previous computational works (Liu and Marshall, 2010b; Kawamoto, 2008). Also, this assumption was in accord with a previous work in which time variation of particle charge was neglected in a computational model that produced results that were qualitatively similar to results of experiments (Kawamoto, 2008). Another justification for neglecting particle charging with time is supported by inspecting results of an experimental study showing that tribocharging of dust on an EDS subject to a traveling wave with f = 1000 Hz increased the charge by at most 100% after 10 s (Kawamoto et al., 2006). Considering that the frequency in our current study was 1000 times smaller and that we used the same timeframe of 10 s, particles likely would collide with the EDS about 1000 times less, which would reduce the effect of tribocharging such that an increase in charge of at most only 0.1% would be expected. Particles were subject to van der Waals force with an adhesion energy per particle surface area of 3.7  106 J m2. The total mass of particles divided by the surface area of the EDS (mass loading) was 0.215 g m2, which is the average mass loading of dust on a PV panel during one day in summer months measured at our location of interest and is on the same order of magnitude of the average value of 0.387 g m2 during one day in spring months measured on solar concentrators in Riyadh, Saudi Arabia (El-Shobokshy et al., 1985). Because particle mass loading was the same for all simulation cases and because pitch affected EDS surface area simulated, the numbers of particles were 25, 100,

390, 900, and 1610 with pitches of 3.5, 7, 14, 21, and 28 mm, respectively. Simulations were performed for 10 wave periods or cycles (10 s for the baseline case). As a measure of cleaning efficiency, the average distance traveled by particles down the inclined surface in the negative xdirection, called transport distance (X), was calculated at the end of the simulation (10 cycles), given by

X¼

N 1X x0 ; N i¼1 i

ð2Þ

where N is number of particles, and x0i is the net distance that the ith particle traveled down the inclined surface in the negative x^ was defined as direction. Normalized transport distance (X) ^ ¼ X=nk, where n = 10 is the number of cycles, such that a value X of unity indicated particles traveled an average distance of one electrode pitch during each half cycle. One way a particle could yield a normalized transport distance of unity would be by hopping from one electrode directly to the adjacent electrode located down the inclined surface, during each half cycle. Another way a particle could yield a normalized transport distance of unity would be by hopping from one electrode, landing on the surface, and then rolling down the inclined surface to reach the adjacent electrode, during each half cycle. Another measure of cleaning efficiency, transport velocity (U), was defined as U ¼ Xf =n, which is transport distance per time simulated. Levitation height (Y) was defined as the ycomponent of a particle’s location averaged over time, then averaged over particles, given by

Y¼

nt N 1X 1X y ; N i¼1 nt j¼1 i;j

ð3Þ

where nt is the number of timesteps in the simulation, and yi;j is the y-component of the ith particle during the jth timestep. Proportion of levitated particles (L) was defined as the proportion of particles that were airborne at a given time averaged over time, given by

L¼

nt 1 1X Nlev ;j ; N nt j¼1

ð4Þ

where N lev ;j is the number of airborne particles during the jth timestep. Because each case simulated the same number of cycles, the amount of time simulated decreased as frequency increased. Hence, to determine the frequency that gave the best performance per 10 cycles, transport distance X was compared between simulation cases, and to determine the frequency that gave the best performance per time, transport velocity U was compared between simulation cases. To determine the effects of EDS design parameters, the baseline case was compared with cases in which a specific design parameter was varied to determine its effect. For parameters that yielded significant results, the case with the parameter value that yielded the highest transport distance was chosen as a superior design case. To determine the effects of EDS operating parameters and determine optimal EDS set-ups, superior design cases were compared with cases in which either voltage was varied between 0.7 and 11.8 kVp-p or frequency was varied between 0.5 and 10 Hz. Simulated particle trajectories over time were visualized using particle positions that were recorded at the end of each of 30 uniform time intervals per cycle. 3. Results and discussion 3.1. Modes of particle transport As observed through visualizations of particle trajectories over time for each simulation case, particles were transported by vari-

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ous modes that primarily depended on values of EDS design and operating parameters. The following modes of transport during a half cycle are the modes observed most frequently and do not constitute an exhaustive list. In Mode A, a particle hopped from electrode to electrode. Specifically, the particle was located on the surface above a positive electrode at the start of the half cycle, was repelled from the electrode, became airborne, and landed on the surface above an adjacent negative electrode by the end of the half cycle. This adjacent negative electrode was located either up or down the inclined surface with respect to the repelling electrode. In Mode B, a particle hopped from one electrode to the surface. Specifically, the particle was located on the surface above a positive electrode at the start of the half cycle, was repelled from the electrode, became airborne, and landed on the surface before reaching an adjacent electrode. After landing on the surface, the particle rolled toward the adjacent electrode, either reaching the electrode or not by the end of the half cycle. In Mode C, the particle was located on the surface above a positive electrode at the start of the half cycle, was repelled from the electrode, and remained airborne at the end of the half cycle. In Mode D, the particle was already airborne at the start of the half cycle and then landed on the surface above the electrode from which it was repelled in the previous half cycle. In Mode E, the particle was already airborne at the start of the half cycle, landed on the surface between the same electrode from which it was repelled in the previous half cycle and an adjacent electrode, and then possibly rolled toward an electrode, perhaps reaching the electrode. In Mode F, the particle was located on the surface far from an electrode at the start of the half cycle and it rolled toward the nearest negative electrode, either reaching the electrode or not by the end of the half cycle. In Mode G, a particle remained on the surface far from an electrode without moving during the half cycle. Table 2 lists each mode with a brief description. Although EDS design and operating parameters were the main determinants of the most frequent mode of transport observed under given simulation conditions, not all particles during all half cycles exhibited the most frequent mode because particle-particle collisions and particle-particle adhesions also affected particle trajectories. Hence, particle trajectories and modes of transport could not be predicted solely by EDS design and operating parameters, even for two particles that began at the same location in two different half cycles. 3.2. Particle dynamics of baseline case For the baseline case, visualizations of particle trajectories over time showed that most particles traveled by hopping from one electrode to the adjacent electrode located down the incline (Mode A). Particles possessed a positive charge such that at the start of the simulation most particles were attracted to and rested on the surface above the negative electrode. At each half cycle, most particles were repelled from the surface above the electrode that just switched to positive voltage, were attracted to an adjacent negative electrode, and came to rest on the surface above this electrode before the next half cycle. At each half cycle, about 65–95% of particles were attracted to the adjacent negative electrode down, rather than up, the incline due to gravity, while the remaining particles were attracted to the adjacent negative electrode up the incline. During each half cycle, a few particles (5% or less) did not complete their hop to an adjacent electrode and instead remained airborne before the next half cycle (Mode C). 3.3. Effects of EDS design 3.3.1. Electrode pitch Electrode pitch was varied for the baseline case. The maximum electric field strength and the region over which the electric field

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Table 2 Main modes of particle transport during a half cycle (non-exhaustive list). Mode

Brief description

A

Repelled from one electrode and landed on an adjacent electrode (hopped from electrode to electrode) Repelled from electrode, landed on surface, then rolled toward an adjacent electrode, possibly reaching the electrode (hopped from electrode to surface) Repelled from electrode and remained airborne Began airborne and landed on the electrode it was repelled from in previous half cycle Began airborne and landed between electrodes, possibly rolling and reaching an electrode Rolled on surface toward an electrode, possibly reaching the electrode Remained on surface without moving

B

C D E F G

strength magnitude was above a given value decreased with increasing pitch (Fig. 2). With pitches less than or equal to 14 mm, visualizations of particle trajectories over time showed that most particles (93%) hopped from one electrode to an adjacent electrode during each half cycle (Mode A), while a few particles (7%) returned to the same electrode from which they were repelled during each cycle (Mode C followed by Mode D). With P  14 mm, for particles that hopped (Mode A), most particles hopped to the adjacent electrode down the incline (73%), while some particles hopped to the adjacent electrode up the incline (20%). With the largest two pitches (21 and 28 mm), no particles hopped directly from electrode to electrode (Mode A) due to low electric field strength. Some particles hopped from an electrode to the surface (Mode B), while about 36% and 73% of particles did not hop during each half cycle for pitches of 21 and 28 mm, respectively. Particles that did not hop were located on the surface too far from an electrode to experience large enough Coulomb forces to repel them from the surface. With a pitch of 21 mm, during each half cycle, only about two thirds of particles (64%) reached either an adjacent electrode (through Modes B, E, and F) or the same electrode from which they were repelled previously (Mode D), while about 25% of particles remained airborne (Mode C), and about 11% of particles rolled on the surface (Mode F) without reaching an electrode. With a pitch of 28 mm, during each half cycle, a far less percentage of particles (27%) reached either an adjacent electrode (through Modes B, E, and F) or the same electrode from which they were repelled previously (Mode D), while about 15% of particles remained airborne (Mode C), and about 58% of particles either rolled on the surface (Mode F) without reaching an electrode or remained on the surface without moving (Mode G) during the half cycle. Pitch significantly affected transport distance X and levitation height Y, as determined by analysis of variance, which produced p-values less than 0.001. As pitch increased, transport ^ and levitation height distance X, normalized transport distance X, Y each increased to a peak then decreased (Fig. 3a-c). The peak in transport distance occurred due to opposing trends with increasing pitch, which were (1) an increase in distance traveled during each half cycle provided particles traveled to the electrode down the incline, and (2) a decrease in electric field strength. As pitch increased from 3.5 to 14 mm, the decreasing electric field strength (Fig. 2a) was still sufficiently large to increase transport distance (Fig. 3a) because enough particles were attracted over the increasing distance to the electrode down the incline at the change in electrode voltage at the cycle or half cycle. As pitch increased from 14 to 28 mm, the decreasing electric field strength (Fig. 2a) was not large enough to continue to increase transport distance (Fig. 3a), with many particles remaining on the surface or hopping without reaching the electrode down the incline. Because the pitch of 14 mm produced the maximum transport dis-

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Fig. 2. Measurements of electric field strength including (a) maximum electric field strength normalized by maximum electric field strength for the case with a pitch of 3.5 mm, versus pitch P, and (b-d) contours of electric field strength magnitude for different pitches P including (b) 3.5, (c) 7, and (d) 14 mm. Electrodes are located below the surface at x/P = ±0.5 in (b-d). Parameter values other than pitch are the same as the baseline case.

^ (c) levitation height Y, and (d) proportion of levitated particles L. Parameter Fig. 3. Effect of electrode pitch on (a) transport distance X, (b) normalized transport distance X, values other than pitch are the same as the baseline case. Error bars in (a)-(c) are standard deviations.

tance (Fig. 3a), this case was called the superior-pitch design case for which optimal voltage and frequency were determined. The optimal pitch was twice the pitch of the baseline case of 7 mm. As pitch increased from 3.5 to 21 mm, levitation height increased (Fig. 3c) because the strength of attraction of particles to an adjacent negative electrode decreased, which caused particles to be transported less in the direction tangent to the EDS and more in the direction normal to the EDS, spending more time airborne. For this same reason, proportion of levitated particles L increased as pitch increased from 3.5 to 21 mm (Fig. 3d). The decreased levitation height with pitch of 28 mm compared with 21 mm was due to a larger proportion of particles remaining on the surface due to lower repulsion forces from the positive electrode at a half cycle, which reduced levitation height overall.

3.3.2. Electrode width The electrode width of the baseline case (D = 0.3 mm) was compared with widths of 0.1 and 0.5 mm. Maximum electric field strength decreased with increasing width because voltage was a constant in all three cases (Fig. 4a). In contrast, the region over which the electric field strength magnitude was above a given value increased with increasing width (Fig. 4b-c) due to a larger width covering a larger area. Visualizations of particle trajectories over time showed that during each half cycle with all widths, most particles hopped to the electrode down the incline, while some particles hopped to the electrode up the incline (Mode A). With widths of 0.1 and 0.3 mm, a few particles did not complete their hops during each half cycle (Mode C), while with the largest width (0.5 mm), only for some half cycles did one or two particles not complete their hops. Width significantly affected transport dis-

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Fig. 4. Effects of electrode width. (a) Maximum electric field strength versus electrode width, (b-c) contours of electric field strength magnitude for different electrode widths ^ (right axis) versus electrode width and (e) levitation height Y versus including (b) 0.1 and (c) 0.5 mm, (d) transport distance X (left axis) and normalized transport distance X electrode width. Parameter values other than electrode width are the same as the baseline case. Electrodes are located below the surface at x/P = ±0.5 in (b) and (c). Error bars are standard deviations in (d) and (e).

tance X and levitation height Y, as determined by analysis of variance, which produced negligible p-values. As width increased, transport distance increased (Fig. 4d), levitation height increased and then plateaued (Fig. 4e), and proportion of levitated particles L remained nearly the same with each width, ranging between 0.28 and 0.30 (not shown). Hence, with the two largest widths, the larger electric field strength per area applied larger repulsion forces to particles at more locations on the surface that increased their levitation heights compared with the smallest width, despite the larger maximum electric field strength with the smallest width. The proportion of levitated particles remained nearly constant as width increased instead of increasing along with the increase in transport distance. This result occurred because, as width increased, the increase in electric field strength per area more strongly attracted particles to the negative electrode, which resulted in particles traveling a longer distance in the same amount of time. Because the width of 0.5 mm produced the maximum transport distance, this case was called the superior-width design case for which optimal voltage and frequency were determined. The optimal width was larger than the width of the baseline case of 0.3 mm.

3.3.3. Electrode shape The planar strip electrode shape of the baseline case was compared with a cylindrical shape that had the same diameter (D = 0.3 mm) as the width of the planar strip electrode and the same minimum distance from the EDS top surface (H = 0.1 mm). Transport distances X were 84 ± 23 mm and 87 ± 23 mm for planar strip and cylindrical shapes, respectively. Levitation height Y was 1.4 ± 0.2 mm for both shapes. Analysis of variance showed that shape produced no significant differences in transport distance or

levitation height, which was due to nearly identical electric fields with each shape. 3.3.4. Dielectric material The dielectric material of the baseline case, PET, was compared with rayon and glass, which affected the electric field through their relative permittivities (ranging from 1.3 to 10). Transport distances X were 86 ± 27 mm, 84 ± 23 mm, and 86 ± 24 mm for rayon, PET, and glass, respectively. Levitation height Y was 1.4 ± 0.2 mm for all materials. No significant differences in transport distance or levitation height due to material were found by analysis of variance. Visualizations of particle trajectories over time showed that particle transport was similar for each material, with particles generally traveling from one electrode to the adjacent electrode down the incline at each half cycle (Mode A). 3.4. Effects of EDS operating parameters 3.4.1. Voltage As voltage increased for the superior-pitch design case (P = 14 mm, D = 0.3 mm, f = 1 Hz), transport distance increased from close to zero to a peak and then decreased (Fig. 5a). A voltage of 2.8 kVp-p produced the largest transport distance X, followed closely by a voltage of 5.6 kVp-p. With V = 2.8 kVp-p, visualizations of particle trajectories over time showed that, in general, particles hopped from one electrode toward the adjacent negative electrode down the incline (Modes A and B). At the end of a hop, particles either reached the negative electrode or landed near the negative electrode and then rolled or slid down the surface toward the electrode due to gravity and electrostatic attraction. A few particles landed close enough to the negative electrode located up the

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^ (right axis), and (b) and (d) levitation height Y. Parameter values for Fig. 5. Effect of voltage on (a) and (c) transport distance X (left axis) and normalized transport distance X (a-b) are those of the superior-pitch design case and include P = 14 mm and D = 0.3 mm. Parameter values for (c-d) are those of the superior-width design case and include D = 0.5 mm and P = 7 mm. Frequency is f = 1 Hz. Error bars are standard deviations.

incline to move up the surface due to electrostatic attraction that overcame gravity. With V = 5.6 kVp-p, visualizations of particle trajectories over time showed that most particles (80%) hopped from one electrode directly to the adjacent negative electrode down the incline (Mode A). Compared with the higher voltages examined, low voltages (0.7, 1.4, and 1.75 kVp-p) yielded low transport distances X and low nor^ (less than 13 mm and 0.05, respecmalized transport distances X tively). For these low voltages, visualizations of particle trajectories over time indicated that the electric field was not strong enough to repel particles off the surface at every location nor strong enough to transport particles to the negative electrode after a half cycle for those particles that were repelled. As calculated by the computational model, a force greater than approximately 104 pN in the positive y-direction was required from the electric field to overcome forces due to van der Waals adhesion and gravity (see Eq. (1)) in order to lift a particle that was resting on the surface. Particles on the surface located farther than a critical distance away from each electrode did not move, provided other particles did not collide with them. As voltage increased from 0.7 to 1.75 kVp-p, this critical distance increased from about 2 to 6 mm, or about 0.1 to 0.4 pitches. On the other hand, the highest voltage tested, 11.8 kVp-p, generated an electric field that was too ^ Visualizations of strong to yield a maximum transport distance X. particle trajectories over time with the highest voltage showed that particles were repelled a higher distance from the positive electrode, as demonstrated by an increase in levitation height Y as voltage increased (Fig. 5b). As compared with voltages of 2.8 and 5.6 kVp-p that produced the highest transport distances, the highest voltage caused many more particles to remain above the surface without completing a hop before the next half cycle. Hence, fewer particles moved down the incline because they were attracted to the same electrode from which they were previously repelled (Mode C followed by Mode D). In addition, the highest voltage caused more particles to be attracted to the negative electrode up the incline. Though it is unknown whether, under the simulated EDS configuration, 11.8 kVp-p is below the breakdown strength of the dielectric material simulated (PET), this voltage served at the least as a theoretical value. This highest voltage was chosen to examine a wide range of voltages to ensure trends were captured, which was shown to be necessary to capture the sharp decrease in transport distance from intermediate voltages (2.8 and 5.6 kVp-p) to the highest voltage (11.8 kVp-p) (Fig. 5a). Similarly constructed experimental EDSs with glass cover sheets of the same thickness as the simulated EDS with PET cover sheet possessed threshold breakdown voltages per pitch of 1.20 and 0.98 kVp-p/mm with pitches of 7 and 10 mm, respectively (Kawamoto and Shibata, 2015). These values are higher than the highest voltage per pitch of the simulated EDS, which was

11.8 kVp-p/14 mm = 0.84 kVp-p/mm. Because simulation results showed that dielectric cover sheet material did not significantly affect transport distance X or levitation height Y, simulation results are still meaningful even if the breakdown strength with PET were lower than that with glass, as PET could instead be replaced by glass and produce similar results. The superior-width design case (P = 7 mm, D = 0.5 mm, f = 1 Hz) produced similar trends in transport distance X (Fig. 5c) and levitation height Y (Fig. 5d) as the superior-pitch design case. For the superior-width design case, a voltage of 1.4 kVp-p produced the largest transport distance, followed closely by a voltage of 2.8 kVp-p. With V = 1.4 kVp-p, visualizations of particle trajectories over time showed that, after a short time, all particles hopped from one electrode toward the adjacent negative electrode down the incline. With V = 2.8 kVp-p, visualizations of particle trajectories over time showed similar particle motions as with V = 1.4 kVp-p, except that about 5% of particles traveled toward the adjacent negative electrode up the incline or to the same electrode after a half cycle. The smallest voltage (0.7 kVp-p) was not strong enough to continually move particles, while the largest voltage (11.8 kVp-p) was too strong such that several particles were transported up the incline. The maximum of transport distance X was higher with the superior-pitch case (182 mm) than with the superior-width case (133 mm) due to the pitch with the superior-pitch case that was twice that of the superior-width case. However, the smaller pitch of the optimal superior-width case helped to more effectively transport particles to the adjacent electrode down the incline as ^ which was demonstrated by normalized transport distance X, 0.95, compared with 0.65 with the optimal superior-pitch case. Also due to smaller pitch, the optimal superior-width case required a lower voltage (1.4 kVp-p) than the optimal superior-pitch case (2.8 kVp-p). 3.4.2. Frequency Results regarding frequency followed similar trends with both the superior-pitch (P = 14 mm, D = 0.3 mm, V = 5.6 kVp-p) and superior-width (P = 7 mm, D = 0.5 mm, V = 5.6 kVp-p) design cases. Transport distance X generally decreased as frequency increased (Fig. 6a-b). With low frequencies (0.5 and 1 Hz for superior-pitch and 0.5 Hz for superior-width) that produced the largest transport distances, visualizations of particle trajectories over time showed that most particles hopped from one electrode directly to the adjacent negative electrode down the incline during each half cycle, while some particles hopped directly to the adjacent negative electrode up the incline (Mode A). With these low frequencies, all particles completed their hops to an adjacent electrode during almost all half cycles with the superior-width design case, while about 3– 11% of particles did not complete a hop before the next half cycle with the superior-pitch design case (Mode C), and some of these

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^ (right axis) and (c-d) transport velocity U. Parameter Fig. 6. Effect of frequency during 10 cycles on (a-b) transport distance X (left axis) and normalized transport distance X values for (a) and (c) are those of the superior-pitch design case and include P = 14 mm and D = 0.3 mm. Parameter values for (b) and (d) are those of the superior-width design case and include D = 0.5 mm and P = 7 mm. Voltage is V = 5.6 kVp-p. Error bars are standard deviations.

particles were attracted toward the negative electrode up the incline. As frequency increased, the number of particles that did not complete their hops before the next half cycle increased because of quicker half cycles compared with lower frequencies. With the highest frequencies (3, 5, and 10 Hz for superior-pitch and 5 and 10 Hz for superior-width) that produced the smallest normalized transport distances close to zero (<0.03), visualizations of particle trajectories over time showed that particles were attracted to the same electrode from which they were repelled during each cycle due to the short time interval between half cycles and changes in electrode polarity that did not allow particles to be transported to an adjacent negative electrode before the next half cycle (Mode C followed by Mode D). Transport velocity U was higher with the lowest three frequencies compared with higher frequencies, though the relationship was not monotonic (Fig. 6cd). The highest transport velocities were achieved with frequencies of 1 and 3 Hz for the superior-pitch and superior-width design cases, respectively.

3.5. Comparison with previous studies A study in which an EDS electric field was analytically solved for inter-electrode spacings between 0.05 and 1.05 mm and electrode widths between 0.01 mm and 0.2 mm found that as width increased for a given inter-electrode spacing, the maximum magnitude of electric field strength on the EDS surface decreased, with the decrease being more substantial with smaller widths (Sayyah et al., 2016). In agreement, our study showed a decrease in the maximum electric field strength magnitude as electrode width increased. Also in agreement, smaller widths yielded larger decreases in maximum electric field strength magnitude in our study. Specifically, the change in width from 0.1 to 0.3 mm and from 0.3 to 0.5 mm yielded a 22% and 12% decrease in maximum electric field strength magnitude, respectively. A recent experimental laboratory study showed that after EDS activation the median diameter of the residual dust particles was reduced to 10.4 lm from the median diameter of the deposited particles of 31.1 lm (Sayyah et al., 2017). This result illustrates the possibility of removal (i.e. transport) of 20 mm particles investigated in our simulations. The experimental EDS operated under a three-phase rectangular wave, V = 1 kV, f = 5 Hz, P = 0.48 mm, D = 0.08 mm, and inclination angle of 20°. Experimental results also showed that an increase in voltage from 1 to 1.5 kV for this set up (and a similar set up with P = 0.6 mm and 30° inclination angle) removed more particles; their result was in accord with our increase in transport distance with increased voltage, provided particles hopped from one electrode to the next down the incline. Parameter values that produced optimal results and had the largest effect on transport distance X in our study included V = 1.4 and

2.8 kVp-p, f = 1 and 3 Hz, and P = 7 and 14 mm. Previous experimental studies with horizontal EDSs and either two- or three-phase rectangular waves utilized voltages of 0.7–3 kVp-p, frequencies of 5–100 Hz, and pitches of 0.1–2 mm (Wu et al., 2015, 2014; Mazumder et al., 2014). Comparing these parameter values with our optimal parameter values, our study indicated that similar voltages, fewer electrodes (i.e. larger pitches), and fewer cycles (i.e. lower frequencies) can be used to clean inclined EDSs under our conditions due to the beneficial effect of gravity that promoted dust transport down the incline. Taking both pitch and voltage into consideration for the baseline, superior-pitch, and superior-width cases, values of voltage per pitch (V/P) that were from 0.15 to 0.4 kVp-p mm1 gave the largest transport distances X, 0.05 to 0.125 kVp-p mm1 gave the smallest transport distances, and 0.8 to 1.7 kVp-p mm1 gave intermediate transport distances (Fig. 7). In contrast, experiments and computational simulations of a previous study with some conditions (D = 0.3 mm, P = 7 or 10 mm, f = 1 Hz, inclination angle of 20°) similar to ours found that cleaning efficiency (mass of particles removed divided by mass of particles loaded) increased as V/ P increased from 0 to 1 kVp-p mm1 (Kawamoto and Shibata, 2015). In agreement with the decrease in transport distance as frequency increased in our study, the previous work with V/ P = 0.86 kVp-p mm1 observed a decrease in cleaning efficiency as frequency increased. However, with the previous work, frequencies between 0.1 and 20 Hz gave cleaning efficiencies of 80%, and only a decrease to 50% efficiency occurred as frequency increased from 20 to 100 Hz, whereas our study found transport distances close to zero with larger frequencies. Differences in results between our study and the previous study may be because our study focused on particles that are difficult to remove (20-mm diameter) and dust accumulated in one day (mass loading of 0.215 g m2), while the previous study utilized the wide range of particle sizes (<25 mm to >300 mm) present in sand and dust accumulated in a much longer time (mass loading of 100 g m2). Although the previous study found high cleaning efficiencies (80%) with voltages of 6 kVp-p or higher and pitches of 7 or 10 mm, our study suggested that lower voltages (1.4 or 2.8 kVp-p) and the same or higher pitches (7 or 14 mm) may also be effective at cleaning inclined PV panels. Our parameter values give the added benefits of reduced EDS operating costs due to lower voltage and reduced EDS fabrication costs due to fewer electrodes.

4. Conclusions The effects of EDS parameters on dust transport distance (cleaning efficiency) for PV panels soiled by desert dust representative of that in Doha, Qatar were determined by computational simulation, and optimal EDS parameters were identified. As electrode pitch

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Innovation Program, each of which had no role in the conduct of the research nor preparation of the article. Simulations were performed using computational codes developed by J.S. Marshall’s group at The University of Vermont. University of Florida Research Computing provided computational resources and support that contributed to this work. W. Javed at Texas A&M University at Qatar provided the data of dust accumulated on PV panels in Doha, Qatar. Conflict of Interest This research was conducted in the absence of any commercial or financial relationships that could be construed as potential conflicts of interest.

Fig. 7. Transport distance X versus voltage V divided by pitch P for (circles, solid line) the baseline case with different pitches, (squares, dashed line) the superiorpitch design case with different voltages, and (triangles, dashed-dotted line) the superior-width design case with different voltages.

increased, a peak transport distance occurred with P = 14 mm due to the decreasing electric field strength being strong enough with small pitches to transport particles the increasing pitch distance to an adjacent electrode. However, the decreasing electric field strength was not strong enough with large pitches to as efficiently transport particles the increasing pitch distance. A larger electrode width produced a larger transport distance due to a stronger electric field. Electrode shape and EDS dielectric material did not significantly affect transport. Optimal voltage was 2.8 kVp-p/1.4 kVpp with the superior-pitch/superior-width design case, while particles remained adhered to the surface with small voltages (0.7 kVp-p) but were repelled and attracted by the same electrode with high voltages (11.8 kVp-p). Transport distance per 10 cycles generally decreased as frequency increased due to the decreasing time between half cycles that decreased the number of particles that completed their hops to an adjacent electrode before a change in electrode polarity at a half cycle. However, an intermediate frequency of 1 Hz/3 Hz was optimal with the superior-pitch/superiorwidth design case. The two cases that gave the highest values of transport distance and transport velocity, which were nearly the same for each case, differed by voltage (2.8 and 5.6 kVp-p) with remaining parameters being the same (f = 1 Hz, P = 14 mm, and D = 0.3 mm). Due to lower operating cost and reduced possibility of electrical breakdown, the case with the lower voltage of 2.8 kVp-p would be preferred. Our study was the first to describe the motion of individual particles under varying combinations of EDS design and operating parameters to improve cleaning of small, difficult to remove particles from inclined PV panels, unlike previous studies to the best of our knowledge. Conditions specific to a location of interest (Doha, Qatar) were simulated, including particle properties and panel inclination angle. In future work, additional important environmental conditions should be incorporated, such as wind velocity, relative humidity, particle size distribution, and electrostatic properties of particles with respect to particle composition. Our study revealed various ways in which individual dust particles were repelled and attracted by electrodes under different conditions that produced different transport patterns, which can be used to improve the efficiency of dust mitigation for PV panels. Acknowledgments This work was supported by grants from Qatar National Research Fund’s National Priorities Research Program (grant number NPRP7-987-2-372) and the 2015 Wells Fargo Clean Tech and

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