Numerical investigation of installation and environmental parameters on soiling of roof-mounted solar photovoltaic array

Abstract A study of dust deposition on solar photovoltaics as influenced by the installation tilt angle, azimuth angle and the dust particles sizes was carried out. A 3-dimensional Computational Fluid Dynamics (CFD) simulation model was used with the Shear Stress Transport k-ω turbulence model being employed for wind flow analysis and discrete phase model was used for dust motion prediction. Response surface modelling was used to analyse the relationships between the installation parameters, dust particle sizes and dust deposition. The investigation revealed that in a 3-dimensional simulation, the influence of tilt angle is almost similar to the effect of azimuth angle for multi-storey rooftop photovoltaic arrays. Dust particle size of 100 µm had the most deposition resulting in more soiling compared to the 10 µm size dust particles. Soiling of roof-mounted solar PV modules is less on multi-storey building installations compared to ground-mounted solar PV arrays which experienced 13% more deposition. Manipulation of the installation azimuth and tilt angles on roof-mounted installations can be effectively used for soiling minimisation.


PUBLIC INTEREST STATEMENT
Solar energy derived from the sun has found many uses including power generation water heating and space heating. However, the issue of soiling can be a deterrent factor to the wider adoption of solar energy. Soiling reduces the amount of irradiance converted into useful energy due to its shading effect. It is therefore technically and economically justifiable to develop new ways of mitigating the negative effects of soiling to allow maximum utilisation of the installed capacity of the solar collectors. For rooftop solar photovoltaics, cleaning is more difficult and hence there is a need to develop mitigation strategies that take advantage of the natural cleaning mechanisms such as wind and rain. This study seeks to evaluate and analyse the soiling characteristics of different installation configurations on a rooftop photovoltaic array. Further, the configurations and variables, which give the maximum and minimum soiling, are identified and analysed.

Introduction
Solar photovoltaic (PV) energy is among the preferred alternative energy sources due to its abundance and renewable nature. In the past ten years, there has been a 50% average increase in the global PV market (Connolly, Lund, Mathiesen, & Leahy, 2010) and by year 2019, about 112 GW global solar PV demand is anticipated (Enkhardt, 2018). However, the wider adoption of solar PV energy can be slowed down due to the influence of soiling which is the accumulation of dust and other foreign materials on a solar PV module surface (Sarver, Al-Qaraghuli, & Kazmerski, 2013;Tanesab, Parlevliet, Whale, & Urmee, 2019). The influence of soiling on solar PV arrays can have drastic effects (Mussard & Amara, 2018;Said, Hassan, Walwil, & Al-Aqeeli, 2018). For example, Adinoyi and Said (2013) reported a soiling power loss of 50% in Saudi Arabia while losses ranging from 5%-70% were also recorded in different places with varying climatic conditions and time of exposure (Adinoyi & Said, 2013;El-Nashar, 1994;Pavan, Mellit, De Pieri, & Kalogirou, 2013). A study in Saudi Arabia revealed a 32% decrease in PV power efficiency due to soiling after several months of exposure (El-Nashar, 1994). A different study by Pavan et al. (2013), reported annual power losses between 1% and 5% for poly-crystalline PV collectors. Soiling is therefore a phenomenon which is dependent on the place of occurrence and the time of exposure.
There are several variables influencing soiling and these were investigated in different researches. The influence of dust particle sizes on soiling was studied by El-Shobokshy and Hussein (1993) and it was reported that small particles have more detrimental effects compared to larger-sized particles. The influence of wind speed was also considered in solar PV soiling studies. An investigation by Said et al. (2018) indicated that the influence of wind velocity on solar PV module performance is dependent on its speed and direction. A different study evaluated the effect of wind speed on dust deposition and higher wind speeds were reported to cause more soiling (Goossens & Kerschaever, 1999). However, other studies on wind speed reported otherwise (Maghami et al., 2016;Mani & Pillai, 2010).
The installation configuration, i.e. the tilt angle and azimuth angle also affect dust deposition on solar PV module. The effects of tilt angles on soiling were investigated and it was reported that higher tilt angles have lower soiling rates compared to lower tilt angles (Elminir et al., 2006;Mekhilef, Saidur, & Kamalisarvestani, 2012). Further studies on the influence of tilt angles on soiling were performed by Xu et al. (2017) and a model relating the tilt angle and dust deposition density was developed and integrated into the PV output model. Investigations on the influence of installation azimuth indicated that surfaces facing away from the wind experience less soiling compared to the surfaces facing the direction of wind flow (Goossens, Offer, & Zangvil, 1993;Mailuha, Murase, & Inoti, 1994;Mani & Pillai, 2010). The azimuth angle of a solar PV surface is the angle between a line due south passing through the PV module and the horizontal projection of the normal to the PV surface. A study to evaluate the influence of installation tilt, azimuth and height on ground-mounted PV modules was carried out by Chiteka, Arora, and Jain (2019) and it was reported that tilt angle is more influential on dust deposition compared to azimuth for heights of installation between 1 m and 5 m.
Simulations and experimental investigations were performed on particle deposition characteristics on surfaces including solar PV modules. Particle adhesion characteristics were reported to be dependent on impact velocity of the particle onto the surface for both normal and oblique impact (Li, Dunn, & Brach, 2000). A general study by Klinkov, Kosarev, and Rein (2005) developed a method to determine the fate of a particle on impact with a surface based on its impact velocity and particle diameter.
A limited number of simulation studies in dust deposition on solar PV collectors were reported in literature. For example Lu, Lu, and Wang (2016) performed a numerical investigation of dust deposition on an isolated building-mounted solar PV array. The study revealed that smaller sized particles of 10 µm had more deposition compared to 50 µm sized particles. In another study, Lu and Zhang (2018) studied the dry deposition by Computational Fluid Dynamics (CFD) simulation of monodisperse and polydisperse dust on rooftop PV collectors and reported no distinction between monodisperse and polydisperse dust deposition characteristics. Deposition characteristics on groundmounted PV collectors were also investigated and a 13.71% deposition rate was recorded on 100 µm sized dust at a velocity of 1.3m/s while a deposition rate of 14.28% was recorded on 150 µm dust particles at a velocity of 2.6m/s (Lu & Zhao, 2019). Dust deposition characteristics on ground-mounted multi-row solar PV installations was investigated using CFD simulation and the study reported 13.18% more deposition on front rows compared to the rear rows (Lu & Zhang, 2019). Further, large-sized dust particles deposited more on the front rows and smaller sized particles settled on the rear rows.
In another study by Heydarabadi, Abdolzadeh, and Lari (2017), the influence of varying tilt angles, wind direction, dust concentration and particle size was evaluated using CFD on ground-mounted PV modules. The results showed that different particle sizes have different deposition characteristics. Further, it was found that higher wind speeds require higher tilt angles for maximum deposition.
Soiling mitigation of soiled solar PV systems is of utmost importance in solar PV power generation. However, studies indicate that the size of the solar PV array and the height of the building contribute to the complexity and tediousness experienced in soiling mitigation (Kumar, Sudhakar, Samykano, & Sukumaran, 2018). The cleaning of PV installations on high rise buildings is complex and expensive as it require specialised pumping of cleaning water (Williams, n.d.). Further, the existing robots are difficult to employ on building integrated and building applied PV arrays as these robots are designed for open space PV installations (Kumar et al., 2018).
The use of novel dust mitigation procedures such as electrodynamic shield, electrostatic cleaning, super hydrophilic and superhydrophobic coatings was found to yield positive results (Chen, Chesnutt, Chien, Guo, & Wu, 2019;Guo, Javed, Khoo, & Figgis, 2019;Kawamoto & Guo, 2018;Mozumder, Mourad, Pervez, & Surkatti, 2019;Wang et al., 2018), however, their use has not received wider application to date. Further, literature has revealed that although a number of approaches exist, there is no one clear approach to soiling mitigation and the economic feasibility of these approaches need further consideration (Said et al., 2018).
Although CFD simulations have been performed on soiling of solar PV collectors, these were mainly focused on single storey rooftop and ground-mounted PV collectors (Heydarabadi et al., 2017;Lu et al., 2016;Lu & Zhang, 2018Lu & Zhao, 2019). The present study focuses on simulation studies on soiling of PV arrays mounted on multi-storey buildings which is scarce in literature. The wind profiles and dust deposition characteristics on ground-mounted photovoltaics and single-storey mounted photovoltaics is different to that on a multi-storey building. Wind flow profiles on PV collectors mounted on a single storey building are influenced by the roof characteristics such as its inclination. However, on a multi-storey building, both inclined and flat roofs are common and a different mounting structure is normally used. The use of a different mounting structure and the height of multi-storey buildings makes wind flow characteristics different and more complex.
The cleaning mechanism required on ground-mounted and single-storey rooftop PV modules is simpler and different to that required on a multi-storey rooftop-mounted photovoltaic array. The cleaning equipment normally used for ground-mounted and single-storey buildings usually traverses on the ground while this is inapplicable to multi-storey buildings which require specialised equipment and water pumping. Citing this difficulty, it is therefore important to evaluate and analyse the factors affecting dust deposition on a multi-storey building and take advantage of natural cleaning agents such as wind and rain. Soiling mitigation methods that can utilise the natural cleaning agents such as rain and wind are important for immediate application in the short term and thus need to be explored extensively. Arora and Arora (2018) accomplished energy and exergy investigations on 1 kW installed rooftop SPV plant in Northern India. Further, Arora, Arora, and Sridhara (2019) carried out performance assessment of 186 kWp power plant in Northern India. The SPV systems can also be integrated with various energy conversion systems viz. Stirling heat engines in view of fabricating a hybrid system. (Arora, Kaushik, & Kumar, 2016a, 2016b.
The effects of installation tilt and azimuth angle as well as the dust particle sizes on both ground mounted and multi-storey building were investigated in this study and a comparative analysis was also carried out. Literature has indicated that 3-dimensional CFD simulation of dust deposition on solar photovoltaics is still limited. Azimuth is important in dust deposition studies on a PV array because it influences wind flow characteristics and the effective area of exposure to dust deposition. It is therefore required to evaluate and analyse the effects of the installation tilt, azimuth as well as the influence of high rise building installations on dust deposition. These factors motivated the investigators to take up the current investigation.
This study is organized as follows: Section 1 outlines the introduction, which also consists of the literature review leading to the identified area of research. Section 2 discusses the materials and methods employed in this study. Section 3 has the results and discussions of the outcomes of the CFD investigation, and lastly, section 4 gives the conclusion of this investigation.

Experimental design
A full factorial face centred central composite experimental design was employed in the design of experiments and a total of 27 simulation experiments were conducted. Parameters including tilt, azimuth and dust particle size were investigated at a constant wind speed of 5m/s. The tilt angle was varied between 5°and 30°while azimuth was varied between 0°and 22.5°. In this study, the azimuth angle was measured with respect to North where 0°means 0°North. The azimuth and tilt angles were selected within the acceptable limits that do not significantly affect the solar radiation incident on the solar PV module. Calcium carbonate dust particles with a density of 2800 kg/m 3 were used in this study. Dust particle sizes were studied in the range 10 µm to 100 µm. Table 1 outlines the parameters used in this study.

Fluid flow and turbulence modelling
The Reynolds Averaged Navier Stokes (RANS) governing equations were used in fluid flow analysis. Turbulence modelling was performed using the Shear Stress Transport (SST) k-ω turbulence model. This model was used due to its better performance compared to other turbulence models on dust deposition applications (Karava, Jubayer, & Savory, 2011;Lu & Zhao, 2019). Dust motion tracking was performed using the Discreet Phase Model (DPM) and particle-particle interactions were ignored. The DPM was employed due to its suitability in modelling two-phase flow problems consisting of a single continuous phase and a discrete phase with a negligible volume fraction of less than 12%. In this DPM modelling, particle-particle interactions were considered negligible and the existence of the suspended particles did not affect fluid flow field (Zhu, Li, & Wang, 2018). The Discreet Random Walk model (DRW) was utilised in modelling the turbulent dispersion of particles for accurate prediction of deposition behaviour of dust particles.
The fluid flow was analysed using RANS governing equation (Equation 1) (Heydarabadi et al., 2017) which describes the relationship between velocity, pressure, temperature and density. The RANS equations used are based on laws of conservation of mass, momentum, and energy. These are shown by Equations 2-4 (Heggøy, 2017). Where; ρ (kg/m 3 ), u (m⋅s −1 ) and κ (Wm −1 K −1 ) are, respectively, density, velocity vector and thermal conductivity while t (seconds), Φ, and Γ ,eff (m 2 /s) represent time, the independent flow variable and the effective diffusion coefficient. S Φ (kg/m 3 s) is the source term.
The formulation of the SST k-ω turbulence model used is shown in Equations 5 and 6 (Zhao, Zhang, Li, Yang, & Huang, 2004). Where;G k andG ω respectively represent the generation term for turbulent kinetic energy k (m 2 /s 2 ), and the generation term for specific dissipation rate. ω (s −1 ). Γ ω and Γ k are the effective diffusivity of ω and k. User-defined source terms N k and N ω are taken as zero in this study while K ω is the cross-diffusion term.
The SST k-ω turbulence model exhibit the best of k-ε and k-ω two-equation models (Lee, Wray, & Agarwal, 2016). Such a model simplifies the prediction of the commencement and amount of flow separation occurring at adverse pressure gradients.

Dust deposition and dust motion modelling
Motion of dust particles was predicted using the DPM model and the formulation of such a model is shown in Equations 7 and 8 (Heydarabadi et al., 2017). The wind-dust particles interaction was considered in the CFD numerical computation. In this investigation, however, dust particle to particle interactions were considered insignificant because the dust concentration in the fluid air was considered as dilute. In the CFD simulation, forces including drag force, gravitational force, and thermophoresis were accounted for.
Where; u f j ¼ u i þ u 0 j ; u 0 j is the mean flow at the particle's position. t (s) is the time; u p j (m/s) is centre velocity of particle; u 0 j (m/s) is velocity flow fluctuation; x p j is the particle position; d is the diameter and S is the particle to fluid density ratio; g i (m/s 2 ) is the gravitational acceleration; and the Stokes-Cunningham slip correction factor is given by C c which modifies the exerted drag due to slip on very fine particles and is outlined in Equation 9. λ represents the mean free path of gas molecules in (µm) and d (cm) is the diameter of the dust particle in cm.
The gravitational force in Equation 8 is given by 1 À 1 s À Á g i . The DRW model was employed in modelling the turbulent dispersion of particles for accurate prediction of dust particle deposition behaviour (Zhao et al., 2004). Respective values of 0.5 and 0.55 were assumed for the roughness constants (C s ) for the PV module and the wall since the solar PV module surface is more uniform compared to the building wall. Moreover, roughness lengths z o of, respectively, 0.0001 and 0.001 were used for the solar PV surface and the building wall and the formulation in Equation 10 was employed in determining the roughness height k s for both the solar PV and the building wall (Liu et al., 2018;X. Zhang, 2009).
A constant wind velocity, U of 5m/s was used in this present study while the initial pressure was set as the standard atmospheric pressure. The wind speed at the solar PV height was determined using Equation 11 (Twidell & Weir, 2015) which describes the variation of wind speed with height where U z is the wind velocity at height z, U is the characteristic speed, z o is the roughness length and d is the zero plane displacement and its value is slightly less than the height of the local obstructions.
The inlet wind velocity and the Turbulent Kinetic Energy (TKE) profiles were compared to the results of an experimental investigation by Tominaga, Akabayashi, Kitahara, and Arinami (2015). The results are displayed in Figures 1 and 2 where Z(m) represent the height from the ground in the computational domain at any particular location of interest, h(m) is the PV module height, U h (m/s) is the velocity at PV module height and K(m 2 /s 2 ) is the turbulent kinetic energy. There was 0.25% and 0.38% difference between the results of the experiments by Tominaga et al. (2015) and the simulations, respectively, for the wind velocity profile at inlet and the Turbulent Kinetic Energy (TKE) profile.

Computational domain
The computational geometry used in this study was developed using ANSYS design Modeller 17. The schematic of the building model of a 3-storey building with an installed rooftop solar PV array is shown in Figure 3. domain was developed to produce the same mean pressure coefficient obtained in the study by Abiola-Ogedengbe et al. (2015).
The height (h) of installation of the PV module measured from the ground was given by H + 0.5 m thus h = 10.5 m. The length, height and width of the computational domain was given by 21.4h, 6h and 9h respectively and this corresponds to 224.7 m, 63 m and 94.5m, respectively. A distance of 5h (52.5 m) was put between the computational inlet and the building while Experimental data was adopted from by Tominaga et al. (2015). a distance of 15h (157.5 m) was left between the rear of the building and the outlet of the computational domain. These dimensions were selected to make sure that there is no airflow obstruction on the solar PV collector by the channel wall boundary layers as shown in Figure 4.

Solution strategy
Resolving of the conservation equations of wind flow was done using the Finite Volume Method (FVM) and the SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm was used in decoupling the pressure and velocity fields. The second-order upwind scheme represented by Equation 12 (Tominaga et al., 2015) was used to discretize the diffusion and convection terms. The Runge-Kutta technique was used in resolving the motion equations of the dust particles. The solution convergence criteria of 10 −6 for Residual Mean Square Error (RMSE) values was used for the fine mesh selected.
where f , SOU andrrespectively represent the face value (using second-order upwind, SOU) and the displacement vector from the upstream cell centroid to the face centroid; & Ñ are the cellcentred value and its gradient in the upstream cell.

Grid independence study
Grid independence study was carried out to determine the minimum grid size that can give the best results. Three grids were tested and these were identified in the study as fine (628 435), medium (492 729) and coarse (152 964). For each mesh size, the number of particles collected on the solar PV collector was recorded and a comparative analysis was done on the different mesh sizes as shown in Figure 5. The results revealed that a fine grid was superior to other mesh sizes with a respective difference of 3.1% with the medium mesh and 17% with the coarse mesh. It was therefore concluded that a fine mesh would give the best results.
Simulations of airflow fields around the solar PV module were performed to evaluate solar PV soiling and validation of the simulations was done using. Abiola-Ogedengbe et al. (2015) experimental results of wind tunnel experiments as shown in Figure 6, where w and W p are, respectively, the distance from the leading edge measured along the solar and the solar panel width. The pressure coefficient (C p ) profile of the simulation results correctly resembled the experimental results and hence it was concluded that the CFD simulation model was capable of accurately predicting the airflow fields near the PV module.

Insolation yield on varying azimuth angles
Annual insolation received by a tilted solar PV on different azimuth angles was computed using Angstrom's model for radiation on a tilted plane represented by Equation 13. H d , H b andK T are respectively the diffuse irradiance, beam irradiance, and the clearness index. R b ; R d and R r are the tilt factors for beam, diffuse and reflected irradiance.

Experimental design and dust deposition analysis
The influence of installation tilt and azimuth as well as the influence of dust particle sizes on soiling of solar photovoltaics was studied using CFD simulations. Simulation experiments amounting to 27 with varying tilt and orientation (wind direction) at a constant wind speed of 5m/s were performed and wind flow was predicted using the RANS equations. The SST k-ω turbulence model was employed in resolving wind flow turbulence near the solar PV collector. Dust particle trajectories were tracked using the DPM model while the DRW model predicted the turbulent dispersion. Design of experiments was done using Design Expert v10.0. and Software Fluent v.17 was used in the simulation experiments. PVSyst v.6.70 was used in computation of the annual solar irradiance yield for the different azimuths used. The results of the solar irradiance yield for different azimuths at an optimised tilt angle of 23°for Harare, Zimbabwe are shown in Table 2. The percentage difference in energy yield between the optimum azimuth and azimuths of 157.5°and 202.5°was also computed. It was found that variation in azimuth angle by up to 22.5°yield a marginal loss in irradiance of up to an annual maximum of 0.69%. The simulation results of the designed experiments and CFD simulations are also highlighted in Table 3. Figure 7 gives the generated response surfaces used in analysing the contribution of the tilt, azimuth and dust particle sizes.
It is noted that the three parameters used in this study have an extent to which they affect dust deposition. In Figure 7, response surfaces are displayed showing the relationships between the different variables. The red dots indicate the design points above the predicted values of the quadratic model. The colour gradient from blue to red shows the region of increasing dust  deposition where blue shows the region of low dust deposition and red is the region of high dust deposition. In Figure 7(a), it is shown that decreasing the tilt angle of the PV panel has an effect of increasing dust deposition. This is due to the effect of gravitational force having more influence on steeper gradients. It can therefore be concluded that tilt angle is inversely proportional to dust deposition a result which was also reported in other studies (Jiang, Lu, & Lu, 2016;Maghami et al., 2016;Mekhilef et al., 2012;Sayyah, Horenstein, & Mazumder, 2014). On the other hand, increasing the azimuth reduces dust deposition. This is because increasing the azimuth angle in relation to wind flow reduces the effective surface area for wind action on the PV collector. The reduction of soiling with wind flow direction agrees well with results reported in literature (Goossens et al.,Figure 7. Response surfaces for the accumulated particles with varying tilt, azimuth and dust particle sizes. 1993; Mailuha et al., 1994;Mani & Pillai, 2010). The results in Figure 7(a) also indicate the need for both low tilt and azimuth angle for maximum soiling. Huge amounts of soiling can also be obtained if either tilt angle or azimuth angle assumes a low value. Further, the results indicate that tilt and azimuth angles have almost equal contribution to soiling on PV installations on multistorey building rooftops. However, tilt angle is slightly more influential compared to azimuth angle.
The results shown in Figure 7(b and c) show that dust particle sizes have a significant influence on dust deposition. However, its influence cannot be equated to that of either tilt or azimuth angle. It is shown that increase in dust particle size resulted in increasing rate of dust deposition with minimum deposition experienced on 10 µm dust particles while maximum deposition rate being recorded for the largest particles sizes of 100 µm. This result shows the differences in deposition characteristics between single-storey and multi-storey buildings. For example, a similar study on a single storey building by Lu et al. (2016) reported maximum deposition occurring at 10 µm particle size which is different for multi-storey buildings considered in the present study. The increase in deposition with increasing dust particle size was also reported in a different study by Lu and Zhao (2018).
The result shown in Figure 7(c) shows that the combination of a low tilt angle and large particle sizes results in higher deposition levels of the dust particles. Larger sized particles are more affected by the force of gravity and hence they tend to deposit more compared to smaller sized particles which may remain suspended in the fluid air for a longer period (Lu & Zhang, 2019;Lu & Zhao, 2018).
The parameters used in this study can be listed in order of their importance in soiling, respectively, as tilt angle, azimuth angle and dust particle size. However, there is only a small difference of 14.6% in the contribution of tilt angle compared to the contribution of azimuth angle. When compared to the previous studies by Chiteka et al. (2019) on groundmounted PV modules, this present study indicates that the influence of tilt angle is significantly less when compared to ground-mounted PV modules. Parameter correlation analysis was performed and the results are shown in Table 4. There was an 11% decrease in the relevance of the tilt angle while, the influence of azimuth angle became more significant with its relevance increasing by 24% when compared to previous studies . This result indicated the importance of azimuth angle in soiling studies on rooftop PV modules on a multi-storey building.

Solar PV module wind flow fields and dust deposition
The characteristic wind flow fields near the PV module were used to interpret the soiling rates and the soiling behaviour of the various configurations and particle sizes used. Figure 8 shows the velocity fields on the PV module at varying tilt and azimuth angles. There are complex velocity fields near the PV module caused by the existence of the building and the solar PV module as wind barriers and this phenomenon was also reported elsewhere (Lu & Zhao, 2019).
The velocity fields on the rooftop solar PV array are different from velocity fields for groundmounted PV module. The velocity variations are more pronounced on roof-mounted PV array compared to the ground-mounted array. Further, lower impact velocities are experienced on the ground-mounted PV collector compared to the roof-mounted collectors. This is the reason for 11.8% more deposition recorded on the ground-mounted PV collector compared to the roofmounted PV module. This scenario is due to the effect of surface roughness of the ground which significantly reduces the wind velocity near the ground (Justus & Mikhail, 1976). Frictional resistance affects airflow near the ground surface. The velocity is thus reduced and this phenomenon is known as wind shear (Twidell & Weir, 2015). As previously reported, higher wind velocities tend to reduce deposition compared to lower wind velocities (Maghami et al., 2016;Mani & Pillai, 2010). The significantly more deposition on the ground-mounted PV collectors is attributed to the wider spectrum of impact velocities ranging from 1.8m/s to 3.7m/s. These speeds are more influential on dust deposition for all particles sizes below about 150 µm. On rooftop solar PV collectors, the speed range was a bit narrower (1.6m/s to 2.2m/s) and this limits the number of particles depositing on the solar collectors. This phenomenon agrees well with results obtained by Klinkov et al. (2005).
The velocity fields for the roof-mounted solar collectors shown in Figures 9 and 10 are almost similar for all configurations although some slight differences can be noted which resulted in the differences in particle deposition rates. Figure 11 shows the Turbulent Kinetic Energy (TKE) profiles which are also almost similar for all configurations like the case for velocity fields for the roof-mounted solar PV collectors. The groundmounted PV module has lower values of TKE compared to the roof-mounted solar collectors. However, for the ground-mounted PV module, the TKE profile is close to the PV collector compared to the roof-mounted configurations. This occurrence may increase dust deposition on groundmounted PV collectors due to higher turbulent particle fluctuations near the PV collector surface (Z. Zhang & Chen, 2009). The velocity streamlines of airflow near the solar PV collector are highlighted in Figure 12. Streamlines represent the path followed by particles suspended in the fluid and they describe flow in terms of velocity and direction. The spacing between the streamlines is inversely proportional to the flow velocity. There are turbulent eddies near the PV module and these occurred behind the installation for all configurations. At 0°azimuth, the turbulent eddies were much closer to the PV module and this had an effect of causing more deposition on 0°azimuth compared to other azimuth angles. The turbulent eddies for 22.5°azimuth were much weaker compared to those at 0°resulting in less deposition compared the 0°azimuth. The 5°tilt angle had apparently larger turbulent eddies compared to the other tilt angles. This could be the reason for more deposition of dust particles (Lu & Zhao, 2019). TKE is related to flow velocity and turbulent eddies and their variations result from the solar PV module inversion (Lu & Zhang, 2019).

Conclusions
The study investigated dust deposition phenomenon and turbulent airflow characteristic behaviour on a multi-storey building using a 3-dimensional CFD simulation model. The influence of installation tilt,  azimuth and dust particle sizes on soiling was analysed. In this investigation, the following observations were noted: • The wind flow fields and hence the soiling characteristics are completely different for roof-mounted and ground-mounted PV collectors. Rooftops experience higher wind velocities unlike groundmounted installations. Ground-mounted installations experience a wider spectrum of impact velocities and hence more deposition is experienced with 11.8% more soiling compared to roof-mounted PV arrays.
• On rooftop installations, there are very small differences on the velocity fields, TKE profiles as well as the velocity streamlines. This is attributed to the relatively larger building height which influences wind flow compared to the PV array size used which has less influence on wind flow compared to the building.
• Tilt and azimuth angles had a significant influence on dust deposition compared to dust particle size. Particle sizes of 100 µm had more deposition at lower impact velocities compared to other particle sizes while lower tilt angles of 5°experienced more soiling.

Funding
The authors received no direct funding for this research.