# CFD-DEM Simulation of Dust Deposition on Solar Panels for Desert Railways
## 3 Numerical Simulation Results and Discussion
### Deposition Characteristics of Fine Sand Particles on Solar Panels  
The deposition process of fine sand with a particle size of 100 um under flow with a fixed friction velocity of \(u_{*}=0.25\) m/s was discussed, for which the dust particles were released along the x-direction, the initial particle velocity obeyed a normal distribution with a mean \(\overline{v}=3\) m/s and a standard deviation \(\sigma=1.5\) m/s, and the calculation time step was \(3.0\times 10^{-7}\) s. According to [PERSON] et al. [29], it can be assumed that the concentration of 100 um particles in dusty weather with 1 km visibility is 0.62 mg/m\({}^{3}\). Then, given that \(U=3\) m/s, \(m=1.07\times 10^{-3}\) mg and by following Formula (11), the number of dust particles entering from the entrance section per unit time was \(1.043\times 10^{4}\)/s. When \(K=0.5\times 10^{6}\) J/m\({}^{3}\), the results of the particle deposition number vs. velocity at different times are shown in Figure 8. From this, we can see that at the beginning of the coupling calculation (0.02 s, Figure 8a), the particle velocity basically followed a normal distribution, but after 0.2 s and 1.0 s through the acceleration of air flow, the high-speed dust particles accounted for a larger proportion (Figure 8b,c). However, the influence of the flow field around the solar panel and the impact of the dust particles on the ground and on the solar panel caused the number-velocity histogram to become irregular. It is particularly noteworthy that there were some particles that were basically at rest, such as the dust particles that stayed on the panel after the dust particles hit the solar panel, as shown in  
Figure 6: Movement of dust particles with particle size of 10 μm around the solar panel, \(u_{*}=0.25\) ms\({}^{-1}\), \(K=0.5\times 10^{6}\) Jm\({}^{-3}\). (**a**) Side view. (**b**) Back view. Figure 7: The total number of particles deposited on the solar panel. Figure 8d. Figure 9 shows the settlement of 100 \(\upmu\)m sand particles on the solar panel. It can be seen that there were indeed some dust particles deposited on the solar panel. Due to the short simulation time, the deposition amount was less. For 100 \(\upmu\)m fine sand, increasing the wind speed led to an increasing in the speed of the sand impacting the solar panel. Figure 10 shows the streamlines of the sand particles around the solar panel and the number of particles deposited on the panel surface. We chose that \(u_{*}=0.40\) m/s and \(K=0.5\times 10^{6}\) J/m\({}^{3}\). From Figure 10a, it can be seen that the dust particles basically rebounded after hitting the solar panel, and few particles were deposited on the panel surface after 2 s, as shown in Figure 10b. Therefore, due to the weak cohesion force between the sand particles and the PV glass panels, the fine sand particles could deposit on the solar panel at low wind speeds, but it would be difficult for them to be deposited when the wind speed increases. This phenomenon has also been reported by [PERSON] [23]. For medium and stronger cohesion forces, the deposition of fine sand particles was different, which can be seen from Figures 11 and 12, where the fine sand particles could also be deposited on the solar panel at the same time with less rebound. Figure 8: Velocity distribution of fine particles at different times in the flow field. Figure 9: Movement of dust particles around solar panel. (**left**) Particle streamlines; (**right**) dust particles settled on the solar panel, where the red point indicates dust particles. The number of deposited sand particles on the different parts of the solar panel were changed into distribution data; then, a cloud chart of the number of particles was drawn based on the data, see Figure 13. Figure 13 shows the concentration distribution of fine sand particles deposited on the solar panel in a day when \(u_{*}=0.40\) m/s and \(K=3.5\times 10^{6}\) J/m\({}^{3}\), for which we can see that along incline of the solar panel, the concentration gradually decreased.