# CFD-DEM Simulation of Dust Deposition on Solar Panels for Desert Railways
## 3 Numerical Simulation Results and Discussion  
### Deposition Characteristics of Dust Particles (Clay) on Solar Panels  
The calculation of wind-blown dust/sand flow was a two-step process. First, the steady CFD method was used to calculate the flow field with a fixed friction velocity around the solar panel until the flow field achieved convergence. Second, the transient \begin{table}
\begin{tabular}{c c} \hline \hline
**Name** & **Value** \\ \hline Dust diameter \(dp_{1}\) & 0.01 mm \\ Dust density & 2000 kg/m\({}^{3}\) \\ Dust shear modulus \(G_{1}\) & 3.5 \(\times\) 10\({}^{6}\) Pa \\ Dust Poisson ratio & 0.42 \\ Recovery factor \(e\) & 0.5 \\ Fine sand diameter \(dp_{2}\) & 0.1 mm \\ Fine sand density & 2050 kg/m\({}^{3}\) \\ Fine sand shear modulus \(G_{2}\) & 3.0 \(\times\) 10\({}^{7}\) Pa \\ Fine sand Poisson ratio & 0.28 \\ Panel glass density & 2700 kg/m\({}^{3}\) \\ Panel glass shear modulus \(G_{3}\) & 3.0 \(\times\) 10\({}^{10}\) Pa \\ Panel glass Poisson ratio & 0.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Physical parameters of dust particles. Figure 4: The deposition of dust particles on the solar panel of 100 \(\upmu\)m fine sand particles under static wind with different coherent energy parameters. (**a**) \(K\) = 0.5 \(\times\) 10\({}^{6}\) Jm\({}^{-3}\). (**b**) \(K\) = 1.05 \(\times\) 10\({}^{6}\) Jm\({}^{-3}\). (**c**) \(K\) = 3.5 \(\times\) 10\({}^{6}\) Jm\({}^{-3}\). Figure 3: (**a**) The deposition of dust particles on the solar panel of 10 \(\upmu\)m clay particles under static wind with coherent energy parameter \(K\) = 0.5 \(\times\) 10\({}^{5}\) Jm\({}^{-3}\), and (**b**) the total number of particles deposited on the solar panel varying with time. CFD method was used to simulate the wind flow including a large number of moving clay particles with a radius 10 \(\upmu\)m, whose moving trail, velocity and force were calculated by an EDM method. The release speed of dust particles was along the x-direction with a fixed value of 1.75 m/s, and the calculation time step was as small as \(1.25\times 10^{-7}\) s, which could prevent dust particles from passing through the surface of the solar panel or sticking inside the panel. The visibility of typical dusty weather was assumed to be 1 km; then, according to [PERSON] et al. [29], it was estimated that the TSP concentration of the incoming flow was about 2\(\sim\)3 mg/m\({}^{3}\). It was reasonably assumed that the concentration of dust with a diameter of 10 \(\upmu\)m is 2 mg/m\({}^{3}\). So, the number of dust particles entering from the entrance section in unit time was  
\[N=cUA/m \tag{12}\]  
In which \(U=1.75\) m/s, \(A=6\) m\({}^{2}\), \(c=2\) mg/m\({}^{3}\) and \(m=1.152\times 10^{-6}\) mg. Then, \(N=1.82\times 10^{7}\)/s. In order to improve the efficiency of the calculation, a ratio of 1:3500 was used for the calculation, that is, the number of released particles at the inlet was 5220/s. The flow-field contour map of the x-y plane and z-y plane is shown in Figure 5. From Figure 5a, it can be seen that the air flow above the solar panel accelerated gradually along the upper surface because of the wing-flow effect, but the air flow below the solar panel formed a high-speed flow area and a subsequent low-speed zone because of the attack angle of the solar panel and its shading effect, while a low-speed and swirling zones existed, as shown in Figure 5b, behind the solar panel due to the solar panel's blocking of the air flow. In order to better display the particle trajectory around the solar panel, the friction velocity \(u_{*}=0.25\) ms\({}^{-1}\), \(K=0.5\times 10^{6}\) J/m\({}^{3}\) and the particle radius was set as 10 \(\upmu\)m. The simulation results are shown in Figure 6, in which the rectangular panel is the solar panel, the streamline color represents the magnitude of the dust particle movement speed and the speed range was from 1.21 m/s (blue line) to 2.08 m/s (red line).