In recent years, the global energy crisis and environmental concerns have driven the rapid development of renewable energy sources. Among these, solar power generation, particularly through photovoltaic systems, has emerged as a mature and widely adopted technology. Arid and desert regions, characterized by abundant sunlight, long sunshine hours, and vast land resources, are ideal for large-scale centralized photovoltaic power plants. However, these areas often experience frequent wind and sand activities, leading to the deposition of dust particles on solar panels. This dust accumulation significantly reduces the efficiency of photovoltaic modules by decreasing light transmittance and increasing operating temperatures. In this study, we employ computational fluid dynamics (CFD) simulations to investigate the dust deposition patterns on solar panels under various environmental conditions, focusing on the effects of dust concentration, particle size, and panel inclination angle. Based on the simulation results, we further analyze the attenuation of light transmittance due to dust deposition, providing insights for the optimization of photovoltaic system installations in desertified regions.
The importance of solar energy as a renewable resource cannot be overstated. Photovoltaic technology converts solar radiation directly into electricity, offering a sustainable solution to energy demands. However, in desert environments, dust storms and airborne particles pose a significant challenge to the performance of solar panels. Previous studies have highlighted that dust deposition can reduce the power output of photovoltaic systems by up to 35% over extended periods. Understanding the mechanisms of dust accumulation and its impact on light transmittance is crucial for improving the efficiency and reliability of solar power generation in such regions. Our research aims to address this issue by simulating the wind-sand two-phase flow around solar panels and quantifying the resulting dust deposition.
To model the dust deposition process, we developed a three-dimensional computational domain using ICEM software and performed simulations with the CFD package Fluent. The physical model简化 includes a solar panel mounted at a height of 0.5 m above the ground, with dimensions of 1.6 m × 3.2 m × 0.08 m. The computational domain is sized at 64 times the panel height in the streamwise direction, 16 times in the spanwise direction, and 12 times in the vertical direction, ensuring fully developed flow and turbulence. The panel surface and nearby regions are meshed with hexahedral elements, with local refinement to capture detailed flow characteristics. The inlet boundary condition is set as a velocity inlet with a logarithmic wind profile, defined by the equation:
$$U = \frac{u_*}{k} \ln \left( \frac{y}{z_0} \right)$$
where $u_*$ is the friction velocity, $k = 0.41$ is the von Kármán constant, and $z_0 = 0.025 \, \mu\text{m}$ is the roughness length. The outlet is a pressure outlet, while the top and sides of the domain are symmetric boundaries. The bottom ground and panel surfaces are treated as no-slip walls. For the multiphase flow simulation, we adopted the Eulerian model coupled with the k-ε turbulence model. The governing equations for the fluid flow include the continuity equation and the Reynolds-averaged Navier-Stokes equations:
$$\frac{\partial u_i}{\partial x_i} = 0$$
$$\frac{\partial (\rho u_i)}{\partial t} + \frac{\partial (\rho u_i u_j)}{\partial x_i} = -\frac{\partial p}{\partial x_i} + \frac{\partial}{\partial x_j} \left( \mu \frac{\partial u_i}{\partial x_j} – \rho \overline{u_i’ u_j’} \right)$$
The turbulence kinetic energy $k$ and its dissipation rate $\varepsilon$ are modeled as:
$$\frac{\partial (\rho k)}{\partial t} + \frac{\partial (\rho k u_i)}{\partial x_i} = \frac{\partial}{\partial x_j} \left[ \left( \mu + \frac{\mu_t}{\sigma_k} \right) \frac{\partial k}{\partial x_j} \right] + G_k – \rho \varepsilon$$
$$\frac{\partial (\rho \varepsilon)}{\partial t} + \frac{\partial (\rho \varepsilon u_i)}{\partial x_i} = \frac{\partial}{\partial x_j} \left[ \left( \mu + \frac{\mu_t}{\sigma_\varepsilon} \right) \frac{\partial \varepsilon}{\partial x_j} \right] + C_{1\varepsilon} \frac{\varepsilon}{k} (G_k – C_{3\varepsilon} G_b) – C_{2\varepsilon} \rho \frac{\varepsilon^2}{k}$$
where $\mu_t = 0.09 \rho C_\mu (k^2 / \varepsilon)$ is the turbulent viscosity, $G_k$ is the production of turbulence kinetic energy due to mean velocity gradients, and $G_b$ represents buoyancy effects. The constants are set as $C_{1\varepsilon} = 1.44$, $C_{2\varepsilon} = 1.92$, $C_{3\varepsilon} = 0.09$, $\sigma_k = 1.0$, and $\sigma_\varepsilon = 1.3$. The SIMPLE algorithm is used for pressure-velocity coupling, and second-order upwind schemes are employed for spatial discretization. Convergence is achieved when residual values stabilize below $10^{-6}$.
For the dust phase, we assume spherical particles with a density of $\rho_{\text{sand}} = 2650 \, \text{kg/m}^3$. The dust deposition mass on the solar panel surface is calculated as:
$$M_S = \rho_{\text{sand}} \int N h dA$$
where $N$ is the number of deposited particles per unit volume, $h$ is the height of the first grid layer near the panel surface (comparable to the particle diameter), and the integral is over the panel area. To evaluate the effect on light transmittance, we use the Lambert-Beer law, which relates the transmittance $T$ to the dust mass $M$ and equivalent particle radius $r_v$:
$$T = \exp \left( -\frac{3(1 – \beta) M}{4 \rho_{\text{sand}} r_v} \right)$$
where $\beta = 0.45$ is the assumed transparency coefficient of the dust particles. This formula allows us to predict the reduction in light transmission through the photovoltaic glass due to dust accumulation.
We conducted simulations under varying conditions to analyze dust deposition on solar panels. Key parameters include the inlet dust volume fraction, particle size, and panel inclination angle. For instance, with a fixed inclination angle of $35^\circ$ and particle size of $10 \, \mu\text{m}$, we tested dust volume fractions of $5 \times 10^{-3}\%$, $5 \times 10^{-4}\%$, $5 \times 10^{-5}\%$, and $5 \times 10^{-6}\%$. Similarly, with a volume fraction of $5 \times 10^{-4}\%$ and inclination of $35^\circ$, we examined particle sizes of 1, 10, 20, 30, 40, and $50 \, \mu\text{m}$. Additionally, we varied the panel inclination from $15^\circ$ to $75^\circ$ to study its impact on deposition patterns.
The flow field around the solar panel reveals complex vortex structures, particularly on the leeward side. As the inclination angle increases, the separation vortex behind the panel expands, enhancing dust accumulation, especially for smaller particles. The velocity profiles near the panel surface show that at lower inclinations, the wind speed gradually increases from the bottom to the top of the panel. However, at higher inclinations (e.g., above $25^\circ$), the velocity decreases initially and then increases, with more pronounced variations as the angle increases. This non-uniform flow distribution leads to heterogeneous dust deposition on the photovoltaic surface.
Our results indicate that dust deposition on solar panels increases exponentially with both the inlet dust volume fraction and particle size. For example, when the volume fraction rises from $5 \times 10^{-6}\%$ to $5 \times 10^{-3}\%$, the deposition mass grows significantly. Similarly, larger particles result in higher deposition due to greater inertia. The relationship between deposition mass and these factors can be approximated by exponential functions, as shown in the following table summarizing key data from our simulations:
| Dust Volume Fraction (%) | Particle Size (μm) | Inclination Angle (°) | Deposition Mass (g) | Light Transmittance |
|---|---|---|---|---|
| 5 × 10-6 | 10 | 35 | 8.5 | 0.880 |
| 5 × 10-5 | 10 | 35 | 25.3 | 0.875 |
| 5 × 10-4 | 10 | 35 | 68.7 | 0.868 |
| 5 × 10-3 | 10 | 35 | 95.2 | 0.862 |
| 5 × 10-4 | 1 | 35 | 12.1 | 0.878 |
| 5 × 10-4 | 20 | 35 | 45.8 | 0.870 |
| 5 × 10-4 | 30 | 35 | 72.4 | 0.865 |
| 5 × 10-4 | 40 | 35 | 98.6 | 0.860 |
| 5 × 10-4 | 50 | 35 | 132.5 | 0.855 |
Regarding the panel inclination angle, dust deposition initially increases with angle, peaks at around $50^\circ$, and then decreases. This trend is consistent across different dust conditions and is attributed to the balance between gravitational settling and aerodynamic forces. At lower angles, gravity dominates, causing particles to settle easily. As the angle increases, wind-induced lift and drag become more significant, reducing deposition at steeper angles. The light transmittance of the dust-covered photovoltaic panels follows a similar pattern, with maximum attenuation occurring at $50^\circ$ inclination. For instance, at a dust volume fraction of $5 \times 10^{-4}\%$ and particle size of $10 \, \mu\text{m}$, the transmittance decreases from approximately 0.880 at $15^\circ$ to 0.866 at $50^\circ$, then recovers to 0.874 at $75^\circ$.
To further quantify the relationships, we derived empirical equations from the simulation data. The deposition mass $M_S$ as a function of dust volume fraction $C_v$ and particle diameter $d_p$ can be expressed as:
$$M_S = A e^{B C_v} + C e^{D d_p}$$
where $A$, $B$, $C$, and $D$ are constants determined through curve fitting. For example, with $35^\circ$ inclination, we found $A = 10.2$, $B = 0.15$, $C = 5.8$, and $D = 0.08$ for typical desert conditions. Similarly, the transmittance $T$ relative to deposition mass $M$ and particle size $d_p$ is given by:
$$T = \exp \left( -\alpha \frac{M}{d_p} \right)$$
where $\alpha$ is a coefficient that incorporates the transparency factor $\beta$ and dust density. Our analysis yields $\alpha \approx 0.0023$ for the studied photovoltaic panels.
The distribution of dust on the solar panel surface is non-uniform, with higher accumulation near the bottom edge due to the impact of incoming sand-laden flow. As the flow moves upward, deposition decreases, resulting in stratified dust layers. This pattern is more pronounced at higher dust concentrations, leading to localized shading that can hotspots and reduce the overall efficiency of photovoltaic modules. In practical terms, this means that regular cleaning schedules for solar panels in desert areas should account for inclination angles to minimize energy losses.
In discussion, our findings align with previous studies that report exponential decay in photovoltaic performance due to dust. However, our CFD approach provides a more detailed spatial understanding of deposition patterns. The identification of $50^\circ$ as the critical angle for maximum dust accumulation offers valuable guidance for optimizing panel tilt in wind-sand environments. Moreover, the integration of fluid dynamics with light transmittance models allows for predictive maintenance strategies, enhancing the economic viability of solar power in arid regions.
In conclusion, we have successfully simulated the dust deposition process on solar panels under various wind-sand conditions using computational fluid dynamics. Our results demonstrate that dust accumulation increases exponentially with airborn dust concentration and particle size, while the panel inclination angle has a non-monotonic effect, peaking at $50^\circ$. The associated reduction in light transmittance follows similar trends, underscoring the importance of angle selection in photovoltaic system design. These insights contribute to the improved performance and sustainability of solar energy installations in desertified areas, supporting global efforts to transition to renewable energy sources. Future work could explore the effects of panel surface coatings or automated cleaning systems on mitigating dust-related efficiency losses.