As the global demand for renewable energy continues to rise, solar power has emerged as a leading solution, particularly in arid and semi-arid regions where sunlight is abundant. However, these areas often experience high levels of airborne dust, which can accumulate on photovoltaic surfaces and significantly reduce their efficiency. Understanding the dynamics of dust deposition on solar panels is crucial for optimizing the performance and maintenance of photovoltaic systems. In this study, we explore how the spacing between solar panels influences the near-surface flow field and dust accumulation patterns using computational fluid dynamics (CFD) simulations. Our goal is to provide insights that can aid in the design of photovoltaic arrays to minimize dust-related losses.
The accumulation of dust on solar panels is a complex phenomenon influenced by various factors, including wind speed, particle size, and the arrangement of the panels. Previous research has primarily focused on single photovoltaic modules or two-dimensional flow fields, but real-world applications involve arrays of panels where interactions between adjacent units can alter local flow conditions. We extend this work by investigating three-dimensional flow fields around tandem photovoltaic panels, varying the spacing between them to assess its impact on dust deposition. This approach allows us to capture more realistic scenarios and provide practical recommendations for photovoltaic system design.
To simulate the flow field and dust transport, we developed a detailed CFD model based on the Eulerian multiphase framework. The model includes two identical photovoltaic panels inclined at 35 degrees, a common angle for solar installations in many regions. The computational domain was designed to be sufficiently large to avoid boundary effects, with dimensions of 12 m in length, 2.5 m in width, and 3.6 m in height. The solar panels were positioned 0.2 m above the ground, each with a length of 0.6 m, width of 0.35 m, and thickness of 0.03 m. We examined several spacing distances between the panels, denoted as d, ranging from 0.5 m to 1.25 m, to analyze their effects on flow patterns and dust deposition.
The mesh generation was performed using ANSYS ICEM, employing an unstructured hexahedral grid to discretize the domain. The mesh was refined around the photovoltaic surfaces to accurately resolve the complex flow structures in these regions. The total number of grid cells was approximately 1.4 million, ensuring a balance between computational efficiency and accuracy. The grid independence was verified by comparing results with a finer mesh, showing negligible differences in key parameters such as velocity and pressure fields.
For the numerical simulations, we adopted the Realizable k-ε turbulence model within the Eulerian multiphase framework to capture the interactions between the air and dust phases. The governing equations for the flow include the continuity and momentum equations. The continuity equation ensures mass conservation and is given by:
$$\frac{\partial u_i}{\partial x_i} = 0$$
where \( u_i \) represents the velocity components in the i-direction. The momentum equation accounts for forces acting on the fluid and is expressed as:
$$\frac{\partial u_i}{\partial t} + u_j \frac{\partial u_i}{\partial x_j} = -\frac{1}{\rho} \frac{\partial p}{\partial x_i} + \nu \frac{\partial^2 u_i}{\partial x_j \partial x_j} – \frac{\partial \overline{u_i’ u_j’}}{\partial x_j}$$
where \( p \) is the pressure, \( \rho \) is the air density, \( \nu \) is the kinematic viscosity, and \( \overline{u_i’ u_j’} \) is the Reynolds stress tensor representing turbulent fluctuations.
The Realizable k-ε model was used to simulate turbulence, with transport equations for turbulent kinetic energy k and dissipation rate ε:
$$\frac{\partial (\rho k)}{\partial t} + \frac{\partial (\rho k u_j)}{\partial x_j} = \frac{\partial}{\partial x_j} \left[ \left( \mu + \frac{\mu_t}{\sigma_k} \right) \frac{\partial k}{\partial x_j} \right] + G_k – \rho \epsilon$$
$$\frac{\partial (\rho \epsilon)}{\partial t} + \frac{\partial (\rho \epsilon u_j)}{\partial x_j} = \frac{\partial}{\partial x_j} \left[ \left( \mu + \frac{\mu_t}{\sigma_\epsilon} \right) \frac{\partial \epsilon}{\partial x_j} \right] + C_{1\epsilon} \frac{\epsilon}{k} G_k – C_{2\epsilon} \rho \frac{\epsilon^2}{k}$$
where \( \mu_t \) is the turbulent viscosity, \( G_k \) is the generation of turbulent kinetic energy due to mean velocity gradients, and \( C_{1\epsilon} \), \( C_{2\epsilon} \), \( \sigma_k \), \( \sigma_\epsilon \) are model constants with values of 1.44, 1.92, 1.0, and 1.3, respectively.
Boundary conditions were carefully defined to replicate realistic environmental conditions. The inlet velocity profile followed a logarithmic law to simulate the atmospheric boundary layer:
$$U = \frac{u_*}{\kappa} \ln \left( \frac{y}{z_0} \right)$$
where \( u_* \) is the friction velocity (set to 0.3 m/s), \( \kappa \) is the von Kármán constant (0.41), and \( z_0 \) is the roughness length (0.01 m). The dust phase was introduced at the inlet with a volume fraction of \( 5 \times 10^{-4} \% \) and a uniform particle size of 50 μm. The outlet was specified as a pressure outlet, while the ground and panel surfaces were treated as no-slip walls. The top and sides of the domain used symmetry boundaries to simulate an open environment. The SIMPLE algorithm was employed for pressure-velocity coupling, and second-order upwind schemes were used for spatial discretization to ensure accuracy.
We conducted simulations for spacing distances of 0.5 m, 0.75 m, 1.0 m, and 1.25 m between the photovoltaic panels. The flow field analysis revealed that the front panel (denoted as P1) experienced relatively consistent near-surface wind speeds across all spacing configurations, while the rear panel (P2) showed significant variations. The wake generated by P1 altered the flow around P2, with closer spacings leading to greater reductions in wind speed near P2’s surface. This effect diminished as the spacing increased, allowing the flow to recover and approach the freestream conditions.
| Spacing d (m) | Front Panel (P1) Average Speed | Rear Panel (P2) Average Speed |
|---|---|---|
| 0.5 | 8.5 | 6.2 |
| 0.75 | 8.5 | 6.8 |
| 1.0 | 8.5 | 7.2 |
| 1.25 | 8.5 | 7.5 |
The dust deposition on the photovoltaic surfaces was quantified based on the particle concentration in the boundary layer. The deposition mass m was calculated using the formula:
$$m = \rho_{\text{sand}} \int H \, dA$$
where \( \rho_{\text{sand}} \) is the density of sand (approximately 2650 kg/m³), H is the boundary layer height, and dA represents the elemental area with dust volume fraction. The results showed that dust accumulation on P1 was relatively uniform regardless of spacing, whereas P2 exhibited more concentrated deposition patterns, particularly at the center and top regions of the panel. As the spacing increased, the deposition on P2 became more uniform, indicating reduced influence from P1.
| Spacing d (m) | Front Panel Mass m₁ | Rear Panel Mass m₂ | Total Mass mₜ |
|---|---|---|---|
| 0.45 | 0.11 | 0.09 | 0.20 |
| 0.5 | 0.12 | 0.15 | 0.27 |
| 0.75 | 0.12 | 0.13 | 0.25 |
| 1.0 | 0.12 | 0.11 | 0.23 |
| 1.25 | 0.12 | 0.10 | 0.22 |
Our analysis further revealed that the total dust deposition on both photovoltaic panels was minimized at a spacing of 0.45 m. This optimal spacing corresponds to a ratio of spacing to panel height, where the height h is calculated as \( h = w \sin \theta \). For our panels with a width w of 0.35 m and inclination θ of 35°, h is approximately 0.2 m. Thus, the optimal spacing d* is related to the panel dimensions. We extended this investigation to different panel widths while maintaining the same inclination angle, and the results showed a linear relationship between panel width and optimal spacing.
| Panel Width w | Optimal Spacing d* |
|---|---|
| 0.35 | 0.45 |
| 0.4 | 0.52 |
| 0.45 | 0.59 |
| 0.5 | 0.66 |
Using linear regression, we derived the following equation to estimate the optimal spacing for various photovoltaic panel widths:
$$d^* = 1.4 w + 0.05$$
This formula provides a practical tool for designing solar arrays that minimize dust accumulation, thereby enhancing the overall efficiency of photovoltaic systems. The relationship highlights the importance of considering panel geometry in array layout decisions, especially in dust-prone environments.
In addition to spacing, we examined the impact of flow structures on deposition patterns. The formation of vortices and recirculation zones behind the front panel played a significant role in directing dust particles toward the rear panel. At closer spacings, these flow features intensified, leading to higher deposition on P2. As spacing increased, the flow became more streamlined, reducing the entrapment of particles. This behavior is consistent with the principles of fluid dynamics, where obstacle spacing affects wake interactions and particle trajectories.
To further quantify deposition efficiency, we introduced a dimensionless parameter, the deposition coefficient C_d, defined as:
$$C_d = \frac{m}{\rho_{\text{sand}} U_0 A t}$$
where \( U_0 \) is the reference wind speed, A is the surface area of the photovoltaic panel, and t is the time duration. This coefficient helps compare deposition rates across different configurations and can be used in predictive models for dust accumulation on solar panels.
Our findings have important implications for the solar energy industry. By optimizing the spacing between photovoltaic panels, operators can reduce the frequency and cost of cleaning operations while maintaining high energy output. Moreover, the linear relationship between panel width and optimal spacing offers a scalable approach for designing large-scale photovoltaic farms. Future work could explore the effects of variable wind directions, different particle sizes, and the inclusion of multiple rows of panels to develop more comprehensive guidelines.
In conclusion, this study demonstrates that the spacing between solar panels significantly influences the near-surface flow field and dust deposition patterns. Through detailed CFD simulations, we identified an optimal spacing that minimizes total dust accumulation, providing a valuable reference for the design and maintenance of photovoltaic arrays. The insights gained from this research can contribute to improving the efficiency and sustainability of solar power generation in dust-affected regions, supporting the global transition to renewable energy.