The accumulation of dust on solar panels presents a significant challenge for photovoltaic power generation, particularly in arid and desertified regions. These areas, while offering abundant solar resources, are often characterized by frequent wind-blown sand events. The deposition of particulate matter on the panel surface directly reduces light transmittance, leading to a substantial decline in power conversion efficiency. Consequently, accurately predicting and mitigating dust accumulation is critical for optimal power plant design, realistic energy yield forecasting, and effective operational maintenance strategies. The local aerodynamic environment around a solar panel array is a primary driver of dust transport and deposition. Therefore, a detailed investigation into the flow field structures induced by different panel configurations is essential. This study employs computational fluid dynamics (CFD) to analyze the three-dimensional flow field and subsequent particle deposition on a two-panel array, focusing specifically on the impact of the inter-panel spacing.
The foundation of the numerical analysis lies in solving the governing equations of fluid motion. The wind field is described by the incompressible Reynolds-Averaged Navier-Stokes (RANS) equations. The continuity and momentum conservation equations are given by:
$$
\frac{\partial u_i}{\partial x_i} = 0
$$
$$
\frac{\partial u_i}{\partial t} + u_j \frac{\partial u_i}{\partial x_j} = -\frac{1}{\rho}\frac{\partial p}{\partial x_i} + \nu \frac{\partial^2 u_i}{\partial x_j \partial x_j} – \frac{\partial \overline{u_i’ u_j’}}{\partial x_j}
$$
where \( u_i \) represents the mean velocity components, \( p \) is the mean pressure, \( \rho \) is the air density, \( \nu \) is the kinematic viscosity, and the term \( -\rho \overline{u_i’ u_j’} \) denotes the Reynolds stress tensor, which must be modeled to close the system of equations. For this study, the Realizable \( k-\epsilon \) turbulence model was selected for its improved performance in simulating flows with separation and recirculation. The transport equations for turbulent kinetic energy \( k \) and its dissipation rate \( \epsilon \) are:
$$
\begin{aligned}
\frac{\partial (\rho k)}{\partial t} + \frac{\partial (\rho k u_j)}{\partial x_j} &= \frac{\partial}{\partial x_j}\left[\left(\mu + \frac{\mu_t}{\sigma_k}\right) \frac{\partial k}{\partial x_j}\right] + G_k + G_b – \rho \epsilon – Y_M \\
\frac{\partial (\rho \epsilon)}{\partial t} + \frac{\partial (\rho \epsilon u_j)}{\partial x_j} &= \frac{\partial}{\partial x_j}\left[\left(\mu + \frac{\mu_t}{\sigma_\epsilon}\right) \frac{\partial \epsilon}{\partial x_j}\right] + \rho C_1 S \epsilon – \rho C_2 \frac{\epsilon^2}{k + \sqrt{\nu \epsilon}} + C_{1\epsilon}\frac{\epsilon}{k}C_{3\epsilon}G_b
\end{aligned}
$$
Here, \( \mu_t \) is the turbulent viscosity, \( G_k \) and \( G_b \) represent the generation of turbulence kinetic energy due to mean velocity gradients and buoyancy, respectively, \( Y_M \) accounts for fluctuating dilatation, and \( C_1, C_2, \sigma_k, \sigma_\epsilon, C_{1\epsilon}, C_{3\epsilon} \) are model constants. The particle phase was modeled using a Eulerian multiphase approach, where dust particles are treated as a secondary continuum phase interacting with the primary air phase. The particle deposition flux on the solar panel surface is a function of the local near-wall particle concentration and velocity. The total dust mass \( m_{dep} \) accumulated over a surface area \( A \) can be estimated by integrating the particle mass flux:
$$
m_{dep} = \int_{A} \int_{H} \alpha_p \rho_p \, dz \, dA
$$
where \( \alpha_p \) is the local volume fraction of the particle phase, \( \rho_p \) is the intrinsic density of the dust particles, and \( H \) represents the height of the concentration boundary layer above the surface. The simulation domain was constructed to model two identical, tilted solar panels with an inclination angle \( \theta = 35^\circ \), a length \( l = 0.6 \, \text{m} \), and a width \( w = 0.35 \, \text{m} \). The panels were mounted at a height of 0.2 m above the ground. The key variable was the center-to-center spacing \( d \) between the two panels. Multiple configurations were analyzed, with spacing ratios \( d/h \) (where \( h = l \sin \theta \approx 0.2 \, \text{m} \) is the vertical height of the panel) ranging from approximately 2.25 to 6.25. The inlet wind profile was prescribed using a logarithmic law of the wall to simulate a realistic atmospheric boundary layer:
$$
U(z) = \frac{u_*}{\kappa} \ln\left(\frac{z}{z_0}\right)
$$
where \( U(z) \) is the velocity at height \( z \), \( u_* \) is the friction velocity, \( \kappa \) is the von Kármán constant, and \( z_0 \) is the surface roughness length. A uniform dust volume fraction of \( 5 \times 10^{-6} \) with a monodisperse particle diameter of 50 μm was specified at the inlet. The boundaries were set as follows: a no-slip wall condition for the ground and panel surfaces, a pressure outlet at the downstream boundary, and symmetry conditions on the lateral and top boundaries to minimize domain size effects. The mesh was highly refined around the solar panels to resolve the critical boundary layer and wake regions.
The simulation results reveal a profound influence of the leading solar panel on the aerodynamic environment of the trailing panel. The flow field around the upstream (first) panel remained relatively consistent across different spacing values, characterized by flow stagnation at the lower edge, acceleration over the top surface, and a region of flow separation and recirculation in the immediate wake. However, the flow encountered by the downstream (second) solar panel was drastically modified. At small inter-panel spacing, the second panel was immersed in the low-velocity, highly turbulent wake of the first. This significantly reduced the wind speed magnitude across its entire surface compared to the isolated or widely-spaced condition. As the spacing \( d \) increased, the flow had more distance to recover, leading to higher wind speeds at the second panel’s leading edge. The near-surface wind speed profiles along the centerline of each panel clearly demonstrate this effect. While the profile for the first panel showed minimal variation with spacing, the profile for the second panel exhibited a strong dependency, with both the magnitude and the location of the stagnation point shifting.
The altered flow field directly governs the dust deposition patterns and total mass accumulated on each solar panel. The deposition on the first panel was largely insensitive to the spacing, showing a relatively uniform distribution across its surface. In contrast, the deposition on the second panel was highly non-uniform and spacing-dependent. At close spacing, dust accumulation was concentrated in specific zones, particularly on the upper-central region of the panel, corresponding to areas of low flow velocity and specific particle trajectories within the complex wake. As spacing increased, the deposition pattern on the second panel became more uniform, resembling that of an isolated panel, but the total mass remained affected. The quantitative analysis of total deposited dust mass yields the most critical finding for system optimization. The total mass deposited on the two-panel array as a function of spacing is non-monotonic.
The following table summarizes the key deposition metrics for different spacing configurations:
| Spacing, d (m) | Spacing Ratio (d/h) | Mass on Panel 1, m₁ (arb. units) | Mass on Panel 2, m₂ (arb. units) | Total Mass, m₁ + m₂ (arb. units) |
|---|---|---|---|---|
| 0.40 | 2.00 | 1.02 | 1.65 | 2.67 |
| 0.45 | 2.25 | 1.01 | 1.25 | 2.26 |
| 0.50 | 2.50 | 1.03 | 1.40 | 2.43 |
| 0.55 | 2.75 | 0.99 | 1.55 | 2.54 |
| 0.75 | 3.75 | 1.04 | 1.60 | 2.64 |
| 1.00 | 5.00 | 1.02 | 1.63 | 2.65 |
| 1.25 | 6.25 | 1.01 | 1.62 | 2.63 |
The data indicates that a distinct minimum in total array deposition occurs at a specific spacing, identified here at \( d = 0.45 \, \text{m} \) ( \( d/h \approx 2.25 \) ). This optimal spacing represents a compromise where the wake interaction between the solar panels modifies the flow in a way that minimizes the particle residence time and deposition efficiency over the combined surface area of both panels. At closer spacing, the second panel’s high deposition outweighs any minor reduction on the first. At larger spacing, while the second panel’s deposition decreases slightly, the benefit is offset by the loss of the synergistic flow effect that reduced deposition at the optimal point. This finding is crucial for maximizing the energy output of a solar panel array under soiling conditions, as it suggests an arrangement that naturally mitigates dust buildup. Furthermore, the relationship between the optimal spacing \( d^* \) and the physical dimensions of the solar panel can be generalized. For a fixed tilt angle, the optimal spacing scales linearly with the panel’s characteristic width or height. A derived correlation based on parametric studies can be expressed as:
$$
d^* = C \cdot w
$$
or, more fundamentally,
$$
\frac{d^*}{h} = K
$$
where \( C \) and \( K \) are constants dependent on the tilt angle \( \theta \) and inflow conditions. For \( \theta = 35^\circ \), the analysis suggests \( K \approx 2.25 \). This provides a practical design rule: the optimal center-to-center spacing between rows of solar panels should be approximately 2.25 times the vertical height of a single panel to minimize combined soiling losses for this configuration. It is important to contextualize these simulation results with real-world conditions. In the field, dust deposition on a solar panel is influenced by a multitude of additional factors not captured in this steady-state simulation, such as time-varying wind speed and direction, humidity, particle adhesion and cohesion forces, rainfall, and complex terrain. For instance, long-term natural soiling often leads to a more uniform distribution across a single panel surface, as deposition occurs from multiple wind directions over time. However, the fundamental aerodynamic principle revealed—that wake interference can be tuned to minimize deposition—remains valid. The optimal spacing identified here is likely a lower bound for a prevailing wind direction; actual array layout must consider seasonal wind roses. The non-uniform deposition pattern predicted for the downstream solar panel under unidirectional flow is a significant finding, as localized heavy soiling can contribute to the formation of hot spots, potentially accelerating the degradation of the photovoltaic cells and leading to permanent power loss or safety hazards.
In conclusion, this numerical investigation demonstrates that the spacing within a solar panel array is a critical design parameter that significantly influences the near-surface flow field and, consequently, the dust deposition characteristics. The aerodynamic wake from an upstream solar panel drastically alters the environment for a downstream panel, primarily reducing its surface wind speed in a spacing-dependent manner. This interaction leads to a non-linear relationship between inter-panel spacing and total dust accumulation on the array. Importantly, an optimal spacing exists that minimizes the combined soiling mass for the two-panel system. For panels tilted at \( 35^\circ \), this optimal spacing was found to be approximately 2.25 times the vertical height of the panel. This result provides a valuable theoretical guideline for optimizing the layout of solar panel arrays in dust-prone environments. By strategically determining the distance between rows based on panel geometry and tilt, it is possible to leverage aerodynamic effects to naturally reduce the rate of dust accumulation, thereby enhancing the long-term energy yield and reducing the frequency and cost of cleaning operations. Future work should extend this analysis to full multi-row arrays, incorporate transient and multidirectional wind effects, and validate the findings through controlled wind tunnel experiments and long-term field monitoring at operational solar power plants.