In this study, we conduct a comprehensive numerical investigation into the wind pressure characteristics of a large-scale solar panel array using computational fluid dynamics (CFD). The motivation arises from the critical role that wind loads play in the structural design of photovoltaic (PV) support systems, particularly in open desert and gobi terrains where most solar farms are located. Accurate determination of wind load coefficients directly influences the safety and economy of the support structures. Our work focuses on a regularly arranged solar panel array consisting of 10 rows and 10 columns, each panel tilted at a fixed elevation angle of θ = 35°. We simulate twelve wind directions ranging from γ = 0° to 180° in 15° increments. The results reveal significant spatial variation of wind pressure coefficients across the array due to shielding effects. Based on the data, we propose a regional division of the array with corresponding reduction factors for the shape coefficients, which can lead to considerable economic benefits in practical engineering design.
The computational domain is set to 1000 m × 600 m × 55 m, with the solar panel array placed at one‑third of the length from the inlet. The blockage ratio is 0.6%, well within acceptable limits. The domain is divided into three sub‑regions: a fine mesh around the panels (sub‑domain 1), a cylindrical region of radius 360 m containing the array (sub‑domain 2), and the outer region (sub‑domain 3). Sub‑domain 2 uses tetrahedral elements for flexibility, while sub‑domains 1 and 3 employ structured hexahedral meshes with local refinement to capture boundary layers. The total mesh count is approximately 14 million cells. Boundary conditions include a velocity inlet with a freestream wind speed of 37 m/s, symmetry at the lateral and top boundaries, and a pressure outlet at the outflow. The ground roughness is set as Class B (smooth wall), and the panels are modeled as rough no‑slip walls. The RNG k‑ε turbulence model is adopted, with second‑order upwind discretization for momentum, turbulent kinetic energy, and dissipation rate, and the SIMPLEC algorithm for pressure‑velocity coupling.
The wind pressure coefficient at any monitoring point on a panel surface is defined as:
$$
C_{p,i} = \frac{P_{f,i} – P_{\infty}}{\frac{1}{2} \rho v_0^2}
$$
where \(P_{f,i}\) is the static pressure at the measurement point, \(P_{\infty}\) is the reference static pressure, \(v_0\) is the freestream wind speed, and \(\rho\) is the air density. The overall shape coefficient for a given panel is obtained by area‑weighted averaging:
$$
\mu_s = \frac{\sum_{i} C_{p,i} \cdot A_i}{\sum_{i} A_i}
$$
Here, \(A_i\) is the surface area associated with the pressure tap \(i\). This weighted approach ensures that regions of larger area contribute proportionally to the total force.
The array arrangement is depicted in the schematic (not reproduced here). Each solar panel is 20 m long and 3.3 m wide, with a tilt angle of 35°. The clear spacing between front and back rows is set to 13 m, which is typical for high‑latitude regions such as Xinjiang, and also represents a conservative case where shielding is most pronounced. The lower edge of the panels is 0.3 m above the ground. Walkways of 1.5 m width are placed between columns, and the gap between adjacent panels in the same row is 150 mm (simplified in the model). The array is arranged in 10 rows and 10 columns, forming a square matrix.
We performed simulations for twelve wind directions: 0°, 15°, 30°, 45°, 60°, 75°, 105°, 120°, 135°, 150°, 165°, and 180°. The range 0°–90° corresponds to positive pressure (wind striking the front face), while 90°–180° corresponds to negative pressure (wind striking the rear face). The results show that the shape coefficients vary significantly across the array due to mutual shielding. For brevity, we present only the most representative cases below.
At a wind direction of 0° (wind perpendicular to the panel rows), the first row experiences the largest shape coefficient, averaging 0.93. The second row is deeply affected by the wake of the first row, resulting in much smaller coefficients, with some panels even showing negative values. From row 2 to row 10, the coefficients are far smaller than those of the first row. Edge panels in the array generally have larger coefficients than interior panels. The central region of the array exhibits very low coefficients, around 0.13, and they are nearly uniform.
At 30°, the first row and the first column show elevated coefficients due to flow separation at the walkways. The panel at position (row 1, column 1) reaches 1.1, which is higher than at 0°. However, the average coefficient of the first row is lower than at 0°, while the average of the first column is higher, indicating a stronger shielding effect from the column. Coefficients gradually decrease along the wind direction.
At 60°, the trend is similar, with the first column averaging 0.86, significantly larger than the first row average of 0.52. The remaining panels average only 0.1. Again, coefficients decrease along the wind direction.
At 75°, because the wind direction is nearly parallel to the panel surface, coefficients are much smaller. The first column averages 0.24, while other panels average only 0.04.
At 120° (wind from the rear), the rear face of the panels is exposed. The panels at the upstream edges (first column and tenth row) experience the strongest forces. The first column averages 0.82, while the tenth row averages 0.45. The second and fourth columns show slightly higher values (0.3 and 0.25) than the inner columns, which average only 0.08.
At 150°, the tenth row average rises to 1.3, much larger than the 0.45 observed at 120°. The corner panel (row 10, column 1) reaches a maximum of 1.72. This extreme local coefficient is critical for structural design, as neglecting corner reinforcement could lead to wind‑induced damage.
At 180°, the coefficient distribution is symmetric. The tenth row averages 1.34, slightly larger than at 150°, but the corner peak (row 10, column 1) is 1.3, lower than the 150° case. The edge panels are consistently larger than interior ones.
To provide quantitative guidance, we tabulate the maximum shape coefficient for each panel across all wind directions from 0° to 180°. The values are obtained by taking the envelope of all 12 wind angles for each panel position.
| Row\Column | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 1.13 | 0.95 | 1.02 | 0.95 | 1.05 | 0.95 | 1.05 | 0.94 | 0.99 | 0.89 |
| 2 | 1.05 | 0.34 | 0.22 | 0.29 | 0.19 | 0.15 | 0.24 | 0.12 | 0.20 | 0.36 |
| 3 | 1.02 | 0.36 | 0.39 | 0.25 | 0.20 | 0.23 | 0.19 | 0.23 | 0.17 | 0.37 |
| 4 | 1.01 | 0.32 | 0.46 | 0.25 | 0.21 | 0.16 | 0.23 | 0.18 | 0.20 | 0.40 |
| 5 | 1.01 | 0.50 | 0.41 | 0.24 | 0.18 | 0.23 | 0.20 | 0.23 | 0.22 | 0.41 |
| 6 | 1.00 | 0.63 | 0.26 | 0.24 | 0.26 | 0.20 | 0.15 | 0.20 | 0.13 | 0.38 |
| 7 | 0.99 | 0.40 | 0.30 | 0.23 | 0.31 | 0.15 | 0.29 | 0.19 | 0.30 | 0.21 |
| 8 | 0.99 | 0.31 | 0.28 | 0.37 | 0.29 | 0.46 | 0.27 | 0.43 | 0.25 | 0.37 |
| 9 | 0.98 | 0.31 | 0.26 | 0.29 | 0.30 | 0.25 | 0.28 | 0.24 | 0.29 | 0.23 |
| 10 | 1.72 | 1.40 | 1.58 | 1.35 | 1.61 | 1.34 | 1.63 | 1.33 | 1.54 | 1.30 |
From the table, it is clear that the edge panels, especially those at the windward corners (row 10, column 1 for negative pressures; row 1, column 1 for positive pressures), have the highest coefficients. The interior panels (rows 2–9, columns 2–9) show much lower values, typically below 0.4. This observation motivates the need for a regional reduction scheme.
For wind directions in the range 0°–90°, the average shape coefficient of the outer windward panels is 0.92, which is consistent with the Chinese load code GB 50009 (0.9) and the Japanese design guide (0.96), but lower than the value of 1.3 given in the PV power station design code GB 50797. For wind directions in the range 90°–180°, the windward outer panels (now on the rear side) have an average coefficient of 1.26, in good agreement with GB 50797 (1.3) and the Japanese guide (1.27), but higher than the GB 50009 value (1.0).
Based on the distribution pattern and engineering convenience, we divide the array into two zones:
- Zone A: The outermost row and column (i.e., all panels in row 1, row 10, column 1, and column 10).
- Zone B: The remaining interior panels (rows 2–9, columns 2–9).
Taking the shape coefficient of 1.3 recommended by GB 50797 as a baseline (this is commonly used in Chinese PV design), we calculate the reduction factor for each zone as the ratio of the actual envelope coefficient to 1.3. For Zone A, the envelope values are close to or exceed 1.3, so no reduction is applied (factor = 1.0). For Zone B, the interior panels have much smaller coefficients; the maximum envelope value among interior panels is typically around 0.62 (e.g., panel row 2, column 6 reaches 0.63). To be conservative, we propose a reduction factor of 0.48, which corresponds to an average coefficient of approximately 0.62 for the most loaded interior panels. This factor is derived from the ratio of the average maximum interior coefficient (0.62) to the baseline 1.3, but we round it to a safe value for design.
| Wind direction range | Zone A (outer edge) | Zone B (interior) |
|---|---|---|
| 0°–180° | 1.00 | 0.48 |
We emphasize that the reduction factor of 0.48 for Zone B applies for all wind directions. This is because, regardless of wind angle, the interior panels are always shielded by the surrounding panels at the array periphery. The proposed factor can lead to significant material savings in the design of support structures for large solar farms, as only the perimeter panels require full wind resistance.
Our numerical results show that for wind directions 90°–180°, the average shape coefficient of the tenth row (1.48) is higher than both the GB 50009 value (1.0) and GB 50797 value (1.3). Moreover, at 150°, the corner panel (row 10, column 1) exhibits an extreme coefficient of 1.72. Therefore, in practical design, special attention must be given to the negative‑pressure windward edges, particularly the corners, to avoid structural failure. Reinforcement measures such as stronger brackets or additional anchoring should be applied to these vulnerable locations.
In summary, we have performed a systematic numerical study of wind pressure characteristics on a 10×10 solar panel array with a tilt angle of 35° and row spacing of 13 m. Key conclusions are:
- For wind directions 0°–90°, the windward outer panels have shape coefficients averaging 0.92, consistent with GB 50009 and Japanese guidelines but lower than GB 50797. For 90°–180°, the coefficients of the outer panels average 1.26, in line with GB 50797 and Japanese values, but higher than GB 50009.
- The tenth row experiences particularly high coefficients for oblique rear winds (150°), with a peak of 1.72 at the corner. Structural reinforcement of these panels is necessary.
- The interior panels (Zone B) are substantially shielded, with coefficients far lower than those at the edges. Using the GB 50797 baseline of 1.3, we recommend a reduction factor of 0.48 for the interior region, which can yield considerable economic benefits in large‑scale solar projects.
Our findings are based on numerical simulations; further validation through wind tunnel tests is recommended to ensure the reliability of the proposed design guidelines.