In the construction of large-scale photovoltaic power stations, the mutual shielding among solar panels significantly influences the wind loads they experience. Understanding this group shielding effect is crucial for optimizing the structural design of support frames, reducing steel consumption, and improving economic efficiency. In this study, I employ Computational Fluid Dynamics (CFD) using the Reynolds-Averaged Navier-Stokes (RANS) approach to systematically investigate the wind load shape coefficients of both fixed and tracking solar panel arrays under various pitch angles and wind directions. The goal is to quantify how the presence of upstream panels modifies the pressure distribution on downstream panels, and to provide guidance for differentiated design strategies.
1. Introduction
The wind load is a dominant factor in the design of solar panel support structures. In typical photovoltaic (PV) power plants, arrays are densely arranged with small row-to-row spacings, leading to significant aerodynamic interference between panels. For the same basic wind pressure, the shape coefficient directly determines the magnitude of the wind load. Therefore, accurately evaluating the group shielding effect can allow designers to reduce safety margins for downstream panels, thereby decreasing the overall steel weight. Traditional wind tunnel tests are expensive and time-consuming; CFD offers a flexible, cost-effective alternative that can simulate full-scale models under controlled conditions. This study uses the commercial code FLUENT 14 to analyze the pressure coefficients on arrays of fixed and tracking solar panels.
2. Numerical Model Setup
2.1 Geometry and Configuration
Two types of solar panels are considered: fixed panels and tracking (solar tracker) panels. The fixed panel dimensions are 2.18 m (width) × 3.32 m (height) (B × L), following typical Chinese PV standards. In most calculations, arrays of 5 rows and 1 column (5×1) or 5 rows and 2 columns (5×2) are used. The minimum edge height above ground is 500 mm. Row spacing (front-to-back) is 7 m, and column spacing (side-to-side) is 200 mm for fixed panels. For tracking panels, dimensions are 4 m × 3 m, with row spacing 7 m and column spacing 11 m (larger gap for tracking mechanism). The pitch angle θ (tilt angle) ranges from 0° to 40°, and wind azimuth angles γ include 0°, 45°, 90°, 135°, and 180°.
2.2 Computational Domain and Mesh
For the fixed 5×1 array, the fine computational domain extends 5H upstream, 10H downstream, 5D laterally on each side, and 10H vertically, where H is the panel height and D is the panel width. The total domain is large enough to avoid blockage effects. For wind directions of γ=0° and 180°, a fully structured hexahedral mesh is used, with cells gradually increasing in size away from the panel surfaces. For γ=45° and 135°, an unstructured mesh with prisms near walls is applied. The mesh density ensures that y+ values are within the log-law region. The total number of cells varies between 2 million and 4 million depending on the configuration.
2.3 Boundary Conditions and Turbulence Model
The inlet velocity profile follows a power law corresponding to Terrain Category B (exponent 0.16). However, to reduce the Reynolds number and improve turbulence model accuracy, the inlet speed is scaled to 27 m/s at reference height, resulting in a Reynolds number based on panel chord of about 5×10⁵. Turbulence intensity is set as I(z) = 0.23 at reference height. The turbulent kinetic energy k and dissipation rate ε are specified using empirical relations: k = 57.85 m²/s² and ε = 344.3 m²/s³. The outlet uses pressure outlet, sides and top use symmetry, and the panel surfaces and ground use no-slip walls with standard wall functions. The RNG k-ε model is employed for its improved performance in flows with separation and recirculation. The SIMPLEC algorithm handles pressure-velocity coupling. Second-order upwind discretization is used for momentum, k, and ε. Convergence is achieved after about 8000 iterations with residuals below 10⁻⁴.
2.4 Derivation of Shape Coefficients
The wind pressure coefficient Cp is obtained from CFD as
$$C_p = \frac{p – p_0}{0.5 \rho U_{ref}^2}$$
where p is the static pressure on the panel surface, p0 is the reference static pressure, ρ is air density (1.225 kg/m³), and Uref is the reference wind speed at 10 m height. Since the height of the panels is less than 10 m, the height variation factor for Terrain B is unity. Hence, the shape coefficient μs equals Cp directly. The final shape coefficient for each panel is the area-weighted average of Cp over the panel surface. Positive values indicate windward pressure (toward the panel), negative values indicate suction (away from the panel).
3. Results for Fixed Solar Panel Arrays
3.1 Effect of Pitch Angle at γ=180°
At wind direction γ=180° (wind blowing from front to back, i.e., normal to the first row), I examine pitch angles θ=0°, 10°, and 40° for a 5×1 array. Table 1 summarizes the shape coefficients for each row. At θ=0°, the panels are nearly horizontal, and the entire array experiences very small suction forces (≈ -0.01). As θ increases to 10°, the first row experiences a moderate pressure (0.47), while subsequent rows show decreasing values. At θ=40°, the first row has a high positive coefficient of 0.97, but the second row drops to -0.13 (suction), and the third to fifth rows stabilize around 0.10–0.13. This indicates that the shielding effect is much stronger at larger pitch angles. The second row is in the recirculation zone behind the first row, leading to negative pressure. For smaller pitch angles, the wake is less pronounced.
| Row | θ = 0° | θ = 10° | θ = 40° |
|---|---|---|---|
| 1 | -0.01 | 0.47 | 0.97 |
| 2 | -0.007 | 0.32 | -0.13 |
| 3 | -0.006 | 0.22 | 0.10 |
| 4 | -0.005 | 0.17 | 0.12 |
| 5 | -0.004 | 0.15 | 0.13 |
It is clear that the ratio of the fifth row to the first row is about 32% at θ=10° and only 13.4% at θ=40°, confirming that the group shielding effect is more significant at higher tilt angles. The velocity vector plot at θ=40°, γ=180° shows a large vortex behind the first panel, causing suction on the second panel. Beyond the second row, the flow reattaches and pressures become slightly positive.
3.2 Effect of Wind Direction at θ=40°
Now I fix the pitch angle at 40° and vary the wind direction: γ=0°, 45°, 90°, 135°, 180°. Table 2 lists the shape coefficients for a 5×1 fixed array. Note that γ=0° means wind blowing from the back of the panels (i.e., approaching from the rear), which typically creates large suction on the first row. Indeed, at γ=0°, the first row has μs = -1.24 (strong suction). The second row shows 0.15 (pressure), and rows 3–5 gradually decrease to around -0.05. At γ=180°, as discussed, the first row has 0.97 (pressure) and the second row -0.13. At oblique directions γ=45° and 135°, the values are intermediate: the first row experiences about -0.98 and 0.66 respectively, and the downstream rows are around 0.37–0.46 for the second row, then stabilize near 0.42–0.46. The pattern is that the windward face of the first array always experiences the largest magnitude, and the second row has the minimum (often changing sign). From the third row onward, values converge to a nearly constant level, indicating that after two rows the flow becomes fully developed.
| Row | γ=0° | γ=45° | γ=135° | γ=180° |
|---|---|---|---|---|
| 1 | -1.24 | -0.98 | 0.66 | 0.97 |
| 2 | 0.15 | -0.42 | 0.37 | -0.13 |
| 3 | -0.11 | -0.46 | 0.42 | 0.10 |
| 4 | -0.05 | -0.47 | 0.46 | 0.12 |
| 5 | -0.04 | -0.46 | 0.46 | 0.13 |
3.3 Effect of Column Number at γ=135°
To examine the influence of multiple columns, I simulate a 5×2 fixed array at θ=40°, γ=135°. The two columns are separated by a gap of 200 mm. Table 3 compares the shape coefficients for the windward column (first encountered by wind) and the leeward column. The wind direction is oblique from the front-left. The first row of the windward column shows a coefficient of 0.78, while the leeward column has a lower value of 0.47. For rows 2–5, the windward column values are around 0.40–0.49, and the leeward column values are much smaller, around 0.04, indicating strong shielding from the windward column when the columns are closely spaced. Interestingly, the values of the windward column in the 5×2 array are very similar to those of the 5×1 array (0.66, 0.37, 0.42, 0.46, 0.46) if we consider the average of the two columns? Actually, the 5×1 for γ=135° gave 0.66 for row1, 0.37 for row2, etc. In the 5×2 array, the windward column has 0.78, 0.40, 0.46, 0.49, 0.49, which are slightly higher. This is because the two columns act as a single wider panel, increasing the effective width-to-height ratio, which tends to increase shape coefficients. The leeward column, however, benefits from the shelter of the windward column and experiences much lower loads.
| Row | Windward column | Leeward column |
|---|---|---|
| 1 | 0.78 | 0.47 |
| 2 | 0.40 | 0.04 |
| 3 | 0.46 | 0.04 |
| 4 | 0.49 | 0.04 |
| 5 | 0.49 | 0.04 |
4. Results for Tracking Solar Panel Arrays
Tracking solar panels (solar trackers) have a larger aspect ratio and greater spacing between columns (11 m) compared to fixed panels. Table 4 presents the shape coefficients for a 5×2 tracking array at θ=40° for wind directions γ=0°, 45°, 135°, and 180°. Note that the geometry is different: each panel is 4 m × 3 m, and the gaps are larger, so the aerodynamic interaction is weaker.
| Row | γ=0° (col1/col2) | γ=45° (col1/col2) | γ=135° (col1/col2) | γ=180° (col1/col2) |
|---|---|---|---|---|
| 1 | -1.10 / -1.10 | -1.06 / -0.69 | 0.99 / 0.69 | 1.10 / 1.10 |
| 2 | -0.32 / -0.33 | -1.06 / -0.56 | 0.99 / 0.58 | 0.35 / 0.25 |
| 3 | -0.74 / -0.78 | -1.06 / -0.56 | 0.99 / 0.58 | 0.58 / 0.49 |
| 4 | -0.70 / -0.68 | -1.10 / -0.56 | 1.01 / 0.61 | 0.67 / 0.63 |
| 5 | -0.68 / -0.67 | -1.10 / -0.56 | 1.01 / 0.61 | 0.67 / 0.63 |
At γ=0° (wind from rear), the first row of tracking panels experiences a suction of -1.10, which is similar in magnitude to fixed panels (-1.24). The second row shows only -0.32 (suction), much less than the fixed panel case (0.15 pressure). The third to fifth rows have values around -0.7, indicating that for tracking arrays, the shielding effect is less pronounced: the pressures do not diminish as sharply. This is because the large gap between columns allows wind to flow through, reducing the sheltering. At γ=180° (wind from front), the first row has a positive pressure of 1.10, and the second row also shows positive pressure (0.35 for column1, 0.25 for column2), quite different from the fixed panels where the second row was in suction. The positive pressure indicates that the recirculation zone is weaker due to the larger gaps.
At oblique angles γ=45° and 135°, the tracking panels show distinctive behavior. For γ=45°, the first row of the windward column (col1) has -1.06, and the leeward column (col2) has -0.69. The second row of col1 is also -1.06, indicating almost no reduction from row1 to row2; this is because the oblique wind can pass through the gaps and load the second row almost as heavily as the first. In contrast, for fixed panels at γ=45°, the second row had -0.42, a significant reduction. For γ=135°, similar trends are observed: the first row of the windward column has 0.99, and the second row also has 0.99, again showing minimal shielding. The leeward column values are about 0.58–0.61, which are higher than the fixed panel leeward column (0.04). Overall, the tracking panel arrays experience larger shape coefficients on downstream rows compared to fixed arrays, meaning the group shielding effect is much weaker for trackers.
5. Comparative Analysis and Discussion
To summarize the key findings, I compare the shape coefficients of fixed and tracking solar panels under identical conditions (θ=40°, γ=45° and 135°). Table 5 provides a side-by-side comparison of the first two rows of a 5×1 fixed array and a 5×2 tracking array (windward column). At γ=45°, the first row of fixed is -0.98, tracking is -1.06 (slightly larger magnitude). The second row of fixed is -0.42 (reduction of 57%), but tracking is still -1.06 (no reduction). At γ=135°, the first row is 0.66 vs. 0.99; the second row is 0.37 vs. 0.99. Clearly, tracking panels provide very poor shielding for downstream rows because of the large inter-column spacing (11 m) and the smaller width-to-height ratio (B/L = 4/3 ≈ 1.33) compared to fixed panels (B/L = 2.18/3.32 ≈ 0.66). The larger gaps allow wind to penetrate and load all rows almost equally.
| Row | γ=45° | γ=135° | ||
|---|---|---|---|---|
| Fixed | Tracking | Fixed | Tracking | |
| 1 | -0.98 | -1.06 | 0.66 | 0.99 |
| 2 | -0.42 | -1.06 | 0.37 | 0.99 |
Another important observation is the behavior at normal wind directions (γ=0° and 180°). For fixed panels, the second row always has the minimum shape coefficient (often negative) because the large, closely spaced panels create a strong wake. For tracking panels, the second row may still have a positive coefficient (at γ=180°) or a smaller negative value (at γ=0°), indicating that the wake is weaker. The size of the separated region behind a solar panel is strongly influenced by the panel’s aspect ratio and the spacing to the next row. The fixed panels, with a smaller gap (7 m row spacing) and smaller width-to-height ratio, generate a longer wake that persists for multiple rows.
6. Design Recommendations
Based on the numerical results, I propose the following:
- For fixed solar panel arrays, the group shielding effect is significant, especially at large pitch angles (≥40°). The second row experiences the smallest loads, and from the third row onward values stabilize at about 10–15% of the first row’s magnitude (for γ=180°). Therefore, a differentiated design is justified: the first row (and possibly the second row if it experiences suction) should be reinforced, while downstream rows can be designed with lighter supports. This can lead to substantial steel savings.
- For tracking solar panel arrays, the shielding effect is weak due to large inter-column gaps and smaller width-to-height ratios. The loads on all rows are relatively uniform, especially at oblique wind directions. Hence, a uniform design for all rows is appropriate, and the benefits of differentiated design are limited.
- The wind direction has a strong influence. At γ=0° (wind from rear), the first row experiences high suction, which can be critical for uplift resistance. At γ=180°, the first row experiences high pressure. Designers should consider the worst-case combination.
- The presence of multiple columns (e.g., 5×2) can further increase loads on the windward column due to the effective increase in panel width. The leeward column benefits from shielding but the magnitude depends on the gap size. For fixed panels with small gaps, the leeward column loads are very low; for trackers with large gaps, the leeward column still experiences moderate loads.
7. Conclusions
In this study, I performed CFD simulations to investigate the group shielding effects on wind load shape coefficients of solar panel arrays. The main conclusions are:
- At wind direction γ=180°, the shielding effect is stronger at larger pitch angles. For θ=40°, the second row exhibits a negative shape coefficient (suction), while the third to fifth rows have small positive values around 0.10–0.13, about 13% of the first row. For θ=10°, the reduction is only to 32%.
- At both γ=0° and γ=180°, the second row always has the minimum shape coefficient. Beyond the third row, the values become nearly constant. This supports the idea of designing only the first two rows for the maximum load.
- For oblique wind directions (γ=45° and 135°), the first row still experiences the largest magnitude, but the downstream rows show roughly 50–60% of the first row’s value for fixed panels. For tracking panels, the downstream rows show almost no reduction due to the large gaps, with values up to 100% of the first row.
- Tracking solar panel arrays have larger shape coefficients than fixed arrays under the same conditions, and the shielding effect is poor. Therefore, differentiated design for trackers is not effective.
- The numerical methodology using the RNG k-ε turbulence model, structured/unstructured meshes, and appropriate boundary conditions can reliably predict these interference effects. Future work could include validation with wind tunnel tests and extension to different panel layouts and terrains.
Appendix: Governing Equations and Turbulence Model
The incompressible Reynolds-averaged Navier-Stokes equations are:
$$
\frac{\partial U_i}{\partial x_i} = 0
$$
$$
\rho \frac{\partial U_i U_j}{\partial x_j} = -\frac{\partial p}{\partial x_i} + \frac{\partial}{\partial x_j}\left[ (\mu + \mu_t)\left( \frac{\partial U_i}{\partial x_j} + \frac{\partial U_j}{\partial x_i} \right) \right]
$$
where Ui is the mean velocity, p is the mean pressure, μ is dynamic viscosity, and μt is turbulent viscosity. The RNG k-ε model solves transport equations for turbulent kinetic energy k and dissipation rate ε:
$$
\frac{\partial (\rho k U_j)}{\partial x_j} = \frac{\partial}{\partial x_j}\left( \alpha_k \mu_{eff} \frac{\partial k}{\partial x_j} \right) + G_k – \rho \epsilon
$$
$$
\frac{\partial (\rho \epsilon U_j)}{\partial x_j} = \frac{\partial}{\partial x_j}\left( \alpha_\epsilon \mu_{eff} \frac{\partial \epsilon}{\partial x_j} \right) + C_{1\epsilon} \frac{\epsilon}{k} G_k – C_{2\epsilon}^* \rho \frac{\epsilon^2}{k}
$$
where μeff = μ + μt, μt = ρ Cμ k²/ε, and constants are Cμ=0.0845, C1ε=1.42, C2ε=1.68, αk=αε=1.393. The term Gk represents production of turbulent kinetic energy. The RNG model provides better performance for flows with strong separation and recirculation compared to the standard k-ε model.
Data Availability
The complete set of shape coefficients for all simulated cases is available from the author upon request. Additional tables can be constructed for other pitch angles and wind directions. The numerical setup files (mesh, boundary conditions, solver settings) are documented in the project repository.