Using ANSYS DesignModeler, a three-dimensional rectangular computational domain was developed around the tracker geometry, sized to minimize blockage and far-field boundary interference (Fig. 1). The inlet was positioned five panel-chord lengths upstream, the outlet fifteen chord lengths downstream to allow full wake development, and the lateral/top boundaries eight chord lengths from the panel centerline, giving a blockage ratio below 3% for all tilt angles. A uniform velocity-inlet condition with a specified turbulence intensity was applied at the inlet, a pressure-outlet condition at the exit, symmetry conditions on the top and side boundaries, and no-slip wall conditions on the ground and panel surfaces, with a locally refined boundary-layer and wake mesh region around the panel to resolve near-wall gradients and separated shear layers (Table

Panel/torque-tube surface No-slip wall Smooth, stationary for each simulated tilt angle

The flow was modeled using the incompressible, steady/transient Reynolds-Averaged Navier–Stokes (RANS/URANS) equations, closed with the Shear-Stress Transport (SST) k-ω turbulence model, which combines the near-wall accuracy of the standard k-ω formulation with the free-shear-layer robustness of the k-ε model and is well suited to flows involving boundary-layer separation, as expected on the leeward face of the panel at moderate-to-high tilt angles. The governing continuity and momentum equations were discretized using a finite-volume, pressure-based solver with SIMPLE pressure–velocity coupling and second-order upwind spatial discretization for momentum and turbulence quantities; transient cases used a bounded second-order implicit time scheme. Air was treated as an incompressible ideal gas at standard atmospheric conditions (ρ = 1.225 kg/m³, ν = 1.5 × 10⁻⁵ m²/s). Solver settings and convergence criteria are summarized in Table 2.

The reference tracker module consists of a horizontal, north–south oriented torque tube supporting a PV panel row that rotates about its long axis to track the sun from sunrise to sunset. The rotation angle θ, measured from the horizontal (stow) position, was varied from 0° (panel edge-on to a horizontal wind, minimum frontal area) to 90° (panel broadside to the wind, maximum frontal area) in 5–15° increments, as illustrated for four representative positions in Fig. 2. Geometric and material properties of the reference module, used to convert aerodynamic coefficients into forces, moments and structural response, are listed in

Pylon / hub height above ground 1.5 m Panel areal mass 12 kg/m² Torque-tube material Galvanized steel (E = 200 GPa) Rotation range 0–90° (single-axis, horizontal N–S)

Using ANSYS DesignModeler (see Fig. 3), an unstructured, predominantly hexahedral-dominant mesh was generated for each tilt angle, with local refinement in the wake and near-panel region and ten prismatic inflation layers on the panel and torque-tube walls to resolve the viscous sublayer (target y⁺ = 1). A mesh-independence study was conducted at the representative θ = 60° position by refining the domain from 0.4 to 5.9 million elements and monitoring the predicted drag coefficient, the change in CD between the two finest meshes was below 0.3%, and the 4.1-million-element mesh, providing a variation of less than 2% from the finest case, was selected for all subsequent production runs as an acceptable balance between accuracy and computational cost.

For each tilt angle, the flow field was initialized from a hybrid initialization and solved to full convergence of the scaled residuals, after which surface-integrated forces and moments (drag, lift, resultant wind load, and torque about the tracker rotation axis) were extracted for wind speeds of 5, 10, 15, 20 and 25 m/s. Bending and overturning moments were computed by integrating the local pressure and shear distribution along the torque-tube span and about the foundation base, respectively. Energy-yield sensitivity to tilt angle and wind-induced deflection was estimated by combining the CFD-derived aerodynamic loads with a simplified structural-deflection and shading-loss model. Model accuracy was assessed by comparing the CFD-predicted drag coefficients against independent experimental/wind-tunnel reference data reported in the literature for equivalent flat-plate and tracker geometries, using percentage deviation as the validation metric; a deviation below 10% was adopted as the acceptance criterion for the numerical model.

Fig. 4 presents pressure-coefficient contours and velocity streamlines around the panel at θ = 0°, 30°, 60° and 90° for a reference wind speed of 15 m/s. At θ = 0°, the panel is nearly edge-on to the flow and the pressure field remains close to ambient, with only a thin, attached wake; the flow accelerates smoothly around the leading and trailing edges and no significant recirculation is observed. As the tilt angle increases to 30° and 60°, a high-pressure stagnation region develops on the windward (lower) face while a pronounced low-pressure suction zone forms over the leeward (upper) face and trailing edge, and the velocity streamlines show flow separation at the upper edge with a growing recirculating vortex in the near wake. At θ = 90°, the panel presents its full broadside area to the wind, producing the largest windward stagnation pressure and the strongest leeward suction observed across the angular sweep, together with a large, well-organized wake vortex extending well downstream of the panel. Turbulence intensity within the wake increases correspondingly with tilt angle, from near free-stream levels at 0° to values 3–4 times higher within the separated shear layer at 60– 90°, indicating progressively unsteady, vortex-dominated wake behavior that is consistent with the increase in drag and the onset of flow-induced vibration.

From Table 4, the drag coefficient increases monotonically and near-monotonically with tilt angle, from CD = 0.06 at θ = 0° (minimum frontal area) to CD = 1.96 at θ = 90° (maximum frontal area), consistent with classical bluff-body behavior of a flat plate rotating from edge-on to broadside orientation. The lift coefficient follows a markedly different, non-monotonic trend, rising from near zero at θ = 0° to a maximum of CL = 1.15 near θ = 40–45°, before decreasing back toward zero as the panel approaches the symmetric broadside orientation at 90°. The resultant wind load depends on the vector combination of drag and lift, and shows a load envelope that grows continuously with angle and does not peak at an intermediate angle, reaching its maximum magnitude at θ = 90°.

Fig. 5a shows the torque about the tracker rotation axis as a function of tilt angle for wind speeds of 5, 10, 15 and 20 m/s. Torque increases with both tilt angle and wind speed, consistent with the quadratic dependence of aerodynamic force on velocity. The sensitivity to wind speed grows sharply at higher speeds: At θ = 90°, the axis torque increases from approximately 34 N·m at 5 m/s to roughly 528 N·m at 20 m/s, an increase of more than fifteen-fold for only a four-fold increase in wind speed. The torque curves rise steeply between 20° and 70° and begin to plateau approaching 90°, reflecting the combined influence of the drag-coefficient growth and the changing moment arm of the resultant pressure center.

Fig. 5b presents the corresponding bending-moment distribution along the torque-tube span as a function of tilt angle, obtained by integrating the local pressure and shear loads; the bending moment increases both with distance from the support bearing and with tilt angle, reaching its maximum near the tube mid-span at the highest tilt angles, which is consistent with typical torque-tube failure locations reported for tracker installations in high-wind regions. These results indicate that structural design checks for single-axis trackers should explicitly consider the angle-dependent torque and bending-moment envelope rather than a single bounding wind-load case, since the governing angle for torsional versus overturning failure modes is not the same (θ = 25° and θ = 45°, respectively).

Fig. 5a. Wind-induced torque about the tracker rotation axis for wind speed of 5-20 m/s, and 5b, contour of bending-moment distribution along the torque-tube length as a function of tilt angle.

Fig. 6a compares the ideal, solar-only energy-yield curve (a function of tracking tilt angle alone, peaking near 35° for the reference site latitude and tracking algorithm) with the net energy yield after accounting for wind-induced deflection and micro-shading losses estimated from the CFD-derived aerodynamic loads.

The two curves are nearly coincident at low tilt angles, where aerodynamic loads and structural deflection are small, but diverge increasingly beyond approximately 40–50°, where growing drag and torque produce measurable torque-tube twist and consequent tracking-angle error and inter-row micro-shading. At θ = 90°, the net yield is approximately 10–12 percentage points below the ideal solar-only curve.

Fig. 6b quantifies this effect directly as efficiency degradation versus wind speed for four representative tilt angles (20°, 40°, 60°, and 80°). Degradation is small (< 1%) at low wind speeds and low tilt angles, but grows supra-linearly with wind speed at all angles and is consistently highest at the steepest tilt (80°), reaching approximately 10.5% at 25 m/s, compared with 5.5% at 20° for the same wind speed.

These results confirm that aerodynamic drag and inclination angle jointly govern wind-related energy loss, and that this loss becomes significant specifically in the high-tilt, high-wind-speed operating corner that trackers must pass through during morning/evening tracking or when stow logic is delayed.

The CFD-predicted drag coefficients were compared against independent experimental/wind-tunnel reference data at seven tilt angles spanning the full rotation range (Fig. 7a, Table 5). Agreement between the CFD and experimental CD values is close across the entire angular range, with the percentage deviation (Fig. 7b) ranging from a minimum of 2.0% at θ = 90° to a maximum of 7.5% at θ = 75°, and remaining below the 10% acceptance threshold at every angle tested.

The largest deviations occur at intermediate-to-high tilt angles (60–75°), where flow separation and wake unsteadiness are most pronounced and are correspondingly the most sensitive to turbulence-model assumptions and experimental blockage/support-interference effects; the closest agreement is obtained at the two extreme angles (0° and 90°), where the flow topology is simpler and more symmetric.

Overall, the validation results confirm that the SST k-ω RANS model, together with the mesh and boundary-condition setup described in Section 2, provides drag-coefficient predictions of acceptable engineering accuracy across the full tracker rotation range, supporting the use of the CFD results for structural and operational assessment.

Fig. 7a. Comparison of CFD-predicted accuracy drag coefficient with experimental/wind-tunnel data and 7b percentage deviation at each tilt angle, confirming model accuracy within 10% threshold.

Fig. 8a overlays the normalized energy-capture curve and the normalized wind-load curve as functions of tilt angle, highlighting the range in which energy capture remains close to its maximum while wind load remains comparatively low.

Energy capture exceeds 90% of its peak value between approximately 15° and 55°, whereas wind load remains below roughly 60% of its maximum value only below approximately 45°; the intersection of these two constraints, together with the critical-angle findings (avoidance of the θ = 25° vibration band and the θ = 45° overturning-moment peak), defines a recommended safe and efficient operating range of approximately 15– 45° for continuous tracking under moderate-to-strong wind conditions.

Fig. 8b expresses this recommendation as a safe operating envelope of allowable wind speed versus tilt angle, showing that the maximum permissible wind speed for continued tracking decreases from approximately 25 m/s near 0° to below 10 m/s near 90°, reinforcing the need for angle-dependent (rather than fixed) wind-speed stow thresholds.

Building on the optimal-range and critical-angle findings, Table 6 summarizes practical design guidelines for improved single-axis tracker systems intended for deployment in high-wind regions, covering structural material selection, stow strategy, axis height and damping requirements; Fig. 8c presents the corresponding high-wind stow-control logic as a flowchart linking real-time wind-speed monitoring to automatic stow rotation and mechanical locking.

Structural material High-strength galvanized or stainless steel torque tube; corrosion-and fatigue-resistant fasteners and bearings.

Stow position Near-horizontal, 0–5°, engaged automatically when sustained wind speed exceeds site-specific threshold (e.g., 15 m/s).

Axis / hub height Minimize consistent with ground clearance and shading requirements, to reduce overturning moment arm.

Damping requirements Passive tuned-mass or hydraulic dampers targeted at θ = 20–30° vortex-induced vibration band.

Control / stow logic Real-time anemometer-triggered automatic stow with fail-safe mechanical locking (Fig. 9c).

Operating tilt range Restrict continuous tracking to approximately 15–45° under moderate-to-strong wind; stow outside this range at high wind speed.

Site / layout Increase row spacing or provide windbreaks in high-turbulence or complex terrain; periodic structural health monitoring at bearings and foundations.