The imperative for decarbonization within the global maritime industry necessitates the exploration and integration of innovative renewable energy solutions. One promising avenue involves the deployment of solar photovoltaic (PV) systems on the expansive, unobstructed deck areas of large vessels, such as oil tankers. These marine environments often present excellent solar irradiance, offering significant potential for auxiliary power generation and reducing reliance on fossil-fueled generators. The adaptation of flexible support structures, proven in terrestrial applications for complex terrains, presents a compelling solution for shipboard installation due to their inherent advantages: cost-effectiveness, reduced structural weight, and adaptable configuration to accommodate deck equipment. However, the operational environment for a marine solar system is considerably more severe than its land-based counterpart, subjecting it to combined wind, wave-induced vessel motions, and corrosive saline conditions. Among these, wind loads represent a primary design driver for the structural integrity of the flexible supports and the PV modules themselves.
This investigation employs Computational Fluid Dynamics (CFD) to numerically simulate and analyze the wind load characteristics on marine solar photovoltaic flexible support arrays. The core focus is on arrays with a panel tilt angle of 0°, an optimal configuration chosen to minimize wind-induced forces while considering the variable geographical positions of transoceanic vessels where tracking an optimal sun angle is impractical. The study systematically examines the influence of two critical layout parameters—the longitudinal spacing between panel rows and the total number of rows in the array—on the distribution of wind pressures and resulting forces. The objective is to derive practical engineering guidelines for the design and arrangement of these marine solar systems to ensure structural reliability under extreme wind conditions representative of high sea states.
The fundamental methodology involves modeling a representative section of a flexible support array. The PV panels are simplified as rigid, flat plates with dimensions of 2.200 m (length, L) by 1.100 m (width, B). The support cables, clamps, and columns are omitted from the fluid domain as their contribution to the overall pressure distribution on the panels is secondary for this global load analysis. A two-dimensional approach is justified for studying the longitudinal interference effects, significantly reducing computational cost while capturing the essential flow physics. The computational domain is constructed with a substantial inflow section to ensure uniform flow development and an extended outflow section to allow for complete wake dissipation. The boundary conditions are set as follows: a velocity inlet with a uniform wind speed of 37.0 m/s (corresponding to a Beaufort 8 gale), a pressure outlet, no-slip walls at the panel surfaces and the ground plane (simulating the deck), and slip walls for the top and sides of the domain. The SST k-ω turbulence model is selected for its accurate prediction of flows with adverse pressure gradients and separation. The simulations use the SIMPLE algorithm for pressure-velocity coupling and second-order discretization schemes for accuracy.
The analysis centers on key aerodynamic coefficients and resultant forces. The lift and drag coefficients for a PV panel are defined as:
$$C_L = \frac{F_L}{\frac{1}{2} \rho V^2 B L}$$
$$C_D = \frac{F_D}{\frac{1}{2} \rho V^2 B L}$$
where $F_L$ and $F_D$ are the lift and drag forces (per unit width in 2D simulation), $\rho$ is the air density (1.225 kg/m³), and $V$ is the freestream velocity. The net force $F_{net}$ and its direction angle $\gamma$ relative to the horizontal, as well as the pitching moment $M$, are also critical for structural design of the flexible cable system.
Influence of Longitudinal Spacing Ratio
The longitudinal spacing is a crucial parameter affecting wake interference between rows. It is defined by the spacing ratio $s = a / L$, where $a$ is the center-to-center distance between rows. A parametric study is conducted for an array of 10 rows, varying $s$ from 0.45 to 2.73. A mesh independence study was first performed, confirming that solution accuracy was achieved.
The results reveal a complex interaction. For the upstream rows (P1-P3), wind loads are highest and show a strong dependence on spacing. As $s$ increases, the lift coefficient ($C_L$) for these front rows decreases, while the drag coefficient ($C_D$) for rows behind the first increases. This indicates that at close spacing, the first row shields downstream rows, reducing their drag, but the accelerated flow over the top creates significant lift on all rows. The net wind load force on each row evolves with spacing, as summarized in the following table for key rows at different spacing ratios.
| Long. Spacing Ratio (s) | Net Force on P1 (N/m) | Net Force on P5 (N/m) | Net Force on P10 (N/m) | Overall Array Force Dir. Angle $\gamma$ (°) |
|---|---|---|---|---|
| 0.45 | 105.2 | 38.1 | 10.5 | 58.7 |
| 1.14 | 98.8 | 31.4 | 18.2 | 49.8 |
| 1.82 | 94.5 | 30.1 | 22.7 | 43.8 |
| 2.73 | 91.8 | 29.8 | 24.1 | 38.2 |
The data shows that for $s < 1.8$, forces change rapidly. Beyond $s \approx 1.8$, the forces on intermediate and downstream rows stabilize. The overall direction of the resultant force on the array becomes less vertical (smaller $\gamma$) as spacing increases, meaning drag becomes more dominant relative to lift. This is advantageous for a marine solar system as vertical forces compound with vessel heave and pitch motions, creating dynamic cable loads. The pitching moment on panels, critical for clamp design, shows an even more dramatic spacing effect. At close spacing ($s=0.45$), the moment on the first row can be an order of magnitude larger than on the last row. For $s \geq 1.8$, this disparity reduces to less than a factor of three, promoting a more uniform and manageable structural demand across the entire array.
The flow field visualization explains these trends. At small spacing, the strong wake from an upstream panel directly impinges on the next panel, creating a large low-pressure region on its windward side and altering its effective angle of attack. As spacing increases, this wake has room to dissipate and develop, reducing its disruptive influence on downstream panels. A small, consistent region of reverse flow is observed immediately behind each panel’s trailing edge, but its length (~0.057L) is independent of array spacing.
Influence of the Number of Longitudinal Rows
The second parameter investigated is the total number of rows, $n$, in the array (5, 10, 15, and 20), for a fixed optimal spacing ratio of $s = 1.8$. The total cumulative force on the entire array scales approximately linearly with the number of rows. However, the distribution of loads along the array changes significantly with $n$.
For a very short array (e.g., n=5), every row experiences a distinct and rapidly changing flow condition. There is no developed “interior” flow regime. As the number of rows increases, a quasi-steady flow condition develops in the central portion of the array. For arrays with $n \geq 15$, the lift and drag forces on rows P4 through P(n-4) exhibit a very gradual, almost linear decay. This indicates that the flow has reached a periodically developed state within the array’s core. The following table illustrates the stabilization of forces in the middle of a long array.
| Array Size (n rows) | $C_L$ on Row P2 | $C_L$ on Central Row* | $C_D$ on Central Row* | Force Decay Rate in Core |
|---|---|---|---|---|
| 5 | 0.185 | Row P3: 0.102 | Row P3: 0.088 | High |
| 15 | 0.180 | Row P8: 0.135 | Row P8: 0.121 | Low (~5% per row) |
| 20 | 0.179 | Row P10: 0.133 | Row P10: 0.119 | Low (~5% per row) |
*Central row is P(n/2) approximated to nearest integer.
This finding has a direct implication for designing a robust marine solar PV system. Short arrays lead to highly non-uniform loading, where front-row components are disproportionately stressed. For a durable and reliably engineered flexible support system, it is advisable to design arrays with a sufficient number of rows (e.g., 15 or more) to allow this stabilized core flow to develop, leading to more predictable and evenly distributed wind loads across the majority of the structure.
The integration of a large-scale solar system onto a marine vessel symbolizes the convergence of traditional maritime engineering with modern renewable energy technology. The image above conceptually represents the ambitious scope of harnessing solar power, akin to tapping into a fundamental energy source within our own celestial neighborhood. Translating this potential to the maritime domain requires meticulous engineering, where understanding and mitigating environmental loads like wind is paramount. The flexible support structure is the critical enabling technology that makes such an installation feasible on a moving ship, allowing for large, lightweight arrays that can withstand harsh ocean conditions.
Engineering Design Synthesis and Conclusion
Based on the comprehensive numerical analysis, targeted recommendations can be formulated for the engineering of marine-based solar photovoltaic flexible support systems under high wind loads:
- Front-Row Reinforcement: The first row of panels consistently experiences the highest wind loads and moments. Therefore, the support cables for the first one or two rows should be specified with a higher safety factor, potentially using a cable with greater diameter, breaking strength, and corrosion resistance.
- Optimal Longitudinal Spacing: A longitudinal spacing ratio of $s \approx 1.8$ is recommended. This spacing effectively balances the competing needs of deck space utilization and aerodynamic performance. At this ratio:
- The disparity in pitching moments between the first and last rows is reduced to within a factor of three, promoting design uniformity.
- The overall wind load on the array has largely stabilized with respect to spacing changes.
- The resultant force direction is less vertical, reducing the additive dynamic loads from vessel motion.
- Minimum Array Length: The solar system array should comprise a minimum of 15 rows of panels. This ensures the development of a stabilized flow regime in the central section of the array, leading to a more gradual and predictable gradient in wind loading across the structure. This avoids the highly uneven loads seen in very short arrays and simplifies the structural analysis and cable design for the majority of the support system.
In conclusion, this numerical study provides foundational insights into the wind load dynamics of zero-tilt-angle photovoltaic arrays on flexible supports in a marine context. The findings highlight that through strategic geometric design—specifically by implementing a sufficient longitudinal spacing and a sufficient number of rows—the aerodynamic loads can be managed to become more uniform and predictable. This is essential for the safe, reliable, and economical design of marine solar systems. The derived guidelines offer a practical framework for naval architects and renewable energy engineers integrating large-scale photovoltaic power generation onto commercial vessels, contributing directly to the maritime industry’s sustainability goals. The CFD methodology and results also establish a basis for future, more complex fully coupled fluid-structure interaction (FSI) analyses of these flexible support systems under combined wind and wave-induced motion loads.