3.1. Vortex Distribution
Figure 6a depicts a schematic diagram illustrating the positions of three observation planes. All three planes are perpendicular to the photovoltaic panel. Among them, Cross-Section 3 is located on the symmetry plane of the computational model, Section 1 passes through the side edge of the panel, and Cross-Section 2 is positioned between Cross-Sections 1 and 3.
Figure 6b illustrates the establishment of the section coordinate axes, with the lower left corner of the computational domain as the origin, the bottom as the horizontal axis, and the left side as the vertical axis.
Figure 7 displays pressure contour maps on various sections for each computational scheme. The streamlines depicted in the figure represent velocity streamlines.
In scheme A-1, no vortices were observed at Section 1; a vortex was observed at Section 2, with its center located approximately at coordinates (2, 0.41), affecting an area extending from the top to the bottom of the panel. At Section 3, two vortices were observed, with their centers located at (2.2, 0.38) and (2.3, 0.79), respectively. The influence areas of these two vortices extend from the top of the panel to the junction between the bracket and the panel. For this scheme, the pressure distribution on the solar panel exhibits a minimum value of 99.8007 kPa and a maximum value of 103.0034 kPa, with a ratio of approximately 1.032 between the two.
In scheme A-2, no vortices were observed at Section 1; a vortex was observed at Section 2, with its center located approximately at coordinates (2.3, 0.39), affecting an area extending from the top to the bottom of the panel. At Section 3, three vortices were observed, with their centers located roughly at coordinates (1.3, 0.21), (2.8, 0.12), and (3, 1.02), respectively. The leftmost vortex only affects the bottom of the panel to the junction between the panel and the bracket, while the other two vortices collectively affect the top of the panel to the junction between the panel and the bracket, with their vortex centers located further away from the panel. For this scheme, the pressure distribution on the solar panel exhibits a minimum value of 99.9870 kPa and a maximum value of 103.3878 kPa, with a ratio of approximately 1.034 between the two.
In scheme A-3, a vortex was observed at Section 1, with its center located approximately at coordinates (2.49, 0.91), exerting a significant influence on the part of the panel above the longitudinal coordinate of 0.5. At Section 2, a vortex was observed, with its center roughly at coordinates (2.4, 0.9), significantly affecting the part of the panel above the longitudinal coordinate of 0.45. The airflow at Section 3 was turbulent, with a prominent vortex center located around coordinates (2.3, 1.08), which had a significant impact on the range from the junction between the panel bracket and the panel to the top of the panel. For this scheme, the pressure distribution on the solar panel exhibits a minimum value of 100.9489 kPa and a maximum value of 103.7747 kPa, with a ratio of approximately 1.028 between the two.
In scheme A-4, it was observed that, at Sections 1, 2, and 3, each had only one vortex. The vortex centers were located approximately at coordinates (2.05, 1.22), (2.03, 1.29), and (2, 1.3), respectively. These vortex centers at these sections were relatively far from the panel, with only a slight impact on the solar panel at the edge of the vortices. For this scheme, the pressure distribution on the solar panel exhibits a minimum value of 101.0598 kPa and a maximum value of 104.0550 kPa, with a ratio of approximately 1.030 between the two.
In scheme B-1, no vortex was observed at Section 1; at Section 2, two vortices were observed with their centers located approximately at coordinates (2.1, 0.72) and (2.35, 0.3), jointly affecting the entire panel surface; at Section 3, two vortices were observed with their centers located approximately at coordinates (2.4, 0.81) and (2.3, 0.31), jointly affecting the entire panel surface. For this scheme, the pressure distribution on the solar panel exhibits a minimum value of 99.9805 kPa and a maximum value of 103.3897 kPa, with a ratio of approximately 1.034 between the two.
In scheme B-2, two vortices were observed at Section 1, with their centers located approximately at (2.4, 0.66) and (2.15, 0.18), jointly affecting the entire panel surface; at Section 2, two vortices were observed with their centers located approximately at (2.05, 0.72) and (2.75, 0.12), jointly affecting the entire panel surface; at Section 3, two vortices were observed with their centers located approximately at (2.3, 0.9) and (2.15, 0.2), jointly affecting the entire panel surface. For this scheme, the pressure distribution on the solar panel exhibits a minimum value of 100.1062 kPa and a maximum value of 103.8123 kPa, with a ratio of approximately 1.037 between the two.
In scheme B-3, it was observed that there is only one vortex at Sections 1, 2, and 3, with their centers located approximately at coordinates (1.8, 1.12), (1.7, 1.3), and (1.7, 1.31), respectively. These vortex centers are relatively far from the panel surface, and their influence on the solar panel is only minimal around the edges of the vortices. For this scheme, the pressure distribution on the solar panel exhibits a minimum value of 101.1967 kPa and a maximum value of 104.2234 kPa, with a ratio of approximately 1.030 between the two.
In scheme B-4, it was observed that there is only one vortex at Sections 1, 2, and 3, with their centers located approximately at coordinates (1.7, 1.3), (1.75, 1.32), and (1.71, 1.36), respectively. These vortex centers are relatively far from the panel surface, and their influence on the solar panel is minimal around the edges of the vortices. For this scheme, the pressure distribution on the solar panel exhibits a minimum value of 101.2013 kPa and a maximum value of 104.2906 kPa, with a ratio of approximately 1.031 between the two.
In computing schemes A-1 to A-4 and B-1 to B-4, it is evident that, as the installation tilt angle of the solar photovoltaic panel increases, the pressure on the windward side also increases. This correlation stems from the fact that a larger installation tilt angle of the solar panel leads to a larger effective force area on the panel surface. As a result, the pressure on the windward side intensifies, due to the increased surface area exposed to the wind flow.
In computing schemes A-1 to A-4, no vortex is generated at Section 1 for schemes A-1 and A-2, while vortices are generated at Section 1 for schemes A-3 and A-4, with the vortex at Section 1 of scheme A-3 being relatively larger. Although no vortex is generated at Section 1 for scheme A-2, the distortion of velocity streamline on the leeward side of the panel surface is significantly higher than that of Section 1 for scheme A-1. For Sections 2 and 3 of schemes A-1 to A-3, significant vortices are generated on the leeward side of the panel surface, especially two vortices at Section 3 for schemes A-1 and A-2. As for scheme A-4, vortices are generated at all three sections, with smaller vortex ranges and the vortex centers located relatively high at the top of the panel surface.
In computing schemes B-1 to B-4, vortices are generated at all sections except for Section 1 of scheme B-1, where no vortex is formed on the leeward side of the panel surface. The vortices generated at Sections 2 and 3 of scheme B-1, as well as Sections 1 to 3 of scheme B-2, are relatively larger, and all of them consist of two vortices. On the other hand, the vortices generated at the leeward side of the panel surface at all sections of schemes B-3 and B-4 are smaller, with the vortex centers located higher than the top of the panel surface.
Since the existence of wind vortices may cause oscillations on the solar photovoltaic panel [
38], frequent oscillations can lead to material fatigue and damage, significantly reducing the lifespan of the solar panel. Moreover, a decrease in the tilt angle results in less force on the windward side. In this case, a smaller tilt angle is preferable. Additionally, excessively high tilt angles may reduce the efficiency of solar energy absorption by the solar panel. Therefore, when the direction of the wind flow is determinable, it is advisable to install the solar photovoltaic panel with a front tilt angle of 30° or 45° facing the wind, and a back tilt angle of 60° facing the wind.
3.3. Pressure Distribution
The schematic diagram of the pressure collection lines on the panel is presented in
Figure 9. In this figure, images labeled 1 and 2 illustrate the method for determining the frontal collection lines on the panel, while images labeled 3 and 4 demonstrate the method for determining the rear collection lines on the panel. The collection lines on the panel are represented by bold lines in the figure.
The pressure variation curve on the collection line in computational scheme A-1 is depicted in
Figure 10. It is important to emphasize that, in
Figure 10b,d, the abrupt changes in the data curves of lines III and V are due to the contact between the collection line and the panel support; similar situations thereafter will not be elaborated. The horizontal axis
l/L in the figure represents the relative position of the sampling points on the collection line, i.e., the ratio of the distance from the starting point to the sampling point to the length of the collection line.
Through meticulous observation of each graph, it is evident that there is a significant difference in pressure between the windward and leeward sides of the solar photovoltaic panel. The pressure on the windward side is mostly concentrated in the range of 101~103 kPa, while on the leeward side, it is primarily distributed in the range of 100~101 kPa. This indicates that the windward side of the solar photovoltaic panel bears a significantly higher pressure than the leeward side, with a maximum difference of up to 3.2027 kPa.
Analyzing the pressure variation along the transverse collection line on the front face of the panel depicted in
Figure 10a, it is observed that the pressure gradually increases from the top to the bottom. The pressure at the top is minimal, averaging 100.78 kPa, while at the bottom, it is highest, averaging 102.48 kPa. Additionally, lower pressure is observed on the sides of the solar photovoltaic panel. This trend indicates that the pressure along the transverse direction of the front face of the panel gradually increases with position and exhibits a noticeable gradient.
Examining the pressure variation along the vertical collection line on the front face of the panel depicted in
Figure 10c, it is observed that the pressure change is consistent from line 2 to line 5, indicating a gradual increase in pressure with height along the vertical direction of the front face. Overall, the pressure increases from approximately 100.4 kPa at the top to 103 kPa at the bottom. However, the pressure variation along line 1 is irregular due to its proximity to the edge of the panel, where vortexes exist, leading to unstable pressure changes.
Regarding the pressure variation depicted in
Figure 10b,d, no discernible patterns are evident, with significant differences in pressure values among the curves. This irregular variation may increase the risk of material fatigue and damage, as uneven pressure distribution may lead to certain areas of the solar photovoltaic panel bearing excessive pressure, exacerbating stress concentration and damage to the material.
Through conducting detailed observation and analysis of the pressure distribution at different positions of the solar photovoltaic panel, it can be concluded that there is a significant difference in pressure between the windward and leeward sides, and there are certain regularities in the transverse and vertical pressure variations on the front face of the panel. However, irregular pressure changes may increase the risk of fatigue damage to the solar photovoltaic panel, emphasizing the need for attention and control during design and usage.
The pressure variation curve on the collection line in calculation scheme A-2 is depicted in
Figure 11. Observing the graphs, it can be noted that on the wind-facing side, the pressure mostly ranges from 100.6 to 103 kPa, while on the leeward side, the pressure mostly ranges from 100 to 101 kPa. This indicates that the pressure on the wind-facing side of the solar panel is significantly higher than that on the leeward side, with a maximum difference of 3.4008 kPa.
In
Figure 11a, the pressure variations along the transverse acquisition lines on the front side of the panel are observed. There is a gradual increase in pressure from the top to the bottom, indicating an average pressure of 100.96 kPa at the top and 102.67 kPa at the bottom. It is noteworthy that the pressure at the sides of the solar photovoltaic panel is relatively lower, possibly due to design or environmental factors. Additionally, there is more turbulence in the pressure variation along line 5, likely due to its proximity to the edge of the panel, making it susceptible to vortex effects.
In
Figure 11c, the pressure variations along the vertical acquisition lines on the front side of the panel are observed. The pressure changes from line 2 to line 5 are consistent, showing a gradual increase from 100.8 kPa at the top to 103.4 kPa at the bottom. However, line 1 exhibits irregular pressure changes, attributed to its position near the edge of the panel, making it susceptible to vortex effects and resulting in unstable pressure fluctuations.
In
Figure 11b,d, no clear pattern in pressure variation is observed, with significant differences in pressure values among the curves. This suggests the presence of significant vortices near the back of the panel, increasing the risk of material fatigue and damage.
Pressure fluctuations at diverse locations on the solar photovoltaic panel are influenced by various factors, including panel design, surrounding environment, and the presence of vortices. Comprehending these fluctuations is of utmost importance for optimizing the design and upkeep of solar photovoltaic panels, with the aim of minimizing the risk of material fatigue and damage, and thereby enhancing the efficiency and dependability of solar photovoltaic systems.
The pressure variation curve on the collection line in calculation scheme A-3 is depicted in
Figure 12. Observing the graphs, it can be noted that, on the wind-facing side, the pressure mostly ranges from 101 to 104 kPa, while, on the leeward side, the pressure mostly ranges from 101 to 101.5 kPa. This indicates that the pressure on the wind-facing side of the solar panel is significantly higher than that on the leeward side, with a maximum difference of 2.8258 kPa.
Figure 12a illustrates the pressure variation along the horizontal line on the front of the solar photovoltaic panel. From the top to the bottom, the pressure gradually increases, with the average pressure at the top being about 101.59 kPa, while the average pressure at the bottom is about 103.39 kPa. This suggests that the lower part of the solar photovoltaic panel experiences greater pressure, which might be related to the supporting structure or installation method. The pressure at both sides of the panel is relatively lower, possibly due to air movement along the edges. Notably, the pressure variation on Line 5 is more irregular compared to other lines, possibly because it is located at the edge of the solar panel, within the influence range of wind vortices.
Figure 12c exhibits pressure variation along the vertical line on the front of the solar photovoltaic panel. From top to bottom, the pressure gradually increases, with the overall pressure rising from about 101.6 kPa to about 103.6 kPa. The pressure variations from line 2 to line 5 are relatively consistent, indicating that the vertical pressure distribution on the solar panel is relatively uniform. However, the pressure on line 1 is more irregular, possibly because it is at the edge of the solar panel, where wind vortices have a greater impact.
In
Figure 12b,d, apart from lines I and V having significant pressure differences due to their edge positions, the pressure curves in the rest of the figures show minor differences. This indicates that the pressure distribution across the solar photovoltaic panel is relatively uniform, reducing the risk of material fatigue and damage.
In general, the pressure distribution on the solar photovoltaic panel is affected by multiple elements, such as the supporting structure, the method of installation, and the surrounding environment. The rational design and optimization of these factors are capable of enhancing the stability and durability of the solar photovoltaic panel.
The pressure variation curve of the online collection line in scheme A-4 is depicted in
Figure 13. Observing the graphs, it can be seen that the pressure on the windward side is mostly between 101.4 and 104 kPa, while, on the leeward side, it is mostly between 101.2 and 101.4 kPa. This indicates that the pressure on the windward side of the solar panel is significantly higher than that on the leeward side, with a maximum difference of 2.9952 kPa.
In
Figure 13a, the pressure variation along the transverse collecting lines on the front face of the solar photovoltaic panel is presented. It is observed that the pressure at the top of the panel is relatively low, averaging 101.92 kPa, while it is higher at the bottom, averaging 103.75 kPa. Additionally, the pressure at the sides of the solar photovoltaic panel is relatively lower, possibly due to the flow conditions around the panel edges. Overall, there is a gradual decrease in pressure from the bottom to the top of the panel, likely influenced by the forces acting on the solar photovoltaic panel and aerodynamic effects.
In
Figure 13c, the pressure variation along the vertical collecting lines on the front face of the solar photovoltaic panel is depicted. The pressure changes on lines 2 to 5 are consistent, indicating a gradual increase in pressure from the top to the bottom of the panel. However, the pressure variation on line 1 is irregular, likely due to its position near the panel’s edge where there may be airflow disturbances such as vortices, leading to unstable pressure changes.
In
Figure 13b,d, the pressure values among the pressure curves are relatively consistent and low, indicating a relatively uniform and stable pressure distribution on the solar photovoltaic panel. This stable pressure distribution helps reduce material fatigue and damage risks, thereby extending the lifespan of the solar photovoltaic panel.
Consequently, analyzing the pressure variation along the transverse collection lines on the front side of the solar photovoltaic panel is able to offer an understanding of the panel’s stress distribution, facilitating the implementation of suitable measures to optimize the design and utilization of the solar photovoltaic panel, thereby enhancing its performance and dependability.
The pressure variation curve on the collection line in calculation scheme B-1 is depicted in
Figure 14. Observing the graphs, it can be seen that, on the lee side, the pressure is mostly between 100 and 100.6 kPa, while, on the windward side, the pressure is mostly between 100 and 103.4 kPa. This indicates that the pressure on the windward side of the solar panel is significantly higher than on the lee side, with a maximum difference of 3.4092 kPa.
Figure 14a illustrates the pressure distribution along a transverse line on the front face of the board. From the graph, it can be observed that the pressure is relatively higher towards the center of the board, approximately 100.5 kPa, whereas it is lower along the sides of the board, around 100.2 kPa. Overall, the pressure variation across the board exhibits weak regularity.
Figure 14c exhibits the pressure variation along a vertical line on the front face of the board. Apart from significant fluctuations at the edges (line 1), the pressure remains quite uniform along other collection lines. Notably, the pressure increases with distance from the board’s edge and decreases towards the center, ranging from 100.2 kPa at the edge to 100.5 kPa at the center.
Figure 14b displays the pressure variation along a transverse line on the back face of the board. Similarly, there are notable fluctuations at the edges (line I), while lines II to V exhibit an interesting trend: higher pressure at the upper end of the board, reaching up to 103.2 kPa, and lower pressure at the lower end, down to 100.36 kPa.
Figure 14d demonstrates the pressure variation along a vertical line on the back face of the board. Like before, there are significant fluctuations at the edges (line I), but the pressure variation along other collection lines is relatively uniform. Notably, the pressure is lower towards the outer edges of the back face and higher towards the center, with higher pressure at the top compared to the bottom. Overall, the pressure on the back face decreases gradually from 103.2 kPa at the top to 101 kPa at the bottom.
To sum up, there is a clearly identifiable pattern in the pressure distribution throughout the board, ranging from the front to the back and from the top to the bottom. A higher pressure is noticed towards the center, while a lower pressure is observed towards the edges, which is likely to be affected by the board’s structure and external factors. The design and application of the board should take into consideration these characteristics of pressure distribution to guarantee its performance and stability.
The pressure variation curve of the online collection line in scheme B-2 is depicted in
Figure 15. Observing the graphs, it can be seen that on the leeward side, the pressure mostly ranges from 100.2 to 100.8 kPa, while on the windward side, the pressure mostly ranges from 100 to 104 kPa. This indicates that the pressure on the windward side of the solar panel is significantly higher than that on the leeward side, with a maximum difference of 3.7061 kPa.
In
Figure 15a, the pressure variation along the transverse acquisition lines on the front surface of the panel is depicted. The pressure fluctuations appear highly chaotic, indicating the presence of significant vortices at this location. It is noteworthy that these vortices result in relatively low pressure at the location, ranging only between 100.2 kPa and 100.8 kPa. This implies a lighter wind load on the solar panel surface at this point, although wind instability may also be a factor.
Figure 15c illustrates the pressure variation along the vertical acquisition lines on the front surface of the panel. Two distinct vortices can be observed, with one vortex centered around relative position 0.5 and another around relative position 0.9. This suggests a complex and variable wind field on the front surface of the solar panel, with multiple rotating flow structures significantly influencing the pressure distribution.
Figure 15b displays the pressure variation along the transverse acquisition lines on the back surface of the panel. Due to line I being located at the edge of the panel, pressure fluctuations are more erratic. However, from line II to line V, it can be observed that the pressure is higher towards the top end of the panel, averaging 103.43 kPa, while it is lower towards the bottom end, averaging only 100.97 kPa. This indicates a noticeable pressure gradient on the back surface of the panel, possibly due to local wind speed variations caused by the panel’s contact with the ground.
Figure 15d presents the pressure variation along the vertical acquisition lines on the back surface of the panel. Apart from the erratic pressure changes at line I near the edge of the panel, pressure variations along the other lines are relatively uniform. It is noteworthy that the pressure is lower towards the outer side of the back surface, at only 101.04 kPa, while towards the middle and upper side, it reaches 103.81 kPa and 103.6 kPa, respectively, with relatively lower pressure towards the lower side averaging 101 kPa. This indicates significant spatial differences in the wind load on the back surface of the panel, which are related to the panel’s shape and surrounding environment.
Finally, it is evident that there are notable disparities in the wind loads endured by the solar panel in different areas, which are closely associated with the panel’s configuration, the surrounding environment, and the intricacy of the wind field. Hence, in the design of solar energy systems, it is of utmost importance to take into account the panel structure and the characteristics of the wind field in a comprehensive manner to guarantee the stability and functionality of the system.
The pressure variation curves of the online data collection in scheme B-3 are depicted in
Figure 16. Observing the graphs, it can be seen that the pressure on the leeward side is mostly between 100.2 and 100.4 kPa, while the pressure on the windward side is mostly between 101.6 and 104.4 kPa. This indicates that the pressure on the windward side of the solar panel is significantly higher than that on the leeward side, with a maximum difference of 3.0267 kPa.
Figure 16a reveals the pressure variation along the horizontal collection lines on the front side of the solar panel. The results indicate minimal pressure differences between the collection lines, with an overall low pressure averaging 101.31 kPa. This suggests a fairly uniform distribution of wind-induced pressure on the front side.
Figure 16c illustrates the pressure variation along the vertical collection lines on the front side of the solar panel. It is worth noting that the edge of the panel at collection line 1 is affected by swirling winds, resulting in lower external pressure averaging 101.24 kPa. However, minimal pressure differences are observed on other collection lines, with an overall average pressure of 101.32 kPa. This indicates a relatively uniform distribution of wind-induced pressure on the front side, albeit with some pressure reduction in the edge area.
Figure 16b displays the pressure variation along the horizontal collection lines on the back side of the solar panel. The results show that collection lines I and V, located at the edge of the panel, are affected by swirling winds, resulting in lower average pressures of 102.67 kPa and 102.76 kPa, respectively. Conversely, lines II to IV exhibit relatively higher pressures, averaging 103.80 kPa, indicating higher pressures in the central region of the back side compared to the front side.
Figure 16d illustrates the pressure variation along the vertical collection lines on the back side of the solar panel. The results show that line I at the edge of the panel experiences lower and unstable pressure, averaging only 101.76 kPa. Pressure variations on other collection lines are relatively uniform and higher, with lower pressure near the outer edge of the back side, averaging 103.56 kPa, and higher pressure in the central position, reaching a maximum of 104.19 kPa.
When exposed to wind loads, there exist notable differences in the pressure distribution between the front and rear sides of the solar panel. The front side undergoes relatively even pressure, whereas the central area of the rear side undergoes higher pressure, and the edge region undergoes pressure reduction as a result of swirling winds. These discoveries are of great significance for the design and optimization of the performance of the solar panel.
In scheme B-4, the pressure variation curve on the collection line is depicted in
Figure 17. Observing the graphs, it can be seen that, on the leeward side, the pressure mostly ranges from 100.2 to 100.4 kPa, while, on the windward side, the pressure mostly ranges from 101.6 to 104.4 kPa. This indicates that the pressure on the windward side of the solar panel is significantly higher than that on the leeward side, with a maximum difference of 3.0893 kPa.
Figure 17a exhibits the pressure variation along the transverse collection lines on the front side of the panel. It is observed that there is minimal pressure difference between the collection lines, with an average pressure of 101.32 kPa, indicating good uniformity of wind distribution across the transverse direction of the panel’s front side.
Figure 17c presents the pressure variation along the vertical collection lines on the front side of the panel. Despite line 1 being affected by wind eddies at the edge of the panel, resulting in a lower pressure of only 101.23 kPa, the pressure variation along the other collection lines is also minimal, with an average pressure of 101.32 kPa, suggesting overall stability in the wind loading characteristics along the vertical direction of the panel’s front side.
Regarding the transverse pressure variation on the back side of the panel, as depicted in
Figure 17b, it is observed that lines I and V located at the panel’s edge are affected by wind eddies, resulting in lower and more erratic pressure. Specifically, the average pressure on line I is 102.81 kPa, while on line V it is 103.39 kPa. However, the pressure on lines II to IV is relatively higher, reaching up to 104.27 kPa, indicating higher pressure in the central region of the back side, possibly due to turbulence caused by the back side structure.
Figure 17d illustrates the pressure variation along the vertical collection lines on the back side of the panel. Similar to the front side, line I at the panel’s edge exhibits lower and more erratic pressure, with an average pressure of 101.89 kPa. However, pressure variation along other collection lines is more uniform and higher, especially in the central region of the back side, with the highest pressure on line II reaching approximately 103.74 kPa, and on line IV approximately 104.27 kPa.
By conducting in-depth analysis of the transverse and vertical pressure information on both the front and rear sides of the solar panel, it is clearly shown that the front side displays favorable wind uniformity, whereas the rear side is greatly influenced by wind vortices at the edges and demonstrates higher pressure in the central area. These discoveries have significant implications for the design and improvement of solar panels.