Wind loads on a solar PV panel with side plates

This study determines the lift force on a tilted solar PV panel with/without side plates (upward and downward types). The tilt angles are 15° and 30°andthewindincidenceisatanangleof0–180°(inincrementsof15°).Measurementsofmeansurfacepressureareconductedinaclosed-loopwindtunnel.Thecornervorticesarelessenedwiththepresenceofupwardordownwardsideplatesforthewindangleofincidenceof0°.Themeansurfacepressureonthelowersurfacewithdownwardsideplatesismorepositive(greaterwindloads).Withupwardsideplates,thereislesssuctionontheuppersurfacenearthewindwardcornerforthewindangleofincidencefrom15°to60°,resultinginsignificantlyreducedwindloads.


INTRODUCTION
Solar energy is one of the most promising renewable energy resources. The capacity of PV systems installed per annum was 100 GW in the period 2016-18 [1]. Electricity generation is expected to reach 4000 TWh in 2050 [2]. PV systems are usually installed on rooftops or the ground. Tilted panels face south in the Northern Hemisphere and the tilt angle relative to the horizontal surface, α, is approximately the same as the local latitude. The optimal tilt angle for PV panels can also be determined using a third-order polynomial empirical model [3].
Power efficiency for PV systems is of great concern for electricity generation. However, natural hazards, such as typhoons or hurricanes, significantly affect proper function for tilted PV panels. A large upward force is detrimental to a tilted panel, which is also critical for the design of supporting structure. Previous studies determined wind loads depending on α [4,5], the wind angle of incidence, β [6][7][8], the spacing, the degree of sheltering and the clearance between the PV array and building roof. Note that there is a reduction in wind loads near the front edge for a tilted panel with greater aspect ratio [9]. On the upper surface, Chung et al. [10] indicated there is flow separation near the leading edge and an inverted U-shape spanwise pressure distribution for β = 0°, corresponding to side-edge vortices. A pair of high fluctuating pressure zones is located in the first half region due to interactions of leading-edge flow separation and side-edge vortices [11,12]. For greater α (=40-80°), the leading-edge flow separation or reattachment was not observed [13]. The downward force increases with an increase in α. Chou et al. [11] determined the effect of β; greater suction on the upper surface is due to the windward vortex for β = 15-60°, resembling conical vortices generated on the flat roof for a low-rise building [14,15]. If the spanwise pressure distribution is unsymmetrical, the bending moment is increased.
The lift force for a tilted panel is mainly due to local wind loads near the front edge. For α = 15-30°and β = 0°, a guide plate was used by Chung et al. [16,17]. There is a reduction in suction force in the one-third region on the upper surface. Attenuation of leading-edge flow separation results in an increased lift coefficient, C L . Moreover, it is known a winglet can be used to alleviate wingtip vortices [18,19]. This study proposes a similar concept to lessen the effect of the side-edge vortices. The transverse velocity component near the side edges for a tilted panel with side plates can be inhibited. The wind loads on a tilted panel, corresponding to uplift force, with/without side plates are then determined. The data are useful for the detailed structural design of PV panels under severe wind loads.
The remainder of this paper is organized as follows. Section 2 gives a brief description of the experimental setup, including the facility, the test models, the instrumentation, and data analysis. The longitudinal and spanwise pressure distributions are presented in Section 3. The lift coefficient for a tilted panel with/without side plates is determined. Conclusions are drawn in Section 4.

E XPERIMENTAL SETUP
The experiments were conducted in a closed-loop wind tunnel, located at the Architecture and Building Research Institute, Tainan, Taiwan. There are a honeycomb and three screens upstream of a convergent nozzle. The contraction ratio is 4.7 and the constant-area test section is 2.   Fig. 1. The panel was tilted at 15°and 30°, in which the maximum blockage ratio was 4.8%. When β = 0°, the lower surface of the tilted panel faced the wind direction. The wind incidence was at an angle of 0-180°(in increments of 15°). Case A corresponds to the baseline configuration, in which there are no side plates installed. Chung et al. [10] showed that there are strong suction forces on the upper surface (the one-third region near the front edge) and slight variation in the mean surface pressure on the lower surface. To lessen the effect of the side-edge vortices, Fig. 2 shows the setup for upward or downward side plates (thickness: 1 mm; height: 2D; length: L/2). A tilted panel with downward side plates is denoted as the downward case (or Case B), while the installation for upward side plates corresponds to the upward case (or Case C).
The tilted panel was located 2.8 m from the inlet and 3 cm above the tunnel floor. The boundary layer thickness in the measurement location was ∼7 cm. The freestream velocity, U (=14.0 ± 0.1 m/s), was measured by a Pitot-static tube, which was at the same height as the model. A SCANIVALVE multichannel pressure scanner system (model ZOC33/64Px 64-port; model RAD3200) was used to measure the mean surface pressures. The Reynolds number, Re L , was 8.79 × 10 5 . Chung et al. [16] showed there is Reynolds number independence (U = 20-50 m/s) for a tilted-panel flow. The full-scale range for the pressure sensors is ±2490 Pa and the accuracy is ±0.15% of the full scale (or 3.7 Pa). The sampling rate was 250 Hz with a record length of 32 768 data points. There were 159 pressure taps machined, respectively, on the upper and lower surfaces, as shown in Fig. 3. All the pressure tapings were connected using flexible polyvinyl chloride tubes of 1.1 mm in diameter and 0.3 m in length. Irwin et al. [20] determined the effect of phase distortions was minor for tube lengths <0.3 m.
The mean pressure coefficient, C p , is denoted as (p − p ∞ )/q, where p ∞ is the freestream static pressure and q is the dynamic pressure of the incoming flow [21]. The uncertainty for C p is ∼3%. The value of C L ([ = (1/A) ∫ A C p cos(α)dA] is determined by integrating differential mean pressure distribution ( C p = C p,up − C p,low ) on the upper and lower surfaces [21]. Since there were no pressure taps on the side edges of the tilted panel, the value of C L is subject to greater error than that for C p .   the upward case, i.e. greater wind loads. The C p,up distribution for both the downward and upward cases is almost the same as x/L ≥ 0.5 (no side plates). The presence of the side plates has a minor influence on C p,low distribution. This is also true for α = 30°, as shown in Fig. 4b, but the level of C p,low is greater than that for α = 15°. In other words, wind loads on the lower surface increase as α increases. On the upper surface, less suction for the upward and downward cases is observed for x/L < 0.5. The presence of upward or downward side plates for α = 30°t ends to alleviate leading-edge flow separation or results in an increase in the value of C p,up . In particular, the suction force at x/L = 0.16-0.24 is significantly reduced for the downward case. This implies alleviation for side-edge vortices.

Longitudinal mean pressure distributions
For α = 15°and β = 30°, Fig. 5a shows the variation in C p,up and C p,low is similar to that for β = 0°. An increase in β results in a reduction in the value of C p,up at x/L < 0.33. The C p,up distribution for the downward case resembles that for the baseline case. For the upward case, there is a lower value of C p,up (greater suction) in the one-third region near the front edge, followed by greater C p,up at x/L = 0.41-0.67. On the other hand, the C p,low distributions for the baseline and upward cases are almost the same. An increase in the value of C p,low for the downward case is observed. For α = 30°, Fig. 5b shows a flatter C p,up distribution for all three test cases. This is due to a combined effect of the leading-edge flow separation, side-edge vortices and windward vortex [10]. This implies upstream movement for flow reattachment. The value of C p,up for the upward case is slightly greater than those for the baseline and downward cases. On the lower surface, there is slightly more positive pressure for the downward case, which is the same for α = 15°.
For α = 15°and β = 60°, Fig. 6a shows there is a plateau for the C p,up distribution at x/L = 0.16-0.41 for the baseline case, followed by a decrease. The presence of side plates results in upstream movement for flow reattachment. For the downward case, there is greater suction on the upper surface near the front edge (x/L ≤ 0.06) and more positive pressure on the lower surface. This corresponds to greater upward force. For α = 30°, Fig. 6b shows a minor effect on the C p,up distribution as the downward side plates are installed. On the other hand, the presence of upward side plates lessens the suction on the upper surface near the front edge, i.e. x/L ≤ 0.16. On the lower surface, there is an increase in the value of C p,low for the downward case. For β = 135°, the wind blows over the upper surface. The value of C p,up is greater than that of C p,low . Figure 7 shows the presence of side plates for α = 15°results in lower C p,low in the one-third region. There is greater value of C p,up for the upward case. This corresponds to greater downward force. For α = 30°, the C p,low distributions are similar for all test cases. The effect of side plates on the variation in C p,up resembles that for α = 15°.

Spanwise mean pressure distributions
Installation of side plates for a tilted panel aims to lessen the side-edge vortices. For β = 0°, the spanwise mean surface pressure coefficient distributions at x/L = 0.41 are shown in Fig. 8. C ps,up and C ps,low denote respective mean spanwise pressure coefficient on the upper and lower surfaces. There is an inverse U-shape C ps,up distribution for the baseline case due to the side-edge vortices. The value of C ps,up increases near the side edges for both the downward and upward cases. The leftright asymmetry of the curves for y/W > 0.3 and y/W > 0.7 is observed. This demonstrates the side-edge vortices are attenuated with the presence of side plates, also resulting in an increase in the value of C ps,up near the central region. For α = 15°, this is not true for the upward case, in which the value of C ps,up near the side edges decreases slightly. On the lower surface, the C ps,low distributions are approximately the same for all three test cases, but not near the side edges for the downward case, i.e. greater value of C ps,low . It means that the flow on the lower surface for the downward case is more two-dimensional.
For the baseline case, there is greater suction on the upper surface for β = 15-60°due to the windward vortex. The C ps distributions at x/L = 0.244 for α = 15°and β = 30°are shown in Fig. 9a. The windward vortex results in the lowest C ps,up of −2.5 near the right edge. For both upward and downward cases, there is a reduction in the value of C ps,up from y/W = 0.5 to 0.9, i.e. greater suction. The presence of the upward side plates results in an increased C ps,up value near the right edge, i.e. a reduction in the right-edge vortex. On the lower surface, the C ps,low distribution for the upward case resembles that for the baseline case. Lower value of C ps,low near the left edge is due to     the blocking effect of a tilted panel [11]. An increased C ps,low value in the left half region for the downward case means there is an increase in the upward force. Figure 9b shows the results for α = 30°. There are flattened C ps,up distributions for all three cases and the presence of the side plates results in a slight increase in the C ps,up value in the right half region. On the lower surface, the effect of the side plates shows a similar feature as that for α = 15°.
For β = 135°, Fig. 10a shows the C ps distribution for α = 15°. The value of C ps,up near the right edge for both the upward and downward cases decreases. For the upward case, there is an increase at y/W = 0.03-0.83. The effect of the windward vortex on the C ps,low distribution is visible. There is a decrease in the C ps,low value near the central region and an increase near the right edge. For α = 30°, the effect of side plates on C ps,up distribution resembles that for α = 15°. A slight reduction in the C ps,low value for the upward case in the right half region is observed.

The lift coefficient
C L is determined by integrating the upper and lower surface pressure coefficients. The effect of β is shown in Fig. 11. For α = 15°, there is a decrease in the C L value from β = 0°to β = 45°. The lowest C L is observed for β = 45°, followed by an increase until β = 165°for the baseline and downward cases and until β = 135°for the upward case. For β = 15-120°, the presence of the downward side plates results in a decrease in the C L value (or greater wind loads). This is also true for the upward side plates for β = 0°and 15°. For α = 30°and β = 0-135°, there is an increase in the C L value as β increases. The presence of the upward side plates results in greater C L (less wind loads), but not for β = 0°. For the downward case, this is true only for β = 0°and 15°. It is also noted that the absolute value of C L for β = 180°(a flip-over panel) is not the same as that for β = 0°, which is due to ground effect.
The deviation in C L with respect to the baseline case, C L (=C L − C L,baseline ), is shown in Fig. 12. A positive value of C L corresponds to reduced wind loads (or less upward force). For α = 15°, the downward side plates are only effective in reduced wind loads for β = 135°and 150°. On the other hand, the upward side plates are favored in reduced wind loads, but not for β = 0°. For α = 30°, there is a reduction in wind loads for the upward case and also for the downward case for β = 0°and 15°.

CONCLUSIONS
Wind loads on a tilted panel are affected by the flow separation near the front edge, the side-edge vortices and the windward vortex. To lessen the side-edge vortices, an experimental study was conducted using upward or downward side plates. The presence of upward side plates is beneficial for a reduction in wind loads for a tilted panel, but not for α = 15°and β = 0°. Note that downward side plates are effective only for α = 30°and β = 0°and 15°. A combination of a guide plate and side plates can be used to alleviate wind loads on a tilted panel. Future study is required.

NOMENCL ATURE
C L = lift coefficient C p = pressure coefficient, (p − p ∞ )/q C p,low = longitudinal pressure coefficient on the lower surface C p,up = longitudinal pressure coefficient on the upper surface C ps,low = spanwise pressure coefficient on the lower surface C ps,up = spanwise pressure coefficient on the upper surface D = thickness of tilted panel L = length of tilted panel p ∞ = freestream static pressure q = dynamic pressure W = width of tilted panel x = coordinate in the longitudinal direction y = coordinate in the spanwise direction α = angle of tilt β = wind incidence angle C L = deviation in C L with respect to the baseline case C p = differential pressure, C p,up − C p,low