PEAK NEGATIVE PRESSURE COEFFICIENTS ON LOW-TILTED SOLAR ARRAYS MOUNTED ON FLAT ROOFS: THE EFFECTS OF BUILDING SIZE AND MODEL SCALE

Thorsten KRAY, Jantje PAUL I.F.I. Institut für Industrieaerodynamik GmbH, Department of Aerodynamics and PV Wind Loading,

Welkenrather Straße 120, 52074 Aachen – Germany kray@ifi-aachen.de

ABSTRACT

Pressure coefficients corresponding to peak uplift on low-tilted solar panels mounted on flat-roofed buildings were determined based on boundary layer wind tunnel testing. The solar panels were arranged in arrays of 8 panels by 12 rows. A total of 9 array positions on a total of 11 buildings of different sizes with sharp roof edges were studied. The testing was conducted on a geometrical scale of 1:100 with parts of the testing being repeated at a larger scale of 1:50. Significant effects of array location on the roof, row and panel position within the array, tributary area and building size on peak negative pressure coefficients were found. A refined method for plotting pressure coefficients over normalized tributary area is proposed. In addition, it is shown that at a model scale of 1:50 peak negative pressure coefficients are higher for all array positions and building sizes. This finding may partly be associated with the effects of additional high-frequency turbulence which is not present at the smaller 1:100 scale.

INTRODUCTION

Wind loads on solar panel arrays mounted on flat or sloped roofs have been the subject of many experimental studies. Full-scale studies are rare with some notable exceptions (Geurts and Steenbergen, 2009 [1]; Moravej et al., 2015 [2]). The most common tool for evaluation of wind loads on solar panels is the atmospheric boundary layer wind tunnel. Some of the recent wind tunnel research focused on wind loads and on pressure equalization for roof-parallel panels (Wood et al., 2001 [3]; Stenabaugh et al., 2011 [4]; Erwin et al., 2011 [5]; Ginger et al., 2011 [6]; Geurts and Blackmore, 2013 [8]; Oh and Kopp, 2014a [9]; Oh and Kopp, 2014b [10]; Oh and Kopp, 2015 [11]; Stenabaugh et al., 2015 [12]; Kray, 2015 [13]; Stenabaugh and Kopp, 2015 [14]). However, most of the research focused on wind loads on tilted solar panels mounted on flat roofs such as the pioneering studies of Radu et al. (1986) [15] and Radu and Axinte (1989) [16] in the late eighties. More recent research has been concerned about quantifying parameters relevant to the wind loading of such structures. Wind tunnel results by Saha et al. (2011) [17] pointed out the effects of panel location and tilt angle on wind force coefficients. Kopp et al. (2012) [18] identified aerodynamic mechanisms relevant to the maximum wind loading on tilted, roof-mounted solar arrays. In particular, array generated turbulence, pressure equalization, the presence of the building and the setback of the array

from the roof edge were found to be causing the aerodynamic loads. Mostly northern cornering winds were critical to the solar panels. However, wall normal wind directions result in critical loads on panels within the separation bubble (Pratt and Kopp, 2013) [19]). Banks (2013) [20] highlighted the importance of the corner vortices in causing the peak uplift on solar panels. Moreover, it was found that common parapet heights increased wind loads compared to sharp-edged roofs. Larger aspect ratio buildings were observed to increase wind loads on solar panels compared to smaller ones. Browne et al. (2013) [21] studied the effect of parapets on tilted roof-top solar arrays in more detail and found higher parapets to increase wind loads on the array. Furthermore, location of panels on the roof, within the array and array geometry itself were significant parameters affecting solar panel wind loads. Cao et al. (2013) [22] considered design parameters including tilt angle and distance between arrays in their wind tunnel study and found the increase of both to be causing increasing negative module forces. However, the study did not reveal any significant effects of building depth and parapet height on negative module forces. Peak negative module force coefficients were higher than the recommendation values in the Japanese “Design Guide on Structures for Photovoltaic Arrays”, JIS C 8955 (2011) [23]. Stathopoulos et al. (2014) [24] recommended simplified provisions for the design of solar panels on roof or on ground to be included in ASCE 7. These provisions were based on wind tunnel testing of stand-alone panel surfaces attached to flat building roofs of different heights. Cao et al. (2015) [25] provided a similar design recommendation for roof-mounted solar arrays. Warsido et al. (2014) [26] studied the effects of lateral and longitudinal spacing between panels on the wind loading of roof and ground mounted arrays. For larger array setback from the roof edge, wind load coefficients on the roof mounted array were found to decrease. Based on a paper by Geurts et al. (2005) [27] wind loads on tilted, roof-mounted PV arrays were included in some European standards, such as the Dutch pre-standard NVN 7250 [28], BRE digest 489 [29] and ÖNORM B 1991-1-4:2013-05-01 [30]. In 2014, Geurts and van Bentum introduced a novel guideline for wind loads on solar energy systems [31], NEN 7250:2014 [32]. This Dutch standard contains net pressure coefficients for the design of roof-parallel or tilted solar collectors on flat and pitched roofs with roof angles up to 75°. In 2012, the Australian/ New Zealand Standard AS/NZS 1170.2 (2012) [33] was amended by the introduction of provisions for wind loads on roof-parallel solar panels which were based on a study of Ginger et al. (2011) [6]. The overall results from that study were described by Leitch et al. (2016) [7]. Wind load calculation methods and wind tunnel testing procedures for low-profile photovoltaic racking systems were codified in the SEAOC PV2-2012 report (SEAOC, 2012 [34]), the guideline developed by the Structural Engineers Association of California. It is largely based on work by Kopp et al. (2012) [18], Kopp (2014) [35] and Kopp and Banks (2013) [36]. One important aspect of the SEAOC PV2-2012 report is that peak pressure coefficients on roof mounted solar panels do not only scale with tributary area, but also with building size. The scaling with tributary area normalized by building size is assumed to be independent of array position on the roof. Moreover, roofs are divided into zones whose sizes depend on building dimensions with the building height being the dominant parameter. As this is a simplified and essentially conservative procedure, the present study aims at refining and improving this methodology based on a solar panel array tilted at 5deg which is studied in 9 roof positions for a total of 11 buildings of different sizes in the large I.F.I. boundary layer wind tunnel. Another recent discussion focuses on the effects of high-frequency turbulence on wind loads of roof- and ground-mounted solar panels (Aly and Bitsuamlak, 2013 [37]; Banks, 2011 [38]; Banks et al., 2015 [39]) due to model scales which are in some cases larger by up to a factor of ten than the scale of

the flow simulation in the atmospheric boundary layer wind tunnel. Generally, the increased spectral content of the test flow at high frequencies is expected to increase peak pressures compared to a correctly scaled flow simulation. As pointed out by Tieleman and Akins (1996) [40], Tieleman et al. (1996 [41], 1997 [42]) and Tieleman (2003) [43] in a series of papers, flow modelling criteria at large geometrical scales of around 1:50 can be relaxed if one is interested in peak pressures. Wind tunnel simulation of the atmospheric surface-layer flow lacks the capability of duplicating the large- and small-scale eddies at the same dimensionless frequencies. Therefore, concentrating on the duplication of the horizontal turbulence intensities and the small-scale turbulence parameter at those heights where the wind loads are being measured on the model can attain the best wind tunnel simulation of the peak pressures. Furthermore, exaggeration of the small-scale turbulence tends to give better agreement with full-scale measurements, especially in high suction areas on flat roofs under the influence of the corner (delta wing) vortices (Tieleman et al., 1996 [41]). This may be partly attributed to the fact that at large geometrical scales a better match of the Reynolds number is achieved (Cheung et al., 1997 [44]). However, if peak pressures are normalized by using a mean dynamic pressure as it is common practice in wind engineering, the ratio of 3-second gust pressure to mean dynamic pressure becomes smaller for large model scales subjected to high-frequency spectral densities much higher than the target, a correctly scaled boundary layer flow (Richards et al., 2007 [45]). Thus conversion of pressure coefficients from one wind speed reference duration to another using a gust factor is known to produce an un-conservative error, i.e. the calculated pressure coefficients which refer to a 3-second gust duration are too low at large model scales. Therefore, the present study also focuses on comparing code-compliant peak negative pressure coefficients determined based on testing at a more traditional geometrical scale of 1:100 with results from a model scale of 1:50. As will be illustrated in the results and discussion section, the conservative error of increased high-frequency turbulence at a scale of 1:50 compensates for the use of a (non-conservative) gust factor for all array locations on the roofs and building sizes. As the focus of the present paper is the design of ballasted rooftop solar arrays, downward-acting loads are not addressed.

EXPERIMENTAL PROCEDURE

Wind tunnel set-up

The wind tunnel tests were conducted in the large I.F.I. boundary layer wind tunnel in Aachen, Germany. The flow is generated by 6 axial fans. The wind tunnel has a cross section of 2.7 m x 1.6 m and the test model was placed at 10 m downstream of an assembly consisting of flow-straighteners, turbulence screens, Counihan-turbulence generators and a barrier wall. The tunnel floor was covered with rough materials, which can be exchanged depending on the boundary layer wind profile that has to be simulated. For the present study, upwind terrain with a power law exponent of 0.14 was simulated. FIGURE 1(a) shows the mean wind velocity profile. FIGURE 1(b) shows the profile of the streamwise turbulence intensity along with equation (C2-6) of ASCE 49-12 [46]. FIGURE 1(c) and (d) show the streamwise wind spectrum measured with a hot-film probe in the wind tunnel incident flow, along with spectra specified in the relevant literature (Kaimal et al.,1972 [47]; Simiu and Scanlan [48], 1985; Olesen et al. [49], 1984; Tieleman, 1995 [50]) at heights of z = 100 mm and z = 200 mm above the tunnel floor. The scale of the flow simulation was calculated to be about 1:200 in the height range up to z = 200 mm by using the method of Cook (1978) [51], but becomes smaller for larger heights above the tunnel floor. The agreement between the measured and target spectra is better at the 1:100 geometrical scale compared to the 1:50 scale.

FIGURE 1 - (a) Mean wind velocity profile; (b) streamwise turbulence intensity profile; (c) spectrum of the streamwise velocitiy fluctuations at z = 100 mm; and (d) spectrum of the streamwise velocitiy fluctuations at z = 200 mm compared with data from Kaimal et al. (1972) [47], Simiu and Scanlan (1985) [48], Olesen et al. (1984) [49] and Tieleman (1995) [50]. The modules of the solar arrays tested in the present study were arranged in landscape orientation and were tilted south at 5°. Full details of the modeling cannot be given in the present paper, as the wind tunnel study was partly proprietary. FIGURE 2 provides the geometric details of the solar roof mount system that can be revealed. System dimensions and relevant venting gaps were reproduced to correct scale in the wind tunnel models as far as possible. At the 1:100 scale the module thickness had to be increased, but roof clearance was matched. As depicted in FIGURE 2, gaps between modules were not modeled over the full length. In the wind tunnel scale models solar panels were arranged on a flat roof in a configuration of eight modules per row and twelve rows behind one another. Six rows were fitted with 248 pressure taps on the upper and lower surfaces of the modules. The other rows were designed as dummies without any pressure taps. The positions of pressure tapped rows and dummy rows were interchanged in the testing.

The representative 8x12 solar arrays studied in the wind tunnel test were placed at an offset distance of a = 1.0 m from the roof edges in positions 1, 2, 3, 4 and 8 as depicted in FIGURE 3. A total of 9 different array locations on the roofs were studied. The instrumented array was placed in each of these locations for a separate test. The main axes of the arrays were parallel to the roof edges in all studied positions. All array locations were chosen such that the north and east array edges were aligned with the symmetry lines on either the 34.1 m x 34.1 m, 60 m x 60 m or 120 m x 120 m roof, but set back by a = 1.0 m from the roof edges in positions 1, 2, 3, 4 and 8. Positions 1, 2 and 5 were identical on all roofs in terms of distance from the north and east roof edges. Moreover, positions 3, 6 and 8 were identical on the 60 m x 60 m and 120 m x 120 m sized roofs.

FIGURE 3 - Plan view of the array layout for buildings with lengths and widths of Lb = Wb =120m (a), Lb = Wb =60m (b) and Lb = Wb =34.1m (c). Roof and parapet heights, H and Hp, were varied as given in TABLE 1. Array locations used in the testing are numbered on all roofs. The array is depicted in position 8 on the 120m x 120m roof.

FIGURE 2 - Drawing showing the pressure tap layout of the instrumented rows alongside the most important geometric dimensions of the test array. In these tests, lc ~ 1.0 m, hl ~ 0.15 m, hu ~ 0.25 m, wm ~ 2.0 m, s ~ 1.3 m, wa ~ 16.5 m, la ~ 15.5 m. Locations of instrumented and dummy rows were interchanged in the testing.

The studied building configurations are given in TABLE 1 in full-scale and model scale dimensions. The roof-edges were either sharp-edged or consisted of perimetric parapets. Tested building heights were in a (full-scale) range of H = 5 m to H = 12.5 m for the 1:50 model, whereas for the 1:100 model roof heights in a range of H = 7.5 m to H = 35 m were studied. Perimetric parapets were only studied for H = 10 m and roof dimensions of 60 m x 60 m at both, the 1:100 and 1:50 model scales. TABLE 1 - Summary of test building configurations with dimensions given in full-scale and for model scales of 1:100 and 1:50

The models were mounted on a turntable. Wind tunnel testing was conducted at 15° intervals for 13 wind directions from 0° to 180° where 0° corresponded to wind blowing from the north, see FIGURE 3. In this way the effects of corner vortices and reattached flow were accounted for. FIGURE 4 shows one model in the wind tunnel. Close-ups of the wind tunnel models at scales of 1:100 and 1:50 are depicted in FIGURE 5. The present measurements were conducted in a partially open test section (open roof) with blockage ratios of less than or about 5% at the 1:100 model scale. The only exceptions were buildings with roof heights of 15 m and 20 m and roof dimensions of 120 m x 120 m where blockage ratios of 5.89% and 7.86%, respectively, were present. As Hunt (1982) [52] and Tieleman and Akins (1996) [40] indicated that the upper bound for acceptable blockage is about 8-10% in the case of squat models (cubes) or prisms, this range was met at the 1:50 model scale for the largest buildings with heights of 10 m and 12.5 m and roof dimensions of 60 m x 60 m. For all other roof height and area combinations, blockage was below 8% at the 1:50 model scale.

model scale model scale34.1 x 34.1 60 x 60 120 x 120 34.1 x 34.1 60 x 60 120 x 120

341 x 341 600 x 600 1200 x 1200 682x682 1200 x 1200 2400 x 2400

5 50 - - - 100 X X -7.5 75 X X - 150 X X -10 100 X X X 200 X X -

12.5 125 - - - 250 X X -15 150 X X X 300 - - -20 200 - X X 400 - - -25 250 X X - 500 - - -30 300 - - - 600 - - -35 350 X - - 700 - - -

10 1 100 - X - 200 - X -10 2 100 - X - 200 - X -

1:100 model 1:50 model

model scale roof dimensions [mm x mm]model scale roof dimensions [mm x mm]roof height

H [m]

full scaleparapet height

Hp [m]roof height

H [mm]roof height

H [mm]

sharp-edged roof

roof with perimetric parapet

full scale roof dimensions [m x m] full scale roof dimensions [m x m]

FIGURE 4 - Wind tunnel model of one flat-roofed building with sharp roof edges and with the solar array in roof position 2 at the 1:100 model scale. Full-scale roof dimensions are 60 m x 60 m at a roof height of H = 10 m. Upstream of the model roughness elements, a barrier wall, Counihan-turbulence generators and turbulence screens are visible.

Using brass tubes and flexible tubes the pressure taps were connected to PSI DTC-Initium pressure scanners. The measuring chain – pressure tap, brass tube, flexible tube, pressure scanner – is a vibratory system. The internal diameters of the brass tubes and of the flexible tubes corresponded to 1.0 mm. To avoid artificial amplification or damping of pressure signals the method of Holmes and Lewis (1987) [53] was applied by inserting restrictors with an internal diameter of 0.4 mm. The total length of the tubing of different internal diameters was 200 mm. In this way a flat frequency response was achieved up to 225 Hz. The pressure taps were scanned computer-controlled via the PSI DTC-Initium system. The pressure transducers are piezo-resistive differential sensors with a full-scale pressure range of ±1000 Pa. Each individual pressure scanner is equipped with 32 pressure ports. In this study, the maximum number of eight pressure transducers scanning simultaneously was used. All pressure taps were sampled simultaneously at a rate of 650 Hz. The velocity scale was calculated by assuming a mean wind velocity of 40 m/s at a height of 10 m in an open country exposure and a mean wind velocity in the wind tunnel measured by means of a Pitot-static tube at the respective height as given in FIGURE 1(a). The number of sampling values per data series was set such that a 24-25 minute sampling in full-scale was achieved. Therefore, sampling times varied between approximately 124 s at the 1:50 scale and 68 s at the 1:100 scale.

FIGURE 5 - Photographs of the wind tunnel models of the generic solar ballasted roof mount system with tilt of 5° at geometrical scales of 1:100 (on the left) and 1:50 (on the right).

Data analysis

For the calculation of peak pressure coefficients the method of Cook and Mayne which is largely based on work by Cook (1990) [54] was adopted. The method was refined as suggested by the Dutch wind tunnel guideline (CUR, 2005) [55] and by Peng et al. (2014) [56]. The Gumbel distribution is often used to fit the distribution of peak wind pressure coefficients

( ) ( ) ( )ˆ ˆˆ = +1.4/p Cp t Cp tC t U a

(1)

where ( )Cp ta is the dispersion and ( )Cp tU is the mode determined from a series of observed peaks,

( )ˆpC t is the pressure coefficient, and t is the duration in which a single peak is observed (reference

duration). Equation (1) corresponds to a 78 % probability of non-exceedance as expressed by the reduced variate which is equal to y = 1.4. ( )Cp ta and ( )Cp tU are determined based upon N observed peaks using the Lieblein BLUE formulation (Lieblein, 1974 [57]), as listed in the schematic in FIGURE 6.

FIGURE 6 - Observed peak method (Gumbel method) with refinement by Peng et al. (2014) [56]. This method requires a total record duration of ttotal = N⋅t. The resultant cumulative distribution function corresponds to the reference duration of t. For example, ˆ

pC representing a 78% probability of non-exceedance within a one minute reference duration could be estimated by dividing a 24 min record into 24 1-minute segments, observing the largest peak in each segment, estimating the Gumbel parameters using these peaks, and identifying the 78% probability of non-exceedance from the Gumbel cumulative distribution function. Subsequently, a procedure has to be applied which converts the Gumbel parameters between different reference durations. This allows the estimation of ( )Cp ta and ( )Cp tU using a sufficient N within a relatively short data record, followed by a conversion to the desired longer reference duration T. For the two reference duration values (t, T, t ≤ T), the conversion is

( ) ( )ˆ ˆCp T Cp ta a= (2)

( ) ( ) ( ) ( )ˆ ˆ ˆ= +1/ ln /Cp T Cp t Cp tU U a T t⋅ (3)

( )ˆpC T is then identified by combining equations (1), (2) and (3) as follows:

( ) ( ) ( ) ( )ˆ ˆˆ = +1/ ln / +1.4p Cp t Cp tC T U a T t ⋅ (4)

As in the present study the two reference duration values, t and T, both correspond to 1 min, ( )ˆpC t

and ( )ˆpC T are identical. All pressure coefficients refer to a velocity pressure which is averaged over

the full-scale sampling time of 1 min of the respective 1-minute segment. As in wind loading codes such as ASCE 7-10 (ASCE, 2010 [58]) and EN 1991-1-4 (CEN, 2005 [59]) the design velocity pressure corresponds to the 3-second-gust, the pressure coefficients calculated by equation (4) need to be converted into pseudo-steady pressure coefficients, ( )3pC s% . For this conversion, the Durst curve as given in Figure C26.5-1 of the ASCE 7-10 standard was used:

( ) ( )ˆ3 = 0.68p pC s C T ⋅% (5)

Equation (5) shows that the pseudo-steady pressure coefficients, ( )3pC s% , are lower by 32% compared

with the pressure coefficients ( )ˆpC T as calculated by equation (4). All net pressure coefficients

presented in this paper correspond to pseudo-steady pressure coefficients, ( )3pC s% , and are averaged over the tributary areas assigned to the taps on the upper and lower panel surfaces.

RESULTS AND DISCUSSION

As can be seen from FIGURE 3, array positions 1, 2 and 5 were tested on roofs with full-scale plan view dimensions of 34.1 m x 34.1 m, 60 m x 60 m and 120 m x 120 m. As in addition array positions 1, 2 and 5 were tested on geometrical scales of 1:50 and 1:100, the focus of the present analysis shall be placed on results from these array positions. First, results relevant to the refined methodology of scaling pressure coefficients with tributary area and building size are given. Then, pressure coefficients for the 1:100 and 1:50 model scales are compared and discussed.

Scaling of pressure coefficients with tributary area and building area

Pressure coefficients were found to be a function of both, tributary area and building area. The ratio of both is termed normalized tributary area, An, as expressed by equation (6).

( )( )

2 2

1000

max ;4max ; min ; 4 ; 4

tn

L S

AAb H

b H W H Wc

γ

⋅=

⋅ ⋅ ⋅ ⋅

(6)

where: At = tributary area (module area x number of modules which share loads), in m2 H = roof height, in m WL = width of a building on its longest side, in m WS = width of a building on its shortest side, in m b = constant, in m2 c = constant, in m γ = power law exponent Note that equation (6) is a refinement to the SEAOC PV-2 approach [34] which suggests scaling of roof zones with building height. However, the present approach is slightly different as the scaling with (H/c)γ is introduced into the equation for An, and fixed zone sizes are used, but it accomplishes the same goal, which is to account for the tributary area when compared with the size of flow structures above the roof. FIGURE 7 shows pressure coefficients for array position 1 for the 2nd to 6th row from north and for the 1st to 4th module. FIGURE 8 and FIGURE 9 show pressure coefficients for array positions 2 and 5, respectively, for the 7th to 11th row from north and for the 1st to 4th module. The model scale is 1:100. It can be seen that the results for buildings with different plan view dimensions produce very similar enveloping curves for roof heights up to 35 m. All enveloping curves include the strongest peaks from wind directions from 0° to 180°. Primarily, for modules tilted to the south and arrays situated in the north half of the building, the strongest peaks are expected to originate from north corner vortices. The arrays located in positions 2 and 5 on the building with plan view dimensions of 34.1 m x 34.1 m may also be expected to be subjected to strong south corner vortices. However, the data sets in FIGURE 7, FIGURE 8 and FIGURE 9 show no evidence that these south corner vortices produce higher pressure coefficients than north corner vortices as captured by enveloping curves for plan view dimensions of 60 m x 60 m and 120 m x 120 m.

For buildings wider or longer than 4H no further increase of pressure coefficients was found. However, normalization of tributary area works better if an additional dependence on normalized building height scaled by a power law exponent, (H/c)γ, is introduced. The power law exponent accounts for changes in array position on the roof and pressure equalization. In the present testing, a range of γ-values from -2.0 to 0 was observed. The validity of equation (6) can be confirmed from the enveloping curves in FIGURE 7 through FIGURE 9 which almost fall for different building plan view dimensions and roof heights onto a single curve. The effects of array position on the roof are also evident from FIGURE 7 to FIGURE 9. Note that the pressure coefficients cannot be compared directly as values for the power law exponent, γ, vary with array position. However, there is a general trend for pressure coefficients to drop from array position 1 to array position 2 and from array position 2 to array position 5. This trend is most significant at small An-values. Pressure coefficients vary also within an array from edge modules to interior modules and from north to south rows due to sheltering effects and array-generated turbulence. However, these results are not presented herein in detail, and the effects of row or panel position within the array cannot always be discerned from the effects of array position on the roof.

FIGURE 7 - Pressure coefficients, ( )3pC s% , vs. normalized tributary area, An, for array position 1; 2nd to 6th row from north, 1st to 4th module; scale 1:100.

FIGURE 8 - Pressure coefficients, ( )3pC s% , vs. normalized tributary area, An, for array position 2; 7th to 11th row from north, 1st to 4th module; scale 1:100.

FIGURE 9 - Pressure coefficients, ( )3pC s% , vs. normalized tributary area, An, for array position 5; 7th to 11th row from north, 1st to 4th module; scale 1:100.

Comparison of pressure coefficients at scales of 1:50 and 1:100

FIGURE 10, FIGURE 11 and FIGURE 12 show pressure coefficients plotted over An for those configurations only which were tested at both geometrical scales, 1:50 and 1:100. Values for the power law exponent, γ, were deduced from 1:100 data. To enable full comparison of both data sets, enveloping curves for 1:50 data were plotted based on normalized tributary area, An, as deduced from 1:100 data. It is obvious that 1:50 testing leads to more conservative enveloping curves. Depending on array position and normalized tributary area, An, peak negative pressure coefficients at 1:50 are on average higher by 10% to 20% compared with the 1:100 scale. From additional testing at the 1:100 scale, it was confirmed that the numerous tubes protruding above the models, see FIGURE 5, interfered with the flow over the panels. The error associated with the tubing was quantified to be on average 10% at the 1:100 scale, but was not evaluated at the 1:50 scale. At the 1:50 scale, the tubes were also present, but smaller relative to the model. Therefore, the real difference between enveloping curves for 1:100 and 1:50 scales may be smaller than the differences depicted in FIGURE 10 through FIGURE 12. The remaining offset between enveloping curves at both scales may be partly attributed to the additional high-frequency turbulence at the 1:50 scale. However, the approach flow profile may be less important than the effects of the corner vortices which are known to cause the peak net pressure coefficients at any scale. In addition, the 0.68 conversion factor from equation (5) applies, strictly speaking, only to a model scale which is adjusted to the scale of the boundary layer simulation. This was more or less the case at the 1:100 geometrical scale where the mismatch with the scale of the modeled atmospheric boundary layer was within a factor of 2. At the 1:50 scale, the scale mismatch corresponded rather to a factor of 4 suggesting that the 0.68 conversion factor may not be conservative [45]. In conclusion, at the 1:50 scale, the added high-frequency turbulence seems to outweigh the likely overprediction of the 0.68 reduction factor from equation (5).

FIGURE 10 - Pressure coefficients, ( )3pC s% , vs. normalized tributary area, An, for array position 1; 2nd to 6th row from north, 1st to 4th module; both scales.

FIGURE 11 - Pressure coefficients, ( )3pC s% , vs. normalized tributary area, An, for array position 2; 7th to 11th row from north, 1st to 4th module; both scales.

FIGURE 12 - Pressure coefficients, ( )3pC s% , vs. normalized tributary area, An, for array position 5; 7th to 11th row from north, 1st to 4th module; both scales.

CONCLUSIONS

Zoning of roof pressures in codes and standards depends usually on building dimensions. This is to account for the size of flow patterns such as reattachment lengths and extent of corner vortices into the roof interior. However, the method presented for plotting pressure coefficients over normalized tributary area using fixed zone sizes works well for the range of building sizes tested in the present study and is also likely to be applicable to some extent to building sizes beyond the tested range. Besides building size, the array location on the roof has the strongest effect on the magnitude of pressure coefficients corresponding to peak uplift on low-tilted solar panels deployed on flat roofs. It was also found that that the effects of row or panel position within the array are significant with regard to the magnitude of peak negative pressure coefficients. The 1:50 geometrical scale used in a modeled atmospheric boundary layer at a scale of 1:200 along with equation (5) is appropriate for studying peak pressure coefficients on pressure-equalizing roof mounted systems. 1:50 testing leads to more conservative enveloping curves compared with 1:100 testing. This is due to the fact that the additional high-frequency turbulence which is not present at the smaller 1:100 scale compensates for the error associated with the use of the 0.68 conversion factor. However, this conclusion is not true anymore for even larger geometrical scales, i.e. in the range of 1:10 to 1:30, which are frequently used in wind tunnel studies on solar structures. If such scales are used in a boundary layer wind tunnel which was designed for conventional scales in the range of 1:200 to 1:400, the use of a gust factor from a building code or from the Durst curve is un-conservative and will lead to an underestimation of the real loads which increases with increasing magnitude of the conversion factor. The use of 1-min as reference duration takes into account that studies on solar structures are generally conducted at large geometrical scales where energy at low frequencies is missing and is expected to be applicable if the scale mismatch does not exceed a factor of approximately 4. Thus modifications to standard analysis methods developed for conventional scales of boundary layer simulation are necessary and were achieved by the present approach.

REFERENCES

[1] C.P.W. Geurts and R.D.J.M. Steenbergen, 2009, “Full scale measurement of wind loads in stand off pv systems”, 5th European African Conference on Wind Engineering, July 19-23, Florence, Italy.

[2] M. Moravej, A. Chowdhury, P. Irwin, I. Zisis, G. Bitsuamlak, 2015, “Dynamic Effects of Wind Loading on Photovoltaic Systems”, Proceedings of the 14th International Conference on Wind Engineering, June 21-26, Porto Alegre, Brazil.

[3] G.S. Wood, R.O. Denoon and K.C.S. Kwok, 2001, “Wind loads on industrial solar panel arrays and supporting roof structure”, Wind and Structures, vol. 4, 481-494.

[4] S.E. Stenabaugh, P. Karava, and G.A. Kopp, 2011, “Design wind loads for photovoltaic systems on sloped roofs of residential buildings”, 13th International Conference on Wind Engineering, July 11-15, Amsterdam, The Netherlands.

[5] J. Erwin, A.G. Chowdhury, G. Bitsuamlak and C. Guerra, 2011, “Wind effects on photovoltaic panels mounted on residential roofs”, 13th International Conference on Wind Engineering, July 11-15, Amsterdam, The Netherlands.

[6] J. Ginger, M. Payne, G. Stark, B. Sumant and C. Leitch, 2011, Investigation on wind loads applied to solar panels mounted on roofs, Report No. TS 821, Cyclone Testing Station, School of Engineering and Physical Sciences, James Cook University, reviewed by J. Holmes, December 22, Townsville, Australia.

[7] C.J. Leitch, J.D. Ginger, J.D. Holmes, 2016, “Wind loads acting on solar panels mounted parallel to pitched roofs, and acting on the underlying roof”, Wind and Structures, vol. 22, 307-328.

[8] C. Geurts and P. Blackmore, 2013, “Wind loads on stand-off photovoltaic systems on pitched roofs”, Journal of Wind Engineering and Industrial Aerodynamics, 123 Part A, 239-249.

[9] J.H. Oh and G.A. Kopp, 2014, “An experimental study of pressure equalization on double-layered roof-system of low-rise buildings”, CWE 2014, June 8-12, Hamburg, Germany.

[10] J.H. Oh and G.A. Kopp, 2014, “Modelling of spatially and temporally-varying cavity pressures in air-permeable, double-layer roof systems”, Building and Environment, vol. 82, 135-150.

[11] J.H. Oh and G.A. Kopp, 2015, “An experimental study of pressure distributions within an air-permeable, double-layer roof system in regions of separated flow”, Journal of Wind Engineering and Industrial Aerodynamics, vol. 138, 1-12.

[12] S.E. Stenabaugh, Y. Iida, G.A. Kopp and P. Karava, 2015, “Wind loads on photovoltaic arrays mounted parallel to sloped roofs on low-rise buildings”, Journal of Wind Engineering and Industrial Aerodynamics, vol. 139, 16-26.

[13] T. Kray, 2015, “Peak net pressure coefficients on roof-parallel photovoltaic arrays mounted on a low-rise, 10° gable roof”, Proceedings of the 14th International Conference on Wind Engineering, June 21-26, Porto Alegre, Brazil.

[14] S.E. Stenabaugh, G.A. Kopp, 2015, “The effects of array geometry on net wind loads on individual solar modules within an array mounted parallel to the roof of a low-rise building”, Proceedings of the 14th International Conference on Wind Engineering, June 21-26, Porto Alegre, Brazil.

[15] A. Radu, E. Axinte and C. Theohari, 1986, “Steady wind pressures on solar collectors on flat-roofed buildings”, Journal of Wind Engineering and Industrial Aerodynamics, vol. 23, 249-258.

[16] A. Radu and E. Axinte, 1989, “Wind forces on structures supporting solar collectors”, Journal of Wind Engineering and Industrial Aerodynamics, vol. 32, 93-100.

[17] P.K. Saha, A. Yoshida and Y. Tamura, 2011, “Study on wind loading on solar panel on a flat-roof building: Effects of locations and inclination angles”, 13th International Conference on Wind Engineering, July 11-15, Amsterdam, The Netherlands.

[18] G. Kopp, S. Farquhar and M. Morrison, 2012, “Aerodynamic mechanisms for wind loads on tilted, roof-mounted, solar arrays”, Journal of Wind Engineering and Industrial Aerodynamics, vol. 111, 40-52.

[19] R.N. Pratt and G.A. Kopp, 2013, “Velocity measurements around low-profile, tilted, solar arrays mounted on large flat-roofs, for wall normal wind directions”, Journal of Wind Engineering and Industrial Aerodynamics, vol. 123 Part A, 226-238.

[20] D. Banks, 2013, “The role of corner vortices in dictating peak wind loads on tilted flat solar panels mounted on large, flat roofs”, Journal of Wind Engineering and Industrial Aerodynamics, vol. 123 Part A, 192-201.

[21] M.T.L. Browne, M.P.M. Gibbons, S. Gamble and J. Galsworthy, 2013, “Wind loading on tilted roof-top solar arrays: The parapet effect”, Journal of Wind Engineering and Industrial Aerodynamics, vol. 123 Part A, 202-213.

[22] J. Cao, A. Yoshida, P.K. Saha and Y. Tamura, 2013, “Wind loading characteristics of solar arrays mounted on flat roofs”, Journal of Wind Engineering and Industrial Aerodynamics, vol. 123 Part A, 214-225.

[23] Japanese Industrial Standards Committee, 2011, JIS C 8955:2011 – Design guide on structures for photovoltaic array, Japanese Standards Association, Tokyo, Japan.

[24] T. Stathopoulos, I. Zisis and E. Xypnitou, 2014, “Local and overall wind pressure and force coefficients for solar panels”, Journal of Wind Engineering and Industrial Aerodynamics, vol. 125, 195-206.

[25] C. Cao, S. Cao, Y. Tamura, 2015, “Wind loading characteristics on roof-mounted solar arrays: comparison, interpretation and generalization”, Proceedings of the 14th International Conference on Wind Engineering, June 21-26, Porto Alegre, Brazil.

[26] W.P. Warsido, G.T. Bitsuamlak, J. Barata and A.G. Chowdhury, 2014, “Influence of spacing parameters on the wind loading of solar array”, Journal of Fluids and Structures, vol. 48, 295-315.

[27] C.P.W. Geurts, C. van Bentum and P. Blackmore, 2005, “Wind loads on solar energy systems mounted on flat roofs”, 4th European African Conference on Wind Engineering, July 11-15, Prague, Czech Republic.

[28] NEN, 2007, NVN 7250:2007 – Solar energy systems – Integration in roofs and facades – Building aspects, Delft, The Netherlands.

[29] P. Blackmore, 2004, BRE digest 489 – Wind loads on roof-based photovoltaic systems, BRE Bookshop, London, United Kingdom.

[30] Österreichisches Normungsinstitut, 2013, ÖNORM B 1991-1-4:2013-05-01 – Eurocode 1: Einwirkungen auf Tragwerke – Teil 1-4: Allgemeine Einwirkungen – Windlasten – Nationale Festlegungen zu ÖNORM EN 1991-1-4 und nationale Ergänzungen, Vienna, Austria.

[31] C.P.W. Geurts and C.A. van Bentum, 2014, “A novel guideline for wind loads on solar energy systems”, ICBEST 2014, June 9-12, Aachen, Germany.

[32] NEN, 2014, NEN 7250:2014 – Zonne-energiesystemen - Integratie in daken en gevels - Bouwkundige aspecten, Delft, The Netherlands.

[33] Standards Australia International Ltd., 2012, AS/NZS 1170.2 (Incorporating Amendment Nos 1 and 2) – Structural Design Actions – Part 2: Wind Actions, Australian/ New Zealand Standard, Sydney, Australia.

[34] Structural Engineers Association of California, 2012, SEAOC Report PV2-2012 – Wind design for low-profile solar photovoltaic arrays on flat roofs, SEAOC Solar Photovoltaic Systems Committee, Sacramento, California, USA.

[35] G. Kopp, 2014, “Wind Loads on Low Profile, Tilted, Solar Arrays Placed on Large, Flat, Low-Rise Building Roofs”, Journal of Structural Engineering, vol.140.

[36] G. Kopp, D. Banks, 2013, “Use of the Wind Tunnel Test Method for Obtaining Design Wind Loads on Roof‐Mounted Solar Arrays”, Journal of Structural Engineering, vol. 139.

[37] A.M. Aly and G. Bitsuamlak, 2013, “Aerodynamics of ground-mounted solar panels: test model scale effects”, Journal of Wind Engineering and Industrial Aerodynamics, vol. 123 Part A, 250-260.

[38] D. Banks, 2011, “Measuring Peak Wind Loads on Solar Power”, Proceedings of the 13th International Conference on Wind Engineering, July 10-15, Amsterdam, The Netherlands.

[39] D. Banks, T.K. Guha, Y.J. Fewless, 2015, “A hybrid method of generating realistic full-scale time series of wind loads from large-scale wind tunnel studies: Application to solar arrays”, Proceedings of the 14th International Conference on Wind Engineering, June 21-26, Porto Alegre, Brazil.

[40] H. Tieleman and R. Akins, 1996, “The effect of incident turbulence on the surface pressures of surface-mounted prisms”, Journal of Fluids and Structures, vol. 10, 367-393.

[41] H.W. Tieleman, D. Surry and K.C. Mehta, 1996, “Full/ model scale comparison of surface pressures on the Texas Tech experimental building”, Journal of Wind Engineering and Industrial Aerodynamics, vol. 61, 1-23.

[42] H.W. Tieleman, T.A. Reinhold and M.R. Hajj, 1997, “Importance of turbulence for the prediction of surface pressures on low-rise structures”, Journal of Wind Engineering and Industrial Aerodynamics, vol. 69-71, 519-528.

[43] H.W. Tieleman, 2003, “Wind tunnel simulation of wind loading on low-rise structures: a review”, Journal of Wind Engineering and Industrial Aerodynamics, vol. 91, 1627-1649.

[44] J.C. Cheung, J.D. Holmes, W.H. Melbourne, N. Lakshmanan and P. Bowditch, 1997, “Pressures on a 1/10 scale model of the Texas Tech building”, Journal of Wind Engineering and Industrial Aerodynamics, vol. 69-71, 529-538.

[45] P.J. Richards, R.P. Hoxey, B.D. Connel, D.P. Lander, 2007, “Wind Tunnel modelling of the Silsoe Cube”, Journal of Wind Engineering and Industrial Aerodynamics, vol. 95, 1384-1399.

[46] American Society of Civil Engineers, 2012, ASCE Standard ASCE/SEI 49-12 – Wind Tunnel Testing for Buildings and Other Structures, Reston, Virginia, USA.

[47] J.C. Kaimal, J.C. Wyngaard, Y. Izumi and O.R. Coté, 1972, “Spectral characteristics of surface-layer turbulence”, Quarterly Journal of Royal Meteorological Society, vol. 98, 563-589.

[48] F. Simiu and R.H. Scanlan, 1985, Wind Effects on Structures: An Introduction to Wind Engineering, John Wiley & Sons, New York, USA.

[49] H.R. Olesen, S.E. Larsen and J. Hojstrup, 1984, “Modelling velocity spectra in the lower part of the planetary boundary layer”, Boundary-Layer Meteorology, vol. 29, 285-312.

[50] H.W. Tieleman, 1995, “Universality of velocity spectra”, Journal of Wind Engineering and Industrial Aerodynamics, vol. 56, 55-69.

[51] N.J. Cook, 1978, “Determination of the model scale factor in wind-tunnel simulations of the adiabatic atmospheric boundary layer”, Journal of Industrial Aerodynamics, vol. 2, 311-321.

[52] A. Hunt, 1982, “Wind-tunnel measurements of surface pressures on cubic building models at several scales”, Journal of Wind Engineering and Industrial Aerodynamics, vol. 10, 137-163.

[53] J.D. Holmes and R.E. Lewis, 1987, “Optimization of dynamic-pressure-measurement systems. I. Single point measurements”, Journal of Wind Engineering and Industrial Aerodynamics, vol. 25, 249-273.

[54] N.J. Cook, 1990, The designer’s guide to wind loading of building structures, Part 2 – Static Structures, Butterworths, London, United Kingdom.

[55] Civiel Centrum Uitvoering Research en Regelgeving, 2005, CUR guideline 103: Wind tunnel research. The determination of design wind loads on (highrise) buildings and parts of buildings, CUR NET, Gouda, The Netherlands.

[56] X. Peng, L. Yang, E. Gavanski, K. Gurley, D. Prevatt, 2014, “A comparison of methods to estimate peak wind loads on buildings”, Journal of Wind Engineering and Industrial Aerodynamics, vol. 126, 11-23.

[57] J. Lieblein, 1974, Efficient methods of extreme-value methodology, Report No. NBSIR 74-602, National Bureau of Standards, Washington, USA.

[58] American Society of Civil Engineers, 2010, ASCE Standard ASCE/SEI 7-10 – Minimum Design Loads for Buildings and Other Structures, Reston, Virginia, USA.

[59] CEN, 2005, EN 1991-1-4:2005 – Eurocode 1: Actions on Structures – Part 1-4: General Actions – Wind Actions, Brussels, Belgium.

ACKNOWLEDGMENTS

The continuous support of Wlodzimierz Nawrot in setting up and conducting the experiments is gratefully acknowledged. Special thanks to Sebastian Rockstein for drawing some of the figures countless times.