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Analysis of wind pressure characteristics of typical agricultural greenhouse buildings on tropical islands
Advances in Aerodynamics volume 6, Article number: 1 (2024)
Abstract
Existing studies about wind pressure on agricultural greenhouse buildings concentrate on the mean wind pressure while ignoring the systematic research on fluctuating wind pressure characteristics and the influence of roof shape on the wind pressure characteristics, which are closely associated with the windinduced damage mechanism. In this study, two typical agricultural greenhouse buildings on tropical islands are selected as prototypes to conduct pressure measurement experiments in the wind tunnel. Based on the wind pressure time series for the two greenhouses, the mean and fluctuating wind pressure distribution pattern and the localized highpressure generation mechanism are analyzed. Then, the shape coefficient of the two greenhouses is compared in depth to the standards from four countries. Besides, wind pressure nonGaussian determination criteria for agricultural greenhouse buildings considering the roof shape and wind directions are proposed. Lastly, the differences in wind pressure spectra on the roofs and walls of the two greenhouses are summarized. The results indicate the roof shape has a significant influence on the wind pressure characteristics. Compared with the pitched roof, the vaulted roof will increase the suction effect on the windward front zone and the middle area, mitigate the suction impact on the leeward roof, and weaken the wind pressure nonGaussian characteristics. The experimental shape coefficient of the pitchedroof greenhouse is basically consistent with the standard from the U.S., while that of the vaultedroof greenhouse has some deviation from the existing standards. The results provide a theoretical basis for the windresistant design of agricultural greenhouse buildings on tropical islands.
1 Introduction
Agricultural greenhouse buildings are specific facilities that utilize lighttransmitting covering materials and environmental control equipment to create optimal microclimates for crop growth and development. Influenced by the tropical maritime climate, agricultural greenhouse buildings in Hainan Province of China have suffered severe damage from the strong wind and typhoon [1]. The main reasons for the windinduced damage are the poor understanding of the wind effects on greenhouse buildings on tropical islands and the lack of standardized guidance for the windresistant design and construction of greenhouse buildings. Based on the above, wind pressure measurement tests of agricultural greenhouse buildings are performed in the wind tunnel, and the wind pressure characteristics and distribution patterns on the surface of the greenhouse buildings are summarized, which has significance against windinduced disasters and reducing losses of agricultural greenhouse buildings on tropical islands.
According to the roof shape, the singlespan greenhouse building could be mainly divided into the pitchedroof greenhouse and the vaultedroof greenhouse. Previous studies on wind loads of agricultural greenhouse buildings were conducted by field measurement, wind tunnel test, and numerical simulation. Wells et al. [2] collected wind load data of glass greenhouses of five different crosssections within 0° ~ 90° by field measurement in the natural wind. Richardson et al. [3] measured the surface pressure of the greenhouse with and without shelter of 50% permeability in the natural wind and obtained the corresponding shelter factor. Kwon et al. [4] measured the wind pressure coefficients of four typical singlespan greenhouses with different wind directions, roof slopes, and curvature radii in Korea by wind tunnel tests. Moriyama et al. [5, 6] conducted the wind pressure experiment using the 1:20 scale rigid model of a tubeshed greenhouse building to analyze the influence of sidehill wall openings on internal and external pressure coefficients and the influence of arrangement spacing on wind pressure coefficients of greenhouse buildings. Kim et al. [7] analyzed the design parameters of five greenhouse standards, including the specification of wind loads, correction factors, and shape coefficients, and summarized the differences among the standards. Besides, Kim et al. [8] analyzed the factors affecting the accuracy of numerical simulation, including the thickness of the atmospheric boundary layer, the turbulence model and the size of the computational domain. The reliability of numerical simulation is verified by comparing the simulation results with the wind tunnel results. Yang et al. [9] summarized wind pressure coefficient distribution patterns on the rigid model surface of the greenhouse building and deduced the critical wind speeds for various zones when windinduced damage occurred. Xie et al. [10] carried out wind pressure experiments of a single plastic greenhouse in South China, analyzed the distribution pattern of wind load shape coefficients under 16 wind directions, and discussed the influence of the eave, skylight, and other extensions on the wind loads on the plastic greenhouse. Wu [11] conducted a wind tunnel test to analyze the distribution characteristics of wind pressure on the surface of greenhouse buildings with and without shade curtains. The results show that existing curtains can increase the wind pressure coefficient on the surface of greenhouse buildings.
In summary, existing studies about the wind effect of agricultural greenhouse buildings focus on the mean wind pressure on the surface of buildings while ignoring the systematic research on the statistical properties of the fluctuating wind pressure and the frequency domain characteristics. Based on the previous studies [12], the fluctuating wind pressure and the frequency domain characteristics are closely associated with the structural damage mechanism, which has vital theoretical and engineering significance to the windinduced vulnerable greenhouse buildings. In addition, how the shape of the greenhouse roof influences the wind pressure distribution on the greenhouse building also deserves more scholarly research. It is necessary to lay the foundation for obtaining the windinduced damage mechanism of agricultural greenhouse buildings with different roof shapes.
In this study, rigid model pressure measurement experiments are conducted for agricultural greenhouse buildings with vaulted roofs and pitched roofs on tropical islands. Based on the collected wind pressure time series from the wind tunnel tests, firstly, this paper summarizes the distribution pattern of the mean and fluctuating wind pressure on the surface of two greenhouse buildings, then compares the shape coefficients with the standards from four countries, finally analyzes the influence of roof shape on the wind pressure nonGaussian characteristics and fluctuating wind pressure spectra. The results provide a theoretical basis for the windresistant design of agricultural greenhouse buildings on tropical islands.
2 Wind tunnel tests
2.1 Modelling and pressure tap arrangement
Two typical single greenhouse buildings of an agricultural greenhouse base in Hainan Province of China are selected as research prototypes. The length of the greenhouses is 20 m, the width is 8 m, and the height is 5 m (3 m and 5 m at the eaves and the ridge, respectively). They are divided into vaultedroof and pitchedroof greenhouses according to the roof shape. Figure 1 shows the geometric dimensions of the two roof models. The curvature radius of the vaultedroof greenhouse is 5 m and the slope angle of the pitchedroof greenhouse is 26.6°. The geometry scale ratio of the rigid pressuremeasurement model is 1:25 and the model is made of acrylonitrile–butadiene–styrene (ABS). The maximum blockage ratio of the test model is 2.3%, not exceeding 5% of the crosssectional area, which meets the test requirements. Wind pressure measurement taps are installed on the surfaces of the wall and roof so that a detailed evaluation of wind pressure changes on the surface of the greenhouse building is possible. Considering the flowseparation zone where the strong suction and rapid change of the wind pressure make buildings more vulnerable to damage, dense taps are installed on the corner and verge zone of the models to capture detailed wind pressure changes [13].
Figure 2 shows the pressure tap distribution of the vaultedroof and pitchedroof greenhouse models. The vaultedroof model has a total of 419 pressure measurement taps (247 on the roof and 172 on the walls), and the pitchedroof model has a total of 432 pressure measurement taps (266 on the roof and 166 on the walls). Wind directions vary from 0° to 360° at intervals of 15°, and the test results at wind directions of 0° to 90° are under consideration because of the biaxial symmetry of the models. Because the Reynolds number of the vaultedroof model is not completely consistent with that of the prototype [14], the 18 pieces of meridional rough paper tapes with a width of 8 mm and a thickness of 0.3 mm are pasted to the external surface of the model to compensate for Reynold number differences [15]. The arrangement of meridional paper tapes for the vaultedroof model is shown in Fig. 3.
2.2 Simulation of the wind field in the wind tunnel
Rigid model pressure measurement experiments for the agricultural greenhouse buildings are conducted in the HD3 straightflow wind tunnel at Hunan University, China. The testing section of the wind tunnel is 10 m long, 3 m wide and 2.5 m high. The experiment speed can vary continuously from 0.5 m/s to 20 m/s. A turntable with a 1.8 m diameter is installed in the testing section to simulate the changing wind directions [16]. According to the measured results obtained by Huang et al. [17], the agricultural greenhouse building base on tropical islands roughly conforms to the Class B landform in the Load Code for the Design of Building Structures (GB 50009–2012) [18]. Passive simulation methods including spires, gratings, rough elements and baffles are utilized to generate the profiles of Class B in Chinese standard. The wind pressure signals are measured simultaneously at a sampling frequency of 312.5 Hz. The duration of sampling is 32 s and 10,000 data are collected at each measurement tap. The wind tunnel sampling time corresponds to the actual sampling time of 13.3 min, which meets the sampling time of not less than 10 min in the Chinese standard (GB 5009–2012). The reference height is 40 cm in the wind tunnel, which corresponds to the actual height of 10 m. The test wind speed is 10 m/s. Figure 4 shows the flow field simulation in the wind tunnel. In Fig. 4b and c, Z and Z_{r} represent the height of the wind speed sampling point and the reference height respectively, in m. U_{z} and U_{r} represent the wind speed at the height of Z and the wind speed at the reference height respectively, in m/s. I_{u} represents the turbulence intensity along the wind. The vertical coordinate fS_{u}/σ^{2}_{u} represents the normalized wind speed spectrum value and the horizontal coordinate fL_{u}/U_{r} represents the reduce frequency, where f is the frequency of fluctuating wind, in Hz, σ_{u} is the standard deviation of the wind speed, and L_{u} is the turbulence integration scale at the reference height, in m. The results show that the wind speed profile, turbulence intensities, and wind speed spectrum simulated by the wind tunnel are consistent with the target values.
3 Results and discussions
3.1 Mean wind pressure coefficient
Four typical wind directions of 0°, 30°, 60° and 90° are mainly discussed because of the biaxial symmetry of the models. Figures 5 and 6 show the mean pressure coefficient contour on the vaulted roof and pitched roof, respectively. At the wind direction of 0°, the mean wind pressure coefficient contour is symmetrical on the vaulted roof due to the influence of the columnar vortex. Large pressure gradients are observed on the windward roof, while small pressure gradients appear on the leeward roof. The positive wind pressure coefficients occur in the zone near the eave and then decrease rapidly to negative pressure with the increasing distance from the windward eave. Finally, the mean pressure coefficients come to a minimum in the ridge. When the wind blows in oblique directions from 30° to 60°, the negative highpressure zone gradually develops from the edge of the west gable to the windward eaves. At the wind direction of 90°, the negative pressure appears in the vast majority of areas on the roof. At the same time, the west gable transforms into the windward side, and the absolute value of the wind pressure coefficient decreases rapidly with the increasing distance from the windward edge until it is near zero at 1/3 of the length of the roof.
The mean pressure coefficient distribution of the pitched roof is similar to that of the vaulted roof at the wind direction of 0°. Unlike a vaulted roof, the incoming flow is separated at the windward eave of the pitched roof so that the negative pressure appears in the windward eave and ridge, and the wind pressure in the middle of the windward roof is close to zero. When the wind blows in oblique directions from 30° to 60°, the negative highpressure zone moves to the leeward area near the west gable and ridge. It is because the gable size of the windward edge is small, which is beneficial to the rapid entrainment and development of the separation shear layer. Besides, the ridge prevents the conical vortex from moving forward, and the downwind momentum of the conical vortex transforms into crosswind vorticity, so strong suction induced by the vortex develops along the ridge. At the wind direction of 90°, there are prominent negative pressures near the edge of the west gable because of the direct impact of the incoming flow. The absolute value of the wind pressure coefficient of the pitched roof is greater than that of the vaulted roof, and it gradually decreases along the ridge line, showing a symmetrical distribution.
When the wind directions are 0° and 90°, the mean wind pressure coefficients along the two buildings’ midline are presented to deeply analyze the influence of roof shape on the mean wind pressure of agricultural greenhouse buildings. As shown in Fig. 7, the horizontal coordinate presents the ratio of the horizontal distance of the measuring tap to the windward eave to the building’s span B or length L (the distance in the wall is after the planar unfolding), and the vertical coordinate represents the mean wind pressure coefficient. At the wind direction of 0°, the mean wind pressure coefficients present the same distribution pattern at the windward walls of two greenhouses and both reach the maximum at the second row B16 (near the 2/3 height of the windward wall). The wind pressure coefficient shows a “decrease first, then increase” on the vaulted roof, while a “monotonically decrease” on the pitched roof. The start and end points of the curves nearly coincide with the roof airflow separation and reattachment points, respectively. Compared with the pitched roof, larger negative pressure appears in the vaulted windward roof. As for the leeward roof, the absolute value of the mean pressure coefficient of the vaulted roof decreases slowly and reaches 0 near the leeward eave, while that of the pitched roof gradually increases and reaches a maximum value of 0.75. At the wind direction of 90°, the mean pressure coefficients for the two greenhouses present a similar tendency with decreasing first, then increasing fast, and lastly tending to be uniform. The minimum of the vaulted roof and pitched roof is −0.79 and –1.05, respectively. When the airflow flows over 0.4 L along the length direction, the mean pressure coefficients of the vaulted roof are near 0. The mean pressure coefficients of the pitched roof are significantly less than 0. The absolute values of the mean pressure coefficients of the pitched roof are higher than those of the vaulted roof, which indicates the mean wind pressure is more sensitive to the pitched roof than the vaulted roof.
3.2 Fluctuating wind pressure coefficient
Figures 8 and 9 show the fluctuating pressure coefficient contour on the vaulted roof and pitched roof, respectively. When the wind direction is 0°, the fluctuating wind pressure coefficient contour is symmetrical on the vaulted roof. Two symmetrical highpressure zones occur on the leeward roof near the gable verge, causing the gable to be easily damaged. When the wind blows in oblique directions from 30° to 60°, the contour distribution has similar characteristics, and the fluctuating wind pressure coefficients in most zones are small, about 0.20. Owing to the airflow separation in the corner, large gradients of the fluctuating wind pressure occur in the west gable near the windward zone. At the wind direction of 90°, the high wind pressure zone occurs in the windward corner near the west gable. The fluctuating wind pressure coefficient decreases rapidly with the increasing distance from the windward gable. Similar to the distribution of the mean wind pressure coefficient, the fluctuating wind pressure coefficient tends to flatten after crossing 1/3 of the length of the roof.
When the wind direction is 0°, as for the pitched roof, the fluctuating wind pressure coefficient reaches the maximum in the windward eave and then decreases towards the ridge direction. The fluctuating wind pressure changes slowly on the leeward roof. When the wind blows in oblique directions from 30° to 60°, the highpressure zones move from the middle zones of the west gable and the windward corner to the leeward eave, and a highpressure ribbon is observed on the pitched roof, which deserves to be emphasized in the design of greenhouse buildings. At the wind direction of 90°, similar to the distribution of fluctuating wind pressure coefficients for the vaulted roof, high fluctuating pressure coefficients appear in the windward front zone of the gable and then come to flatten as airflow develops.
Similar to Fig. 7, to analyze the influence of roof shape on the fluctuating wind pressure of agricultural greenhouse buildings, Fig. 10 shows the fluctuating wind pressure coefficients along the two buildings’ midlines at the wind directions of 0° and 90°. When the wind direction is 0°, the fluctuating wind pressure coefficients present a similar distribution pattern at the windward walls of the two greenhouses, and the fluctuating wind pressure coefficients of the pitched model are slightly higher than those of the vaulted model. Between the airflow separation point and reattachment point on the roof, the fluctuating wind pressure coefficients of the vaulted roof show an “increase first, then decrease”, while those of the pitched roof show a “decrease first, then increase slowly”. The inflection points of the two curves are near the ridge, which presents different distribution patterns from the mean wind pressure coefficient. At the same time, the wind pressure fluctuation of the vaulted roof is more significant than that of the pitched roof. It is because the incoming flow is separated locally in the lateral region of the vaulted roof, resulting in a transverse separation shear flow, which forms the vortex shedding in the roof fluid and produces high turbulent kinetic energy [19]. In addition, the distribution of fluctuating wind pressure on the vaulted roof is significantly affected by the Reynolds number, and the flow transition near the airflow separation point leads to high fluctuating wind pressure [14]. When the wind direction is 90°, the fluctuating pressure coefficients for two greenhouses present a similar tendency with increasing first, then decreasing slowly, and lastly tending to be uniform. The fluctuating pressure coefficients of the pitched roof are slightly higher than those of the vaulted roof, which indicates the fluctuating pressure coefficients are more sensitive to the pitched roof than the vaulted roof.
3.3 Wind load shape coefficient
Different countries’ standards have corresponding provisions in determining wind load shape coefficients for agricultural greenhouse buildings with different roof shapes. The surface of the vaultedroof model is divided into several matching zones so that the results for the wind tunnel test can be compared with four countries’ standards: China, Japan, the U.S., and the European Union (EU) [20,21,22,23]. Surface zone definitions of the vaultedroof model are shown in Fig. 11a, b, c and d. As for the pitchedroof model, the four countries’ standards have the same surface zones. Surface zone definitions of the pitchedroof model are shown in Fig. 11e.
Table 1 shows the comparative results of the wind load shape coefficient between the experiment and four countries’ standards and references for the vaultedroof greenhouse. The standards from China and Japan have the same surface zone definitions for the vaultedroof greenhouse and are defined as “Comparison 1” group. Surface zone definitions from Kwon [4] and Blackmore [24] are close to the standard from the EU, so they are defined as “Comparison 3” group. Surface zone definitions from the American standard differ from the above standards and references, so the experiment results are compared separately with the American standard as a “Comparison 2” group.
Combined with Tables 1 and 2, the experiment values in the R1 region are in good agreement with Blackmore’s results, with a small deviation of 25.4% from the Japanese standard and increasing deviations from the EU, U.S., and Chinese standards in that order. The standards of the four countries pay different attention to the geometrical characteristics of greenhouse buildings, which leads to the deviation of the shape coefficient. Regarding the determination of shape coefficients, the Japanese standard is the most detailed in describing the shape coefficients, and involves the main geometrical characteristics of the experimental model, so the deviation between the experiment results and the Japanese standard is the smallest. The rest of the standards reflect partly the geometrical characteristics of the experimental model, so the experiment results deviate significantly from the standards. It should be clarified that although the standards from China and Japan have the same surface zone definitions, the Chinese standard only reflects the effect of the risetospan ratio on wind loads, while the Japanese standard comprehensively reflects the effect of the risetospan ratio and eave heighttospan ratio on wind loads, where the shape coefficient in the R1 zone increases with increasing windward length [23]. The deviations from references may be due to the differences in the geometrical characteristics and Reynolds numbers [14, 25, 26].
The experiment values in the R2 and R3 regions are in good agreement with the standard from the EU. The experiment value in the R2 region shows the largest deviation from Blackmore’s results at 136.6% and the experiment value in the R3 region shows the largest deviation from Kwon’s results at 54.1%. The experiment value in the F1 region matches the standards from China and the U.S., is larger than the standards from Japan and the EU, and has the largest deviation from Kwon’s result at 59.6%. The experiment value in the F2 region matches the standards from China, the U.S. and Japan, with the largest deviation from Kwon’s result at 23.4%. The experiment value in the M region is in agreement with the standards from China and the U.S., with deviations of 9.3%, 12.0% and 19.3% from Kwon’s results, the standards from the EU and Japan, respectively. In summary, the shape coefficient experiment result of the vaultedroof greenhouse shows the smallest deviation from the Japanese standard, with an average deviation of 19.5% for all surface zones, and shows the largest deviation from the Chinese standard, with an average deviation of 104.6%. In conclusion, the results indicate that the standards from China, Japan, the U.S., and the EU all have limitations in determining the wind load shape coefficient for the vaultedroof greenhouse.
Table 3 shows the comparative results of the wind load shape coefficient between the experiment and four countries’ standards and references for the pitchedroof greenhouse. The standards of the four countries pay different attention to the geometrical parameters of greenhouse buildings, which leads to differences in the shape coefficients of greenhouse buildings with the same dimension. The standard from China is only related to the slope angle, and the standards from the U.S. and the EU comprehensively reflect the effect of the slope angle and heighttowidth ratio on wind loads. The standard from Japan reflects the combined effect of the slope angle, lengthtoheight ratio and widthtoheight ratio to meet the requirements of its country. Combined with Tables 3 and 4, the experiment value in the R1 region has the smallest deviation from the standards from the U.S. and the EU at 25.9%, and the largest deviation from Kwon’s result at 74.0%. The experiment value in the R2 region matches the American and Japanese standards as well as Wells’ results, with the largest deviation from the Chinese standard at 20.0%. The experiment value in the F1 region matches the Chinese and American standards, and is greater than the standards from the EU and Japan as well as Wells’ and Kwon’s results, with the greatest deviation from Kwon’s results at 40.4%. The standard from Japan has the most detailed description of the F1 region among the four countries’ standards, which reflects the influence of the variation coefficient along the height direction. The experiment value in the F2 region matches the standards from China, the U.S. and Japan, with the largest deviation from Kwon’s result at 212.5%. The experiment value in the M region shows small deviations from the four countries’ standards and references, with the largest deviation occurring in the standard from the EU at 10.0%. In summary, the shape coefficient experiment result of the pitchedroof greenhouse has the smallest average deviation of all zones from the American standard, at 6.9%, and has the greatest average deviation from Kwon’s result, at 70.4%. In conclusion, the results indicate that the American standard can basically describe the shape coefficients of the pitchedroof greenhouse, while the rest of standards have limitations in determining the shape coefficients of the pitchedroof greenhouse.
To further analyze the influence of roof shape on the shape coefficient, as shown in Fig. 11f, the pitched roof greenhouse is divided into several matching zones with the vaulted roof greenhouse in Chinese and Japanese standards. Table 5 shows that the roof shape has a significant influence on the distribution of the shape coefficients. Compared with the pitched roof, the R1 region in the windward front zone and the R2 region in the middle roof show higher negative pressure in magnitude for the vaulted roof, with a deviation of 161.1% and 272.4%, respectively. The absolute value of the shape coefficient in the R3 region on the vaulted leeward roof is smaller than that on the pitched leeward roof. The results demonstrate that the vaulted roof shape will increase the suction effect on the windward front zone and the middle roof while mitigating the suction effect on the leeward roof.
3.4 Windpressure nonGaussian characteristics
Influenced by flow separation, reattachment and vortex shedding, the windpressure signals collected in the local zone present significant nonGaussian characteristics. As for the lowrise buildings, Kumar [27] considers the zone with the absolute skewness S_{K} > 0.5 and kurtosis C_{K} > 3.5 as the windpressure nonGaussian zone. Agricultural greenhouses are significantly different from general lowrise buildings, so this criterion does not apply to the determination of the nonGaussian characteristics of wind pressure on greenhouses. Additionally, at the same measuring tap, whether the fluctuating wind load conforms to a Gaussian distribution is closely related to the incoming wind direction [28]. Therefore, the concept of statistical cumulative probability is introduced in this study to explore the cumulative probability of different wind directions, and further strengthen the GaussiannonGaussian basis for the classification of skewness and kurtosis. Previous studies have demonstrated that reaching a cumulative probability of 80% serves as a critical point for defining the cumulative distribution of longspan flat roof and cylindrical roof cover skewness and kurtosis as a highprobability event [28,29,30,31,32]. The vaulted and pitched roofs in this study also belong to the abovementioned longspan roofs. Since the study object is similar to the appearance of the longspan roof, the values of the skewness coefficients and kurtosis coefficients corresponding to 80% cumulative probability are selected as the critical points, and then the values are regarded as the criteria of windpressure nonGaussian characteristics.
Figure 12 shows the cumulative probability distribution curves of skewness and kurtosis for the vaultedroof and pitchedroof greenhouses at the wind direction of 0°, from which the critical values at each wind direction are further obtained by 80% cumulative probability. It is observed in Table 6 that the critical values of skewness and kurtosis at wind directions from 15° to 75° are close to each other, so the approximate mean values of the skewness and kurtosis coefficients at wind directions from 15° to 75° are taken as the determination criterion at the oblique wind directions. In this study, the windpressure measurement taps with S_{K} ≤ S and C_{K} ≤ C are regarded as Gaussian points, and the taps with S_{K} > S and C_{K} > C are regarded as nonGaussian points, then the rest of the windpressure taps with S_{K} < S and C_{K} > C or S_{K} > S and C_{K} < C are further systematically judged according to the combination with the windpressure timehistory curve and the probability histogram. The F9 measuring tap (failure to meet the direct determination criterion in Table 6) near the gable verge of the vaultedroof greenhouse at the wind direction of 0° is selected as an example to introduce the judgment procedure. The windpressure timehistory curve and the probability histogram of F9 are illustrated in Fig. 13. The results show that the windpressure timehistory curve presents an asymmetry and the intermittent pulse phenomenon and diverges from the Gaussian distribution curve, which indicates the F9 measuring tap does not follow the Gaussian distribution. NonGaussian characteristics of the measuring taps on the two greenhouse roofs are analyzed according to the determination criteria or the timehistory curve and probability histogram. Figures 14 and 15 show the Gaussian and nonGaussian distribution of wind pressure on the vaulted roof and pitched roof, respectively, among which the shadow area shows the Gaussian distribution and the rest of the areas show the nonGaussian distribution.
As shown in Fig. 14, influenced by the signature turbulence, the vaulted roof presents the following characteristics: (1) At the wind direction of 0°, the nonGaussian zone appears in the windward eave and the leeward eave. The former is caused by the separation of the incoming flow in the windward eaves, and the latter is attributed to the disturbance and mutual interference of wake wind pressure caused by the reattachment of the separated flow in the leeward eaves. (2) When the wind blows in oblique directions from 15° to 75°, nonGaussian zones appear in the edge, corner, and roof middle zones. With increasing wind directions, the windpressure nonGaussian area in the windward gable enlarges, and that in the leeward verge declines, which is attributed to the separation flow in the shear layer, the sidetoside oscillatory motion of the conical vortex axis, and the secondary vortex [33]. (3) At the wind direction of 90°, the symmetrical nonGaussian zones appear in the windward front zone and leeward verge zone. In general terms, as for the vaulted roof, windpressure nonGaussian areas are mainly distributed in the windward front zone, the leeward back zone and the roof middle zone.
As shown in Fig. 15, the pitched roof presents the following characteristics: (1) When the wind direction is 0°, windpressure nonGaussian zones appear in the windward front area and the middle and verge area of the leeward roof. That is because the incoming flow separates and reattaches when the airflow flows over the windward eave and ridge. (2) When the wind blows in oblique directions from 15° to 75°, influenced by the flow separation, a pair of conical vortexes appears in the corner and the ridge, which leads to the windpressure nonGaussian characteristics in the windward front zone and the localized zone of the leeward roof. Besides, the nonGaussian area in the windward edge and corner increases with increasing wind directions. Especially, a nonGaussian ribbon is observed on the leeward roof at the wind direction of 60°, which is the same as the fluctuating wind pressure distribution. (3) At the wind direction of 90°, the symmetrical nonGaussian distribution zones are observed in the windward front zone and leeward back zone. In conclusion, as for the pitched roof, the windpressure nonGaussian zones are mainly distributed in the windward front zone and the leeward roof.
The windward front zones of the vaulted roof and the pitched roof all show nonGaussian characteristics. The difference is that the wind pressure distribution in the middle roof of the vaulted greenhouse is nonGaussian, while that in the leeward roof of the pitched greenhouse is nonGaussian. In a word, compared with the vaulted roof, the pitched roof presents more obvious windpressure nonGaussian characteristics at each wind direction.
3.5 Wind pressure spectrum
The fluctuating wind pressure spectrum is a diagram that not only can depict the wind pressure signal distribution in the frequency domain, but also directly reflects the magnitude of the signal carrying power per unit frequency band. The wind pressure fluctuation on the roof includes the lowfrequency and the highfrequency components. The lowfrequency component comes from the largescale turbulent structure in the incoming flow, and the highfrequency component comes from the smallscale turbulent structure closed to the solid wall, which is caused by the disturbing effect of the structure itself on the incoming flow [33]. Hence, the wind pressure spectrum not only displays the contribution of the wind pressure signal to the fluctuating wind pressure in different frequency components, but also identifies the potential turbulent structure [34]. In this study, the wind pressure spectra at the same measuring taps located on the surface of the vaultedroof and pitchedroof greenhouses at the wind direction of 0° are presented. To obtain accurate wind pressure data, the Butterworth filter is adopted to eliminate the noise influence of the electrical signals in the test system [34,35,36]. As shown in Fig. 16, the horizontal coordinate fB/U_{z} represents the reduced frequency, and the vertical coordinate fS_{p}/σ^{2}_{p} represents the normalized wind pressure spectrum values.
The results show that at the number 1 measuring tap, the wind pressure spectra of the vaultedroof and pitchedroof greenhouses have a similar trend, and the corresponding peak frequencies are all close to 1. However, as the distance between the measuring tap and the windward eave increases, the peak frequency of the pitchedroof greenhouse shows a gradually increasing movement. At the number 3 measuring tap of the vaultedroof greenhouse, it is also found that the faster energy decay occurs in the highfrequency components.
Figure 16a depicts the wind pressure spectra at measuring taps on the windward roof. It is observed that the normalized wind pressure spectrum value of the vaultedroof model is higher than that of the pitchedroof model in the lowfrequency components. However, with the development of airflow (the measuring taps change from 1 to 3), the misalignment between the two curves gradually expands. In the highfrequency components, the wind pressure spectrum value of the pitchedroof model is higher than that of the vaultedroof model. It may be because smallscale turbulence generates some vortices after the airflow separation in the shear layer of the pitchedroof model.
Figure 16b depicts the wind pressure spectra at measuring taps on the leeward roof. The wind pressure spectrum at the number 4 measuring tap has a similar trend as the numbers 1 – 3. However, at the number 5 measuring tap, the wind pressure spectrum value of the vaultedroof model is lower than that of the pitchedroof model in the lowfrequency components, and the corresponding peak frequency of the leeward roof is higher than that of the windward roof for the vaultedroof model. Besides, the wind pressure spectrum value of the pitchedroof model decreases faster in the highfrequency components at the number 5 measuring tap. For both pitched and vaulted roofs, some pronounced peaks appear at specific frequencies, and this may be explained by the Helmholtz resonance phenomenon [37]. The Helmholtz resonance occurs inside the model cavity and the frequency corresponding to the pronounced peaks is the Helmholtz frequency.
Figure 16c, d and e depict the wind pressure spectra at measuring taps on walls. On the windward wall, the wind pressure spectrum value of the vaultedroof model is lower than that of the pitchedroof model in the lowfrequency components; besides, as the measuring tap height increases, the deviation is lower and lower. On the leeward wall, all of the wind pressure spectrum values of the vaultedroof model are lower than those of the pitchedroof model in the lowfrequency components. As for the gables, the wind pressure spectrum value of the vaultedroof model is higher than that of the pitchedroof model in the lowfrequency components. In conclusion, the energy distribution of the vaultedroof and the pitchedroof models presents a similar trend in the middlefrequency and highfrequency components, which indicates the roof shape mainly affects the energy in the lowfrequency components of the walls, while having little effect on the middlefrequency and highfrequency components of the walls.
4 Conclusion
In this study, wind pressure measurement tests of two typical agricultural greenhouse buildings were conducted in a wind tunnel, and the influence of the roof shape on the wind pressure characteristics was analyzed. The results provide a reference for the windresistant design of agricultural greenhouse buildings on tropical islands. The following conclusions can be drawn:

(1)
The mean and fluctuating wind pressure distribution patterns and the localized highpressure generation mechanism for the vaultedroof and pitchedroof greenhouse buildings on tropical islands are clarified.

(2)
The experimental shape coefficient of the pitchedroof greenhouse is basically consistent with the standard from the U.S., while that of the vaultedroof greenhouse has some deviation from the existing standards. It is suggested that the experimental results should be used in the structural design. The vaulted roof shape will increase the suction effect on the windward front zone and the middle roof while mitigating the suction effect on the leeward roof.

(3)
Wind pressure nonGaussian determination criteria for agricultural greenhouse buildings considering the roof shape and wind directions are proposed. Compared with the vaulted roof, the pitched roof presents more obvious windpressure nonGaussian characteristics at each wind direction.

(4)
On the windward roof, the wind pressure spectrum value of the vaultedroof model is higher than that of the pitchedroof in the lowfrequency components, while slightly lower than that in the highfrequency components. In terms of the walls, the roof shape mainly affects the energy in the lowfrequency components, while having little effect on the middlefrequency and highfrequency components.
Availability of data and materials
The data that support the findings of this study are available from the corresponding author upon reasonable request.
References
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Acknowledgements
We would like to thank all the experimental staff of the HD3 Wind Tunnel for their hard work.
Funding
This research was supported by the National Natural Science Foundation of China (52068019) and the Hainan Provincial Natural Science Foundation of China (522RC605, 520QN231 and 521RC502).
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Bin Huang: Supervision, Methodology, Writing – original draft, Writing – review & editing, Funding acquisition. Jinke Liu: Methodology, Writing – original draft, Writing – review & editing. Zhengnong Li: Supervision, Conceptualization. Wenxiang Wang: Writing – review & editing, Software. Xiangjun Wang: Investigation, Writing – review & editing. Xijie Liu: Investigation, Software. Tianyin Xiao: Formal analysis.
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Huang, B., Liu, J., Li, Z. et al. Analysis of wind pressure characteristics of typical agricultural greenhouse buildings on tropical islands. Adv. Aerodyn. 6, 1 (2024). https://doi.org/10.1186/s42774023001700
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DOI: https://doi.org/10.1186/s42774023001700