Open AccessArticle

Study on the Effect of Size on the Surface Wind Pressure and Shape Factor of Wind Load of Solar Greenhouses

Zongmin Liang

Zixuan Gao

¹,

Yanfeng Li

²,

Shumei Zhao

¹,

Rui Wang

¹ and

Jing Xu

^1,*

College of Water Resources and Civil Engineering, China Agricultural University, Beijing 100083, China

Vegetable Research Institute of College of Agriculture and Animal Husbandry of Tibet Autonomous Region, Lhasa 851418, China

Author to whom correspondence should be addressed.

Appl. Sci. 2024, 14(16), 7114; https://doi.org/10.3390/app14167114

Submission received: 25 June 2024 / Revised: 6 August 2024 / Accepted: 11 August 2024 / Published: 13 August 2024

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Abstract

In this paper, the effect of size on the wind pressure coefficient on the surface of solar greenhouses is investigated using numerical simulations. The models were designed with consistent ratios of ridge height to span and north wall height to ridge height across different spans. To effectively understand the impact of dimensions on wind pressure distribution, two wind directions—0° (north wind) and 180° (south wind)—which have previously been shown to impose significant overall wind loads on solar greenhouses, are focused on. It was found that the wind load per unit area increases continuously with greenhouse size. Wind-induced suction is particularly concentrated along the ridge, with greater suction on the leeward side compared to the windward side. The wind suction near the ridge is more significantly affected by greenhouse size. This study provides valuable insights for the practical engineering design of solar greenhouses.

Keywords:

solar greenhouse; size; numerical simulation; wind pressure coefficient; shape factor of wind load

1. Introduction

Solar greenhouses not only play a significant role in facility agriculture production in China but also serve as an exemplary facility for environmentally friendly and low-carbon crop cultivation worldwide [1,2,3]. In 2022, China’s facility horticulture area accounted for more than 80% of the world’s total facility horticulture area, totaling more than 2.8 million hm², of which the total area of solar greenhouses was 0.81 million hm² [4]. The solar greenhouses are considered as flexible structures, with most of their components being long and slender bars. The connecting between these components is primarily achieved through single-bolt connections or spot welding [5]. In windy conditions, the structures of solar greenhouses can be vulnerable to damage [6,7,8], resulting in both economic losses and potential threats to personnel safety. Understanding the mechanisms of wind-induced stresses on solar greenhouse roofing is of significant importance due to their susceptibility to such damage. Many scholars [9,10,11] have carried out relevant research through wind tunnel experiments and numerical simulations. For example, the effect of shape [12], span number [13], and incoming wind direction [14] on the surface wind pressure of the solar greenhouse have been studied. Still, there are fewer studies about the effect of factors such as span, ridge height, and dimensions on wind pressure distribution and shape factors of wind load of solar greenhouses.

Regarding the influence of building dimensions on wind load, You et al. [15] conducted wind tunnel experiments to examine the peak distribution of wind pressure coefficients on the ceilings and walls of end-type and corner-type arcades in buildings of varying heights. Qiu and Wang [16] analyzed the effect of the height of the parapet on the average wind pressure on the surface of a flat roof and found that the wind pressure tended to be uniform when the roof reaches a certain height. Yu et al. [17] investigated the effect of parameters such as long-span ratio and rise–span ratio on shape factor of the roof by numerical simulation and found that the two ratios have a more significant effect on shape factor. Chen et al. [18] investigated the effect of aspect ratio on the surface wind load of the roof through wind tunnel experiments and pointed out that the aspect ratio has a significant impact on the maximum wind pressure coefficient in the roof’s corner regions. McGuill et al. [19] presents a parametric investigation focusing on variations in the length of façade brackets, the length of façade fins, and wind orientation through computational fluid dynamics analysis. The primary objective is to identify the optimal design configuration that mitigates wind pressures acting upon the façade components. Chu et al. [20] studied the effect of the rise–span ratio on the shape factor of wind load of a fan-shaped building through numerical simulation and proved that the shape factors on all the zones of the surface decreased with the increase in the rise–span ratio. Relevant research indicates that the influence of dimensions on the surface wind pressure distribution in solar greenhouses should not be overlooked. However, the current China codes, Load Code for the Design of Building Structures [21] and Code for the Design Load of Horticultural Greenhouse Structures [22], which are applicable to low-rise structures with shapes similar to solar greenhouses, do not account for the influence of dimension of structure on the wind load shape factor.

In recent years, the development of solar greenhouses in alpine cold regions of China has been rapid. The diversity in dimensions of solar greenhouses, including span, ridge height, and north wall height results from variations in construction periods and specific planting requirements. Still, the more common spans for solar greenhouses typically fall in the range of 8 m to 16 m, corresponding to ridge heights of 3.9 m to 7.5 m and north wall heights of 2.8 m to 5.0 m. This paper investigates the distribution of surface wind pressure on solar greenhouses in alpine cold regions as influenced by changes in greenhouse dimensions and aims to optimize the partitioning of wind load coefficients. Five different sizes of solar greenhouses, each with the same ridge-to-span ratio, north wall height, and ridge-to-height ratio, were used as research objects. To effectively understand the impact of size on the distribution of wind pressure coefficients in solar greenhouses, this study focuses on two wind directions identified in previous simulations as prone to significant overall wind loads: 0° (northerly winds) and 180° (southerly winds). Other wind directions, such as 45°, 90°, and 135°, are excluded from consideration. Particular attention is paid to the wind pressure distribution on the front roof of these structures. Research systematically analyzes three distinct methods for zoning the wind load coefficient on the front roof and proposes an improved approach to account for the impact of greenhouse size. The insights from this study provide valuable reference data for the wind-resistant design of solar greenhouses and offer refined wind load coefficients that reflect the crucial influence of size on structural performance.

2. Numerical Model and Parameters

2.1. Computational Domain and Grid Settings

The greenhouse dimensions were based on five commonly used sizes in the alpine cold regions of China, with an east–west length of 60 m. While the spans and ridge heights varied, the ratios of north wall height to ridge height and ridge height to span remained constant. The greenhouse model features a rear roof inclination of approximately 42° (α) and a front roof inclination of approximately 30° (θ). The north wall height is denoted as H₁, the ridge height as H₂, the horizontal projection of the rear slope as B₁, and the north–south span as B₂, as detailed in Table 1. The surface profile of solar greenhouse is shown in Figure 1. Since the greenhouse dimensions were derived from practical applications, strict equal proportions were not maintained, resulting in localized variations in the model. The computational domain was enlarged by three times the model span before the model in the X-axis direction, six times the model span after the model and four times the model length in each of the left/right directions in the Z-axis direction, and more than five times the model height in the Y-axis direction, as shown in Figure 2.

An unstructured grid methodology was employed, with grid sizes determined according to reference [11]. The computational domain featured a maximum grid size of 5 m, while the greenhouse surface grid was refined to 0.3 m [11]. Given the significant gradients in velocities, pressures, and other physical quantities near the greenhouse, a boundary layer was implemented. The initial layer had a thickness of 0.1 m with a growth rate of 1.2, resulting in a boundary layer thickness of 0.74 m. Beyond the boundary layer, the bulk mesh had a growth rate of 1.08, yielding a total grid count exceeding 10⁷. The closer the mesh quality is to 1 [11], the higher the quality of the mesh. More than 80% of the total number of grids for all conditions have a mass of not less than 0.8, with a minimum mass of 0.4.

2.2. Boundary Condition

(1) Inlet boundary conditions: The inlet boundary condition is a velocity-inlet with an exponential rate-averaged wind profile. Refer to Equation (1):

v (y) = v_{b} {(\frac{y}{10})}^{α}

(1)

where z is any height; v(y) is the average wind speed at height y; v_b is the average wind speed at a height of 10 m. As per the specifications in [21], the wind speed obtained after converting the basic wind pressure with a return period of 20 years was 25 m·s⁻¹. The selection of B-type terrain, as specified by the load criteria [21], encompasses fields, villages, forests, hills, and sparsely populated townships and suburban areas, for a B-type terrain with a roughness length coefficient of α = 0.15 [21].

The turbulence characteristics at the inlet are defined by directly giving the turbulent kinetic energy k and the turbulent dissipation rate ε, whose expressions are given in Equations (2) and (3).

k = {[v (y) I (y)]}^{2}

(2)

ε = {0.09}^{0.75} k^{1.5} / l

(3)

l = 100 {(y / 30)}^{0.5}

(4)

where l is the turbulence integration scale, as expressed in Equation (4). I(y) is the turbulence intensity, as shown in Equation (5).

I (y) = \{\begin{cases} 0.23 \\ 0.1 {(y / 350)}^{- α - 0.05} \end{cases} \begin{array}{l} (y \leq 5 m) \\ (5 m < y \leq 350 m) \end{array}

(5)

(2) Outlet boundary conditions: A fully developed outflow boundary condition was used, where the physical quantities do not change along the flow direction.

(3) The top and lateral sides of the fluid domain: The symmetry boundary condition was used, which is equivalent to a free-sliding wall.

(4) Greenhouse model surfaces and floors: Using no-slip wall conditions.

2.3. Ground Roughness

In the near-surface atmospheric boundary layer, the distribution of vegetation can have a large impact on the vertical distribution of wind speeds. The roughness height h is one of the parameters used to characterize vegetation roughness conditions. Alpine shrublands and alpine meadows are widely distributed in alpine cold regions of China, with plant roughness height approximately equal to plant height, which is taken as 15 cm to 20 cm. Aerodynamic roughness length z₀ characterizes the interaction between the Earth’s surface and the atmosphere, reflecting the impact of land surface on the reduction in wind speed. The linear relationship between the aerodynamic roughness and roughness height in the horizontal region is h₀ = α₀z₀, where α is a conversion factor and is related to land cover type; α₀ was taken as 7.5 [23]. Aerodynamic roughness is generally about 1/7–1/8 of the height of the land surface plant [23]. In this study, the plant height is taken as 0.2 m, the aerodynamic roughness is taken as 0.0285 m, and the roughness height used for FLUENT calculation is taken as 0.214 m.

2.4. Turbulence Modeling and Algorithms

Realizable k-ε is chosen for the turbulence model. The solar greenhouse, classified as a low building, resides within the near-surface layer of the atmospheric boundary layer—a region characterized by substantial turbulence and a high Reynolds number. This turbulent region is typically modeled using a two-equation approach. The standard k-ε model, however, tends to be inaccurate when simulating flow fields over curved surfaces such as solar greenhouses. In contrast, the realizable k-ε model better aligns with turbulence physics, particularly under conditions of large time-averaged strain rates. The second-order windward format is used for the discrete format of the convective terms, while the Couple’s algorithm is used for the solution of the coupled pressure–velocity equations [24].

In the near-wall region, the influence of molecular viscosity surpasses that of turbulent pulsation, necessitating the introduction of a wall function to adjust the realizable k-ε model. This function connects physical quantities such as velocity and pressure at the wall to those in the turbulent core region. To account for the pressure gradient effect, this study employs a Non-Equilibrium Wall Function, enhancing the simulation of fluid separation and reattachment phenomena in the ridge and edge regions of the solar greenhouse.

3. Results and Data Analysis

3.1. Calculation Formula for Wind Pressure Coefficient

The wind pressure coefficient C_p on the surface of the solar greenhouse is defined in Equation (6):

C_{p} = \frac{2 (p_{i} - p_{0})}{ρ v_{b}^{2}}

(6)

where p_i is the pressure value on the greenhouse surface; p₀ expresses the static pressure; ρ is air density; and v_b is the average wind speed at a height of 10 m, and is taken as 25 m·s⁻¹.

3.2. Distribution Pattern of Wind Pressure Coefficient at 0° Wind Angle

(1) Figure 3 shows the cloud chart of wind pressure coefficients of the north wall at 0° wind angle with different sizes. As can be seen from Figure 3, the substantial proportion of the surface area on the north wall of the solar greenhouse with five sizes experiences positive pressure. The wind pressure coefficient in the central zone is relatively high, whereas it decreases significantly in the surrounding areas. It is remarkable that the wind pressure coefficient in the central region consistently remains above 0.6. As the height of the wall increases, there is a corresponding rise in the extent of regions experiencing positive wind pressure. To assess the effect of varied north wall height on its wind pressure coefficient, we selected data points at heights of h/2 plotting curve, capturing one point every 0.5 m, resulting in a total of 121 data points, as presented in Figure 4. Remarkably, the north wall positive wind pressure coefficient value exhibited an increase as the height increased.

(2) The cloud chart of wind pressure coefficients at the rear roof, as presented in Figure 5, elucidates that the majority of the rear roof heights of five sizes exhibit wind pressure coefficients around 0. Notably, a discernible pattern of increased negative wind pressure is observed along the east, west, and front boundaries. Comparative analysis of the cloud chart of wind pressure coefficients at various sizes indicates a positive correlation between solar greenhouse size and the areas where the absolute value of the negative wind pressure coefficient is around 0, with the span at 16 m coming out of the wind pressure coefficient greater than 0.2.

(3) Figure 6 illustrates a cloud chart of wind pressure coefficients for a range of front roof sizes, totaling five different configurations. Within these front roofs, specific regions exhibit absolute wind pressure coefficient values below 0.4, and the extent of these regions diminishes as solar greenhouse size increases. Concurrently, there was an evident increase in wind suction per unit area as size expands, indicating a direct correlation between size and wind suction. Moreover, areas featuring absolute wind pressure coefficient values within the 0.4~0.6 range expand with increasing size. In addition, the concentration of wind suction is most pronounced around the crest of the front roof. Intriguingly, as the spans increase from 8 m to 16 m, the extreme value of negative wind pressure coefficient undergoes a gradual transition from −1.8 to −2.4.

3.3. Distribution Pattern of Surface Wind Pressure Coefficient under 180° Wind Angle

(1) Figure 7 presents the wind pressure coefficients distribution cloud chart on the north wall of solar greenhouses with various sizes. This depiction reveals that the absolute negative wind pressure coefficients on the north wall consistently approximate 0.4, and it is noteworthy that the size of the solar greenhouse exerts no discernible impact on the wind pressure coefficients distribution along the north wall.

(2) Figure 8 presents the wind pressure coefficients cloud for a cohort of five front roofs of solar greenhouses with varying sizes, where it can be seen that the absolute value of negative wind pressure coefficient in the middle region of rear roofs of various sizes is around 0.4. Importantly, it is evident that the size of these rear roofs exerts minimal influence on the wind pressure coefficients values within this part of the region.

(3) In Figure 9, the wind pressure coefficient distribution for front roofs at five different sizes of solar greenhouse is compared. It reveals a consistent pattern where wind pressure coefficients for these front roofs are positive in the lower section and negative in the upper portion. Remarkably, the highest positive wind pressure coefficient exceeds 0.4, and an area with a wind pressure coefficient from 0 to 0.4 is observed. This region’s width becomes more pronounced with increasing solar greenhouse size.

3.4. Concentration Analysis of Wind Suction near the Roof Ridge

A notable phenomenon observed pertains to the substantial wind suction near the roof ridge of the solar greenhouse, which can exert a considerable impact on the structural integrity of the building. To investigate the relationship between solar greenhouse size and the concentration of wind suction near the roof ridge, wind pressure coefficients along the longitudinal axis of the roof were measured at intervals of 0.1 m and 0.2 m both before and after the roof ridge line. In the accompanying Figure 10 and Figure 11, the horizontal axis represents the longitudinal distance from west to east, with data points captured at 0.5 m intervals.

(1) The data presented in Figure 10 reveal a noteworthy disparity in wind pressure coefficients along the front roof and the rear roof near the solar greenhouse roof ridge under a 0° wind angle. Specifically, the absolute values of negative wind pressure coefficients at a 0.1 m distance on the front roof range from −1.25 to −1.01, while on the rear roof, these values range from −1.64 to −1.22. Furthermore, it is evident that the absolute value of negative wind pressure coefficients at the 0.1 m longitudinal line from the ridge significantly exceeds that at 0.2 m from the ridge. Interestingly, variations in size do not exert a significant influence on the distribution of negative wind pressure coefficients in the vicinity of the ridge.

(2) As seen in Figure 11, the absolute value of the negative wind pressure coefficient near the ridge of the rear roof is greater than that of the front roof for a 180° wind angle. The absolute values of negative wind pressure coefficients at a 0.1 m distance from the solar greenhouse on the front roof range from −1.05 to −0.84, while on the rear roof, these values range from −1.1 to −0.86. In addition, it is evident that the absolute value of negative wind pressure coefficients at the 0.1 m longitudinal line from the ridge significantly exceeds that at 0.2 m from the ridge. Variations in size do not exert a significant influence on the distribution of negative wind pressure coefficients in the vicinity of the ridge.

4. Analysis of Shape Factor of Wind Load

4.1. Formula for Shape Factor of Wind Load

The surface of the solar greenhouse is partitioned, and the wind pressure coefficients of each partition are weighted and averaged to obtain the partitioned shape factor of wind load μ_s, whose formula is shown in Equation (7):

μ_{s} = \frac{\sum_{i = 1}^{n} C_{p i} A_{i}}{\sum_{i = 1}^{n} A_{i}}

(7)

where μ_s is the zonal shape factor of wind load; C_pi is the wind pressure coefficient value of the representative point of the partition; and A_i is the area represented by the representative point.

4.2. Discussion of Different Front Roof Zoning Methods

The internal structure of the solar greenhouse stems from the standard transverse arch spacing within the range of 0.8 m to 1.2 m, combined with the inherent susceptibility of the east and west extremities of the surface of the solar greenhouse to localized wind pressure coefficient peaks. The partitioning which is the north wall and roofs of the solar greenhouse follows a west–east numbering system, denoted as B, H, QS, and QX. To manage this, the longitudinal 60 m was systematically divided into five lateral segments, resulting in a total of 20 distinct partitions, as shown in Figure 12 [24].

The front roof of the solar greenhouse is a contoured surface, with wind pressure or suction perpendicular to this curvature. Wind load should be directed towards this curved surface. However, partitioning techniques of two current load standards [21,22] rely on dividing the horizontal projection of the curved surface into two equivalent sections. The strategy of the present study introduces novel partitioning approaches, based on arc length of the front roof and calibrated to the longitudinal line with a wind pressure coefficient of 0. This study compared and discussed three partitioning methods about the wind pressure coefficient in the front roof of the solar greenhouse:

Method 1: The initial method entails dividing the front roof into two equal segments according to its arc length. The rationale for this method is that calculating the arc length of the front roof is essential for greenhouse design, thereby facilitating engineering practice.

Method 2: The second method, which represents the current partitioning method, divides the front roof into two equal portions based on its horizontal projection, given by reference [21].

Method 3: The third method entails segmenting the front roof into upper and lower sections, demarcated by the longitudinal line where the wind pressure coefficient is zero. The wind pressure coefficients on the upper section of the front roof are uniformly negative, while those on the lower section are uniformly positive, given by this paper.

The middle portion of the rear roof differs among the three partitioning techniques, depending on its wind pressure coefficient value. Figure 6 depicts a wind angle of 0°, with the middle of the front roof situated within a substantial portion of the region exhibiting a shape factor of wind load ranging from −0.6 to −0.4, resulting in a notably homogeneous distribution of shape factors of wind load. During this scenario, the three zoning techniques for calculating the shape factor of wind load on the front roof have minimal influence, except for in the vicinity of the roof where a more concentrated negative wind pressure is observed. This localized effect can be addressed by modifying the local wind pressure coefficient. The shape factors of wind load of the convection effect of the front roof from bottom to top gradually transition from negative to positive as the wind angle reaches 180°, as shown in Figure 9. Figure 9 illustrates the wind pressure coefficient within the central segment of the front roof’s arc, which ranges from −0.2 to 0.2. This range encompasses a substantial portion of the curve. It is worth emphasizing that these three zoning methodologies significantly influence the computation of temperature loads under these conditions.

In order to gain a more comprehensive insight into the mathematical correlation between the dimensions of the front roof in the greenhouse and the extent of the positive wind pressure zone, the longitudinal coordinates are extracted where the wind pressure coefficient for the leading roof segment reached 0 under varying sizes of solar greenhouse, specifically at a wind angle of 180°. Additionally, the wind pressure coefficient analysis for a 9 m span at a wind angle of 180° with simulation data is augmented. Furthermore, the arc lengths for the lower portion of the leading roof under different zoning techniques is investigated. The following conclusions can be reached from Figure 13:

(1) The bottom arc length of the front roof calculated using Method 2 exceeds that of Method 1 by approximately 0.62 to 0.82 m, and surpasses that of Method 3 by a substantial margin, ranging from 2.1 to 0.6 m.

(2) At a span between 12 m and 14 m, the bottom arc length of the front roof calculated using Method 3 closely aligns with that of Method 1.

This alignment suggests a near coincidence between the longitudinal line associated with a wind pressure coefficient of 0 and the central arc length of the front roof. However, at a span of 8 m, the middle arc length of the front roof obtained by Method 3 was 1.48 m shorter than that achieved through Method 1. This discrepancy indicates a forward shift in the longitudinal line of the wind pressure coefficient.

Considering that the wind load acting upon the front roof of the solar greenhouse is perpendicular to the arc and distributed along its length, the approach for dividing the shape factor of wind load should be based on the arc length. At a wind angle of 180°, the lower section of the front roof consistently experiences positive wind pressure, while the upper part consistently encounters negative wind pressure. In light of these observations, this study recommends the utilization of Method 3. Furthermore, when the wind angle was 0°, the front roof is subjected to suction forces. In such circumstances, it was suggested that Method 1 be employed.

4.3. Comparison of Shape Factors of Wind Load for Different Sizes

Shape factors of wind load were determined for various zones of solar greenhouses with differing sizes, assessed at wind angles of 0° and 180°. Multiple zoning techniques are employed for categorizing the front roof of solar greenhouses, facilitating a comparative analysis of the shape factors of wind load derived from these diverse zoning methods.

4.3.1. North Wall and Rear Roof

(1) At a wind angle of 0°, the shape factors of wind load for all divisions of the northern wall of the solar greenhouses display positive values, as shown in Table 2. Principally, the shape factors of wind load across different partitions of the northern wall display varying responses to the size of the greenhouse. In particular, the shape factors of wind load in regions B1 and B5 exhibit a tendency to initially increase and subsequently decrease with an increase in size. Markedly, for the solar greenhouse with a 10 m span, regions B1 and B5 on the northern wall yield the highest shape factor of wind load, approximately reaching a peak value of 0.23.

At an 8 m span, the shape factors of wind load within the B1 and B5 regions are observed to be smaller than those at a 10 m span. Conversely, when the size falls within the range of 12 m to 16 m, the shape factors of wind load of the B1 and B5 regions exhibit reductions relative to the 10 m span, ranging from 0.02 to 0.09. Furthermore, the shape factors of wind load across the B3 to B4 regions increase as the size extends. Remarkably, the wind pressure coefficients in the B3 region at a 16 m span reach their maximum, with a value of approximately 0.72. Compared to a 16 m span, spans ranging from 8 m to 14 m result in a substantial reduction in the shape factors within the B2 to B4 region, ranging from 2% to 14%.

The shape factor of wind load values on the rear roof partitions of greenhouses with five sizes are observed to be negative and are in proximity to 0. Specifically, at a span of 14 m, the shape factors of wind load within the H2 to H5 region demonstrate the most significant values among the five distinct sizes. Furthermore, shape factor of wind load values reach their minimum in each region at the 10 m span, with the lowest recorded value occurring in the H1 region, approximately −0.19.

(2) At a wind angle of 180°, the shape factor of wind load for the northern wall and rear roof is observed to be negative, as shown in Table 2. The absolute magnitude of the shape factor of wind load within the B3 zone of the northern wall increases with the size, reaching a peak value of 0.36 when the span extends to 16 m. This value was notably larger by 0.02–0.04 compared to the other four size variations. In contrast, for the 14 m span, the absolute magnitude of the shape factor in the remaining regions ranges from 0.39 to 0.40, representing the smallest values.

The size exhibits minimal influence on the shape factor of wind load in the rear roof region. However, for the regions on both sides of the rear roof (H1, H2, H4, and H5), the absolute value of the shape factor of wind load decreases as the size extends. Comparing the shape factor of the 16 m span to that of the 8 m span, it undergoes a change from −0.55 to −0.43.

4.3.2. Front Roof

(1) At a wind angle of 0°, the shape factor of wind load of the solar greenhouse front roof registers below 0, indicating a wind suction force in the upper region significantly surpassing that in the lower area. The absolute magnitude of the upper wind load shape factor experiences a slight reduction with increasing size by Method 2, ranging from 1% to 18% on the front roof. In contrast, for the lower front roof, the absolute value of the shape factor of wind load undergoes a slight increment with an increase in size, changing from −2% to 19%.

(2) At a wind angle of 180°, the lower section of the front roof experiences wind suction at its eastern and western boundaries, while the central region encounters predominantly wind pressure. On the other hand, the upper segment of the majority of the upper roof area was wind suction, resulting in a negative shape factor. An examination of the shape factors derived through the application of Method 2 for roof zoning reveals the following trends: The shape factors of wind load for the upper portion of the front roof remain relatively consistent across various sizes. In contrast, the shape factors of wind load for the middle area of the lower roof (from QX2 to QX4) exhibit an increase corresponding to the size increment. Markedly, the increment in shape factors of wind load for the 16 m span, compared to that of the 8 m span, reaches a significant range of 82% to 108%.

4.4. Comparison of Shape Factors from Different Zoning Methods for Front Roofs

Methods 1 and 2 were applied to segment five solar greenhouse sizes under a wind angle of 0°, resulting in the acquisition of shape factor values for these segments, as presented in Table 3. Significantly, the disparity between the shape factor values obtained through the two partition methods was found to be exceedingly marginal. The most substantial deviation in shape factors of wind load among the two partition methods is observed for a span measuring 8 m, with variations amounting to only from 0 to 0.05.

At a wind angle of 180°, the upper section of the front roof was partitioned using three distinct methods to determine the shape factor of wind load. These shape factors are presented in Table 4, revealing that the variations between the values are relatively minor, with differences of less than 0.09. The assessment of the lower part of the front roof presents a more intricate scenario. Particularly, the disparity between the shape factors of wind load obtained through Method 1 and Method 2 is relatively modest, with variances of less than 0.09. However, for an 8 m span, the discrepancy between the shape factors of Method 3 and Method 1 ranges from 0.11 to 0.18, resulting in relative errors of 45% to 88%. Additionally, the distinction between the shape factors of Method 2 and Method 3 varies between 0.14 and 0.22, corresponding to relative errors of 55% to 100%. In the case of spans between 10 m and 16 m, the differences in shape factor of wind load are not substantial. Specifically, the disparities in shape factor for each partition between Method 3 and Method 1 are less than 0.02, while the errors between Method 2 and Method 3 are less than 0.09.

It is important to note that while there is little value difference in shape factors of wind load across most areas of the solar greenhouses’ surface using different zoning methods, significant shape factor discrepancies are present in the upper and lower parts of the front roof. Therefore, the shape factors of wind load calculations present considerable disparities. This study advocates the utilization of Method 1 when the wind angle was set at 0°. In this approach, shape factor is derived by bisecting the size length of the front roof. Meanwhile, for a wind angle of 180°, Method 3 was recommended. Under this method, shape factor is ascertained by partitioning the front roof into upper and lower segments along the longitudinal axis where the wind pressure coefficient reaches zero.

4.5. Localized Shape Factors in the Vicinity of the Roof Ridge

As illustrated in Figure 6, under a wind angle of 0°, a distinct region near the crest of the front roof exhibits wind pressure coefficients with absolute values exceeding 0.6. The horizontal projection length of this region measures approximately 1.6 m. In response to the observed wind suction concentration near the ridge of the front roof, the front roof was partitioned into upper and lower sections, with a demarcation line positioned 1.6 m from the horizontal projection of the ridge. The upper portion of the front roof was further divided into five partitions (from QWJ1 to QWJ5), spanning from east to west, and the shape factors of wind load for this area are depicted in Table 5. It is noteworthy that the shape factors of wind load in this region exhibit a marginal decline as the size increases across the ten partitions, with the maximum decrease amounting to only 0.13. Importantly, the absolute values of the derived shape factors from this method are 28% to 41% greater than those obtained through Method 1 for each region of the upper front roof.

5. Conclusions

In this study, numerical simulation was used to identify the patterns of surface wind pressure and wind load shape factors for five sizes of solar greenhouses at 0° and 180° wind angles. Various zoning methods for the front roof of solar greenhouses were discussed, and an improved zoning method was proposed, accounting for the effect of greenhouse size on the wind load shape factor of the front roof. The main conclusions are as follows:

(1) At a coming wind angle of 0°, with spans growing from 8 m to 16 m, the value of the positive wind pressure coefficient of the north wall increases with the increase in size. The shape factors of wind load within the B3~B4 region of the north wall also display an increase as the size length grows. Simultaneously, the region of negative wind pressure coefficients on the front roof, with an absolute value less than 0.4, diminishes as size length increases. Conversely, the region, with an absolute between 0.4 and 0.6, expands with increasing size. Separately, the region, with an absolute value exceeding 0.6, is almost unaffected by changes in size length.

(2) At a coming wind angle of 180°, the size exhibits minimal influence on the distribution of wind pressure coefficients along the north wall and the rear roof. Particularly, the width of the positive wind pressure coefficient region on the front roof expands proportionally with the size length. In contrast, the shape factor within the central region (H3) of the rear roof remains relatively constant, irrespective of size length. However, the regions at both ends (H1, H2, H4, and H5) experience a reduction in shape factor as the size increases, with a decrease of approximately 22%, when comparing the 16 m span to the 8 m span.

(3) Regarding the shape factors of wind load, at a coming wind angle of 0°, the absolute value of the localized shape factors along the 1.6 m width of the front roof exhibits a substantial increase, ranging from 28% to 41%, compared to the shape factors of the upper portion of the front roof determined using Method 1.

(4) The proposed zoning approach for the front roof involves the following criteria: at a coming wind angle of 0°, Method 1 is applied, dividing the entire arc length of the front roof into two equal segments; at a coming wind angle of 180°, Method 3 is employed, where the boundary for the front roof’s wind pressure coefficient was set at 0. In summary, variations in the dimensions of the greenhouse have a discernible effect on its surface wind pressure and shape factor. As size increases, the wind load per unit area shows a consistent upward trend. Wind-induced suction is particularly concentrated along the roof ridge, with greater intensity observed on the leeward side in comparison to the windward side. Furthermore, this suction effect becomes more pronounced closer to the roof ridge. Special attention should be paid to the wind resistance design of greenhouses in areas with significant wind suction and wind pressure.

This paper focuses on two wind directions, highlighting the necessity to investigate the effects of additional wind directions and dimensional variations on surface wind pressures and the shape factor of wind load in groups of solar greenhouses.

Author Contributions

Conceptualization, Z.L. and J.X.; software, Z.G.; investigation, Y.L.; writing—original draft preparation, Z.G.; writing—review and editing, Z.L. and J.X.; visualization, Z.G. and R.W.; supervision, S.Z. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the National Natural Science Foundation of China (U20A2020), the Beijing Innovation Consortium of Agriculture Research System (BAIC01-2023-20), the Cangnan County Modern Agricultural Industry Research Institute (2023CNYJY02), and the Ministry of Education of the People’s Republic of China (C21JB0100060).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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Figure 1. Surface profile of solar greenhouse.

Figure 2. Size of calculation domain under 0° wind angle. Note: X-axis is parallel to the direction of incoming wind, Y-axis is height direction, Z-axis is perpendicular to the direction of incoming wind; 10 L, 9 W, 5 H are the length, width, and height of the calculation domain, respectively; L is the length of the greenhouse profile perpendicular to the incoming flow, m; W is the length of the greenhouse profile parallel to the incoming flow, m; and H is the height of the greenhouse, m.

Figure 3. Cloud chart of wind pressure coefficients on the north wall of solar greenhouse with five different sizes under 0° wind angle.

Figure 4. Wind pressure coefficient curve at h/2 height of north wall with different sizes.

Figure 5. Cloud chart of wind pressure coefficients on the rear roof of solar greenhouses with five different sizes under 0° wind angle.

Figure 6. Cloud chart of wind pressure coefficients on the front roof of solar greenhouses with five different sizes under 0° wind angle.

Figure 7. Cloud chart of wind pressure coefficients on the north wall of solar greenhouses with five different sizes under 180° wind angle.

Figure 8. Cloud chart of wind pressure coefficients on the rear roof of solar greenhouses with five different sizes under 180° wind angle.

Figure 9. Cloud chart of wind pressure coefficients on the front roof of solar greenhouses with five different sizes under 180° wind angle.

Figure 10. Extreme wind pressure at the ridge with 0° wind angle.

Figure 11. Extreme wind pressure at the ridge with 180° wind angle.

Figure 12. Surface zoning plan of solar greenhouse.

Figure 13. Comparison of the arc length of the lower part of the front roof with different zoning methods under 180° wind angle.

Table 1. Dimensions of different greenhouse models.

Span (m)	H₁ (m)	H₂ (m)	B₁ (m)	B₂ (m)	α (°)	θ (°)	H₁/H₂	H₂/B₂
8	2.8	3.9	1.2	8	43	30	0.7	0.49
10	3.4	4.8	1.6	10	41	30	0.7	0.48
12	4	5.7	1.9	12	42	29	0.7	0.48
14	4.5	6.6	2.4	14	41	30	0.7	0.47
16	5	7.5	2.8	16	42	30	0.7	0.47

Table 2. Shape factor of wind load of the north wall and rear roof partition under 0° and 180° wind angles.

Wind Direction	Span (m)	B1	B2	B3	B4	B5	H1	H2	H3	H4	H5
0°	8	0.20	0.55	0.63	0.54	0.22	−0.16	−0.11	−0.09	−0.16	−0.17
	10	0.23	0.57	0.65	0.57	0.22	−0.18	−0.17	−0.14	−0.14	−0.19
	12	0.21	0.61	0.70	0.61	0.18	−0.13	−0.05	−0.03	−0.04	−0.14
	14	0.17	0.60	0.69	0.60	0.17	−0.16	−0.03	−0.01	−0.01	−0.14
	16	0.14	0.63	0.72	0.63	0.16	−0.16	−0.03	−0.01	−0.03	−0.16
180°	8	−0.43	−0.46	−0.32	−0.46	−0.43	−0.55	−0.55	−0.39	−0.56	−0.55
	10	−0.42	−0.43	−0.32	−0.43	−0.41	−0.49	−0.51	−0.41	−0.50	−0.48
	12	−0.40	−0.41	−0.34	−0.41	−0.39	−0.46	−0.47	−0.41	−0.47	−0.44
	14	−0.40	−0.39	−0.34	−0.40	−0.39	−0.43	−0.44	−0.41	−0.46	−0.45
	16	−0.41	−0.40	−0.36	−0.40	−0.40	−0.43	−0.44	−0.41	−0.43	−0.43

Table 3. Comparison of shape factors of wind load of the front roof for different zoning methods under 0° wind angle.

Partition Method	Span (m)	QS1	QS2	QS3	QS4	QS5	QX1	QX2	QX3	QX4	QX5
Method 1	8	−0.66	−0.64	−0.50	−0.64	−0.67	−0.49	−0.48	−0.35	−0.48	−0.49
	10	−0.60	−0.60	−0.49	−0.60	−0.60	−0.49	−0.47	−0.37	−0.48	−0.50
	12	−0.60	−0.59	−0.50	−0.59	−0.60	−0.50	−0.49	−0.40	−0.49	−0.50
	14	−0.57	−0.57	−0.50	−0.56	−0.55	−0.49	−0.49	−0.42	−0.48	−0.48
	16	−0.58	−0.58	−0.48	−0.57	−0.58	−0.52	−0.51	−0.44	−0.50	−0.51
Method 2	8	−0.69	−0.66	−0.52	−0.69	−0.69	−0.49	−0.48	−0.36	−0.48	−0.49
	10	−0.62	−0.62	−0.51	−0.62	−0.63	−0.49	−0.48	−0.37	−0.48	−0.49
	12	−0.61	−0.61	−0.51	−0.60	−0.60	−0.50	−0.49	−0.41	−0.49	−0.50
	14	−0.58	−0.58	−0.50	−0.56	−0.56	−0.49	−0.49	−0.42	−0.48	−0.48
	16	−0.59	−0.59	−0.48	−0.58	−0.59	−0.52	−0.51	−0.43	−0.50	−0.51

Table 4. Comparison of shape factors of wind load of the front roof for different zoning methods under 180° wind angle.

Partition Method	Span (m)	QS1	QS2	QS3	QS4	QS5	QX1	QX2	QX3	QX4	QX5
Method 1	8	−0.25	−0.31	−0.26	−0.32	−0.26	0.02	0.18	0.21	0.17	0.03
	10	−0.25	−0.29	−0.26	−0.29	−0.25	0.02	0.24	0.27	0.24	0.02
	12	−0.27	−0.29	−0.27	−0.28	−0.25	−0.01	0.25	0.29	0.25	−0.01
	14	−0.25	−0.28	−0.28	−0.29	−0.24	−0.03	0.28	0.32	0.28	−0.02
	16	−0.26	−0.27	−0.27	−0.27	−0.26	−0.04	0.30	0.35	0.30	−0.04
Method 2	8	−0.27	−0.35	−0.27	−0.33	−0.26	0.01	0.13	0.17	0.13	0
	10	−0.27	−0.34	−0.3	−0.33	−0.28	−0.01	0.19	0.22	0.19	0
	12	−0.31	−0.36	−0.34	−0.35	−0.29	−0.05	0.17	0.2	0.17	−0.04
	14	−0.27	−0.31	−0.31	−0.32	−0.28	−0.04	0.24	0.28	0.24	−0.03
	16	−0.28	−0.30	−0.30	−0.3	−0.28	−0.06	0.27	0.31	0.27	−0.06
Method 3	8	−0.23	−0.28	−0.22	−0.27	−0.24	0.16	0.35	0.38	0.35	0.14
	10	−0.25	−0.29	−0.25	−0.28	−0.25	0.02	0.25	0.28	0.25	0.02
	12	−0.27	−0.28	−0.27	−0.28	−0.26	−0.01	0.26	0.30	0.26	−0.01
	14	−0.25	−0.28	−0.28	−0.29	−0.24	−0.03	0.28	0.32	0.28	−0.02
	16	−0.27	−0.28	−0.28	−0.28	−0.26	−0.05	0.29	0.33	0.29	−0.05

Table 5. Local shape factors of wind load for a width of 1.6 m on the front roof ridge with 0° wind angle.

Span (m)	QWJ1	QWJ2	QWJ3	QWJ4	QWJ5
8	−0.87	−0.81	−0.64	−0.85	−0.87
10	−0.83	−0.79	−0.67	−0.78	−0.77
12	−0.79	−0.78	−0.66	−0.78	−0.78
14	−0.78	−0.76	−0.66	−0.75	−0.74
16	−0.79	−0.81	−0.66	−0.79	−0.82

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Liang, Z.; Gao, Z.; Li, Y.; Zhao, S.; Wang, R.; Xu, J. Study on the Effect of Size on the Surface Wind Pressure and Shape Factor of Wind Load of Solar Greenhouses. Appl. Sci. 2024, 14, 7114. https://doi.org/10.3390/app14167114

AMA Style

Liang Z, Gao Z, Li Y, Zhao S, Wang R, Xu J. Study on the Effect of Size on the Surface Wind Pressure and Shape Factor of Wind Load of Solar Greenhouses. Applied Sciences. 2024; 14(16):7114. https://doi.org/10.3390/app14167114

Chicago/Turabian Style

Liang, Zongmin, Zixuan Gao, Yanfeng Li, Shumei Zhao, Rui Wang, and Jing Xu. 2024. "Study on the Effect of Size on the Surface Wind Pressure and Shape Factor of Wind Load of Solar Greenhouses" Applied Sciences 14, no. 16: 7114. https://doi.org/10.3390/app14167114

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