Development of a Machine Learning Natural Ventilation Rate Model by Studying the Wind Field Inside and Around Multiple-Row Chinese Solar Greenhouses

Abstract

This paper experimented with a methodology of machine learning modelling using virtual samples generated by fast CFD (Computational Fluid Dynamics) simulations in order to predict the greenhouse natural ventilation. However, the output natural ventilation rates using fast two-dimensional (2D) CFD models are not always consistent with the three-dimensional (3D) one for all the scenarios. The first contribution of this paper is a proposed comparative modelling methodology between two-dimensional and three-dimensional CFD studies, regarding its validity, especially when buildings are in rows. The results show that the error of the ventilation rate prediction could exceed 50%, if 2D models are not properly used. Subsequently, in those scenarios where the 2D and the 3D models had equal accuracy, nearly one thousand samples were generated using fast 2D CFD simulations to train a natural ventilation rate regression tree model. This model is efficient to deal with the combined effect of wind pressure and thermal gradients under various vent configurations, with only four necessary inputs. In addition, by analyzing the wind speed distribution contour of the outdoor wind field around the greenhouse rows, the optimal wind speed-measuring locations were determined to eliminate interference for predicting the natural ventilation rate.

1. Introduction

The horticultural greenhouse facility area in China is now 3.7 million hectares. Solar greenhouses are the major type in northern provinces due to their heat preservation and low energy cost [1]. In recent years, agriculture production facilities have progressively evolved towards greenhouse clusters, which impact the ventilation of each greenhouse (Figure 1). The spacing among them is usually small, which makes it necessary to study the validity of two-dimensional CFD (Computational Fluid Dynamics) in this ubiquitous scenario. To date, most of the current CFD studies focus on a single greenhouse, especially for the typical Chinese solar greenhouse (CSG), but the wind field and ventilation rate around and inside multiple greenhouses have not been fully studied [2]. However, the model is usually used in greenhouse clusters, which causes differences compared to ideal experiments.

The estimation of the ventilation rate is an indispensable part in modelling the greenhouse climate, as well as for controlling the climate inside the greenhouse, which is essential for cooling and dehumidification. Ventilation is achieved either by natural ventilation or by forced ventilation facilities (e.g., exhaust fan and fan-pad cooling system) [3]. Natural ventilation is currently widely preferred by farmers in practical production, given its low energy cost [4,5,6]. Natural ventilation is driven by two forces induced by wind and thermal gradients [7,8]. In contrast to mechanically forced ventilation, natural ventilation is characterized by varied input conditions, which makes it difficult to quantify the flow rate.

Gas tracing and energy balance were common methods used to determine the ventilation rate before CFD techniques were adopted over the last two decades to simulate greenhouse flow fields [9]. The gas tracing method requires that the tracer gas distribution be uniform inside the greenhouse before opening the vents and that its concentration be measured at a given operational point [10]. The energy balance method relies greatly on the accuracy of the flux sensors or the greenhouse model [11]. In addition to the inconvenient practice, both methods have an error of up to 30% [12]. Compared to the above methods, the cost of the CFD method is lower, and in addition, this approach guarantees a high level of accuracy, provided that the quality of the mesh, the optimal design of the model in the flow field, and the convergence of the solution are correctly checked.

The CFD technique has been widely applied in the optimal design and the simulation of ventilation since the 1990s [7,13]. In the 21st century, more comprehensive models were developed including the interaction between the microclimate and the crop [14,15,16,17,18,19,20]. By using the CFD method, the impact of wind speed, vent opening configuration, and greenhouse structures on the airflow pattern have been investigated by many researchers [8,21,22]. Bournet and Boulard (2010) reviewed optimum solutions for designers and analyzed the effect of ventilator configurations on the distributed climate inside greenhouses from CFD simulations published over 25 years [23].

To date, a vast majority of the current research has focused on 2D models [23,24,25], with some of them being especially applied to CSG [26,27,28,29]. With the progress in computing power, there are more and more 3D studies available [28]. Improving the quality of the 3D mesh requires designers with proficient skills. For the CSG, the fan-shaped geometry of the south roof makes it a challenge to create boundary layer grids. In addition, the calculation load of the three-dimensional CFD model is heavy. This is why two-dimensional models have been widely used. Moreover, the impact of the surrounding buildings on the wind velocity distribution and on the greenhouse ventilation has been hardly considered in previous two-dimensional CFD models. It is known, however, that the ventilation rate of a greenhouse with restricted vent-opening areas is greatly reduced when neighboring objects are high enough to disturb the flow [30]. In the present study, the impact of building obstacles in front and behind the greenhouse on the ventilation rate is studied separately using 2D and 3D modelling. Twenty cases were selected (ten cases for 2D and ten cases for 3D) to compare their corresponding predicted natural ventilation rate and the wind field with the aim to validate the model. In cases where the 2D models have been proven to effectively replace 3D models, fast two-dimensional CFD simulations allow for large sample sizes, facilitating the study of natural greenhouse ventilation.

Using the CFD model to obtain the ventilation rate involves complex steps such as geometric modeling, meshing, coding functions, and defining boundary conditions. It also relies on the modeler’s skill in mesh design and problem understanding and formalizing. It usually requires mesh reconstruction and boundary condition redefining when vent configuration or building structures are different, which necessitate relatively heavy workloads and, hence, makes it be primarily implemented for research purposes rather than for practical use [31]. From enough CFD samples, it could be possible to develop a black box model for natural ventilation. Indeed, conducting virtual wind tunnel simulations to obtain comprehensive and orderly samples is feasible, whereas it would be difficult to obtain a sufficient number of samples in field experiments, due to unstable and unpredictable weather conditions [32]. Machine learning models are widely used to predict the temperature and humidity inside greenhouses, but there is limited research on simulating natural ventilation rates [33,34]. In this study, from a high number of CFD simulations (990 cases), a natural ventilation rate model was developed using a nonlinear regression tree model [35]. By combining CFD simulations and regression tree models, it becomes possible to assess the ventilation characteristics while avoiding the need to identify several difficult-to-measure parameters (e.g., wind pressure and thermal pressure), representing a significant advancement in the optimal design of and real-time greenhouse climate simulation.

2. Materials and Methods

2.1. Experimental Greenhouses and Vent Configurations

The object considered for the present study was the typical single-slope solar greenhouse in China (Figure 2). These greenhouses are arranged in rows along the east–west direction. Both the roof vent (upper vent) and side vent (lower vent) are equipped with a rolling film. The full vent opening width for both the upper and the lower vents is 0.6 m. The ventilation rates for 9 different vent configurations were assessed in the experiment (

Table 1. Simulated greenhouse size and vent opening configurations.

Width (m)	Ridge Height (m)	Length (m)	Depth (m)	Vent Type	Vent Opening Area (m2)
					Lower Vent	Upper Vent
7	3.6	50	0.5	Rolling Film	10	10
						20
						30
					20	10
						20
						30
					30	10
						20
						30

). Crops were not included in this experiment, as the goal was to develop a general ventilation rate model applicable to most CSGs. Including specific crop heights or leaf area indexes could influence the ventilation rates and limit the model’s applicability.

2.2. Calculation Domain

The CFD mesh was generated based on a 1:1 scale greenhouse, i.e., considering the actual size of the greenhouse. In this study, three greenhouses were meshed in the flow field, spaced 4 m apart. Nine different vent combinations, involving both upper and lower vents, were designed (as detailed in Table 1) and applied uniformly across all three greenhouses. The calculation domain had a height of 14 m. The upstream portion extended 3 times the ridge height (10.8 m), while the downstream portion extended 10 times the ridge height (36 m, Figure 3). Indeed, it was established that the backflow cannot form inside the computational domain within 10 times of the ridge height [36]. Based on the same size as the above 2D domain, the 3D domain included three greenhouses with a width of 50 m and an extension of 86 m on both sides of the greenhouses.

2.3. Models, Solver, and Materials

The Reynolds-averaged Navier–Stokes equations for mass, momentum, energy, and standard k-ε turbulence model combined with buoyancy effect (g = −9.81 m s⁻²) were solved by the SIMPLEC (Semi-Implicit for Pressure Linked Equations Consistent) method using the Fluent^TM pro [37]. The k-ε turbulence model has been proven to be suitable for simulating the greenhouse flow pattern [28]. The flow in the near-wall region was solved using the Standard Wall Function. The incompressible ideal gas model was used as state law to link the temperature and pressure. The corresponding physical properties of the air specified in the model are gathered in

Table 2. Physical properties of the air.

Material	Density (kg m−3)	Specific Heat (J kg−1 K−1)	Thermal Conductivity (W m−1 K−1)	Viscosity (kg m−1 s−1)
Air	Incompressible ideal gas	1006	0.024	1.7894 × 10−5

.

2.4. Generation of the Mesh File

The mesh file was generated by the ICEM pro (Ansys Inc., Canonsburg, PA, USA). The blocks were associated with a set of grids, which were then converted to unstructured grids when generating the mesh file. The height of the cell in the first boundary layer was estimated from the y⁺ value, which is expressed by the following equation [38],

$$y_c={\displaystyle \frac{y^{+}\mu }{\rho u_{*}}}$$

(1)

where y_c is the estimated height of the first cell in the boundary layer and y⁺ is a non-dimensional distance, which must satisfy 30 < y⁺ < 300 for the Standard Wall Function [37]. μ is the dynamic viscosity, Pa s⁻¹; ρ is the density of the fluid, kg m⁻³; and u_* is the friction velocity, m s⁻¹. The friction velocity is determined by the aerodynamic roughness length and reference wind speed [39]. The roughness length was determined as 0.0193 m for the simulation of greenhouse ventilation and its surrounding flow field [16]. In the present study, a value of 0.02 m was used for H₀.

The first step in creating a mesh file is to build a geometric model. Then, the geometric model is associated with created blocks, including associating points with vertex, associating curves with edges, and associating surfaces with faces (Figure 4a). The former is the name corresponding to the geometric model, and the latter is the name corresponding to the block. The next key step is to split the blocks. Given the complexity of the semi fan-shaped south roof and in order to obtain a high-quality meshing of the boundary layer around, the ‘Ogrid Block’ splitting method was used along the side wall of the greenhouse (Figure 4b) [37]. Finally, it is beneficial to move the vertex in order to find the optimal quality and check the global association (Figure 4c). The vertex movements were based on the geometric optimal solution under multiple criteria, e.g., avoiding sharp angles and reducing aspect ratios.

Tests of Boundary Layer Thickness and Grid Independence

The height of the first cell from the wall in the boundary layer was determined by conducting iteration tests of the results regarding the wall y⁺ value. The tested case corresponded to a windward flow for which a wind profile was imposed at the entrance of the calculation domain as follows [40],

$$u={\displaystyle \frac{u_{*}}{\kappa }}\mathit{ln}\left({\displaystyle \frac{H+H_0}{H_0}}\right)$$

(2)

where u is the wind speed, m s⁻¹; κ is the von Karman constant, 0.42; H is the reference height, m; and H₀ is the aerodynamic roughness length.

The turbulent kinetic energy k and dissipation rate ε distributions at the entrance are defined by the following equations [41],

$$k={\displaystyle \frac{u_{*}^2}{\sqrt{C_{\mu }}}}$$

(3)

$$\epsilon ={\displaystyle \frac{{u_{*}}^3}{\kappa (H+H_0)}}$$

(4)

The wind speed at 2.5 m height (u_2.5) was 5 m s⁻¹ for the tested case. The criterion for the convergence residual was 1 × 10⁻³ for the continuity, k, and ε equations, and it was 1 × 10⁻⁶ for the energy equation.

The steady-state solution was generally reached within 500 steps for the 2D case and within 900 steps for the 3D case. The first cell height providing the optimum y⁺ solution was 0.025 m based on the iteration tests. Figure 5 shows that the wall y⁺ satisfies 30 < y⁺ < 300 for the Standard Wall Function. The total number of elements is shown in

Table 3. Number of elements of the 2D and 3D meshes.

Mesh	Windward Mesh	Leeward Mesh
2D	36,722	36,726
3D	16,807,531	16,776,673

and the mesh files are shown in Figure 3 both for the windward and leeward cases.

2.5. Sample Data

In the first step, 2D and 3D modelling were conducted in parallel. Twenty cases were selected (ten cases for 2D and ten cases for 3D) to compare their natural ventilation rate and the wind field. The objective was to experiment on the validity of 2D modellings when buildings are in rows. For these cases, the vents of the 3 greenhouses were fully open, with 30 m² opening areas for the upper and lower vents. Windward and leeward wind directions were applied, with a log law wind profile at the inlet (see

Table 4. Boundary conditions.

Boundary	Boundary Condition
	Momentum	Thermal
Wall	No-slip wall	Fixed temperature
South roof	No-slip wall	Fixed temperature
North roof	No-slip wall	Fixed temperature
Ground	No-slip wall	Fixed temperature
External top, both sides	Symmetry
Inlet of the external domain	Velocity at inlet: Wind profile, Equations (2)–(4); Temperature 300 K
Outlet of the external domain	Pressure at outlet; Temperature 300 K

). Also, five values of the reference velocity u_2.5 from 1 to 5 m s⁻¹ were chosen for the simulations. The temperature difference between indoors and outdoors was 0 K (300 K inside both the indoor and outdoor domain). The ventilation rate through the vents of each greenhouse was monitored. The criterion of the quality estimation of the fit between the 2D and the 3D models was defined as follows (Equation (5)),

$$e=\left|{\displaystyle \frac{L_2-L_3}{L_3}}\right|$$

(5)

where e is the ratio error; L₂ is the ventilation rate simulated by the 2D case, m³ s⁻¹; and L₃ is the ventilation rate simulated by the 3D case, m³ s⁻¹.

In the second step, 990 samples were collected using 2D simulations. The objective was to study the greenhouse natural ventilation from a large sample size. These samples include natural ventilation rates under the coupling of gradient wind pressure, thermal pressure and vents opening combinations. A natural ventilation rate model was then developed using a nonlinear regression tree model (see Section 2.7). For these cases, there was only one greenhouse in the calculation domain. Eleven temperature differences between a fixed temperature of 300 K at the inlet and the average temperature inside the greenhouse from 0 to 10 K were tested. The steady indoor temperature was simulated by defining the fixed wall temperature (Table 4). When the fluid flows through the fixed temperature wall, a thermal boundary layer is formed near the wall due to temperature differences. In the thermal boundary layer, the fluid temperature is directly affected by the wall temperature and gradually diffuses away from the wall. The indoor average temperature was monitored by conducting iteration tests until it reached the targeted value. Combined with the 9 vent-opening configurations described in Table 1, the windward and leeward directions were tested, with a log law wind profile at the inlet, and 5 values of u_2.5 from 1 to 5 m s⁻¹. This means in total 11∗9∗2∗5 = 990 cases. The area ventilation rate was monitored and calculated by the following equations,

$$L={\displaystyle \frac{f_m}{\rho }}{\displaystyle \frac{l_g}{A_g}}$$

(6)

where L is the area ventilation rate, m³ s⁻¹ m⁻²; f_m is the simulated mass flow rate through the vents, kg m⁻¹ s⁻¹; l_g is the length of the greenhouse, m; A_g is the area of the greenhouse, m²; and ρ is the density of the fluid (incompressible ideal gas), kg m⁻³, which is calculated by the following equation [37],

$$\rho ={\displaystyle \frac{P_{op}}{\frac{R}{M_w}T}}$$

(7)

where R is the universal gas constant, 8.31 m³ Pa K⁻¹ mol⁻¹; M_w is the molecular weight of the gas, kg mol⁻¹; and P_op is the operating pressure, Pa.

2.6. Monitoring of Wind Speed at 2.5 m Height

The wind speed is a critical parameter of the natural ventilation model. The height of 2.5 m is usually is an easier one for placing wind speed sensors on the outdoor weather stations. Meanwhile, the wind speed at 2.5 m height (u_2.5) can be used to establish the inlet velocity profile. It is crucial to judge whether the measured wind speed is affected by buildings. Although the appropriate distance of anemometers from objects is common knowledge in wind engineering, in most practice experiments, due to the variable structure of greenhouses and different experimental scenarios, it is necessary to specify a standard to provide a brief guidance for researchers who study the CSG climate prediction but have little knowledge in wind engineering. The method is to monitor the change in wind speed with a position at the 2.5 m height horizontal plane, thus helping to determine a limited area to ensure that the wind speed is in the free stream. The red lines in Figure 6 show the monitoring locations at 2.5 m height, which cross the external domain and the whole greenhouse in two orthogonal directions. Ten groups of samples were monitored, which were u_2.5 = 1~5 m s⁻¹ as the inlet input under windward and leeward flows.

2.7. Ventilation Model Establishment Using Regression Trees

Regression trees and classification trees belong to a particular kind of nonlinear predictive model, namely prediction trees. Regression trees are a way of making quantitative predictions, which use the trees to represent the recursive partition. Each of the leaves represents a cell of the partition and has attached to it a simple model that applies to that cell only [42]. The inputs are wind speed and directions, the upper and lower vent-opening ratio areas (vent area/greenhouse area), and the temperature difference between indoors and outdoors. The output is the area ventilation rate, m³ s⁻¹ m⁻². In this work, this technique was used to obtain the natural ventilation rate model.

2.8. Statistics and Machine Learning Toolbox

MATLAB’s “Statistics and Machine Learning Toolbox” (ver. 2021b) provides functions and applications to describe, analyze, and model data. It contains a Regression Tree Predict block that calculates responses to given input data. The regression trees model was trained and predicted by following the tree from the root node down to a leaf node. At each node, the model decides which branch to follow using the rule associated with that node and it continues until it arrives at a leaf node. Each step in a prediction involves checking the value of one predictor variable [43].

2.9. Evaluation of the Regression Tree Ventilation Model

The evaluation of regression tree model was conducted to compare its output with an existing validated theoretical model used to simulate the ventilation rate of the CSG. The equations are shown below [5], which assume that the indoor and outdoor air temperature distribution is uniform:

$$L_T=f_u\sqrt{{\displaystyle \frac{2g∆H_v(T-T_o)}{T}}}$$

(8)

where

$$f_u={\displaystyle \frac{1}{\sqrt{\frac{1}{u_j^2{F}_j^2}+\frac{1}{u_p^2{F}_p^2}}}}$$

(9)

where L_T is the thermal gradient ventilation rate, m⁻³ s⁻¹; f_u is the coefficient of the thermal pressure ventilation rate; g is the gravitational acceleration, m s⁻²; ∆H_v is the height difference between the upper vent and the lower vent, m; T is the indoor air temperature, K; T_o is the outdoor air temperature, K; u_j is the flow coefficient of the air inlet; F_j is the effective area of the air inlet, m²; u_p is the flow coefficient of the air outlet; and F_p is the effective area of the air outlet, m².

The wind pressure ventilation rate is estimated by an empirical value assigned by NY/T 1451-2018 [44],

$$L_w=\beta F_{j}u$$

(10)

where L_w is the wind pressure ventilation rate, m⁻³ s⁻¹; and β is the wind pressure coefficient.

The area ventilation rate is the square root of the quadratic sum divided by the area of the greenhouse,

$$L={\displaystyle \frac{\sqrt{{L_T}^2+{L_w}^2}}{A_g}}$$

(11)

The evaluation aimed to calculate the averaged absolute error (AE) and root mean square error (RMSE) of the predicted ventilation rate by entering the same inputs to the regression trees and the theoretical model, including gradient wind speeds, vent-opening areas, and temperature differences between indoors and outdoors, under leeward and windward conditions (Figure 7).

3. Results and Discussion

This section describes the main results for the numerical analysis of the wind field in rows of the CSG, and the development of a natural ventilation model. First, the wind flow pattern around and inside multiple greenhouses and the ventilation rate are compared using 2D and 3D cases. Afterward, the limited area ensuring that the wind speed is in the free stream is demonstrated. Finally, a regression trees natural ventilation rate model is developed and evaluated.

3.1. Ventilation Rate and Airflow Pattern Under the Windward Condition

The airflow pattern is analyzed under windward conditions. Figure 8 shows the comparative analysis between the 2D and 3D cases. The vent openings are 100% in this comparative analysis section. The first row in Figure 8 represents the windward condition. The ventilation rates for the 2D and 3D cases are very close for greenhouse A, for which the ratio errors are below 0.1 (Figure 8) for 1–5 m s⁻¹ u_2.5 wind speeds. However, for greenhouses B and C (different positions in building clusters), the ratio errors are above 0.5. Additionally, the errors for greenhouse B are greater than those for greenhouse C and are positively correlated with the wind speed. This result demonstrates that 2D cases are sufficient when there is no obstacle in front of and behind the greenhouse in windward conditions. However, if there are other greenhouses in front of and behind them, 3D cases must be adopted.

Figure 9 shows the velocity vectors obtained from the 2D and 3D cases and depicts larger differences for greenhouses B and C than for the A one. The airflow patterns calculated from the 2D and 3D simulations are indeed similar in the central vertical section of the front greenhouse (Figure 9a,b). From the results of the 3D case, it can be seen that the greenhouse in the back rows of the greenhouse cluster receives a portion of its air intake from the lateral sides of the greenhouse rows. This information is lost in the 2D model. When adopting the 2D case, for the middle and the back row greenhouses, the airflow pattern in the central section of the greenhouse cannot be regarded as representative of the entire greenhouse. This fact explains why the middle and back row greenhouses show significant errors (Figure 9c) regarding the ventilation rate prediction. This means also that, if the 2D model is used for the windward flow, there must be no obstacles in front of and behind the greenhouse. Otherwise, the error could reach more than 50%.

In Figure 10, it can be seen that, for greenhouse A, all air enters through the lower vent (Figure 10a). For greenhouse C, most of the air enters from the lower vent (Figure 10c). In the center of greenhouse C, there is flow in the opposite direction. Nevertheless, the inflow through the lower vent is significantly greater than the outflow. For greenhouse B, most of the air enters the room from the upper vent and exits through the lower vent (Figure 10b,d). Note that this result is related to the lack of thermal pressure. Additionally, the flow pattern is affected by the turbulence model and time step size.

The above description is when the temperature difference inside and outside the greenhouse is 0 K, meaning that the wind pressure is dominant. Under these conditions, the ventilation rate of greenhouse B is negative (Figure 8). When the thermal pressure is dominant, the flow pattern of greenhouse B changes. Figure 11 shows that, with a temperature difference of 5 K between the inside and outside of the greenhouse, the upper vent is the outlet, and the ventilation rate is positive for greenhouse B. The wind speed is 1 m s⁻¹ and the ventilation rate is 6.5 m³ s⁻¹. The thermal pressure also significantly increased the ventilation rate of greenhouse C from 2.3 m³ s⁻¹ to 8.9 m³ s⁻¹ under windward flow when u_2.5 is 1 m s⁻¹. This illustrates that, in the greenhouse clusters, the influence of the wind pressure on the natural ventilation for the back rows greenhouses is limited. Appropriately increasing the spacing between greenhouses is therefore essential for maintaining ventilation.

3.2. Ventilation Rate and Airflow Pattern Under the Leeward Condition

Under leeward flows, the lower vents are the inlet (Figure 12a,b), and the ventilation rates from the 3D simulations are greater than those from the 2D ones in all the samples. This is probably because, in the 3D cases, the inflow through lower vents comes from both the roof and lateral sides, whereas it comes only from the roof in the 2D cases (Figure 12c). When adopting the 2D simulation, this difference in the flow field is more enhanced inside greenhouses A and C than inside greenhouse B. Additionally, this impact is negatively correlated with the wind speed. In general, the difference in the natural ventilation rate simulation between the 2D and 3D cases under leeward conditions is smaller than that under windward conditions. The ratio errors for greenhouses A, B, and C in all the leeward flow cases were lower than 0.4. Among them, the greenhouse in the middle of the greenhouse rows had the smallest ratio errors, with a value in the range of 0.1–0.2.

Current studies are aimed at a single greenhouse, ignoring the influence of surrounding buildings, and the wind direction is relatively simple [23]. However, the modelling of flow fields in greenhouse clusters is of great relevance for both production and research in the future. Another reason for which most researchers choose a 2D model is that their calculations are transient, and it is known that, with a three-dimensional transient CFD simulation, it is difficult to achieve convergence at each time step, which affects the accuracy [27,45]. Although, with the progress of hardware, these problems are expected to be solved in the next few years, the methodology in this study aimed to include time-consuming numerical computations into the fast transient simulation by training their results in the black box model.

3.3. Analysis of Wind Speed at the Monitoring Location

In the direction perpendicular to the wind, the impact of the building on the wind speed is positively correlated with the wind speed (Figure 13). The gray area in Figure 13a,b shows the recommended area to place wind speed sensors to ensure that the measured wind is in free stream (the greenhouse wall is at 86 m on the western side), i.e., the area where the building does not impact the flow field anymore. Under the windward condition, the distances where the wind speed changes sharply on both sides outside the greenhouse are below 8, 10, 16, 20, and 23 m away from the greenhouse under 1~5 m s⁻¹ wind speed. Under the leeward condition, the distances are below 7, 9, 13, 17, and 20 m under 1~5 m s⁻¹ wind speed. Beyond these distances, the measured wind speed is considered to be in the free stream. The impact of buildings on the air flow on the lateral sides is clearly seen in Figure 14. This disturbance is more obvious for the greenhouse in the rear row. It is recommended to measure the free stream wind speed in the windward upstream of the building clusters.

In the direction parallel to the wind (the inlet is 10.8 m from the greenhouse), whether in the windward or leeward direction, the optimal distance from the greenhouse would be beyond 10.8 m (3 times the ridge height) in the upstream direction and greater than 36 m (10 times of the ridge height) in the downstream portion, ensuring the wind speed is in the free stream (Figure 13c,d). This conclusion was confirmed by Kim et al. [36]. The measurement of the wind speed is a necessary step for simulating the greenhouse climate. Anemometers must be placed in an open area outside of the greenhouse, and this study provides reference values for these distances in various cases.

3.4. Ventilation Model Establishment Using Regression Trees

The estimation of the ventilation rate is a laborious task and usually requires multiple complex parameters. In this section, a regression tree ventilation model was developed from 990 CFD samples. Its inputs were the wind speed at a height of 2.5 m, the ratio area of the upper and lower vents, the area of the greenhouse, and the temperature difference between the inside and outside of the greenhouse. The output was the area ventilation rate in m³ s⁻¹ m⁻². The temperature difference was achieved by the imposed fixed wall temperature. The greenhouse temperature decreased from top to bottom, and the air temperature near the opaque walls was higher than that in other areas [27]. By embedding the buoyancy equation, the contribution of thermal gradients to the ventilation rate was calculated by steady-state simulation.

A total of 990 samples from 2D CFD results was used to train the model. In Figure 15, the so-called “true” response is provided by the CFD results, while the predicted response is provided by the regression tree ventilation model. From left to right in Figure 15, the velocity speed is increased, and from bottom to top, the vent opening area is increased. The points on each short line correspond to the tested temperature differences, which increase from left to right. There are, therefore, 11 points in each short line, representing the temperature difference between 0 and 10 K, with a 1K temperature step. It shows that, at a low wind speed, the temperature difference makes the lines tilt greatly. But, at high wind speeds, all the lines are almost horizontal, which demonstrates that, under a low wind speed, the thermal pressure ventilation becomes predominant, and vice-versa. From bottom to top, the vent-opening areas increase. There are 18 rows (9 vent combination ∗ 2, windward and leeward) at each wind speed. Figure 15 shows that choosing a larger vent area at a high wind speed is more beneficial for increasing the ventilation rate than choosing one at a low wind speed. The RMSE of the regression tree model is 0.002. This model can perfectly deal with the combined effect of wind pressure and thermal gradients. Note that this regression tree model was applied when there were no other greenhouse rows in front, because the previous sections proved that the samples of the 2D model are only reliable when there is no building obstruction in front of the greenhouse. To improve the model, 3D cases must be simulated with the same sample size. However, this is a great challenge due to the limitations of computing power and the workload.

3.5. Comparison Between the Regression Tree and Theoretical Models (Equation (11))

Figure 16 shows 330 pairs of samples. Each pair of samples is a comparison of the two models under the same input. The result shows that the curves of the regression tree and theoretical models are very close, with the AE and RMSE between two models being 0.0077 and 0.0094 m³ s⁻¹ m⁻², respectively (Figure 16a). From samples No. 0–30, it is known that the ventilation models are linear when the wind pressure is the only driving force. For samples No. 31–330, the results show that the regression tree model can totally take over accurate predictions when the wind pressure and thermal pressure act simultaneously, without any theoretical parameters and laborious equation modeling.

4. Conclusions

This paper experimented with a methodology of machine learning modelling using virtual samples generated by fast CFD simulations in order to predict greenhouse natural ventilation. Its main contributions can be summarized as follows:

(i)

Three-dimensional simulations require a vast amount of computation load. It costs more than 30 h to complete 900 iterations to achieve convergence in each 3D case, using an Intel Core I7 CPU and 16 GB RAM. For that reason, two-dimensional CFD simulations are still often adopted to study the wind flow pattern around a greenhouse. The present study compared 2D and 3D simulations, and the results show that the 2D model is sufficient when there is no obstacle in front of and behind the greenhouse, especially for windward flows. But, if there are other greenhouses nearby, the 3D model should be adopted; otherwise, the error could reach 50% for the ventilation rate prediction.

(ii)

Turbulence around buildings makes it difficult to measure the wind speed. So, this paper determined a limited area around the rows of the CSGs ensuring that the wind was in the free stream and provided the recommended distance to place anemometers in a greenhouse.

(iii)

A regression tree natural ventilation model was developed using results from 990 two-dimensional CFD samples. This model perfectly deals with the combined effect of wind pressure and thermal gradients. This regression tree natural ventilation model is embedded in a published greenhouse model [6]. The application shows this tree model performs ideally for a 7-day simulation (Appendix A).

The CFD method provides a theoretical basis for virtual wind tunnel experiments. A vast number of reliable samples can be obtained through virtual wind tunnel experiments. In the future, with the update of computer hardware, a refined ventilation model can be trained through a large number of three-dimensional simulation results, including arbitrary wind direction and better accuracy. Meanwhile, it is also acknowledged that simulation samples have limitations in demonstrating real scenarios. Further studies include experimental testing to enhance the robustness of the model.