Greenhouse Natural Ventilation Models: How Do We Develop with Chinese Greenhouses?

Abstract

Greenhouse technology has advanced over the past few decades in terms of environmental control (e.g., indoor temperature, relative humidity, and CO₂ concentration). Ventilation is an effective way to adjust the indoor climate. Natural ventilation has gained significant research attention recently because of its low energy requirement. To evaluate the ventilation effectiveness, the ventilation rate is often used. This review summarizes the published review papers related to greenhouse ventilation. Ventilation models are reported under different conditions, including wind-induced, buoyancy-induced, and combined effects-induced ventilation in greenhouses. The influencing factors are described, such as the wind and buoyancy strength and distribution, greenhouse geometry, and vent arrangement. Various methods assessing natural ventilation in greenhouses are introduced, consisting of tracer gas techniques, the pressure difference method, the energy balance method, the emptying fluid-filling box method, and numerical simulation. The values of the key coefficients deduced and used in the literature are listed. This paper reports what has been done in the world and where we can start to develop dynamic ventilation models for solar and tunnel-type greenhouses in China. Further valuable investigations are discussed. The pressure distribution function in greenhouses with horizontal openings, a model for cross-ventilation induced by combined wind and buoyancy force, and an analytical plant-considered ventilation model with higher applicability are described. To ensure the accuracy of the ventilation models, other environmental variables, especially geography-dependent ones, can be added. More criteria are suggested to evaluate the ventilation performance rather than the ventilation rate to provide a comprehensive assessment.

1. Introduction

As of 2018, 577,455 and 1,335,663 hectares of land were occupied by small greenhouses, namely Chinese solar greenhouses (CSG) and Chinese plastic greenhouses (CPG), respectively [1] (Figure 1f,g).

CSGs provide a suitable environment for planting in cold regions due to the thick back wall and the thermal insulation quilt. Therefore, CSGs are usually built in the northern plains and western plateau areas in China. A typical CSG has a lower opening toward the south and an upper opening parallel to the ground. In order to improve the ventilation efficiency and thus the production performance, researchers have studied the flow field characteristics, the effects of vent heights on indoor climate, and the structural renovation of vents. However, few theoretical models describe the correct behavior of natural ventilation in typical CSGs (Figure 1(g1)).

There are two forms of CPGs, which are also called tunnel-type greenhouses, with side vents only (Figure 1(f1)) or with both side and roof vents (Figure 1(f2)). Because of the vast area of China, the operating conditions of greenhouses are dramatically different. In the southern rainy regions of China, from plains to plateau areas, CPGs without roof vents are commonly constructed. This kind of tunnel greenhouse (CPG-f1) has been well studied with respect to wind-induced ventilation, while few studies have focused on the buoyancy-induced ventilation performance and its theoretical models.

This paper surveys what has been done, how to understand the ventilation mechanism, and how we might develop ventilation models for small greenhouses in China.

The sensible heat released in greenhouses is mainly induced by the absorbed solar radiation contributed by the cover, the structural elements, the soil, and the crop absorption [2]. The purpose of ventilation in greenhouses is to bring in carbon dioxide and remove excess heat and humidity, and to provide a comfortable environment for plants [3,4]. A sustainable and healthy indoor environment is important for both humans and plants, and natural ventilation is one basic element.

The concept of natural ventilation received increasing attention from scholars starting in the 1990s. Boulard [5] surveyed the approaches to natural ventilation in greenhouses. Sethi and Sharma [6] summarized natural ventilation studies as one of the cooling technologies in greenhouses. Norton et al. [7] performed modeling of the computational fluid dynamics (CFD) applications of ventilation systems and designs in the field of agriculture. Bournet and Boulard [8] summarized the effects of ventilator configurations on greenhouse indoor climate distribution, including greenhouse geometry and opening arrangements. Khanal and Lei [9] discussed solar chimneys as a passive strategy to enhance natural ventilation with respect to the buoyancy effect [10]. Rong et al. [11] discussed natural ventilation mechanisms in livestock buildings and the ventilation coefficients used in the literature. Akrami et al. [12] reported on the methods and technologies used for natural ventilation in greenhouses. Sakiyama et al. [13] provided an overview of natural ventilation investigations with respect to thermal comfort, the efficiency of energy usage, and indoor air quality. Wang et al. [14] summarized the wind pressure coefficients on the surface of different greenhouse types. Zhong et al. [15] discussed papers relevant to single-sided natural ventilation.

Natural ventilation is induced by the wind effect, buoyancy effect, and combined wind and stack effect [16]. The wind action results in a pressure field surrounding the openings, and the buoyancy effect is relevant to the gradient of air density between the indoor and outdoor environments [17]. Ventilation rate is a widely used and well-developed concept in ventilation assessment, namely the frequency of exchanged air volume between the inside and outside per unit of time [18]. Models have been established with the driving forces and influencing factors (Figure 2) for different greenhouses (Figure 1), but not for Chinese greenhouses in particular.

2. Current Models of Wind-Induced Ventilation

2.1. Theoretical Models

The wind action results in a pressure field surrounding the openings [17]. The pressure field is different in various application scenarios, including greenhouse structures and ventilation categories. In addition, the wind-induced ventilation rate is affected by the vent size and arrangement, insect screens, roof geometry, plant characteristics, and wind direction.

According to Bernoulli’s equation, the pressure difference (Δp) decides the mean flow velocity through the opening (V), with a known resistance coefficient (ξ) and air density (ρ) (Equation (1)). The function of ξ for rectangular openings was introduced by Bot [19], with different forms including for the ratio between the length and height of vents L/H > 1 (Equation (2)) and for a hinged flap (Equation (3)), which was also used in later studies [20,21,22].

Δp = 1/2 ξρV²

(1)

ξ = 1.75 + 0.7exp(−L/(32.5H))

(2)

ξ = 1.75 + 0.7exp(−L/(32.5Hsinα))

(3)

When a window is used, covering the vent, the window function f(α) with a value between 1 at full and 0 at closed opening, is applied (Equation (4)) based on the opening angle (α) [19], where ϕ_v is the ventilation rate and A_o the opening effective area.

Δp = 1/2 (ξ/f(α)) ρ(ϕ_v/A_o)²

(4)

The discharge coefficient is often used as a function of resistance coefficient (C_d = 1/ξ^0.5) [17,20,23]. The mean velocity at the opening can be calculated via Equation (5). Gong, et al. [24] estimated the discharge coefficient in different types of greenhouses, with a specific ratio between the height and length of openings and different opening angles, considering the ventilation as the outflow through thin-walled orifices:

V = C_d (2/ρ ∆p)^0.5.

(5)

2.2. Application Scenarios

2.2.1. Mixing Ventilation

The wind turbulence significantly influences the mixing ventilation [19,20,25,26,27,28,29]. When there are only roof vents facing the same direction (Figure 1 (mixing ventilation)), the ventilation is induced by two factors: the static and turbulent wind effect.

At the windward side of the building with external wind speed V_w, the static pressure (p_u) is higher than the barometric pressure, whereas the static pressure is lower at the leeward side [30]. Dimensionless static pressure coefficient (K_p) is positive at the windward side and negative in the contrast. In this case, ventilation is formed only when there are vents on both sides of the construction [25].

p_u = 1/2 K_pρV_w²

(6)

As wind has the nature of fluctuation related to the wind turbulence interacting with the building structure, the momentary pressure (p_u′) outside the openings was considered the driving force [19], with a dimensionless pressure fluctuation coefficient (K_f) defined. Both K_p and K_f can be obtained by experiments only [31,32,33].

p_u′ = 1/2 K_f ρV²

(7)

The wind effect coefficient (C_w) was proposed and clarified as a whole, covering both the static and turbulent effect to compute the ventilation rate caused by wind (Equation (8)) [17,19,29,31,32,34]:

ϕ = C_d A/2 (C_w V_w²)^0.5.

(8)

Differently, Hellickson et al. [35] and Albright [36] gave the ventilation rate in Equation (9), where E is the opening effectiveness, recommended as 0.35 for agricultural buildings. An algorithm was proposed to calculate the opening effectiveness of natural ventilation by Nääs et al. [37]:

ϕ = AEV_w/2.

(9)

2.2.2. Displacement Ventilation

The wind-induced ventilation rate of greenhouses with side and roof vents (Figure 1 (displacement ventilation)) can be estimated according to Equation (10) [38]. Researchers [3,16,17,19,20,23,27,32,33,34,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61] have deduced and applied the discharge coefficient and the wind effect coefficient in greenhouses with vertical openings (see

Table 1. The wind effect coefficient given by various greenhouses. Note: “global” means the global wind effect coefficient in the form of C_dC_w^0.5.

References	Greenhouse	Continuous Roof Vents	Continuous Side Vents	Ventilation Type	Wind	Wind Effect Coefficient	Discharge Coefficient	Opening Effectiveness	Effective Area of Vents	Continuous Buoyancy Source	Combination Method
Bruce [23]	Cattle	Yes	Yes	Mixing and Displacement	No	-	0.6	-	-	Yes	Energy balance
Bot [19]	Multispan	No	-	Mixing	Yes	0.6–1.6	0.64 + 0.001α	-	-	Yes	ϕ = √(ϕw2 + ϕb2)
Zhang, et al. [39]	Swine finishing	Yes	Yes	Displacement	Yes	-	0.605	-	-	Yes	Volume balance
Albright [36]	-	-	-	-	Yes	0.35	-	0.5–0.6; 0.25–0.35	-	-	-
De Jong [20]	Quasi infinite	No		Mixing and Displacement	Yes	0.09	0.74	-	-	Yes	ϕ = √(ϕw2 + ϕb2)
Linden, et al. [3]	Enclosure	-	-	Displacement	No	-	-	-	Yes	Yes	-
Fernandez and Bailey [27]	Multispan	No	-	Mixing	Yes	0.17	-	-	-	Yes	Energy balance
Kittas, et al. [40]	Multispan	Yes	-	Mixing	Yes	0.27	-	-	-	Yes	ϕ = ϕw + ϕb
Boulard and Draoui [41]	2-span	Yes	-	Mixing	Yes	0.21	-	-	Yes	Yes	ϕ(ζ)
Boulard and Baille [17]	2-span	Yes	-	Mixing	2–4; 0–2	0.07–0.1	0.43; 0.45; 0.64	-	-	Yes	ϕ = ϕw + ϕb
Boulard, et al. [34]	2-span	Yes	-	Mixing	2–3	0.2; 0.26; 0.29	-	-	-	-	ϕ = ϕw + ϕb
Papadakis, et al. [33]	2-span	Yes	Yes	Mixing and Displacement	0.1–7.6	0.246, 0.142 (global roof and side); 0.21 (global)	-	-	-	Yes	ϕ = √(ϕw2 + ϕb2)
Kittas, et al. [32]	Multispan	Yes	-	Mixing	Yes	0.2 (global)	-	-	-	Yes	ϕ = ϕw + ϕb
Kittas, et al. [38]	2-span	Yes	Yes	Displacement	0–9.5	0.07	0.74	-	Yes	-	ϕ = √(ϕw2 + ϕb2)
Miguel [42]	2-span	No	-	Mixing	1.27–5.5	1.13–1.52	0.61	-	-	Yes	-
Nääs, et al. [37]	Poultry	-	Yes	Mixing	Yes	-	-	0.25–0.6	-	-	-
Muñoz, et al. [43]	3-span	Yes	-	Mixing	1–4	0.32–0.48; 0.061–0.089 (screened)	ξ = 1.75 + 0.7exp(−L/(32.5Hsinζ))	-	-	-	-
Baptista, et al. [16]	Multispan	No	-	Mixing	0.1–11	0.1; 0.09	0.64; 0.65	0.2	-	Yes	ϕ = ϕw + ϕb; ϕ = √(ϕw2 + ϕb2)
Hunt and Linden [44]	Enclosure	Yes	Yes	Displacement	Yes	-	0.6	-	Yes	Transient	ϕ = √(ϕw2 + ϕb2)
Oca, et al. [45]	Tunnel	Yes	Yes	Displacement	No	-	0.75	-	-	Yes	Energy balance
Teitel and Tanny [46]	4-span	Yes	Yes	Mixing	0–4.2	0.11 (global)	0.7	-	-	Yes	Energy balance
Hunt and Linden [47]	Enclosure	Yes	Yes	Displacement	Yes	-	0.6	-	Yes	Yes	ϕ = √(ϕw2 + ϕb2)
Gladstone and Woods [48]	Enclosure	Holes	Holes	Displacement	No	-	0.5	-	Yes	Yes	Energy balance
Parra, et al. [49]	Multispan	Yes	Yes	Displacement	0–11	0.0017	0.656	-	Yes	Yes	ϕ = ϕw + ϕb
Si and Miao [50]	3-span	Yes	Yes	Displacement	Yes	0.8 (windward); −0.4, −0.5 (leeward)	0.33	-	-	Yes	ϕ = ϕw + ϕb
Liu, et al. [51]	3-span	Yes (screened)	Yes (screened)	Displacement	2	0.038	0.127	-	Yes	Yes	Energy balance
Katsoulas, et al. [52]	Multispan	Yes (screened)	Yes (screened)	Displacement	2.2	0.07	0.363	-	Yes	Yes	ϕ = √(ϕw2 + ϕb2)
Teitel, et al. [53]	Multispan	Yes (screened)	Yes (screened)	Displacement	4.9	0.075	0.253	-	-	Yes	CFD simulation
Wang and Wang [54]	Multispan	Yes (screened)	-	Mixing	1–5	0.178 (window); 0.318 (rolling-up)	-	-	-	Yes	-
Wang and Wang [54]	Multispan	Yes (screened)	-	Mixing	0	-	0.667; 0.863	-	-	Yes	-
Baeza, et al. [55]	3-, 5-, 7-, 10-, 15-, 20-span	Yes (screened)	Yes (screened)	Mixing and Displacement	0	-	0.65; 0.055	-	-	Yes	-
Mashonjowa, et al. [56]	Multispan	Yes	Yes	Displacement	0.35–3.4	0.029	0.414	-	Yes	Yes	ϕ = √(ϕw2 + ϕb2)
Teitel and Wenger [57]	Single span	-	Yes	Cross	1–7	0.6 (windward); −0.35 (leeward)	-	-	-	-	-
Fang, et al. [58]	Chinese solar	Yes	-	Mixing	Yes	0.04; 0.05; 0.07	0.78; 0.60; 0.44	-	-	Yes	ϕ = ϕw + ϕb
Chu, et al. [59]	Single; 2-span; 3-span	-	Yes	Cross	10	0.00623	0.66	-	Yes	-	-
Chu and Lan [60]	Single; 3-span	Yes	Yes	Displacement	7.2	1.15–1.28 (difference)	0.66	-	Yes	-	-
Villagran, et al. [61]	Multispan	No	No	Displacement	0.31–1.47	-	-	-	-	-	CFD simulation

).

ϕ = C_d A_iA_o/√(A_i² + A_o²) [(C_wi−C_wo) V_w²]^0.5

(10)

Typical Chinese solar greenhouses (CSG) have horizontal roof openings. However, the measured wind pressure coefficients of CSG were only used to evaluate the wind load of the greenhouses [14] and to deduce the critical wind speed for wind disasters in various areas of the facility [62,63,64]. The wind pressure coefficient of CSG is often calculated using a scale model with the vents completely closed in the wind tunnel. Studies showed that the wind pressure coefficient decreased with opened vents compared to closed vents [65].

The natural ventilation of typical Chinese solar greenhouses (CSG) has been studied since 2000. With the rapid development of computational fluid dynamics during that time, researchers started to investigate the air flow characteristics of CSG via CFD simulations [66,67] and energy balance models [68] instead of theoretical models. According to the CFD simulations, the functions of the wind pressure coefficient (Equation (11)) and discharge coefficient (Equation (12)) of CSG were proposed according to the angle θ between the vent and the wind direction and the area ratio (R) between the inlet and outlet, respectively [69].

C_w = 0.7486sinθ + 0.0237sin²θ

(11)

C_d = e^{(−0.67403R)}

(12)

2.2.3. Cross-Ventilation

Cross-ventilation (Figure 1 (cross-ventilation)) leads to better cooling and dehumidification uniformity in greenhouses [70], and has often been investigated via CFD simulations [71]. Chu et al. [72] indicated that the discharge coefficient is a function of the Reynolds number, the incident angle of external wind, and the opening positions (Equation (13)). Re_c is the critical Reynolds number, 18,000, leading to the critical discharge coefficient (C_dc) 0.66. The power n is different with inlet, outlet, and wind direction.

C_d/C_dc = (Re/Re_c)ⁿ

(13)

To have effective wind driven cross-ventilation, the rule of thumb is that the length of the building (the horizontal distance between the two openings) should be smaller than five times the ceiling height [73,74]. The internal friction should be considered when the greenhouse length is six-times greater than the height [75].

2.3. Factors Influencing Ventilation Rates

2.3.1. Vent Size, Shape, and Arrangement

When the outdoor wind speed is low, the cooling effect of ventilation with combined roof vents and side vents is better than with roof vents alone [33]. However, when the wind speed exceeds a certain value, the cooling effect of roof vents alone is better [76,77]. With a larger opening area on the roof, the reduction of the temperature and humidity ratio (ventilation effect) increases [46].

A vortex can be produced in greenhouses with the bottom vent or bottom and roof vents, while the air circulation is not strong with the opened roof vent [78]. The most homogeneous distribution of indoor environment was achieved with roof vents only [79], leading to decreased air temperature–humidity ratios over time [46]. The combined roof and side vents caused increased the spatial heterogeneity of the microclimate, increased the air speed, and decreased the temperature inside the greenhouse [70,79,80]. Hence, roof vent ventilation was recommended under cold weather to keep the inside warm and meet the requirements of dehumidifying [70].

The increased vertical distance between the vents [81] resulted in greater ventilation flux. However, Shen et al. [82] found that the ventilation rate is dependent on the ratio between the inlet and outlet sizes, whereas the positions have little impact. Larger side vents resulted in a lower indoor temperature [83]. The indoor air velocity increased with larger side vents, while the effect decreased when the vent width exceeded 1 m [84]. Various outlets did not affect indoor velocities, but inlets influenced the outlet velocities [82].

Increasing the number of roof vents (roof vent area) resulted in a higher overall ventilation rate but weaker air movement at the crop level [85,86]. Yan [87] compared the ventilation performance in CSG with rear slope integral vents, rear slope interval vents, and top end vents (Figure 3a–c). The rear slope vents resulted in a higher daily average wind speed.

The optimal range of area ratio between vents and a greenhouse was recommended as 18–25% in CSG [88]. However, Tian [69] determined that the best area ratio was 11.6% in CSG with wind-induced ventilation, producing the highest air velocity in the crop zone. He also indicated that the best vent area ratio between the inlet and outlet to reach the greatest ventilation rate is 1.

Figure 3. Chinese solar greenhouses with top end vents (a), rear slope integral vents (b), and rear slope interval vents (c) [87], and vents on the back wall (d) [89].

Figure 3. Chinese solar greenhouses with top end vents (a), rear slope integral vents (b), and rear slope interval vents (c) [87], and vents on the back wall (d) [89].

The backwall vents in CSG (Figure 3d) could not improve the ventilation effectiveness, which leads to two low-speed eddy currents at the upper and lower sides of the backwall vents [89].

2.3.2. Insect Screens

Insect screens are often installed over vents, which is of great importance for reducing insect pests and diseases in greenhouses, but results in resistance to the ventilation.

Miguel et al. [90] analyzed the effects of different screen materials on ventilation rate with respect to the porosity of the screen and the pressure drop through it. Based on the motion equation [42,90], Muñoz et al. [43] determined the ventilation rate of greenhouses with insect-proof screens over different types of vents. The discharge coefficient of the screened vent (C_dsv) can be computed with the discharge coefficients of the vent (C_dv) and the screen (C_ds) (Equation (14)) [91]:

1/C_dsv² = 1/C_d² +1/C_ds².

(14)

The total screened vent resistance coefficient is equal to the sum of the resistance coefficients of the vent and the screen (Equation (15)). The screen resistance is higher, with lower wind speed, related to the smaller Re value [92]. The total resistance is also influenced by the incidence angle (θ) of wind (16) [93]. Parra et al. [49] indicated that the ratio between the ventilation rate with and without a screen (Equation (17)) can be represented by the screen porosity (ε).

ξ_total = ξ_vent + ξ_screen

(15)

ξ_θ = ξ₀ cos²θ

(16)

G_screen/G = ε (2 − ε)

(17)

The ventilation rate was reduced by 77–87% with a screened roof and side vents in the buoyancy-ventilated greenhouse, where the reduction depended on the greenhouse size [55]. However, the ventilation rate reduction was much smaller in the wind-driven ventilation.

Reduced spatial heterogeneity was observed in greenhouses with screened roof and side openings [79,94]. The air temperature at the crop level was lower than outside due to the absence of screens, but higher with screens because of the lower ventilation rate and weaker turbulence [79].

2.3.3. Plants and Their Orientation

The fluid loses some momentum due to collisions during the movement through the plant zone, leading to a decreased ventilation rate compared to with no plants. The estimation of air speed profiles in greenhouses was recommended to divide the section area into a crop part and a void part [95].

Researchers [96,97,98,99] have quantified the drag effect of plants by combining Equation (18) [100], corresponding to the pressure gradients term in the Navier–Stokes equation and the porous medium approach. The drag coefficients (C_D) can be measured in wind tunnels, with 0.32 for tomato plants [101], 0.30 for forest trees [102], and 0.2 for plants in general [103]. According to the plant cover characteristics (leaf area density l, C_D), the inertial factor (C_f) and the permeability (K) can be deduced (Equation (19)).

∇P = l C_D ρu²

(18)

C_f/K^0.5 = l C_D

(19)

It was indicated that the plant drag coefficient was not affected by the ranges of pressure drop and crop canopy geometry, but by leaf area density [104]. A taller canopy with greater leaf area density resulted in lower temperature and stronger temperature stratification [105].

The energy model of natural ventilation was modified (Equation (20)) based on crops of different growth heights (x) using crop height coefficient k (Equation (21)) [106].

Q = kϕρC (T_in − T_out)

(20)

k = −0.02667x⁴ + 0.1467x³ − 0.2333x² + 0.02333x + 1

(21)

Chu et al. [89] determined the effects of plants, insect screens, and internal friction on ventilation rates using a resistance model (Equation (22)) [107,108]:

ϕ* = ϕ/(V_wA*) = 1/A* [(C_pw-C_pL)/(ζ_w + ζ_i + ζ_L)]^0.5.

(22)

Although plants are mostly cultivated in the north–south ridge direction in CSGs due to the good lighting conditions, the ridge length in this direction is short [109]. During actual production operations, farmers need to go in and out of the ridges in a cyclical manner, resulting in low work efficiency. Because of the suitability of the east–west crop rows orientation for machine operations in CSGs, it has been favored by researchers in China recently [110]. However, the growth of north–south-oriented tomatoes was indicated to be higher than in east–west rows [111]. Based on data collected from December 2016 to April 2017, no dramatic difference in tomato yield was found between the east–west ridges and the north–south ones [112].

Majdoubi et al. [113] analyzed the influence of plant orientation alone on ventilation performance according to the additive property of the resistance coefficients. The crop rows oriented perpendicular to the direction of indoor air movement resulted in a 50% reduction in the ventilation rate [113].

2.3.4. Roof Geometry and Slope

The geometry and roof slope can influence the natural ventilation efficiency [114,115,116]. The ventilation flow rate of a convex roof was 8.8% higher than that of a concave roof and 3.5% higher than that of a straight roof (Figure 4) [117]. A curved and gothic roof resulted in a 3.4-fold higher ventilation rate than the traditional greenhouse used in Colombia and more homogeneous thermal distribution, with the mean temperature reduced by 2.8 °C [61].

The height and number of spans has dramatic consequences in terms of the climate performance [117,118]. As the greenhouse height and number of spans increase, the ventilation performance increases [118]. However, this does not mean that we can increase them indefinitely, because there is a greater heating requirement [118] and a discrepancy between different roof slopes, with a double-span roof performing better than a straight or concave roof but worse than a convex roof (Figure 4) [117].

2.3.5. Wind Direction

Different wind directions with respect to the lengthwise axis of the tunnel greenhouse result in a clear effect on the inner temperature, humidity, and velocity distributions [119,120,121]. Chu et al. [122] investigated the wind-induced ventilation for buildings with two vents on the same wall. They found that when the wind direction was 22.5–45°, the mean pressure difference across the vent dominated the air entering the room, while the fluctuating pressure entrained the air across the vents when the wind direction was 0° and 67.5–180°.

The discharge coefficient and wind effect coefficient are significantly influenced by the surrounding of the greenhouse and the wind direction close to the openings [123,124]. To take full advantage of the wind, a multispan monoslope greenhouse (Figure 1e) was suggested to use prevailing windward ridge vents [60].

3. Current Models of Buoyancy-Induced Ventilation

3.1. Theoretical Models

The stack effect is caused by the uneven temperature field of the fluid, resulting in an uneven density field, leading to the driving force of the fluid movement [125]. In the case of buoyancy-driven ventilation, the spatial distribution and intensity of sensible heat sources decide the air flow.

The pressure difference at the opening can be calculated via Equation (23), with constant values of interior and exterior air density [19]. According to the Boussinesq approximation, the density difference was expressed as a temperature difference with a thermal expansion coefficient (Equation (24)), where g is the gravitational acceleration.

∆p = p_i − p_e = (ρ_e − ρ_i) gz

(23)

ρβ (T_i − T_e) gz = ξ 1/2 ρV_z²

(24)

The similarity between the scaled model and the full-scale greenhouse ventilated by buoyancy was often defined by the Rayleigh number (Ra) and Archimedes number (Ar) [2]. Hou and Ma [126] reviewed it and concluded that the Ra number of the airflow field in the greenhouse is 2 × 10⁷–6 × 10¹¹. The buoyancy effect was found to be more important as the Rayleigh number increased [127]. Foster and Down [128] summarized the methods of computing the buoyancy-induced ventilation rate [129,130,131,132,133].

3.2. Application Scenarios

3.2.1. Vertical Openings

To simplify the problem, the temperature field was assumed to be homogeneous in greenhouses with one-side vents. The neutral plane determines the direction of air flow, in or out, which can be determined according to the mass balance between the intake air and exhaust air [134]. The positions of neutral planes of rooms with a single vertical opening and with two equal vertical openings follow the symmetrical distribution of the hydrostatic pressure, but are closer to the bigger vent in the case of two unequally sized vertical openings [19,23].

Scholars define the pressure and velocity distribution in three ways: first-order distribution, second-order distribution, and third-order distribution (Figure 5) [17,123]. The first-order distribution has the pressure staying constant at each half of the vent, the second-order distribution integrates it by height, and the third-order distribution introduces a linear change in temperature along the height of the window.

The first-order assumption was verified via experiments by Boulard and Baille [17], leading to the ventilation rate function (Equation (25)):

ϕ = S/2C_d [g∆Th/(2T)]^1⁄2.

(25)

The second-order pressure distribution has been the most popular assumption in natural ventilation studies [17,19], resulting in the ventilation rate function (Equation (26)):

ϕ = L/3 [gβ∆T/ξ] ^1/2 h ^3/2.

(26)

As for the third-order assumption, the function of interior temperature distribution (Equation (27)) was introduced to compute the interior air density (Equation (28)) and pressure (Equation (29)) along the height of the vent [135]. Similarly, the exterior variables were obtained in the same way. Then, the pressure difference could be deduced and applied to Equation (5), resulting in a function of velocity along the opening height (Equation (30)).

T_i (z) = T_0i + b_iz

(27)

ρ_i(z) = ρ₀ − ρβ (T_i(z) − T₀)

(28)

P_i(z) = P_0i − ∫ ρ_i(z)gdz

(29)

V(z) = C_d {2/ρ (P_0i − P_0e) + 2βg[(T_0i − T_0e)y + (b_i − b_e)y²/2]}^0.5

(30)

3.2.2. Horizontal Openings

The horizontal openings (Figure 6) were considered in the study of De Jong [20], while there were not conclusive results here because of the rather complicated and unstable flow conditions at the opening. The heavier air moves downward and the hot air upward, where a release of potential energy forms, providing kinetic energy for the motion. Thus, the pressure and flow distribution cannot be assumed in a steady way; instead, the ventilation flow rate can be quantified in an unbalanced way, considering the growth of perturbations [136].

A typical CSG has a bottom vent and a top vent, which are vertical and horizontal, respectively. The cold air mixes with the hot air at the horizontal roof vent, resulting in a smaller thermal pressure difference than with a vertical opening under the same temperature difference. The interior temperature and air velocity were observed to decrease dramatically near the roof vent in CSG, while the specific humidity increased [137]. The first-order assumption was applied to the ventilation model of CSG with a roof vent only (Figure 7) [58]. The deduced discharge coefficients were 0.78, 0.60, and 0.44 for different widths (3, 5, and 7 cm, respectively) of roof vents, which decreased as the vent width increased [58].

3.3. Factors Influencing Ventilation Rates

3.3.1. Buoyancy Source Strength and Distribution

The flow pattern of natural convection is influenced by the buoyancy strength and position. The normalized temperature gradient increased with mature plants compared to young plants [138]. The Prandtl number (Pr) was found to be a critical variable for thermal convection patterns. When Pr << 1, the heat is mainly transported through large-scale circulation; when Pr >> 1, the heat transport is mainly caused by plumes [139].

The vertical stratification is stable with different entrainments in the displacement ventilation (Figure 8) [3,140,141], while it is weak in the mixing ventilation [3]. The position of interfaces was found to be a function of the effective area of the openings, the height of the enclosure, and the ratio between the buoyancy sources [142,143].

As the heat source in greenhouses is usually areal instead of separate, researchers used a floor with holes (Figure 9a) and a heated floor (Figure 9b) to simulate the real situation. The viscosity and thermal diffusivity can be ignored with a high enough Re (>900) and Pe [45]. Taking the heat loss through the cover into account, the ventilation flux decreased by 25%. Compared to the single buoyancy source, the areal heat source produced warm air with a lower temperature but a greater air flux circulating through the room [48].

3.3.2. Vent Size, Shape, and Arrangement

Boulard et al. [144] investigated the natural ventilation driven by thermal gradients in a greenhouse with a single-sided roof opening and two symmetrical roof vents, respectively. The experimental greenhouse was set according to the Rayleigh–Bénard convection pattern. Different vent arrangements did not influence the convective loop of the incoming air streams.

Baeza et al. [55] tested a multispan greenhouse CFD model with buoyancy-driven ventilation according to the obtained data [130], and concluded that double the ventilation rate could be achieved with combined roof and sidewall vents rather than only roof vents. The combined roof and sidewall ventilation rate was higher with a smaller number of spans. Miao [86] found that increasing the roof opening area enhances the ventilation caused by heat pressure.

4. Current Natural Ventilation Models and Methods of Measurements

4.1. Theoretical Models

The combined force of wind and buoyancy affects the ventilation rate in two ways [17,19,20,35,36,44,145,146], assuming that the wind pressure and thermal pressure ventilation are dependent on each other (Equations (31) and (32)). Ventilation rate models of greenhouses under different ventilation configurations have been proposed in the literature (Equations (33) and (34)) [17,23,38]. The parameters applied in the ventilation models under various conditions are summarized in Table 2.

ϕ = √ (ϕ_w² + ϕ_b²)

(31)

ϕ = ϕ_w + ϕ_b

(32)

Mixing ventilation [16,22]:

ϕ = C_dA/2 [2gΔT/T_o h/4 + C_wV_w²]^0.5.

(33)

Displacement ventilation [37]:

Φ = C_d (A_iA_o)/√(A_i² + A_o²) [2gΔT/T_oh + (C_wi − C_wo)V_w²]^0.5.

(34)

A simplified model (Equation (35)) was proposed with only two variables: the wind speed and temperature difference between the inside and outside [147,148]:

ϕ = A √(f_V²V² + f_T²∆T).

(35)

Air change rate parameters a, b, and c were used (Equations (36)–(38)) to determine the relationships between the buoyancy force, the building heat loss, and the wind force, respectively [149,150]. The ventilation rate drops dramatically when the building heat loss b increases from 0, and drops slowly when b increases further [151].

a = (C_dA*)^2⁄3 (Egh/(ρC_pT_o))^1⁄3

(36)

b = ∑U_wallA_wall/(3ρC_p)

(37)

c = 1/√3 (C_dA*) √(2∆P_w)

(38)

In the case of wind-assisted natural ventilation, Heiselberg et al. [152] determined a hysteresis phenomenon to describe the abrupt switch that happened in the wind-dominated ventilation with continuously increasing buoyancy strength. The mode became buoyancy-driven ventilation with a certain strength of buoyancy, while the decreased buoyancy flux did not return the flow to the mode of wind-dominated ventilation. The driving force of ventilation with opposing wind and buoyancy effects can shift when there is sufficient perturbation [153,154].

4.2. Methods of Measuring Ventilation Rates

4.2.1. Tracer Gas Technique

The ventilation rate can be computed according to the measured tracer gas concentration and the volume of the greenhouse (Equation (39)) [19,20,43]. Accordingly, the wind and temperature factors of the simplified ventilation function [27,148,155,156] and the discharge coefficient were estimated [157,158].

c(t) = c(t₀) e ^−[(t−t₀^)ϕ/V]

(39)

Katsoulas et al. [52] used the N₂O gas tracing method to study the effect of window size and insect screens on ventilation. By comparing the ventilation rate computed via the tracer gas method and energy balance, a correlation was developed (Equation (40)):

ϕ_tracer = 0.81ϕ_energy.

(40)

4.2.2. Pressure Difference Method

The pressure difference method (Figure 10) [159] is usually applied together with tracer gas tracking technology [42] to obtain the discharge coefficient and wind effect coefficient. Researchers have estimated the static pressure coefficient and the turbulent pressure coefficient of a greenhouse with a continuous roof vent [32,33].

4.2.3. Energy Balance Simulation Method

The energy and mass balance was chosen to determine the ventilation rate because of its wide applicability [160]. The measurements of the ventilation rate in the greenhouse using a tracer gas consisting of CO₂ and N₂O showed good agreement with those obtained from the mass balance between the air humidity and tomato transpiration [41]. However, the tracer gas technique has numerous disadvantages, especially the large test space and low ventilation rate in the greenhouse [161], resulting in a low accuracy of around 30% [162].

The ventilation rate deduced from greenhouse energy balance (Equations (41)–(43)) was used to identify the discharge coefficient and wind effect coefficient [163] based on the ventilation model (Equation (44)) [164], with the computed convective heat transfer coefficient C_h [161] and sensible heat loss coefficient C_k [165].

R_net = q_Si,e + q_Si,c + q_Si,w + q_Li,e + F_s

(41)

q_Si,e = (ρ_airC_p∆T_i,eϕ)/A_soil, q_Si,c = C_h∆T_i,c

(42)

q_Li,e = (ρ_airL∆H_Aϕ)/A_soil, q_Si,w = C_k∆T_i,w

(43)

ϕ = C_d ((A_i + A_o)/2) (2gε²∆T/T_e h/2 + C_wV_w²)^0.5

(44)

4.2.4. Numerical Simulation Method

The greenhouse climate can be assessed via various numerical models [25] that have an error as high as 25% [166,167]. A temperature gradient was clearly observed in the vertical direction in the simulated CSG [168] and Venlo-type greenhouse [169] using the DO radiation model. Fatnassi et al. [170] applied the ventilation rate model [171] in a greenhouse CFD simulation, with successful verification via experiments. The plant resistance can be considered using a drag coefficient in the source term of the porous media [172]. According to the target ventilation rate, the required wind speed outside the inlet was estimated using two-dimensional numerical simulation [173].

The major difference between energy balance simulation (ES) and CFD is that it is difficult for ES to consider the detailed flow pattern and heat transfer fluxes, while CFD is not able to provide fluid dynamics information over a long period due to the limited computational resources [174]. It has been indicated by several studies that coupled CFD and ES enhanced the accuracy by taking advantage of each simulation method and reducing their drawbacks [175,176,177,178].

4.2.5. Emptying Fluid-Filling Box Method

The emptying water-filling box method uses water of different densities to simulate the natural ventilation [179,180] with the absence [181] or presence [47] of a continuous buoyancy source (Figure 11). The contribution to total velocity of the effects of buoyance and wind forces were measured by a Froude number Fr [44]: When Fr > 1, wind force dominates the ventilation, while buoyancy dominates when Fr < 1. Considering the surface thermal radiation, the emptying water-filling box model was modified to an emptying air-filling box model [182,183] by applying the node model [140].

4.3. Critical Wind Speed Determining Driving Forces of Natural Ventilation

The dominant driver of natural ventilation is the critical wind speed. The critical wind speed is relevant to the shape and size of the greenhouse, the position and shape of the ventilation openings, and the initial temperature difference between indoors and outdoors. Researchers have defined the critical wind speed under different conditions (Table 2).

Table 2. The critical wind speed defining the dominant drivers of natural ventilation.

References	Ventilation Configuration	Opening Geometry	Driving Force	Critical Wind Speed (m/s)
Meneses and Raposo [184]	Displacement	Continuous	Buoyancy	0.5–1.5
Meneses and Raposo [184]	Displacement	Continuous	Wind	>1.5
Boulard and Baille [17]	Mixing	Continuous	Combined	0.5–2
Boulard and Baille [17]	Mixing	Continuous	Buoyancy	0–0.5
Boulard, et al. [34]	Mixing	Continuous	Wind	>1.2
Kittas, et al. [32]	Mixing	Continuous	Wind	>1.5
Baptista, et al. [16]	Mixing	Discontinuous	Buoyancy	0–1

Table 2. The critical wind speed defining the dominant drivers of natural ventilation.

References	Ventilation Configuration	Opening Geometry	Driving Force	Critical Wind Speed (m/s)
Meneses and Raposo [184]	Displacement	Continuous	Buoyancy	0.5–1.5
Meneses and Raposo [184]	Displacement	Continuous	Wind	>1.5
Boulard and Baille [17]	Mixing	Continuous	Combined	0.5–2
Boulard and Baille [17]	Mixing	Continuous	Buoyancy	0–0.5
Boulard, et al. [34]	Mixing	Continuous	Wind	>1.2
Kittas, et al. [32]	Mixing	Continuous	Wind	>1.5
Baptista, et al. [16]	Mixing	Discontinuous	Buoyancy	0–1

5. Discussion

5.1. Further Research on Ventilation Models of Greenhouses with Horizontal Openings (CSG)

The material of the opening of CSG is mostly plastic, unlike the glass openings of Venlo-type greenhouses. Since the resistance coefficient of the opening is related to the Reynolds number and roughness, the existing resistance coefficient models (Equations (2) and (3)) for rectangular openings are not suitable for CSG. In addition, more studies are needed to investigate wind pressure coefficients at the CSG openings under various conditions. It seems that the ventilation model in CSG can follow the logic of Equation (34), but the buoyancy term needs to be further established.

Compared with the vertical opening in most studies, the air exchange at the horizontal vent in CSG is more complicated. The dense air moves down and the hot air moves up, where the thermal pressure difference under the same temperature difference between inside and outside is smaller than that of the vertical vent. Therefore, the existing first-order, second-order, and third-order hypotheses cannot correctly describe the thermal pressure distribution around horizontal openings. Establishing a buoyancy-induced ventilation model in CSG might require a new function of temperature distribution for horizontal openings.

5.2. Further Research on Cross-Ventilation Models (CPG)

Most cross-ventilation studies have investigated wind force only [185,186,187] or considered buoyancy force via CFD simulations. No analytical model has yet been found to describe the stack effect in cross-ventilation. The cross-ventilated greenhouse climate cannot be well simulated and controlled without such an analytical model.

A hypothesis is proposed for the cross-ventilation model. When the wind force drives it, the air stream goes into the greenhouse via the windward vents and out via the leeward vents, where the ventilation rate might be calculated according to the wind term of Equation (34). If the buoyancy force dominates, there might be two symmetrical vertexes between the two vents, and the air flows in through the lower half vents and out through the upper half. The buoyancy-induced ventilation could be calculated as twice the result of Equation (33), neglecting the wind term. When the air flow is driven by the combined forces, the air flows in via the windward vent, then upward along the tunnel cover, and out via the leeward vent. Different flow patterns result in a change in the ventilation effect—for instance, the age of air for the crop zone and heat accumulation in the zone above plants. The critical wind speeds determining the flow patterns can be classified by the strength ratio between the wind force and the stack force.

5.3. Influence of the Porosity and Height of Plants on Ventilation Models

A plant ventilation model with higher accuracy must be developed. Practically, the fluid loses momentum due to collisions during movement, leading to a changed flow direction. The method considering the leaf area density is able to involve a sink of momentum, but is not yet included in the analytical ventilation models. The sink of momentum was considered in the 2D image processing method; however, the remaining kinetic energy after the collision was ignored because of the underestimated porosity of the plants.

In general, the rows of crops in CSG are parallel to the direction of incoming air, with aisles between rows where the trajectory of air is greatly affected by the wind speed and plant characteristics. When the wind speed is relatively high, the aerodynamic force is strong: The fresh air can pass through the crop area, then up to the roof vent. Accordingly, the plant resistance model in greenhouses with side and roof openings should be investigated according to the porosity and height of plants, the orientation of plant rows, and the wind speed.

5.4. More Variables Considered in Ventilation Models

Other variables should be considered in further ventilation models [188]. This is because the vent size and wind speed were indicated to be the most important variables in air exchange rage, explaining over 50% of variance, whereas the other considered variables explained a further 30% [188].

The geographical variables might have effects on the process of ventilation. Stronger solar radiation resulted in higher buoyancy [21] and a decreased ventilation effect (reduction in temperature and humidity ratio) [46] inside the greenhouse. Under the same indoor temperature, stronger radiation resulted in a higher ventilation rate [189], which may influence the critical wind speed. In addition, with lower air density, the amount of convective heat could be different under the same ventilation rate, leading to a poor ventilation effect.

The physical properties of air change as the altitude increases, leading to lower air pressure, density, temperature, humidity, and heat transfer coefficient, and a higher radiation [190,191,192,193,194]. Greenhouses are considered a tool to provide enough vegetables in high-altitude areas, but there are limited relevant studies [195,196,197], and further investigations are necessary.

5.5. Application of Ventilation Model in Greenhouse Climate Prediction

The purpose of ventilation models involves application in greenhouse climate models as sub-models to analyze and control the indoor climate and control. Greenhouses are intensively coupled Multi-Input, Multi-Output systems that are highly nonlinear and influenced by the outdoor weather and practical limitations [198]. Energy balance models have been widely used to predict the indoor climate of greenhouses [199,200,201,202]. However, these models are limited by the requirement of empirical expressions for convective heat transfer coefficients and the known wind pressure coefficients [178].

By introducing the established ventilation models [17], a dynamic model predicting the indoor environment with insect screen was developed [203]. Wang and Boulard [204] improved the calculations of the Gembloux Greenhouse Dynamic Model [205,206,207,208,209,210,211]. According to the ventilation model proposed by Kittas et al. [38], Singh et al. [212] established a dynamic model to simulate the microclimate in a greenhouse. The simulation results of GGDM fitted well with the measurements [213].

More criteria have been suggested to evaluate the ventilation performance in addition to the ventilation rate, since it is only estimated through the opening surfaces, which might overestimate the real ventilation performance [214,215]. The air speed at the crop level, the crop aerodynamic resistance, the efficiency of ventilation rate, and the temperature difference between the interior and exterior are recommended variables for consideration in further investigations. In addition, the ventilation efficiency is usually computed by the local mean age of air [216,217,218,219].

6. Conclusions

This paper provides a review of the literature on natural ventilation in greenhouses. The wind-induced ventilation models are classified by application scenarios, including mixing ventilation, displacement ventilation, and cross-ventilation. Horizontal vents and vertical vents are considered as application scenarios for buoyancy-induced ventilation models.

The wind-induced ventilation rate of greenhouses is influenced by wind direction, roof geometry, vent size, insect screens, plant properties, and plant row orientation. Buoyancy strengths and distributions, and vent sizes and arrangements, affect the temperature-induced ventilation rate. Key parameters of the ventilation models, including the discharge coefficient, wind pressure coefficient, and opening effectiveness, are summarized according to the driving force and influencing factors.

Methods of measuring ventilation rates that can be used to validate the theoretical models are described, including the tracer gas technique, pressure difference method, energy balance method, emptying water-filling box method, and numerical simulation method. Moreover, the critical wind speeds are summarized, which can determine the driving force simply.

Regarding the development of ventilation models for typical Chinese greenhouses, further investigations are recommended in Section 5. First, for Chinese solar greenhouses (CSG), the pressure distribution function is recommended in greenhouses with horizontal openings. Second, for Chinese plastic greenhouses (CPG), a cross-ventilated model should be established with combined wind and buoyancy force. A hypothesis is proposed for natural ventilation in CPGs. Third, a more accurate plant-considering ventilation model is needed. Fourth, for greenhouses at high altitudes, other environmental variables, especially geography-dependent ones, can be added to ventilation models, including solar radiation and air density. Finally, more criteria are suggested to evaluate the ventilation performance rather than the ventilation rate only. These recommendations offer a development path for ventilation models for Chinese greenhouses.