# 3D Numerical Analysis of the Natural Ventilation Behavior in a Colombian Greenhouse Established in Warm Climate Conditions

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Description of the Greenhouse

^{2}, corresponding to longitudinal and transversal dimensions of 20 m and 25 m, respectively (Figure 1). The PG greenhouse was built in the Caribbean region of Colombia, in the municipality of Seville, department of Magdalena, at the Caribbean Research Center in The Corporación Colombiana de Investigación Agropecuaria—AGROSAVIA (longitude: 74°10′ W, latitude: 10°47′ W and altitude: 18 mamsl). With sides and a maximum height of 9.8 m above the ridge in the central part, the PG was equipped with side and front windows with an opening of 2.5 m, with which the side ventilation area is 225 m

^{2}, which is equivalent to 45% of the covered floor area. On the other hand, the ventilation areas were complemented by four ventilation regions in the PG roof area, two with a maximum opening of 1.54 m and another two with a maximum opening of 0.98 m, with which the roof ventilation area is 100 m

^{2}, which is equivalent to 20% of the covered floor area. All ventilation areas were covered with an insect-proof screen with a thread density (threads cm

^{−1}× threads cm

^{−1}) of 16.1 × 10.2.

#### 2.2. Numerical Model and Governing Equations

_{b}is turbulent kinetic energy generation due to buoyancy, G

_{k}is the generation of turbulent kinetic energy due to velocity gradients,${\sigma}_{k}y{\sigma}_{\u03f5}$ are Prandtl’s turbulent numbers for k and $\epsilon $, $v$ is the coefficient of kinematic viscosity, Y

_{M}is the fluctuating expansion in turbulence due to the overall dissipation rate, and ${C}_{1\u03f5},{C}_{2\u03f5},{C}_{\mu},{\sigma}_{k}y{\sigma}_{\u03f5}$ are constant with empirically determined values and set by default in the simulation software [48]. Likewise, the effect of air buoyancy caused by the force of gravity and air density changes were added to the momentum equation as a source term by Boussinesq’s approximation [49,50]. The presence of insect-proof screens covering the side, front, and roof ventilation surfaces of the structure can be modelled as porous mediums [51]. Taking into account its non-linear moment loss coefficient (Y) and its permeability as a function of screen porosity (K), the airflow through these screens is governed by Equation (4), describing Darcy-Forcheimer’s law.

^{3}), and ∂x the thickness of the porous material (m); the factors K and Y are determined through experimental equations that can be reviewed in the study of Valera et al. [52]. The aerodynamic coefficients requested by the CFD model were established for the type of insect screen used, which is similar to that reported in the study developed by Flores-Velazquez et al. [53]. The species transport equation was activated in order to study the humidity distribution inside PG. This model allows to solve the conservation equation in a turbulent flow for the diffusion, convection, and reactions of the mass fractions for each species defined by the user in the numerical model [54,55]. The mass fraction of the elements can be predicted by the CFD model from Equation (5).

^{−8}W/m

^{2}K

^{4}); $\Phi ,T\text{}\mathrm{and}\text{}\Omega $ are the phase function, the local temperature (°C), and the solid angle, respectively. Likewise, in order to simplify the resolution of the 3D CFD model, no type of crop was included, this in order to speed up the numerical calculation and establish the behavior of the airflow and temperature under the worst possible scenario, which means conditions where there is no presence of plants, a scenario where a large part of the radiation incident on the interior of the greenhouse is converted into heat, which generates an increase in the temperature of the interior air. To solve the pressure-momentum coupled equations, a semi-implicit solution method was adopted for pressure-linked equations through a second-order discretization scheme for momentum, energy, and turbulence, the convergence criteria for these variables were set at 10

^{−6}[57,58].

#### 2.3. Computational Domain and Meshing Process

#### 2.4. Validation of the CFD Model and Simulated Scenarios

^{2}) Equation (9).

## 3. Results

#### 3.1. Data and Model Validation

_{(Dm)}

^{2}= σ

_{(Ds)}

^{2}).

_{0:}µ

_{Dm}= µ

_{Ds}. The p-value obtained was 0.4606 and 0.398 for temperature and relative humidity, values that are greater than the significance level of 0.05, so the null hypothesis is accepted. This test also includes the confidence interval for the difference in means, for the case of temperature is {−0.8690, 1.9054} and for humidity it is {−5.8293, 2.3384}; as both intervals include zero, it can be interpreted that, like the hypothesis test, the difference between the means of the observed and simulated data is not significantly different from zero. Therefore, considering that the mean value of the data sets is statistically similar, the simulation model can be accepted.

^{2}) ranging from 0.87 to 0.97 (Table 3).

#### 3.2. Airflow Pattern Simulations

_{in}) and the normalized speed (V

_{nor}= Velocity inside/Velocity outside) were calculated for each parameter with its respective standard deviation (Table 6). The V

_{in}values ranged from 0.21 ± 0.09 m/s to 0.36 ± 0.13 m/s for the X axis, from 0.15 ± 0.08 m/s to 0.37 ± 0.12 m/s for the Y axis, and from 0.26 ± 0.08 m/s to 0.46 ± 0.18 m/s.

_{nor}), it is observed that the scenarios S01, S02, and S03 that correspond to the hours 7, 8, and 9 respectively, hours of low wind speed outside (0.2 m/s) present values of velocity in the interior greater than those presented in the exterior; this can be an effect of the strong influence of the thermal effect on the natural ventilation for these scenarios. On the other hand, for the remaining scenarios, it was observed that the normalized velocity presented reductions with respect to the velocity of the exterior airflow of 19.7% and 79.6% for the X axis, 38.8% and 87.7% for the Y axis, and 17.5% and 73.1% for the Z axis.

#### 3.3. Spatial Temperature Distribution

_{in}) and the average thermal differential (ΔT

_{m}= Tin − Tout) were determined for each of the axes analyzed (Table 7). These results show that the value of the temperature inside the PG is a function of the temperature of the external environment and the level of solar radiation for each scenario evaluated. Therefore, an increase in temperature between 7 and 14 h and a subsequent decrease until 17 h is observed, which is a characteristic phenomenon of passive greenhouses located in intertropical regions [70]. Tin values ranged from 25.4 ± 0.19 °C to 36.9 ± 0.13 °C for the X axis, from 25.6 ± 0.43 °C to 36.9 ± 1.69 °C for the Y axis, and from 25.5 ± 0.17 °C to 36.5 ± 0.51 °C for the Z axis.

#### 3.4. Spatial Distribution of Relative Humidity

^{in}) and the average relative humidity differential (ΔRH

_{m}= RHin − RHout) were calculated for each of the axes analyzed (Table 8). These values presented a temporal variation along the hours of the day as a function of the external relative humidity; therefore, it is observed that the highest humidity values were obtained for the first hours of the daytime period (7 and 8 h), then a general decrease of the humidity levels begins until reaching the minimum values above 14 h and from the following hour begins again an increase of the relative humidity value. RH

_{in}values ranged from 45.8 ± 2.14% to 77.8 ± 0.90% for the X axis, from 46.8 ± 1.40% to 77.1 ± 0.40% for the Y axis, and from 47.0 ± 1.31 to 77.1 ± 0.81% for the Z axis. This behavior generated negative values from ΔRH

_{m}for all scenarios with magnitudes between −2.54% and −6.26%. These values can be considered low bought with other works where the humidity presents different values up to −13.1 °C [70]. The negative value indicates that the humidity level inside the PG is lower than that of the outside environment.

## 4. Discussion

^{2}values higher than 0.8, values that indicate a high correlation between the data sets. All these results allowed establishing that, in quantitative terms, the numerical model has a great capacity to predict the thermal and hygrometric behavior of the PG greenhouse under the specific conditions of evaluation. Therefore, it was also possible to conclude that the CFD is a robust and versatile tool for the development of these types of studies, as has been recently mentioned by Li et al. [41].

_{m}generated were below 2.0 °C in all scenarios, which is very relevant for this type of climate conditions, this value is much lower than values reported in other studies where values of ΔT

_{m}are reached between 5.0 °C and 10.2 °C, for greenhouses equipped with insect-proof screens [58,92]. Finally, it is observed that the greatest thermal differentials occur in the axis Y. Where the highest temperature values occur near the floor, values that decrease as they approach the ventilation areas located on the roof of PG, this is consistent with the results obtained by Majdoubi et al. [93].

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Overall dimensions of the naturally ventilated flat roof greenhouse PG, (

**a**) Isometric view, (

**b**) Front view, (

**c**) Side view, and (

**d**) Real prototype.

Physical and Optical Properties of the Materials | ||||
---|---|---|---|---|

Air | Ground | Polyethylene | Porous Screen | |

Density (ρ, kg m^{−3}) | 1.225 | 1.400 | 920 | 910 |

Thermal conductivity (k, W/m °K) | 0.0242 | 1.5 | 0.33 | 0.31 |

Specific heat (Cp, J/°K kg) | 1006.43 | 1.738 | 2600 | 1.800 |

Coefficient of thermal expansion (1/K) | 0.0033 | |||

Absorptivity | 0.19 | 0.9 | 0.06 | 0.2 |

Scattering coefficient | 0 | −15 | 0 | 0 |

Refractive index | 1 | 3 | 1.53 | 0.05 |

Emissivity | 0.9 | 0.95 | 0.70 | 0.45 |

Hour | Temperature (°C) | Relative Humidity (%) | Solar Radiation (W/m^{2}) | Wind Speed (m/s) | Wind Direction |
---|---|---|---|---|---|

S01—Hour 7 | 24.9 | 81.4 | 46.6 | 0.2 | WNW |

S02—Hour 8 | 27.8 | 75.6 | 177.8 | 0.2 | WNW |

S03—Hour 9 | 30.1 | 68.6 | 376.7 | 0.2 | W |

S04—Hour 10 | 31.9 | 62.4 | 580.8 | 0.4 | W |

S05—Hour 11 | 33.5 | 56.6 | 713.7 | 0.7 | W |

S06—Hour 12 | 34.8 | 53.1 | 792.1 | 1.01 | W |

S07—Hour 13 | 35.2 | 52.2 | 802.7 | 1.22 | W |

S08—Hour 14 | 35.4 | 50.8 | 719.4 | 1.31 | W |

S09—Hour 15 | 34.9 | 50.2 | 547.6 | 1.13 | N |

S10—Hour 16 | 34.1 | 51.8 | 347.9 | 0.72 | N |

S11—Hour 17 | 33.1 | 54.6 | 184.6 | 0.51 | N |

Scenario | Sensor | T-M * | T-S * | RH-M * | RH-S * | Scenario | Sensor | T-M * | T-S * | RH-M * | RH-S |
---|---|---|---|---|---|---|---|---|---|---|---|

S01—Hour 7 | 1 | 25.2 | 25.1 | 78.8 | 79.1 | S07—Hour 13 | 1 | 35.9 | 35.5 | 50.3 | 51.2 |

S01—Hour 7 | 2 | 25.3 | 25.2 | 78.9 | 79.8 | S07—Hour 13 | 2 | 36.2 | 35.5 | 49.5 | 51.3 |

S01—Hour 7 | 3 | 26.1 | 25.6 | 75.8 | 76.7 | S07—Hour 13 | 3 | 38.4 | 37.1 | 43.8 | 47.9 |

S01—Hour 7 | 4 | 25.7 | 25.3 | 76.9 | 77.9 | S07—Hour 13 | 4 | 38.5 | 37.5 | 43.3 | 45.8 |

S01—Hour 7 | 5 | 25.7 | 25.4 | 77.3 | 78.5 | S07—Hour 13 | 5 | 38.6 | 37.3 | 42.8 | 45.5 |

S02—Hour 8 | 1 | 28.3 | 28.2 | 73.9 | 74.2 | S08—Hour 14 | 1 | 36.4 | 35.8 | 47.5 | 49.9 |

S02—Hour 8 | 2 | 28.3 | 28.4 | 74.2 | 74.1 | S08—Hour 14 | 2 | 36.5 | 35.7 | 47.4 | 49.8 |

S02—Hour 8 | 3 | 29.3 | 28.9 | 69.2 | 70.2 | S08—Hour 14 | 3 | 38.1 | 37.5 | 41.3 | 44.7 |

S02—Hour 8 | 4 | 28.7 | 28.4 | 69.5 | 71.8 | S08—Hour 14 | 4 | 38.0 | 37.6 | 41.5 | 45.9 |

S02—Hour 8 | 5 | 29.5 | 29.2 | 67.3 | 69.4 | S08—Hour 14 | 5 | 37.9 | 37.8 | 42.0 | 45.7 |

S03—Hour 9 | 1 | 30.9 | 30.8 | 67.0 | 67.5 | S09—Hour 15 | 1 | 35.7 | 35.6 | 48.6 | 49.8 |

S03—Hour 9 | 2 | 31.0 | 30.7 | 66.1 | 67.4 | S09—Hour 15 | 2 | 35.6 | 35.4 | 46.4 | 47.9 |

S03—Hour 9 | 3 | 32.4 | 31.8 | 58.9 | 62.0 | S09—Hour 15 | 3 | 36.2 | 35.7 | 45.6 | 46.8 |

S03—Hour 9 | 4 | 31.1 | 30.6 | 64.1 | 65.7 | S09—Hour 15 | 4 | 35.9 | 35.5 | 46.3 | 48.7 |

S03—Hour 9 | 5 | 32.4 | 31.4 | 63.8 | 64.6 | S09—Hour 15 | 5 | 36.6 | 36.5 | 44.7 | 45.5 |

S04—Hour 10 | 1 | 32.5 | 32.3 | 60.1 | 61.3 | S10—Hour 16 | 1 | 35.3 | 34.9 | 47.8 | 49.3 |

S04—Hour 10 | 2 | 32.6 | 32.3 | 59.5 | 61.2 | S10—Hour 16 | 2 | 35.2 | 34.7 | 49.2 | 51.1 |

S04—Hour 10 | 3 | 34.5 | 33.7 | 54.1 | 55.4 | S10—Hour 16 | 3 | 35.9 | 35.1 | 46.8 | 49.4 |

S04—Hour 10 | 4 | 33.9 | 33.6 | 55.6 | 56.8 | S10—Hour 16 | 4 | 35.6 | 34.8 | 48.2 | 50.2 |

S04—Hour 10 | 5 | 34.7 | 33.8 | 54.3 | 56.9 | S10—Hour 16 | 5 | 36.1 | 35.3 | 45.8 | 48.3 |

S05—Hour 11 | 1 | 34.5 | 34.1 | 54.5 | 55.7 | S11—Hour 17 | 1 | 33.9 | 33.8 | 50.3 | 52.1 |

S05—Hour 11 | 2 | 34.3 | 34.1 | 55.1 | 55.6 | S11—Hour 17 | 2 | 33,9 | 33.5 | 51.8 | 53.3 |

S05—Hour 11 | 3 | 36.1 | 35.5 | 50.3 | 51.8 | S11—Hour 17 | 3 | 34.8 | 34.3 | 49.7 | 51.1 |

S05—Hour 11 | 4 | 36.2 | 35.4 | 48.9 | 51.4 | S11—Hour 17 | 4 | 34.4 | 33.7 | 50.7 | 52.8 |

S05—Hour 11 | 5 | 36.3 | 35.5 | 50.2 | 52.0 | S11—Hour 17 | 5 | 35.2 | 34.5 | 49.2 | 51.4 |

S06—Hour 12 | 1 | 36.1 | 35.1 | 48.9 | 52.1 | ||||||

S06—Hour 12 | 2 | 36.0 | 35.1 | 51.2 | 52.0 | ||||||

S06—Hour 12 | 3 | 37.9 | 36.8 | 46.5 | 48.8 | ||||||

S06—Hour 12 | 4 | 37.5 | 37.2 | 46.2 | 46.7 | ||||||

S06—Hour 12 | 5 | 38.1 | 37.3 | 44.9 | 46.5 |

F Test to Compare Two Variances | H_{0}: σ_{(Dm)}^{2} = σ_{(Ds)}^{2} o H_{1}: σ_{(Dm)}^{2} ≠ σ_{(Ds)}^{2} | |

Temperature | Relative Humidity | |

F | 1.095 | 1.101 |

p-value | 0.750 | 0.724 |

95% confidence interval | {0.636,1.870} | {0.642,1.888} |

The null hypothesis (H_{0}) is accepted. | ||

Two Sample t-test | H_{0}: µ_{Dm} = µ_{Ds} o H_{1}: µ_{Dm} ≠ µ_{Ds} | |

Temperature | Relative Humidity | |

T | 0.740 | −0.847 |

p-value | 0.460 | 0.398 |

95% confidence interval | {−0.869,1.905} | {−5.829,2.338} |

Mean (µ) | µ_{Dm} = 33.92 °Cµ _{Ds} = 33.40 °C | µ_{Dm} = 54.77%µ _{Ds} = 56.51% |

The null hypothesis (H_{0}) is accepted. |

Temperature (°C) | Relative Humidity (%) | |||||
---|---|---|---|---|---|---|

MAE* | RMSE* | R^{2} | MAE | RMSE | R^{2} | |

S01—Hour 7 | 0.28 | 0.32 | 0.94 | 0.86 | 0.91 | 0.93 |

S02—Hour 8 | 0.24 | 0.26 | 0.91 | 1.16 | 1.46 | 0.94 |

S03—Hour 9 | 0.50 | 0.58 | 0.87 | 1.46 | 1.71 | 0.96 |

S04—Hour 10 | 0.50 | 0.57 | 0.95 | 1.62 | 1.72 | 0.95 |

S05—Hour 11 | 0.56 | 0.60 | 0.97 | 1.52 | 1.68 | 0.97 |

S06—Hour 12 | 0.82 | 0.86 | 0.92 | 1.68 | 1.94 | 0.84 |

S07—Hour 13 | 0.94 | 1.02 | 0.97 | 2.42 | 2.68 | 0.91 |

S08—Hour 14 | 0.51 | 0.56 | 0.96 | 3.25 | 3.36 | 0.96 |

S09—Hour 15 | 0.26 | 0.30 | 0.82 | 1.42 | 1.52 | 0.87 |

S10—Hour 16 | 0.66 | 0.68 | 0.81 | 2.10 | 2.18 | 0.96 |

S11—Hour 17 | 0.48 | 0.52 | 0.83 | 1.82 | 1.88 | 0.88 |

**Table 6.**Mean velocity (V

_{in}) and normalized velocity (V

_{nor}) values obtained for each simulated scenario.

X-Axis | |||||

Scenario | V_{in}(m/s) | V_{nor}(%) | Scenario | V_{in}(m/s) | V_{nor}(%) |

S01—Hour 7 | 0.26 ± 0.14 | 132 ± 43.1 | S07—Hour 13 | 0.33 ± 0.15 | 27.1 ± 12.9 |

S02—Hour 8 | 0.21 ± 0.09 | 101 ± 13.2 | S08—Hour 14 | 0.32 ± 0.13 | 24.2 ± 11.2 |

S03—Hour 9 | 0.24 ± 0.07 | 122 ± 33.2 | S09—Hour 15 | 0.35 ± 0.13 | 23.9 ± 4.2 |

S04—Hour 10 | 0.32 ± 0.11 | 81.3 ± 27.2 | S10—Hour 16 | 0.31 ± 0.11 | 44.1 ± 13.8 |

S05—Hour 11 | 0.36 ± 0.13 | 51.4 ± 19.3 | S11—Hour 17 | 0.32 ± 0.12 | 61.2 ± 21.2 |

S06—Hour 12 | 0.35 ± 0.17 | 35.2 ± 16.5 | |||

Y-Axis | |||||

Scenario | V_{in}(m/s) | V_{nor}(%) | Scenario | V_{in}(m/s) | V_{nor}(%) |

S01—Hour 7 | 0.23 ± 0.16 | 119 ± 67.1 | S07—Hour 13 | 0.23 ± 0.06 | 19.5 ± 5.6 |

S02—Hour 8 | 0.24 ± 0.07 | 121 ± 34.2 | S08—Hour 14 | 0.15 ± 0.08 | 12.3 ± 6.5 |

S03—Hour 9 | 0.35 ± 0.08 | 161 ± 35.1 | S09—Hour 15 | 0.22 ± 0.09 | 19.1 ± 8.3 |

S04—Hour 10 | 0.37 ± 0.12 | 44.3 ± 28.2 | S10—Hour 16 | 0.24 ± 0.14 | 33.5 ± 21.8 |

S05—Hour 11 | 0.35 ± 0.15 | 51.1 ± 21.3 | S11—Hour 17 | 0.20 ± 0.07 | 61.2 ± 13.2 |

S06—Hour 12 | 0.31 ± 0.16 | 32.1 ± 18.2 | |||

Z-Axis | |||||

Scenario | V_{in}(m/s) | V_{nor}(%) | Scenario | V_{in}(m/s) | V_{nor}(%) |

S01—Hour 7 | 0.29 ± 0.10 | 141 ± 47.1 | S07—Hour 13 | 0.40 ± 0.18 | 33.4 ± 16.1 |

S02—Hour 8 | 0.26 ± 0.08 | 132 ± 34.2 | S08—Hour 14 | 0.46 ± 0.18 | 35.6 ± 13.5 |

S03—Hour 9 | 0.32 ± 0.18 | 157 ± 45.6 | S09—Hour 15 | 0.29 ± 0.11 | 26.9 ± 9.1 |

S04—Hour 10 | 0.33 ± 0.14 | 82.5 ± 29.2 | S10—Hour 16 | 0.30 ± 0.09 | 42.5 ± 11.2 |

S05—Hour 11 | 0.43 ± 0.15 | 60.1 ± 14.3 | S11—Hour 17 | 0.27 ± 0.08 | 51.5 ± 18.2 |

S06—Hour 12 | 0.44 ± 0.17 | 42.4 ± 15.7 |

**Table 7.**Average temperature (T

_{in}) and average thermal gradient values (ΔT

_{m}) obtained for each simulated scenario.

X-Axis | |||||

Scenario | T_{in}(°C) | ΔT_{m}(°C) | Scenario | T_{in}(°C) | ΔT_{m}(°C) |

S01—Hour 7 | 25.4 ± 0.19 | 0.44 ± 0.19 | S07—Hour 13 | 35.6 ± 0.24 | 0.42 ± 0.24 |

S02—Hour 8 | 28.5 ± 0.26 | 0.70 ± 0.26 | S08—Hour 14 | 36.9 ± 0.13 | 1.56 ± 11.2 |

S03—Hour 9 | 31.0 ± 0.39 | 0.90 ± 0.34 | S09—Hour 15 | 35.5 ± 0.21 | 0.65 ± 0.21 |

S04—Hour 10 | 33.3 ± 0.77 | 1.40 ± 0.77 | S10—Hour 16 | 34.8 ± 0.20 | 0.73 ± 0.20 |

S05—Hour 11 | 35.1 ± 0.97 | 1.62 ± 0.97 | S11—Hour 17 | 33.7 ± 0.15 | 0.67 ± 0.15 |

S06—Hour 12 | 36.3 ± 0.82 | 1.48 ± 0.82 | |||

Eje Y | |||||

Scenario | T_{in}(°C) | ΔT_{m}(°C) | Scenario | T_{in}(°C) | ΔT_{m}(°C) |

S01—Hour 7 | 25.6 ± 0.43 | 0.70 ± 0.43 | S07—Hour 13 | 36.7 ± 1.61 | 1.50 ± 1.61 |

S02—Hour 8 | 28.7 ± 0.55 | 0.91 ± 0.55 | S08—Hour 14 | 36.9 ± 1.69 | 1.52 ± 1.69 |

S03—Hour 9 | 31.7 ± 0.86 | 1.62 ± 0.86 | S09—Hour 15 | 36.0 ± 1.06 | 1.12 ± 1.06 |

S04—Hour 10 | 33.6 ± 1.42 | 1.71 ± 1.42 | S10—Hour 16 | 35.4 ± 1.15 | 1.28 ± 1.15 |

S05—Hour 11 | 35.4 ± 1.69 | 1.91 ± 1.69 | S11—Hour 17 | 34.3 ± 0.90 | 1.18 ± 0.90 |

S06—Hour 12 | 36.5 ± 1.66 | 1.67 ± 1.66 | |||

Eje Z | |||||

Scenario | T_{in}(°C) | ΔT_{m}(°C) | Scenario | T_{in}(°C) | ΔT_{m}(°C) |

S01—Hour 7 | 25.5 ± 0.17 | 0.58 ± 0.17 | S07—Hour 13 | 36.1 ± 0.37 | 0.93 ± 0.37 |

S02—Hour 8 | 28.3 ± 0.26 | 0.49 ± 0.26 | S08—Hour 14 | 36.5 ± 0.51 | 1.06 ± 0.51 |

S03—Hour 9 | 31.0 ± 0.47 | 0.89 ± 0.47 | S09—Hour 15 | 35.8 ± 0.69 | 0.86 ± 0.69 |

S04—Hour 10 | 32.7 ± 0.37 | 0.82 ± 0.37 | S10—Hour 16 | 35.1 ± 0.60 | 0.95 ± 0.60 |

S05—Hour 11 | 34.5 ± 0.42 | 1.02 ± 0.42 | S11—Hour 17 | 34.0 ± 0.65 | 0.90 ± 0.65 |

S06—Hour 12 | 35.7 ± 0.36 | 0.86 ± 0.36 |

**Table 8.**Mean temperature values (RH

_{in}) and mean thermal gradient (ΔRH

_{m}) obtained for each simulated scenario.

X-Axis | |||||

Scenario | RH_{in}(%) | ΔRH_{m}(%) | Scenario | RH_{in}(%) | ΔRH_{m}(%) |

S01—Hour 7 | 77.8 ± 0.90 | −3.63 ± 0.90 | S07—Hour 13 | 47.4 ± 2.39 | −4.64 ± 2.39 |

S02—Hour 8 | 71.3 ± 1.11 | −4.26 ± 1.11 | S08—Hour 14 | 45.8 ± 2.14 | −4.95 ± 2.14 |

S03—Hour 9 | 64.2 ± 1.44 | −4.35 ± 1.44 | S09—Hour 15 | 47.6 ± 0.55 | −2.54 ± 0.55 |

S04—Hour 10 | 56.7 ± 2.46 | −5.71 ± 2.46 | S10—Hour 16 | 48.9 ± 0.53 | −2.83 ± 0.53 |

S05—Hour 11 | 50.9 ± 2.78 | −5.61 ± 2.78 | S11—Hour 17 | 51.6 ± 0.42 | −2.94 ± 0.42 |

S06—Hour 12 | 48.1 ± 2.19 | −5.08 ± 2.19 | |||

Y-Axis | |||||

Scenario | RH_{in}(%) | ΔRH_{m}(%) | Scenario | RH_{in}(%) | ΔRH_{m}(%) |

S01—Hour 7 | 77.1 ± 0.40 | −4.29 ± 0.40 | S07—Hour 13 | 48.0 ± 0.75 | −4.09 ± 0.75 |

S02—Hour 8 | 70.8 ± 0.49 | −4.79 ± 0.49 | S08—Hour 14 | 46.8 ± 1.40 | −3.94 ± 1.40 |

S03—Hour 9 | 62.3 ± 0.48 | −6.26 ± 0.48 | S09—Hour 15 | 47.1 ± 0.42 | −3.09 ± 0.42 |

S04—Hour 10 | 56.7 ± 0.96 | −5.69 ± 0.96 | S10—Hour 16 | 48.3 ± 0.56 | −3.51 ± 0.56 |

S05—Hour 11 | 51.0 ± 0.76 | −4.60 ± 0.76 | S11—Hour 17 | 50.9 ± 0.57 | −3.68 ± 0.57 |

S06—Hour 12 | 48.6 ± 0.77 | −4.09 ± 0.77 | |||

Z-Axis | |||||

Scenario | RH_{in}(%) | ΔRH_{m}(%) | Scenario | RH_{in}(%) | ΔRH_{m}(%) |

S01—Hour 7 | 77.1 ± 0.81 | −4.28 ± 0.81 | S07—Hour 13 | 48.6 ± 1.03 | −3.40 ± 1.03 |

S02—Hour 8 | 72.2 ± 1.12 | −3.39 ± 1.12 | S08—Hour 14 | 47.0 ± 1.31 | −3.72 ± 1.31 |

S03—Hour 9 | 64.2 ± 1.74 | −4.37 ± 1.74 | S09—Hour 15 | 47.1 ± 1.78 | −3.10 ± 1.78 |

S04—Hour 10 | 58.5 ± 1.27 | −3.86 ± 1.27 | S10—Hour 16 | 48.4 ± 1.61 | −3.39 ± 1.61 |

S05—Hour 11 | 52.6 ± 1.26 | −3.94 ± 1.26 | S11—Hour 17 | 51.0 ± 1.89 | −3.57 ± 1.89 |

S06—Hour 12 | 49.7 ± 1.01 | −3.48 ± 1.01 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Villagran, E.; Leon, R.; Rodriguez, A.; Jaramillo, J.
3D Numerical Analysis of the Natural Ventilation Behavior in a Colombian Greenhouse Established in Warm Climate Conditions. *Sustainability* **2020**, *12*, 8101.
https://doi.org/10.3390/su12198101

**AMA Style**

Villagran E, Leon R, Rodriguez A, Jaramillo J.
3D Numerical Analysis of the Natural Ventilation Behavior in a Colombian Greenhouse Established in Warm Climate Conditions. *Sustainability*. 2020; 12(19):8101.
https://doi.org/10.3390/su12198101

**Chicago/Turabian Style**

Villagran, Edwin, Rommel Leon, Andrea Rodriguez, and Jorge Jaramillo.
2020. "3D Numerical Analysis of the Natural Ventilation Behavior in a Colombian Greenhouse Established in Warm Climate Conditions" *Sustainability* 12, no. 19: 8101.
https://doi.org/10.3390/su12198101