1. Introduction
Plant growth greatly depends on the temperature and humidity. For winter production in Central Mexico, greenhouses provide better environmental conditions for plant growth compared to most agricultural production systems. Given that a greenhouse is a structure favoring environment for crop production, there are consequences such as heat excess during the day is absorbed by the ground and during the night it is used to meet the heating needs in enclosed greenhouses [
1]. In this way, one of the characteristics of enclosed greenhouses is that they are energy saving compared to greenhouses fully relying on natural ventilation. However, accumulation of energy during the day may become insufficient [
2] with higher frequency during the winter. Therefore, night temperature becomes a critical factor in the efficiency of a crop cultivated in a greenhouse. Adequate greenhouse energy management can serve to avoid low night temperatures and reduce condensation phenomena causing dripping process on crops [
3,
4,
5,
6].
A conventional solution for low-temperature problems is using heating systems inside the greenhouse. Since energy and fuel prices are not cheap [
7], their efficient use directly impacts production costs and should be balanced with the risks of crop loss [
8,
9]. Nonetheless, the amount of heat added to the greenhouse depends on the changing weather conditions, where winter becomes the critical period [
10]. Previous research [
10,
11] have stated that more attention should be given to the night due to significant heat losses, which should be compensated by means of an artificial heat input.
In addition to conventional heating systems (fossil fuels), there are alternative systems used to heat the interiors of greenhouses, among which are renewable energy source systems. These systems allow the use of biomass, solar, and geothermal energy sources [
12,
13,
14,
15,
16,
17], with solar energy being the most recommendable, given that it is a clean, abundant, and safe source. One of the greenhouse heating systems that uses solar energy as a main source and that has been studied by many researchers is rock bed storage. This type of system uses underground rocks to store heat during the day and release it at night, generating an increase in air temperature of up to 3 °C, causing improvement of fruit quality by up to 29% [
18,
19].
In some greenhouse production systems, the energy consumption represents more than 50% of the total cost of production, and it is necessary to calculate its consumption. The more accurate approach is employing mathematical models based on the principle of heat and mass conservation in order to estimate the feasibility of the implementation of control systems during the winter. Numerical models are also used to improve the understanding of convective, radioactive, and conductive phenomena and the environment-plant iteration within the greenhouse [
20,
21,
22,
23]. These findings have allowed us to deepen our understanding of the dynamics of the microclimate and the energy needed to maintain environmental comfort, achieve a high-performance production, and improve the quality and efficiency of heating systems [
24,
25,
26].
Modeling by means of Computational Fluid Dynamics (CFD) has achieved an approach to simulate air movement and temperature variation within the greenhouse and the impact of heating systems on the thermal gradient [
27,
28,
29,
30,
31,
32]. Along with this, it has allowed us to refine sub-systems of the greenhouse such as the heating system to increase its effectiveness and efficiency. Some studies carried out in CFD have allowed us to establish that, by using heating pipes, it was possible to increase the temperature inside the greenhouse by up to 4.5 °C [
11]. In 2018, Yilmaz and Selbas [
33] investigated the thermal performance of a solar collector, a heat pump, and a boiler for heating a greenhouse. The results showed that the solar collector had a greater impact on the thermal gradient of the greenhouse, with a thermal efficiency of 33.11%. Another work in 2017, Tadj et al. [
27] demonstrated that perforated polyethylene duct heating systems generated a uniform temperature compared to other heating systems (hot water pipes and air heaters). These results agreed with what was established in the literature, in which the temperature distribution was more homogeneous in a vertical plane than in a horizontal plane [
34].
In regions with mild winters and at specific periods of the year, an emergent heating system is being needed to mitigate occasional frosts. In central Mexico, it is common to place pop-up heaters aiding to stabilize the internal temperature when the outside temperature drops abruptly in specific hours before sunrise. Even though empirical experience has been gained, there is still scarce research about optimal use of electrical heating systems. For instance, recommendations about the position and direction of heaters to optimize amounts of heat that guarantees thermal homogeneity during these critical periods. Nor it is found related research on the energy and economic costs of this emerging heating system.
Then, the aim of this work was to estimate the necessary energy consumption to maintain thermal homogeneity using an electric heater in the greenhouse under winter conditions in central Mexico, using a model of energy balance and CFD to predict the thermal distribution under different heating scenarios.
2. Materials and Methods
2.1. Experimental Ground Description
The site of the experimental greenhouse was located at Campus Graduate College in the State of Mexico (19°27′45.5″ N, 98°54′12.2″ W) at 2239 masl, situated on flat ground with no structures around it. In the region, the minimum monthly temperatures range between 2.49 °C and 11.24 °C throughout the year.
The prototype greenhouse had an area of 1050 m2. It was of the zenith type with three spans covered with translucent polyethylene on the floor and sides, polycarbonate on the roof, and anti-insect on the windows. The greenhouse had a natural ventilation system based on the closure and opening of the overhead and front windows and a heating system using an electric heater (CM-VAX, Calelec, Monterrey, Mexico) recommended for enclosed spaces with an area of 96 m2. The electric heater was located 3 m above the ground level in span 2 in the windward zone and had a power of 15 kW. Its electrical characteristics were 230/3/60 (Volts/Phases/Cycles), and it had an axial fan with a motor of 1/8 HP that worked with 120 V.
For data acquisition, an Eddy Covariance system 2.4 m away from the windward position with a sonic anemometer (CSAT 3D, Campbell Scientific Ltd., Antony, France), an EC150 gas analyzer (Campbell Scientific Inc., Logan, UT, USA), a temperature and humidity sensor (HMP155A, Campbell Scientific Logan, UT, USA) and four sensors for soil temperature (TCAV thermocouple Campbell Scientific Logan, UT, USA) which were placed inside the greenhouse. Seven temperature sensors (DS18B20, Maxim Integrated, San Jose, CA, USA) and three relative humidity sensors (DHT22, Zhengxinyuan Electronics Co., Ltd., Shenzhen, China) were distributed in the three spans at a height of 3 m (
Figure 1).
Data recording and storage were performed every 5 s for the temperature and humidity and every 100 ms for the anemometer. The monitoring period was from February 3 to February 24, 2019, which was enough time to investigate the emergent heater, since the meteorological data recorded minimum temperatures during this month of below 12 °C. The data was stored with a data logger system (CR3000 Micrologger, Campbell Scientific, Inc., Logan, UT, USA) for the Eddy Covariance system and an Arduino data Logger Shield for the DS18B20 and DHT22 sensors. Outside the greenhouse, a weather station (Vantage Pro2 Plus, Davis Instruments, Hayward, CA, USA) was available and used to record data on temperature, humidity, wind direction, and wind speed—these values were used as the initial boundary condition of the computer model. All data was processed in Microsoft Excel to determine the environmental input conditions of the computational model.
2.2. Heat Calculation
The greenhouse temperature model was developed based on the energy and mass balances [
24,
25,
35,
36] in the completely closed greenhouse without environment-plant iteration, because at the time of data recording there was no crop. The calculation of
Qh was estimated by establishing the necessary energy consumption transferred by the electric heater to attenuate the thermal gradient, expressed as follows:
The thermal radiation transferred from the inside to the outside of the greenhouse (
) depended on the emission of energy into the atmosphere and on the roofing materials.
where
Ssc is the floor area covered (m
2),
is the Stefan–Boltzmann constant (W m
−2 K
−4),
is the transmittance coefficient of the cover material for thermal radiation,
is the emissivity of the atmosphere,
Tatm is the temperature of the emission of energy to the atmosphere (K),
is the emissivity of the roofing material for thermal radiation, and
Tc is the absolute temperature of the roof (K).
The heat transfer by conduction and convection (
Qt) was estimated by the temperature between the inside and outside of the greenhouse.
where
Sdc is the developed area of the greenhouse cover (m
2),
ti is the interior temperature of the greenhouse (K),
te is the exterior temperature of the greenhouse (K), and
kcc is the overall coefficient of heat loss by conduction and convection (W m
−2 K
−1).
The sensitive and latent heat lost by the renewal of indoor air (
Qi) was considered minimal when establishing as an initial condition the closing of the side and overhead windows. However, there is air infiltration through the structure as it is an old construction becoming a partially airtight greenhouse.
where
Vgh is the volume of the greenhouse (m
3),
cpa is the specific heat of the air (J kg
−1 K
−1),
is the density of the air (kg m
−3),
cpv is the specific heat of the superheated steam (J kg
−1 K
−1),
xi xe is the absolute indoor and outdoor humidity (kg kg
−1),
is the latent heat of vaporization (J kg
−1), and
R is the air renewal rate (h
−1).
The heat transfer through the ground (
Qg) is a function of the difference in the indoor and soil temperature.
where
Kts is the coefficient of thermal exchange through the soil (W m
−1 K
−1),
ts is the soil temperature (K), and
p is the depth at which the temperature is estimated (m).
The parameters of the energy balance model were analyzed considering the effect of the greenhouse environment, its characteristics, and the roof materials (
Table 1 and
Table 2).
The heat calculation was made using the average weather condition rates of minimum daily temperature. Inside temperature of the greenhouse was established as 12 °C based on the thermal requirement of the tomato (
Solanum Lycopersicum L.), which, for proper growth, the temperature should be higher than 10 °C at night [
40,
41].
2.3. Computational Model
Building and simulation of the computational model was carried out in ANSYS® Fluent® (ANSYS, Inc., Canonsburg, PA, USA). The geometry was developed in the design modeler tool. The meshing was done in meshing, and the greenhouse had dimensions of 30 × 35 × 5 m, with 490,000 average structured elements, an orthogonal quality of 0.98, and a distortion of 1.935 × 10−0.02.
Model conditions and variables applied to the airflow to solve the transport equations, which were discretized into algebraic equations and calculated by numerical methods, were defined in
Table 3.
Heater simulation included a pressure jump and angular velocity. The pressure jump calculation was estimated considering Equation (6):
where
is the air density (kg m
−3) and
is the fan speed (m s
−1).
Evaluation of the Computational Models
In order to obtain a reliable computational model, two scenarios were assessed: (I) no heat and (II) with heat. The evaluation was carried out by a statistical analysis of both temperature and wind speed using simulated and experimental data. The statistic studios were made by an analysis of variance (ANOVA), with a significance level of 0.05 used to contrast the difference of the variables in the different factors parametrically.
2.4. Simulation Scenarios
The analysis of the distribution of heat flow in the greenhouse was performed by comparing the effect of the position and direction of the heaters; two more heaters were included in the computational model, seeking to improve the system with a uniform temperature (
Table 4). Simulations were carried out in a stationary state, and the provided energy was modified by the heater based on the assessed computational model’s results. The origin of the coordinates (x, y, z) is in the center of the greenhouse, and the flow direction of the evaluated heater is z.