Abstract

Greenhouse plant production involves a number of processes such as transpiration, condensation, photosynthesis, and climate control. Such processes, in turn, set off mass and heat transfer phenomena that influence not only the quality and quantity of crop production but also its environmental cost. While these processes have considerably been analyzed in separate, they strongly interact with one another. For instance, increased radiation (mainly thermal infrared) increases temperature, reduces humidity, consequently increases transpiration, and affects CO2 exchange as well as other reaction rates. Computational fluid dynamics (CFD) is a numerical tool with a solid physical basis which allows, through the construction of a computational model, to simulate the fluid flow environment. Heating, ventilation, and condensation have been analyzed in the greenhouse environment with CFD techniques. The current challenge is the interaction of these processes and their impact on the production system. The present work summarizes some CFD investigations carried out in this topic, in order to analyze the processes of heat and mass transfer in a greenhouse for agronomic purposes.

Keywords: ventilation, heating, crop production, numerical simulation, climate control

## 1. Introduction

The fast expansion of greenhouse technique around of world, as a means to supply food and produce, has posed emerging challenges in the operation and management of greenhouse climate. While such challenges have not changed in essence ever since the onset of agriculture, they have been considerably reshaped by the access to new technologies and information.

In semiarid regions, the main problems are the high temperatures that take place in daily and annual cycles. The same is true for cold temperatures. There are many options to auxiliary climate control systems, the implementation of which depends on many factors such as their cost, crop, location, and management, to name a few.

Greenhouse is an advantageous production system which realistically allows us to produce crops from all over the world during the whole year. Consequently, environment interior conditions such as temperature and humidity have to be controlled at a certain plant-specific level regardless of environmental conditions.

In greenhouse crop production, climate has peculiar considerations, because the most important data is the impact of the environmental factors on the crop cycle. The cultivation of plants requires a sufficient amount of light, a specific range of temperature, humidity, and CO2, among other requirements. These requirements are primarily influenced by the greenhouse design and size and vary according to the local climate conditions. For instance, the radiation quantity inside the greenhouse depends on whether greenhouses are built with PVC or glass, because the surface material is the element to optimally use solar radiation for the required lighting [1].

Recently, heating, ventilation, and air conditioning (HVAC) systems have been extensively used in urban spaces, such as offices or stores, at agriculture area, and specifically in greenhouses. For instance, HVAC has been used in buildings in order to analyze the optimization and comfort inner Officine's and several uses. In greenhouses, the concept is incipient, even though the application of the ventilation and calefaction systems as a method to climate control in cold and warm regions is nothing new.

The climate produced in a greenhouse is the result of complex mechanisms involving the processes of heat and mass exchange. The internal climate is strongly dependent on the outside conditions, especially in unheated greenhouses. In greenhouse climate models, the parameters of the internal climate such as air, soil, and crop temperatures as well as air humidity are calculated using energy and water vapor balances for the various components of the system [2].

Climate in the greenhouse is a consequence of radiation crossing the cover material, usually plastic. After that, climate condition is a strong relationship between several factors, temperature, humidity, wind velocity, and the solar radiation. Environment conditions in the greenhouse depend on the energy management, by the auxiliary calefaction and ventilation systems. The equilibrium of these climate variables is a function of the efficiency of air exchange generating losses and gains of heat (temperature, radiation) and mass (humidity, gases) [3].

The automation in a greenhouse environment involves climate control, lightlevel control, and shade curtain management; gases inside the greenhouse are due to the plant reactions with the environment, requiring control of carbon dioxide (CO2) concentration, irrigation and chemical treatment. Greenhouse automation is a modern, efficient, and accurate disruptive agriculture, which utilizes data collected within the system, to obtain better quality and higher yields, thereby increasing productivity [3].

Every process inside the greenhouse consumes energy and involves a change of mass between the sink or the source. The objective of this work was to show some results on greenhouse mass and energy transfer, using CFD.

## 2. Computational fluid dynamics (CFD) in a greenhouse simulation

Computational fluid dynamics (CFD) is an analysis tool based on numerical methods that show graphically the general and localized air movement inside the greenhouse owing to natural ventilation. Also, it is possible to determine spatial temperature distributions arising from such air movement, all this for any greenhouse type and open/closed configuration of the roof and side windows.

CFD modeling of different parameters in greenhouses has been used to examine various features such as vent configuration [4]; natural and mechanical ventilation [5, 6]; ventilation in screenhouses [7]; condensation, transpiration, and heat and mass transfer [8–10]; and, more recently, calefaction and HCVA [11] and their interactions [12, 13]. The analyses of these systems allow for climate control,

CFD Simulation of Heat and Mass Transfer for Climate Control in Greenhouses DOI: http://dx.doi.org/10.5772/intechopen.86322

Figure 1. Natural and mechanical climate control in greenhouses.

thereby offering the possibility to provide large numbers of high-quality crops with greater predictability.

CFD modeling has been used as a tool to get major details in facilities, for instance [14], uses CFD to analyze ventilation system in greenhouses. Based on CFD, simulation is possible to optimize some characteristics of ventilation systems, such as relationship between volume and vent area of greenhouses [15].

The performance of ventilation in enclosed spaces is affected by the flow of outside air [16], type of cover, height of the installation, and the ventilation opening [18]. Computational parametric studies on greenhouse structures can aid to identify design factors that affect greenhouse ventilation under specific climatic conditions [5, 19].

Modern auxiliary systems used for climate control demand new approaches of study, e.g., to quantify the effect of the back-wall vent dimension on solar greenhouse cooling. Traditional solar greenhouse (Figure 1) uses radiation to store energy and get advantages of its use naturally. Some studies [10] showed that it is possible to reduce averaged air temperature by approximately 1.7°C and the highest temperature drop by approximately 5.8°C, in comparison to a traditional solar greenhouse with brick back wall (TG). These authors also suggest that a back-wall vent of 1.4 m increased internal ventilation efficiency in a solar greenhouse by installing removable back walls [10].

On the other hand, modeling of climate systems is necessary for studying and regulating energy consumption and quality of indoor environment. In urban semiclosed spaces, modeling approaches are used in HVAC systems [20]. Physics-based models offer adequate capabilities for first-hand assessments but suffer from poor accuracy; data-driven models have very high accuracy on training data but suffer from lack of generalization beyond the training domain.

Numerical methods have also been implemented for analyses of crop production in semi-closed spaces. Santolini et al. [7] reviewed the effect of mass transfer in a screenhouse structure with CFD. Alternative computer-based simulation models have been used for examining typical greenhouses with alternative energies such as dynamic photovoltaic (PV) and plant cultivation [21, 22].

## 3. Heat and mass transfer equations and CFD simulations

Heat and mass transfer is investigated using CFD tools. A numerical model is built based on the solution of the governing equations for momentum, energy, and continuity within the greenhouse domain. General equations can be written as the

convection-diffusion equation to simulate mass, velocity, temperature, or other variables inside the greenhouse (Eq. 1):

$$\frac{\partial \rho \mathcal{Q}}{\partial t} + \nabla \left(\rho \dot{v} \mathcal{Q}\right) = \nabla \left(\Gamma \nabla \mathcal{Q}\right) + s\_{\phi} \tag{1}$$

where ∅ transport variable; uj velocity vector (m s�<sup>1</sup> ); Γϕ diffusion coefficient; s<sup>ϕ</sup> source term to variable ∅ (temperature, CO2, etc.).

Specific energy balance simulation is based on the solution of heat and mass balance equations applied to the whole greenhouse system [8].

For the heat balance of greenhouse air, the general equation is shown in Eq. (2):

$$\frac{\rho \mathbf{V} \mathbf{C}\_p \Delta T}{\Delta T} = \sum\_{i} q\_i \mathbf{A}\_i + \phi \left( \mathbf{C}\_p \mathbf{T}\_{out} - \mathbf{C}\_p \mathbf{T}\_{int} \right) \tag{2}$$

Mass balance of greenhouse air is described in Eq. (3):

$$\frac{\partial M\_w}{\partial T} = \Gamma\_{crop} - \Omega\_{cov} + \phi (W\_{air} - W\_{air\_{sa}}) \tag{3}$$

where ρ is the density (kg cm�<sup>3</sup> ); t is the time (s); T is the temperature (°C); Cp is the heat capacity at constant pressure; Ф is the ventilation rate (kg s�<sup>1</sup> ); W (kg m�<sup>3</sup> ); ∑1qi Ai (W) is the sum of the convective contribution; Γcrop (kg s�<sup>1</sup> ) is the transpiration rate; wair (kg kg�<sup>1</sup> ) is the inside humidity ratio; Wair\_out (kg kg�<sup>1</sup> ) is the outside humidity ratio; Mw is the water vapor mass.

The energy transfer process can occur basically in three physical phenomena: radiation, convection, and conduction. In greenhouse inner, convective heat transfer is the main source of temperature and energy. The conduction of energy occurs from the soil layers, and the flow is displaced depending on the quantity, always from higher to lower.

#### 3.1 Conduction energy transfer process

Heat conduction is based on Fourier's law, in which one direction is a simple Eq. 4:

$$q\_x = -kA\frac{\delta T}{\delta \mathbf{x}}\tag{4}$$

where k material conductivity (W m�<sup>1</sup> ); A cross-sectional perpendicular area (m<sup>2</sup> ); <sup>δ</sup><sup>T</sup> thermal gradient (°C). <sup>δ</sup><sup>x</sup>

The convective effect is calculated using the cooling Newton's law (in Eq. 5):

$$Q = hA\_t(T\_t - T\_\infty) \tag{5}$$

where h convective heat transfer coefficient (W m�<sup>2</sup> ); As area (m<sup>2</sup> ); Ts surface temperature (°C); T<sup>∞</sup> fluid temperature (°C).

In a greenhouse, Eqs. (6) and (7) give the convective fluxes:

$$q\_{conv,i} = a\_i (T\_i + T\_{air}) \qquad \left[ \text{W} \text{m}^{-2} \right] \tag{6}$$

$$Q\_{conv,i} = A\_i a\_i (T\_i + T\_{air}) \quad \left[ \text{Wm}^{-2} \right] \tag{7}$$

## 3.2 Radiation: energy transfer process

Outgoing radiation from a surface with nonzero transmissivity cover and sidewalls can be described in Eq. 8 [23]:

$$j\_{i-in} = \varepsilon\_i \sigma T\_i^4 + \zeta\_i \mathbf{g}\_{in} + \pi\_{in} \mathbf{g}\_{ext} \quad \text{[Wm}^{-2}\text{]}\tag{8}$$

where ε<sup>i</sup> is the emissivity, σ is the Boltzmann constant, ζ<sup>i</sup> is the reflectivity, and τ is the transmissivity. The outgoing radiation from opaque surface, soil, external soil, and sky is calculated with Eq. 9:

$$j\_i = e\_i \sigma T\_i^4 + \zeta\_i \text{ [Wm}^{-2}\text{]} \tag{9}$$

Incident radiation on a surface is (Eq. (10)):

$$\mathbf{g}\_i = \sum\_{j-\text{sup}} F\_{i-j} \mathbf{J}\_j \ \left[ \mathbf{W} \mathbf{m}^{-2} \right] \tag{10}$$

where Fi!<sup>j</sup> is the view factor between surfaces j and i (Eq. (11)).

Several factors are involved in these calculations. For instance, the net radiation balance could be simulated with Eqs. (11) and (12):

$$\mathbf{q}\_{rad} = \mathbf{j}\_i - \mathbf{g}\_i \begin{bmatrix} \mathbf{W} \mathbf{m}^{-2} \end{bmatrix} \tag{11}$$

$$\mathbf{Q}\_{rad-i} = \mathbf{A}\_i \mathbf{(j}\_i - \mathbf{g}\_i) \text{ [W]} \tag{12}$$

In addition, the ideal black-body radiation is shown in Eq. 13:

$$E\_{b\lambda} = \frac{C\_1}{\lambda^5 \left(e^{\frac{C\_2}{\lambda T}} - 1\right)}\tag{13}$$

where Eb<sup>λ</sup> spectral emissivity power (W m�<sup>2</sup> ); λ wave longitude (m); T absolute surface temperature (K); C1 3.7405 � <sup>10</sup>�16 (W m2 ); C2 0.0143879 m K.

The power surface emissivity is

$$E\_b = \sigma T\_s^4 \tag{14}$$

where Ts absolute surface temperature (K) and σ Boltzmann constant <sup>2</sup> <sup>K</sup>� (5.6697 � <sup>10</sup>�<sup>8</sup> W m� <sup>1</sup> ).

The simulation of radiative heat exchange between black surfaces is based on Eq. 15:

$$Q\_{1-2} = \sigma A\_1 F\_{12} \left( T\_1^4 - T\_2^4 \right) = \sigma A\_2 F\_{21} \left( T\_1^4 - T\_2^4 \right) \tag{15}$$

where F is the fraction of radiant energy that leaves the area A (m<sup>2</sup> ).

#### 3.3 Mass transfer process in a greenhouse

In a greenhouse, the mass balance between inflows and outflows must be preserved. In general, Eq. 16 represents the mass balance:

Heat and Mass Transfer - Advances in Science and Technology Applications

$$\frac{\partial \not{\rho}}{\partial t} + \frac{\partial}{\partial \alpha\_j} \left( \not{\rho} \not{u}\_j \right) = \mathbf{0} \tag{16}$$

where ρ air density (kg m�<sup>3</sup> ) and uj wind velocity in j direction (m s�<sup>1</sup> ).
