4.2 CFD heating pipe tube simulation

Heating in greenhouses strongly influences crop yields [17], energy consumption, and operation costs; however, this type of systems is essential to achieve sustainable production. A method to prevent low temperatures below a threshold makes use of the forces arising from a temperature or convection gradient.

Figure 4.

Distribution of wind speed vectors (m s ˜1 ) to the center of the module in a frontal (a) and longitudinal (b) plane.

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

The systems that most cold-climate greenhouses use are a collector wall and a heating system based on water or gas driven by a pipe. The heating pipes (pipe heating) is an effective means of keeping the greenhouse warm by promoting convection and radiation of heat. The layout of these tubes and the heating power determine the spatial distribution of temperature and the flow patterns induced by the movement of air due to the convective effect (Figure 4).

Teitel et al. [24, 25] mentioned that the best way to place the tubes is at medium height and under the crop, with the tubes as close as possible to the leaves. Other configurations have been analyzed by various researchers [24, 26, 27], which highlight the influence of the heating system with crops and radiative aspects. These investigations have unveiled the advantages of installing hot water pipes (pipe heating) in the lower part of the crop without promoting excessive evaporation [28]. Such pipe heating systems also favor the removal of humidity, which is known to negatively influence air quality. Moisture transport has been analyzed using computational fluid dynamics (CFD) to address various aspects such as condensation [8] and refrigeration [18], especially in closed greenhouses [5].

Numerical methods have been widely used to study climate variable inner greenhouses [29]. In 2007 and recently 2017 [30, 31] analyzed the heat distribution by three pipes and perforate polyethylene ducts to manage low temperature in tomato crop greenhouses. CFD gets observed as strong thermal gradients near to the ground and roof and well conditions in the crop zone. In this study, the effect of determining the flow and temperature patterns is the location and power of heating devices [31].

Figure 4 shows the air movement in a small greenhouse, with heating system based on five heat water tubes. The air movement and energy transference are due to the convection method, because temperature in the low tubes is higher than the upper pipe tubes. Normally wind velocities in greenhouse oscillation are between 0.1 and 0.5 m s˜<sup>2</sup> , due to pressure effect. In this system, wind velocity, just for convection effect, is 0.2–0.3 m s˜<sup>1</sup> .

A homogeneous temperature distribution is observed throughout most of the day (Figure 5). In a greenhouse almost all of the management processes need energy; in fact, in cool regions, the cost due to the climatic control is nearly 40% of the total production cost or more, depending on the automation grade of sensors and controls.

### 4.3 Transpiration

Transpiration is a special component with enormous importance in the balance of energy and transfer process in the greenhouse system. Crop transpiration is an important process useful not only in the production process but also in the climate

Figure 5. Temperature gradient (K) to the center of module: frontal plane view (a) and longitudinal plane view (b).

control. Actually, transpiration is the first cooling natural system; when the high temperature is increasing, transpiration occurs very fast, and temperature is controlled. In CFD it is possible to simulate this phenomenon as a source term from the crop, as a flow of water. To speed up energy transport calculus use the model Penman-Monteith (Eq. 20) with some simplification.

Simulation in Fluent is based on Eq. 20, and for the simulation of transpiration, it is necessary to make a balance of energy between the plant and the environment, creating a system of equations implemented in the simulation as a "user-defined function" (UDF) so that terms such as transpiration, the consumption of CO2, etc. can be calculated [4]. Nowadays most of the factors and estimated values of latent heat of vaporization in the energy balance equation can be measured using data of density, thermal conductivity and psychometric constant.

$$ET = \frac{\Delta (Rn - G) + \rho\_a c\_p \frac{(e\_i - e\_a)}{r\_a}}{\Delta + \chi \left[1 + \frac{r\_a}{r\_a}\right]} \tag{20}$$

�2 �<sup>1</sup> where ET is the potential evapotranspiration (kg m s o mm s�<sup>1</sup> ); Rn is the net radiation (kW m�<sup>2</sup> ); G is the heat flux in soil (kW m�<sup>2</sup> ); ðes�eaÞ is the vapor pressure deficit (kPa); rc is the crop resistance (s m�<sup>1</sup> ); ra is the aerodynamic resistance (s m�<sup>1</sup> ); Δ is the slope of the vapor pressure saturation (es/T) (Pa °C�<sup>1</sup> ); ρ<sup>a</sup> is the air density (kg m�<sup>3</sup> ); cp is the specific heat of the air (MJ kg�<sup>1</sup> °C�<sup>1</sup> ); and γ is the apparent psychometric constant (kPa °C�<sup>1</sup> ).

In the case of stomatal resistance, it is possible to measure it directly and relate it to the environmental variables involved (solar radiation, VPD, temperature and CO2 concentration). For each crop, the resistance will be different, but in general an average resistance in the canopy can be estimated according to the foliar area index [33]. To estimate external leaf resistance, it has been assumed that temperature of the leaf and air is the same, so it is possible to estimate a coefficient rc with Eq. (21):

$$r\_t = \frac{r\_i}{L} \tag{21}$$

where Rc is the internal resistance of the leaf canopy to the transfer of water vapor (s m�<sup>1</sup> ), L is the leaf area index, and ri internal resistance of the leaf (s m�<sup>1</sup> ). Figure 6 shows the simulated results of the distribution of humidity and mass fraction along the greenhouse using the simplified model of [33]. Numerically it was demonstrated that the Penman-Monteith transpiration model is not particularly sensitive to the variables with the simplification of the model mentioned, which can be an indication of a good result.

Transpiration of the crop is directly affected by the foliar area (Figure 7), and consequently the strict relationship between this and the vapor pressure deficit (VPD) will be the variable to follow for an approximation to the transpiration of greenhouse crops.

The largest source of variation between the models compared is based on the leaf area of the crop; while it is true that transpiration is originally associated with the amount of radiation, the dependence of stomata in this exchange is also founded. Figure 7 shows the variation of the transpiration of the crop as a function of the leaf area index (LAI), in this case a tomato crop.

#### 4.4 Gas simulation (ammonia)

Mass transfer in semi-closed spaces is an important process. Ventilation is the primary mechanism for gas removal. Air movement assumes a mixture of liquid,

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

#### Figure 6.

Contour of relative humidity (%) (A) and transpiration as a mass fraction of H2O (B) using CFD simulation [33].

#### Figure 7.

Variation of transpiration (g m�<sup>2</sup> h�<sup>1</sup> ) of a tomato crop as a function of the leaf area (IAF), when 3 and 6ms�<sup>1</sup> speed is simulated outside of the wind [33].

vapor, and nonconsumable gases. In this case, the species transport model available in ANSYS Fluent was used to simulate the mass transport, beginning from the diffusion flux of species i, which arises due to gradients of concentration and temperature. Such species model uses the dilute approximation (Flick's law) to model mass diffusion. For turbulent flows, mass diffusion can be written as in Eq. 22 [32]:

$$\overline{J}\_i = \rho \mathbf{D}\_{i,m} \nabla Y\_i - \mathbf{D}\_{T,i} \frac{\nabla T}{T} \tag{22}$$

In Eq. (19), Ji is the diffusion flux of species i (m2 s �1 ), ρ is the density of the mixture (kg m�<sup>3</sup> ), Di,m is the mass diffusion coefficient for species i in the mixture m (m2 s ˜1 ), and DT, <sup>i</sup> is the turbulent diffusion coefficient (m2 s ˜1 ). Yi is the mass fraction of specie i, and T is the temperature of the flow (K). CFD can simulate this process and visualization of the movement as shown in Figures 8–10.

The discretization of components in semi-closed facilities can better depict fluxes under different scenarios. Figure 8 shows the air movement along the barn and how the temperature is changing. In addition, air exchange promotes an efficient distribution of gas concentration by the effect of ventilation system.

Figure 8. Wind velocity vectors (m s ˜1 ) under cages and surrounding temperature profiles (°C).

#### Figure 9.

Relative gas concentration by air exchange effect.

#### Figure 10.

CFD results of (A) profile of wind velocity and temperature and (B) relative gas concentration of nitrogen in a vertical profile, under two wind direction configurations (cages are in the 1.1 m height).

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

Performance of the vents is a function of their size, position, and proportion to the whole ground area.

In this study mass and energy transfer was revised to get reduced the negative effect of the ammonia gas in the rabbit barn development. Two climatic variables are responsible to the rabbit's health: temperature and humidity. Both climate variables were got better when the position of windows was changed. These results are consistent with CFD simulations, where the effective renovation rate depends on the position of the window. In some cases more than 50% of the air cannot get in through the inlet vent, producing a ventilation rate of 5.4 kg s˜<sup>1</sup> . As a consequence, a greater dispersion of toxic gases and lower temperature gradients (5 K) are produced.

The air exchange rate is an indicator of gas movement, because it is similar for both the air and the gas being simulated such as the ammonia (Figure 9) with a wind direction normal to the ridge. When the wind is parallel to the vents, the air that enters the vents by pressure difference produces a higher ventilation rate at the zone beneath the cages (Figure 10), even when the ventilation rate is close to zero. In contrast, when the wind flows normal to the ridge, ventilation rates increase.

Numerical models show a representative environmental dynamics, which can supply information for manage and control of several climate factors.

Continuity equation indicates that mass quantity entrance must be the mass in exit; however, with the change in the configuration of orientation of barn, the gas concentration can be better. Using CFD simulation, the concentration of gas under/ over cages is calculated. Figure 10 shows the mass transfer due to natural ventilation systems and the wind direction with respect to the size of the windows. In this case the position of the size of the windows was enough to reduce the mass transference under cages. Results indicated that the rate of mass change is the same, but distribution of gases (mass exchange) can be managed using different configuration of windows.
