**L. Serir**

Applied Research Unit on Renewable Energies, Ghardaia, Algeria

H. Benmoussa

Applied Research Unit on Renewable Energies, Ghardaia, Algeria

P.E. Bournet

Environmental Physics and Horticulture Research Unit, Agrocampus-Ouest, Angers, France

Applied Research Unit on Renewable Energies, Ghardaia, Algeria

H. Benmoussa

Applied Research Unit on Renewable Energies, Ghardaia, Algeria

P.E. Bournet

Environmental Physics and Horticulture Research Unit, Agrocampus-Ouest, Angers, France

Crop growth in greenhouses is strongly influenced by the local inside climate. In the present study, a model for predicting the thermal and water behaviour inside an unheated closed plastic tunnel greenhouse is presented. The energy balance method is applied to each element of the shelter: cover, indoor air and soil surface. Radiative transfers are included by calculating view factors. This model is connected to another model for the subsoil. The corresponding modules were integrated in the TRNSYS (Transient Simulation system) environment. TRNSYS includes weather data and calculates the solar radiation distribution, sky temperature and psychrometric properties. The simulations predict three main parameters under transient conditions: the indoor air temperature, the soil temperature and the indoor humidity. The present study also focuses on the cover temperature in response to the inside and outside conditions. Results provided by the model were validated with fair agreement against experimentations conducted for an unheated closed plastic tunnel greenhouse located in Angers (47.43N, 0.55°E). Based upon the results of the simulations and the experimentation, it is shown that the convective heat transfer between the soil surface and the indoor air affects significantly the indoor climate. Moreover, the use of correlations of this coefficient depends on the direction of heat flow; a specific correlation is applied with upward heat flow and another one with undergoing downward heat flow.

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L. Serir, H. Benmoussa and P.E. Bournet, 2011. Numerical Analysis of the Influence of Soil-Air Convective Heat Transfer Coefficient on the Global Indoor Climate Model of a Closed Plastic Tunnel Greenhouse. *International Journal of Agricultural Research, 6: 458-469.*

**DOI:** 10.3923/ijar.2011.458.469

**URL:** https://scialert.net/abstract/?doi=ijar.2011.458.469

In recent years, the cost of fossil energy considerably increased, making the crop production inside greenhouses more expensive. For that reason, there is an urgent need to implement better practices in energy management in order to reduce energy costs (Heidari and Omid, 2011).

Modeling tools can help to predict the climate evolution inside a greenhouse and adapt a strategy to reduce the energy consumption. The design of a greenhouse depends upon the latitude of the place and the requirement of crop (From a physical point of view, a greenhouse may be considered as a solar energy tank (Kumar *et al*., 2006) and the most of **solar radiation** incident on a greenhouse is absorbed by components (Abdel-Ghany and Al-Helal, 2010). A large amount of this energy reaches the greenhouse during daytime and warms the inside air but most of the energy is not stored and is evacuated through the openings (Rico-Garcia *et al*., 2008). Artificial heating is therefore, sometimes required (Kumari *et al*., 2006), particularly at night time in winter. For that reason, it becomes urgent to optimize the use of unheated greenhouses and better exploit heat storage inside the ground.

Numerous numerical studies on greenhouse indoor climate have been conducted to predict the greenhouse thermal environment. Some of them are based on a global approach which consists in writing the energy balance of the different elements of the greenhouse as well as the water vapour balance inside the greenhouse (Fitz-Rodriguez *et al*., 2010; Shukla *et al*., 2006). The developed thermal-simulation models mainly use measured transmittivity of the cover (Kittas *et al*., 1999) or constant values (Singh *et al*., 2006). Moreover, they usually consider all surfaces of the cover to have the same temperature and assume that internal thermal radiation exchanges only occur between the cover and the ground and exchanges with the outside ground are therefore, neglected. The weakness of these studies is that they do not consider the different components of the greenhouse cover although they to not behave in the same way. Recently however, Kolokotsa *et al*. (2010) took account of the thermal radiation between cover surfaces and introduced view factors as input data and the greenhouse shape is considered as paralleled enclosure.

A greenhouse **simulation model** (GGDM: Gembloux Greenhouse Dynamic Model) was developed by Pieters and Deltour (1999) and used by Wang and Boulard (2000) to describe the evolution of the climatic parameters inside a greenhouse. The model GGDM is implemented in the TRNSYS environment and requires as input data the global and the diffuse radiation. Nevertheless, only the global radiation is measured by the most meteorological stations.

The objectives of the present study were to develop two new modules in the TRNSYS environment, one to simulate the greenhouse behavior and the second one to simulate the subsoil transfers. The inputs of the greenhouse model are provided by the other standard modules and by the subsoil module. To validate the greenhouse module, experimental data were collected and a comparison of the impact of the soil-to-air heat convection by using three different correlations from the literature. The validity of these correlations over the time was also checked.

TRNSYS is a transient simulation program with a modular structure. This modular structure makes it easy for users to add new components to the standard package. In the present study two new modules have been implemented in order to cope with the specificities of the greenhouse system. The first one deals with the greenhouse itself: cover, indoor air and soil surface. The model provides information at each time step on the thermal behavior by calculating the temperature of each component of the greenhouse. The second one provides temperature profile in the subsoil. The aim of these differentiated modules is to separate the low capacity component of the system (i.e., the greenhouse) from the high capacity component of the system i.e., subsoil. The distinction of different portions of cover following the slope and azimuth solar angle makes it possible to take account of both the incident **solar radiation** and the wind direction in the convective coefficient determination.

A greenhouse is a production system made of thee main elements: the transparent cover, the indoor air and the soil surface. The cover acts as an interface between the microclimate and the outside climatic conditions and the soil surface as an interface between the microclimate and the subsoil. The outside climate, the greenhouse (cover, indoor air and soil surface) and the subsoil may then be formalized by using a modular approach. In this prospect, two new modules for the greenhouse and for the subsoil have been implemented in the TRNSYS code.

Fig. 1: | Greenhouse orientation and nomenclature of the different elements of the greenhouse |

Fig. 2: | Heat exchanges between the nodes of the system and the surroundings |

The objective is to connect these new modules to the core of the code in order to carry out simulations of the transient behavior of the greenhouse.

To reach this goal, the energy balance equation is established for each component of the shelter: the cover, the inside air, the plants and the soil. In the present study, the cover is divided into six surfaces as shown in Fig. 1. These elements, together with the inside air and the ground, are assimilated to nodes where calculations proceed. In the same manner the subsoil is decomposed into several layers. As shown in Fig. 2, a greenhouse is a system in which all **heat transfer** modes co-exist, by radiation, convection, with or without phase change and by conduction.

The energy balance equation at each node may be written in the general form provided by Eq. 1:

(1) |

where, m_{i} is the mass (kg), C_{i} is the specific heat of air (J/kg/k), T_{i} is the temperature (K) and Q_{i} is the sensible/latent heat energy (W). Adapted to the different components of the greenhouse, Eq. 1 may then be written:

For the cover surfaces (i = 1,2,..,6):

(2) |

For the indoor air sensible heat:

(3) |

To include the mechanisms of condensation and evapotranspiration on the indoor humidity, an additional energy balance is established for the internal air (Eq. 4):

(4) |

where, m_{ai} (kg) is the mass of humid air, L_{v} is the latent heat of water vaporisation (J kg^{-1}) and is the latent heat energy (W) due to condensation on the cover, evapotranspiration and infiltration:

(5) |

For the soil surface

(6) |

For the subsoil nodes (j = 2,…,N-1):

(7) |

For the subsoil bottom node, j = N:

(8) |

where, ρ is the density (kg m^{-3}), C_{p} is the specific heat (J/kg/k), t is the time, Q^{r} is the thermal radiative heat transfer, Q^{s} is the absorbed solar radiation; Q^{cv} is the heat exchanges by convection, Q_{i}^{cnd} is the **heat transfer** by conduction between the soil nodes, Q^{inf} is the indoor-outdoor heat exchange by infiltration and Q^{l} is the latent heat. The subscripts ai denotes the indoor air, ae the outdoor air, c the cover, e the environment (sky and external soil).

Q^{cv} in Eq. 2 represent the convective **heat transfer** between the element of cover and both outdoor and indoor air:

(9) |

in Eq. 6 represent the convective **heat transfer** between the soil surface and indoor air:

(10) |

where, h_{ae, i}, h_{ai, i} are the convective heat coefficients between the element of cover and the outdoor and indoor air, respectively and h_{ai, s} is the convective coefficient between indoor air and soil.

In the Eq. 8, the heat flux is equal to zero because changes in soil temperature at the deeper layers (>0.3 m) remained almost constant during a day (Gulser and Ekberli, 2004).

**Numerical procedure:** For numerical analysis, two subroutines have been written in FORTRAN and linked to TRNSYS program.

**Simulation tool:** The commercially available TRNSYS software was chosen as numerical tools as it offers a flexible environment to carry out transient simulations. This code makes it possible to split complex models into elementary simpler and interconnected modules (Fig. 3). It is therefore, easy for users to add new components to the standard package. In the present study two new modules have been implemented in order to cope with the specificities of the greenhouse system.

• | The first one deals with the greenhouse itself: cover, indoor air and soil surface. The model provides information at each time step on the thermal behaviour by calculating the temperature of each component of the greenhouse |

• | The second one provides temperature profile in the subsoil. The aim of these differentiated modules is to separate the low capacity component of the system (i.e. the greenhouse) from the high capacity component of the system i.e., subsoil. The distinction of different portions of cover following the slope and azimuth solar angle makes it possible to take account of both the incident solar radiation and the wind direction in the convective coefficient determination |

Fig. 3: | Flow chart of the greenhouse and subsoil interconnected under TRNSYS environment |

Each module is launched independently and coupled with other modules to simulate and solve the entire system problem. The advantage of this procedure comes from the large unit library already implemented that includes some features like **physical properties** calculators (i.e., psychometric properties), radiation processor, sky temperature and other specific routines to calculate the transmitivity and the view factors for instance.

**Numerical technique:** The above differential Eq. 2-8 are coupled through energy fluxes. Given these equations are nonlinear with respect to temperatures and humidity. The corresponding system of differential equations can be solved by a Runge-Kutta method (Sharma and Tiwari, 1999). However, the convergence of this method requires a time step Δt ≤m_{i} Cp_{i}/ΣQ_{i }(Klein *et al*., 2004). For the cover component, of which volume and mass (m_{i} = ρ_{i}. V_{i}) is very small, the corresponding time step required would be also very small and not convenient for the long time simulation. To avoid this situation, several simplifications were adopted in this study in order to linearize the system of Eq. 2-6. Nonlinear terms were expressed as a function of the mean temperature at the previous time step according to the procedures described by Dos Santos and Mendes (2004).

After linearization the equations are reduced to the flowing first-order differential equation of the form of Eq. 11:

(11) |

where, a_{i} is a constant and gathers all terms which depend on the mean temperature or humidity of other nodes:

(12) |

The modified Euler method (predictor-corrector method) was chosen as numerical method. It is adapted to the present analytical method because the analytic solution is used as prediction step. The combination of these two methods results in the so-called semi-analytical method. It makes the numerical resolution of the equations faster and quite robust (Dos Santos and Mendes, 2004).

**Experimental validation:** Experiments were conducted inside a tunnel greenhouse at Agrocampus Ouest in Angers (47.43N, 0.55°E) in the West of France. The climate is moderate oceanic. The greenhouse is oriented N-S and covered with a 200 μm thickness plastic film. It is 24 m long, 9 m wide and 5.5 m high with the gutter at 2 m. The greenhouse is maintained closed during two consecutive days (April 21st and 22nd 2010), the soil remained dry and no crop was grown inside the greenhouse during the experiments.

The global **solar radiation** was measured with a pyranometer (CM-3, Kipp and Zonen, Delft, Netherlands). Wind speed and direction measurements were performed using cup anemometers (HA 430A, Geneq Inc., accuracy 0.11m sec^{-1}), located 10 m above the ground. Dry and wet bulb air temperatures were measured with an aspirated shielded psychrometer (model 225-5230 Assman). The indoor climatic parameters (temperature and relative humidity) were also recorded with a shielded psychrometer every 10 min and 289 observations were collected for each microclimatic parameter.

Measurements were sampled every 10 min by means of a data logger (Delta-T Devices, Cambridge, UK). 289 observations were collected for each microclimatic parameter.

A comparison between calculated and measured values of the indoor temperature, the indoor humidity and the soil temperature was carried out by a regression between calculated and measured data and the Root Mean Square Error (RMSE) were calculated following the Eq. 13:

(13) |

where, n is number of observation and X_{m} and X_{c} is the measured and calculated indoor temperature, the indoor humidity or the soil temperature.

In this study, the model developed under TRNSYS is able to simulate the temporal evolution of three parameters (indoor air temperature, indoor air humidity and soil temperature). The constant parameters used for the numerical study are summarized in Table 1.

The other question studied in this work is the effect of the soil-air convective coefficient correlation (hai, s) on the indoor climate. According to Baille *et al*. (2006), for an air-heated greenhouse and during the night, hai,s varied within a alower and upper limit, corresponding respectively to the functions proposed by de Halleux (hai, s = 1.86 Δ.T^{0.33 }) for a greenhouse equipped with heating pipes and Silva cited by Roy *et al*. (2002) (hai, s = 10. Δ.T^{0.33}) for an unheated plastic greenhouse with bare soil). An intermediate correlation was also proposed by Lamrani *et al*. (2001) (hai, s = 5.2 Δ.T^{0.33}) for a greenhouse with a heating floor. In this study, we have examined the effect of these correlations of the combination of these extreme correlations and of the intermediate correlation on the indoor air temperature calculation.

Table 1: | Constant parameters used in the simulation |

Fig. 4: | Calculated (solid lines) and measured (dashed) dynamic changes for indoor temperature, when: hai, s = 10.Δ.T^{0.33} |

Fig. 5: | Calculated (solid lines) and measured (dashed) dynamic changes for indoor temperature, when hai, s = 5.52 Δ.T^{0.33} |

**Use of upper limit correlation:** Using Silva correlation (hai, s = 10.Δ.T^{0.33}), the inside air temperature predicted by the model is generally in fair agreement with measurements as indicated in Fig. 4 but appears to be slightly overestimated. The difference may come from the infiltrations. The difference after the peak of temperature is probably due to the use of higher soil-air convective coefficient correlation (hai, s = 10.Δ.T^{0.33})

**Use of intermediate correlation:** Using Lamrani correlation (hai, s = 5.2.Δ.T^{0.33 }) to calculate the indoor temperature evolution slightly modifies the results as shown in Fig. 5. The inside air temperature predicted by the model appears to be slightly overestimated and the difference observed is smaller than that observed with Silva correlation.

**Use of lower limit correlation:** Using de Halleux correlation (hai, s = 1.5.Δ.T^{0.33 }) to calculate the indoor temperature evolution considerably modify the results as shown in Fig. 6. Inversely to the precedent case, the use of lower correlation is more appropriate after the peak during the cooling period (upward heat flux) but the difference appeared during the warmed period (downward heat flux).

Fig. 6: | Calculated (solid lines) and measured (dashed) dynamic changes for indoor temperature, hai, s = 1.86Δ.T^{0.33} |

Fig. 7: | Calculated (solid lines) and measured (dashed) dynamic changes for indoor temperature, when hai, s = a Δ.T^{0.33} |

Fig. 8: | Calculated (solid lines) and measured (dashed) dynamic changes for indoor temperature, when hai, s = a Δ.T^{P} |

From Fig. 5 and 6, it can be seen that the use of the Lamrani correlation is more appropriate undergoing downward heat flux while the use of de Halleux correlation is more appropriate with upward heat flux. As consequence, none of the two extreme correlations can be used to properly and accurately reproduce the measured temperatures over a 24 h period. It appears more advantageous to applies the two correlations with the condition of heat flow direction, one during the warming period (upward heat flux) and the other one during the cooling period (downward heat flux), depending on the direction of heat flow, we propose the general expression: hai, s = a.Δ.T^{0.33}. Where, a = 5.52 if (Ts-Tai) <0 or a = 1.5 if (Ts-Tai)>0).

The results of the corresponding simulations are given in Fig. 7 for the indoor temperature, in Fig. 8 for the indoor humidity and in Fig. 9 for the soil temperature. A comparison between calculated and measured values of the indoor temperature is shown in Fig. 10. The RMSE is 3.34°C.

Fig. 9: | Calculated (solid lines) and measured (dashed) dynamic changes for soil temperature |

Fig. 10: | Calculated indoor temperature (T_{c}) Vs measured (T_{m}) |

Fig. 11: | Calculated indoor humidity (Hc) Vs measured (Hm) |

The inside air humidity calculated by the model is in good agreement with measurement as indicated in Fig. 8. The difference may come from infiltrations on the one hand way and from the residual evaporation on the other hand. The comparison between calculated and measured humidity is shown in Fig. 11, the RMSE is 6.72%.

The temperature of the fist subsoil layer calculated by the model is in good agreement with measurement as indicated in Fig. 9. The comparison between the corresponding calculated and measured temperatures is shown in Fig. 12, the RMSE is 0.065°C.

Fig. 12: | Calculated soil temperature (Tc) vs. measured (Tm) |

A new model of closed greenhouse climate was developed in the TRNSYS environment to predict the indoor microclimate of a plastic greenhouse. The use of TRNSYS improves the calculation of model inputs.

Based upon the results of the simulation and the experimentation, it was shown that using different expressions of convective **heat transfer** coefficient between soil and indoor temperature according to the direction of convective **heat transfer** (from soil to indoor air or vice versa) leads to a better accuracy of the predicted indoor climate. We propose the more general expression of convective **heat transfer** coefficient between soil and indoor temperature valid all a day long.

The developed models of closed greenhouse and subsoil can be used for any size with different characteristics of cover and soil but improvements are still needed concerning the case of ventilated greenhouses. Further modelling efforts are also required to integrate a more accurate soil model taking account of the variations of the **soil properties** with soil moisture profile and texture.

The authors are indebted to the EPHor (Environmental Physics and Horticulture) research Unit of Agrocampus Ouest for their invaluable support.

- Kittas, C., A. Baille and P. Giaglaras, 1999. Influence of covering material and shading on the spectral distribution of light in greenhouses. J. Agric. Engng. Res., 73: 341-351.

CrossRef - Singh, G., P.P. Singh, P.P. Singh Lubana and K.G. Singh, 2006. Formulation and validation of a mathematical model of the microclimate of a greenhouse. Renewable Energy, 31: 1541-1560.

CrossRef - Kolokotsa, D., G. Saridakis, K. Dalamagkidis, S. Doliantalis and I. Kaliakatsos, 2010. Development of an intelligent indoor environment and energy management system for greenhouses. Energy Conversion and Management, 51: 155-168.

CrossRef - Pieters, J.G. and J.M. Deltour, 1999. Modelling solar energy input in greenhouses. Solar Energy, 67: 119-130.

CrossRef - Wang, S. and T.Boulard, 2000. Predicting the microclimate in a naturally ventilated plastic house in a mediterranean climate. J. agric. Engng Res., 75: 27-38.

CrossRef - Dos Santos, G.H. and N. Mendes, 2004. Analysis of numerical methods and simulation time step effects on the prediction of building thermal performance. Applied Thermal Engineering, 24: 1129-1142.

CrossRef - Baille, A., J.C. Lopez, S. Bonachela , M.M. Gonzalez-Real and J.I. Montero, 2006. Night energy balance in a heated low-cost plastic greenhouse. Agric. Forest Meteorol., 137: 107-118.

CrossRef - Roy, J.C., T. Boulard, C. Kittas and S. Wang, 2002. Convective and ventilation transfers in greenhouses, part 1: The greenhouse considered as a perfectly stirred tank. Biosyst. Eng., 83: 1-20.

CrossRef - Lamrani, M.A., T. Boulard, J.C. Roy and A. Jaffrin, 2001. Airflow and temperature patterns in a greenhouse. J.agric.Engng. Res., 78: 75-88.

CrossRef - Heidari, M.D. and M. Omid, 2011. Energy use patterns and econometric models of major greenhouse vegetable productions in Iran. Energy, 36: 220-225.

CrossRef - Abdel-Ghany, A.M. and I.M. Al-Helal, 2010. Solar energy utilization by a greenhouse: General relations. Renewable Energy, 36: 189-196.

CrossRefDirect Link - Rico-Garcia, E., I.L. Lopez-Cruz, G. Herrera-Ruiz, G.M. Soto-Zarazua and R. Castaneda-Miranda, 2008. Effect of temperature on greenhouse natural ventilation under hot conditions: Computational fluid dynamics simulations. J. Applied Sci., 8: 4543-4551.

CrossRefDirect Link - Kumari, N., G.N. Tiwari and M.S. Sodha, 2006. Thermal modelling for greenhouse heating by using packed bed. Int. J. Agric. Res., 1: 373-383.

CrossRefDirect Link - Fitz-Rodriguez, E., C. Kubota, G.A. Giacomelli, M.E. Tignor, S.B. Wilson and M. McMahon, 2010. Dynamic modeling and simulation of greenhouse environments under several scenarios: A web-based application. Comput. Electronics Agric., 70: 105-116.

CrossRef - Shukla, A, G.N. Tiwari and M.S. Sodha, 2006. Energy conservation potential of inner thermal curtain in an even span greenhouse. Trends Applied Sci. Res., 1: 542-552.

CrossRefDirect Link - Gulser, C. and I. Ekberli, 2004. A comparison of estimated and measured diurnal soil temperature through a clay soil depth. J. Applied Sci., 4: 418-423.

CrossRefDirect Link - Sharma, P.K. and G.N. Tiwari, 1999. Parametric study of a greenhouse by using Runge-Kutta methods. Energy Conversion Manage., 40: 901-912.

CrossRef - Kumar, A., G.N. Tiwari, S. Kumar and M. Pandey, 2006. Role of greenhouse technology in agricultural engineering. Int. J. Agric. Res., 1: 364-372.

CrossRefDirect Link