# Convective heat transfer in a tunnel cultivated greenhouse.

IntroductionThe final target of environmental control in greenhouses is the optimisation of crop production. The greenhouse cover and heating system cause a change in the climatic conditions compared to those outside, such as increased temperature and water vapour pressure of the air, reduction of radiation and air velocity, and larger fluctuations of the carbon dioxide concentration. These changes have an impact on growth, production and quality of the greenhouse crop (Bakker 1995).

The Perfectly-Stirred-Tank approach of greenhouse climate, widely used since the 80's to model heat and mass transfers, implicitly assumes complete homogeneity of the variables which determines the internal climate. A unique air temperature and velocity is considered for the whole greenhouse volume and the crop canopy is generally represented as a "big leaf". In practice no climatological variables are homogeneous in a greenhouse. Instead there are numerous exchange processes occurring at the surfaces of the plants, glazing covers and heating pipes that are governed by local environments and the physical conditions of the surfaces. As pointed out by Bailey (1985) when management of greenhouse climate control moved towards more insulated structures and sophisticated heating facilities, the response of plants to macro and microclimates was no longer the same as that in conventional greenhouses.

Many greenhouses are heated by pipes in order to keep the canopy temperature at a desired level. The location and the power of the heating devices determine the flow and temperature patterns inside the greenhouse. Not much consideration has been given to the problem of finding the optimal location of heating pipes in greenhouses. Although for crop control the use of heating systems near the growing point of the crop might be preferred, this generally results in an increase of energy loss from the greenhouse due to increased thermal radiation exchange between the heating system and the roof (Bot & Van de Braak, 1995). The location of the pipes based on low- temperature heating fluids has been investigated by Popovski (1986), who concluded that a low location of the heating system has significant advantages. Teitel and Tanny (1998) reported that, from a radiative point of view, the best tube location is near the crop at its mid-height. Kempkes and Van de Braak (2000) reported that the heating requirement increases by 5-10% with overhead pipes and the position of the heating pipes has little or no influence on the total evaporation of the crop, but does influence the distribution of the evaporation within the crop. Boulard et al (1999) investigated experimentally and simulated with a commercial CFD code the flow patterns in a half mono-span greenhouse, as they are created by thermal gradients. They found that most of the temperature drop between the soil and the roof occurred within small distances above the floor and below the roof, and the temperature inside the whole cavity was constant, with a uniform and stable distribution. Computational fluid dynamics programs were also used in closed greenhouse (Boulard et al, 1997) and ventilated greenhouses (Mistriotis et al, 1997, Bartzanas et al., 2004). Roy et al (2000) studied the air flow and temperatures patterns induced by heating pipes in a small-scale greenhouse with Particle Imagery Velocimetery (PIV).

The aim of the present study is to investigate numerically, using a commercial CFD code, the influence of heating system position on airflow and temperature distribution inside a tunnel greenhouse with a tomato crop.

The Numerical Approach

The CFD technique numerically solves the Navier-Stokes equations and the mass and energy conservation equations. The three-dimensional conservation equation describing the transport phenomena for steady flows in free convection is of the general form:

[partial derivative](U[PHI]/[partial derivative]x + [partial derivative](V[PHI]/[partial derivative]y + [partial derivative](W[PHI]/[partial derivative]z = [GAMMA][[NABLA].sup.2][PHI] + [S.sub.[PHI]] (1)

In Eqn (1), [PHI] represents the concentration of the transport quantity in a dimensionless form, namely the three momentum conservation equations (the Navier-Stokes equations) and the scalars mass and energy conservation equations; U, V and W are the components of velocity vector; [GAMMA] is the diffusion coefficient; and [S.sub.[PHI]] is the source term. The governing equations are discretised following the procedure described by Patankar (1980). This consists of integrating the governing equations over a control volume.

The commercially available computational fluid dynamics code CFX is used, in this study, to obtain airflow and temperature patterns. CFX (ANSYS, 2003) is a general purpose commercial CFD package that solves the Navier-Stokes equations using the finite volume method. The discretisation is performed with triangular and quadrilateral elements. In a closed space, like a greenhouse, the flow is turbulent for Rayleigh number Ra > [10.sup.9]. Ra involves the characteristic length of the greenhouse and the temperature difference [DELTA]T between the soil and the cold roof of the greenhouse.

For a greenhouse 3 m high, the flow is already turbulent if [DELTA]T > 0.1 [degrees]C, which means in most cases. Consequently, turbulence models, not considered in equation 1, must be introduced.

The standard k-[epsilon] model (Launder and Spalding, 1974) assuming isotropic turbulence was adopted to describe turbulent transport. The k - [epsilon] turbulence model is an eddy--viscosity model in which the Reynolds stresses are assumed to be proportional to the mean velocity gradients, with the constant of proportionality being the turbulent eddy viscosity. The turbulent viscosity is obtained by assuming that it is proportional to the product of a turbulent velocity and a length scale.

The Boussinesq model, which ignores the effect of pressure changes on density (Launder and Spalding, 1974) was adopted for the buoyancy effect in the computational domain. Non-slip velocity conditions (i.e the normal component of the velocity of the fluid will be the same as the normal component of the velocity of the surface) were applied to all greenhouse surfaces.

The crop was simulated using the equivalent porous medium approach by the addition of a momentum source term, due to the drag effect of the crop, to the standard fluid flow equations (Boulard and Wang 2002). For a greenhouse tomato crop Haxaire (1999) using wind-tunnel facilities evaluated the total drag of the canopy for different leaf area indexes. Using the methodology described by Boulard and Wang (2002) we can estimate the appropriate values for permeability and non-linear pressure-loss coefficient according to the leaf area index of our case.

Greenhouse Characteristics and Boundary Conditions

The simulations were performed for a round-arch with vertical side walls, plastic-covered greenhouse. The greenhouse was identical with one used for experimental purposes and from which realistic boundary conditions were adopted. The geometrical characteristics of the greenhouse were as follows: eaves height = 2.4 m; ridge height = 4.1 m; total width = 8 m; total length = 20 m; ground area Ag =160 [m.sup.2] and volume V = 572 [m.sup.3].

An identical greenhouse, located in the experimental farm of the University of Thessaly in Central Greece, was used for experimental purposes. The experimental greenhouse was heated from a network of black plastic heating pipes (diameter 28 mm), located below the gutter holding the growing substrate (at a distance of 0.5 from the greenhouse soil), with one supply and return lines for each crop row. Tomato plants (cv. Beladonna) were grown in containers filled with perlite with a density of 2.5 plants/[m.sup.2]. Water and fertilisers were supplied by a drip system, which was automatically controlled by a fertigation computer.

Besides the position of the heating pipes during the experiments, two other different heating pipes positions were numerically investigated: a) heating pipes located 1 m and 2 m from the greenhouse soil, respectively.

Wall-type boundary conditions were imposed along the floor, the roof and the heating pipes whereas greenhouse walls were treated as adiabatic. Imposed boundary conditions correspond to the average measured temperature values during 10 days. Selected periods of measurements were located during the night period when the heating system was operated almost continuously. Airflow was assumed to be steady turbulent flow, and all computations were performed at steady-state conditions.

A preliminary grid convergence study was carried out in order to verify that the solution is grid independent. The grid is more refined near the heating pipes, greenhouse floor and greenhouse walls, where strong thermal gradients are supposed to be found (Figure 1). The choice of the final grid was validated after several trials in order to both optimise the computational time and the precision of the model, especially near the crop.

To reduce the computational time necessary for a convergence solution, symmetry conditions were considered to apply at the sides of the domain and the simulations were carried out only for half greenhouse. In table 1 greenhouse characteristics and used boundary conditions are summarized.

[FIGURE 1 OMITTED]

Results

Figure 2 shows the velocity vectors in the tunnel greenhouse for the second tested case (i.e heating pipes located 1 m from greenhouse ground). Velocity vectors shows two symmetric loops. Greenhouse air is heated by the pipes and flows up at the right side of them. At the same time, air flows down from the direction of the roof and continues down the wall. Both airflow loops collide on the greenhouse roof. There the air is cooled, since its temperature is higher than the temperature of greenhouse roof and both move down following the inner surface of the walls. Close to the wall and greenhouse soil the air velocities are the highest, with values up to 0.5 m [s.sup.-1], whereas lower values were observed in the center of the greenhouse. Stagnation zones can be observed at the corners between the roof and the walls, where the values of air velocity reduce to 0.05 m [s.sup.-1].

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

The temperature profile which is presented in figure 3 follows the distribution of air, in agreement with the experimental results of Sase et al (1984) who concluded that the temperature distribution in a greenhouse was largely determined by the air flow pattern. The isotherm spreads along the heating pipes from the centre to the walls. These two regions split off in the middle of the greenhouse to ascend away from the heating pipes to greenhouse roof, forming a thermal plume. The same temperature pattern was observed by Pretot et al (2000) who investigated the natural convection on a horizontal plane. Most of the temperature gradients occurred near the greenhouse ground and the roof while greenhouse air temperature remains almost constant and stable in the whole greenhouse volume. Boulard et al (1999) concluded the same, in a small-scale model greenhouse without plants. They found that, except for strong temperature gradients observed in thin layers near the floor and the roof, the temperature inside the cavity was uniform and stable.

The air velocity near the crop, and the temperature difference between crop an air play a significant role in crop activity since they determine to a large extent the physiological activities of the crop. Spatial heterogeneity of air velocity and climate inside greenhouse interfere with plants activity and influence largely crop behaviour through their effects on crop gas exchanges, particularly transpiration and photosynthesis. For instance, increasing air velocity inside the greenhouse increases convective heat transfer and hence reduces the leaf-air temperature difference. Furthermore, air velocity might be expected to increase photosynthesis because of the reduced boundary layer resistance to the transport of carbon dioxide. But if the increased air speed raises transpiration to such extent that water stress and hence stomatal closure occurs, then photosynthesis will be reduced as a consequence. High air velocities (> 1 m [s.sup.-1]) in the crop canopy should also be avoided, since they lead to reduction in leaf area and dry matter accumulation. Figure 4 presents the average transverse horizontal component of the air velocity for the three different heating pipes locations along the greenhouse width at the middle of the greenhouse. The lower the location of the heating pipes the higher the resulting air velocity within the crop canopy.

Vertical temperature distribution within greenhouse crop is of a great importance; since temperature has a direct effect on the sink strength with respect to assimilates of the individual parts of the plant (De Koning, 1994). For the three tested cases, most of the temperature gradients occurred near the floor and the roof while it remains constant and stable in the whole greenhouse volume (results not shown). The lower the location of the heating pipes, the higher the resulting air velocity in the region near the crop. Locating the heating pipes higher than crop (the 3rd case tested) resulted in slightly higher air temperatures in the crop level, mainly due to the lower air velocities achieved with this configuration.

Conclusions

An attempt was made to instigate the airflow and temperature patterns induced by soil pipe heating. Three different cases, representing three different heating pipes position, were studied for a closed tunnel greenhouse, with a tomato crop. For the three cases tested, the simulations indicated two symmetrical circulation loops of airflow. Stagnation zones can be observed at the corners between the roof and the walls of the greenhouse. The temperature profile is characterized by strong thermal gradients near the floor and the roof and generally it remains constant and stable in the rest greenhouse volume.

References

[1] Boulard, T., Haxaire, R., Lamrani, M.A., Roy, J.C., Jaffrin, A. 1999. Characterization and modelling of the air fluxes induced by natural ventilation in a greenhouse. Journal of Agricultural Engineering Research 74: 135-144.

[2] Launder, B.E and Spaiding, D.B, 1974. The numerical computation of turbulent flows. Comp. Methods in Appl. Mech & Engng. 3: 269.

[3] Boulard, T. and Wang, S. 2002. Experimental and numerical studies on the heterogeneity of crop transpiration in a plastic tunnel. Computers and Electronics in Agriculture, 34: 173-190

[4] ANSYS Inc., 2003, ANSYS Incorporated, 2003. CFX Manuals

[5] Bakker, J.C. 1995. Greenhouse climate control: constraints and limitations. Acta Hortic. 399: 25-37.

[6] Bartzanas, T., Kittas, C., Boulard, T. 2004. Effect of vent arrangement on windward ventilation of a tunnel greenhouse. Biosystems Engineering 88 (4): 479-490.

[7] Bot, G.P.A., Van de Braak, N.J. 1995. Transport phenomena. In: Bakker, J.C., Bot, G.P.A., Challa, H., Van de Braak, N.J. (Eds.), Greenhouse Climate Control: An Integrated Approach. Wageningen Pers, Wageningen

[8] Bailey, B.J. 1985. Microclimate, physical processes and greenhouse technology. Acta Hort. 174:35-42.

[9] Boulard, T., Roy, J.C., Lamrani, M.A., Haxaire, R. 1997. Characterising and modelling the air flow and temperatures profiles in a closed greenhouse in diurnal conditions. Mathematical and Control applications in agriculture and horticulture; IFAC Workshop; Hannover Germany 1997.

[10] De Koning, A.N.M., 1994. Development and dry matter distribution in glasshouse tomato: a quantitative approach. Dissertation, Agricultural University, Wageningen, 240 pp.

[11] Haxaire, R.1999. Caracterisation et modelisation des ecoulements d'air dans une serre. Ph.D Thesis, 149p.

[12] Kempkes, F. L. K. and van de Braak N.J. 2000. Heating system position and vertical microclimate distribution in chrysanthemum greenhouse. Agriculture and Forest Meteorology, 104: 133-142

[13] Mistriotis, A., Bot, G.A., Picuno, P., Scarascia Mugnozza, G. 1997 Analysis of the efficiency of greenhouse ventilation with computanional fluid dynamics Agricultural and Forest Meteorology 85: 317-328

[14] Patankar, S.V 1980. Numerical Heat Transfer. Hemisphere.

[15] Pretot, S., Zeghmati, B., Palec, Le G., 2000. Theoretical and experimental study of natural convection on a horizontal plate. Applied Thermal Engineering, 20: 873891

[16] Popovski, K., 1986. Location of heating installations in greenhouses for low temperature heating fluids. In: Industrial thermal effluents for Greenhouse Heating. European Cooperative Networks on Rural Energy. CNRE Bulletin No.15, pp.51-55. 1986 Procceedings of CNRE Workshop, Dublin, Ireland.

[17] Roy, J.C., Boulard, T., Bailley, Y., 2000. Characterisation of the heat transfer from heating tubes in a greenhouse. E-Proceedings, AGENG 2000, Warwick UK.

[18] Sase, S., Takakura, T., Nara, M.,1984. Wind tunnel testing on airflow and temperature distribution of a naturally ventilated greenhouse. Acta Horticulturae 148: 329 37.

[19] Teitel, M. and Tanny, J., 1998. Radiative Heat Transfer from Heating Tubes in a Greenhouse. Journal of Agricultural Engineering Research 69: 185-188.

N. Tadj (1), T. Bartzanas (2), B. Draoui (1), G. Theodoridis (3) and C. Kittas (4)

(1) University Center of Bechar, Institute of Mechanical Engineer P.O. Box 417, 08000 Bechar, Algeria. E-mail: Tadjnacima@gmail.com.

(2) Centre for Research & Technology-Thessaly, Institute of Technology & Management of Agricultural Ecosystems, Technology Park of Thessaly 1st Industrial Area of Volos-Greece.

(3) Flow Dynamics Hellas S.A. Simulation - Measurement - Optimization-Control 21 Ant. Tritsis str. GR-57001 Thessaloniki Greece.

(4) University of Thessaly, School of Agricultural Sciences, Department of Agriculture, Crop Production and Agricultural Environment, Volos, Greece.

Table 1: Greenhouse characteristics and boundary conditions used in the simulations. Parameters Value Greenhouse characteristics number of spans 1 length, m 20 width, m 8 side height, m 2.4 ridge height, m 4.1 Temperature of the roof, [degrees]C 10 of the ground, [degrees]C 30 of heating pipes, [degrees]C 50 of greenhouse walls, [degrees]C adiabatic Plant canopy height, m 1.5 permeability 0.395 pressure loss coefficient 0.2

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Author: | Tadj, N.; Bartzanas, T.; Draoui, B.; Theodoridis, G.; Kittas, C. |
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Publication: | International Journal of Applied Engineering Research |

Article Type: | Report |

Date: | Sep 1, 2008 |

Words: | 2850 |

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