Measurement and simulation of climate inside Almerı́a-type greenhouses using computational fluid dynamics

Agricultural and Forest Meteorology 125 (2004) 33–51

Measurement and simulation of climate inside Almer´ıa-type greenhouses using computational fluid dynamics Francisco Domingo Molina-Aiz∗ , Diego Luis Valera, Antonio Jesús Álvarez Department of Rural Engineering, University of Almer´ıa, C/Cañada de San Urbano s/n, 04120 Almer´ıa, Spain Received 7 October 2003; received in revised form 16 March 2004; accepted 27 March 2004

Abstract In this paper, the effect of wind speed on the natural ventilation of an Almer´ıa-type greenhouse is analysed by means of computational fluid dynamics (CFD), using the commercial program ANSYS/FLOTRAN v6.1 based on the finite elements method. The experiment was carried out in an Almer´ıa-type greenhouse equipped with top and side ventilation. The vertical profiles of air velocity were measured with a hot bulb anemometer and visualised by means of a smoke tracing technique. The airflow through the insect-proof screens and the crop were described by means of an approach to porous media. Two-dimensional simulations in a steady state, which described the turbulent transfers by means of the standard K − ε turbulence model, were also carried out. Cooler, denser air entered through sidewall openings and left the greenhouse through the roof window when the wind speed exceeded 1 m s−1 . The importance of roof ventilators for efficient ventilation in Almer´ıa-type greenhouses was observed. The air temperature distribution shows a gradient from the sidewalls towards the centre of the greenhouse due to the movement of the hot air rising towards the roof vent, and a vertical gradient due to the movement of the air above the surface of the ground absorbing solar energy at floor-level. Maximum air velocity inside the greenhouse was reached near the side vents, with the lowest values observed in the middle of the greenhouse. The velocity decrease produced in the windward opening between the outside and inside of the greenhouse was 75–85% in every case. The air velocity in the leeward area remained more or less constant around 0.3 m s−1 , as result of the “chimney effect”. The model was verified by comparing the numerical results with experimental data. The differences between values predicted by the CFD models and those measured were from 0.0 to 0.36 m s−1 for air velocities, and from 0.1 to 2.1 ◦ C for air temperatures. © 2004 Elsevier B.V. All rights reserved. Keywords: Greenhouse; Ventilation; Wind speed; Inside climate heterogeneity; Modelling; CFD

1. Introduction Ventilation is the main climatic control method of greenhouses in the province of Almer´ıa where there are more than 27 000 ha of greenhouses. Nowadays the Almer´ıa-type greenhouse is in course of standard∗ Corresponding author. Tel.: +34-950-015449; fax: +34-950-015546. E-mail address: [email protected] (F.D. Molina-Aiz).

isation, since in the few last years Almer´ıa manufacturers are exporting this greenhouse to other countries and climatic areas such as Mexico, Colombia, Morocco and China. Natural ventilation is the system generally used to control the climate of the greenhouse, it requires less energy, less equipment operation and maintenance and it is much cheaper that other systems of controlling greenhouse air temperature. During the summer, the main reasons for its use are to lower temperatures and to increase air humidity; while during

0168-1923/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.agrformet.2004.03.009

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Nomenclature cp Cd Cε1 Cε2 Cφ Cµ gz G h0 k K Kp l0 L P Rx Sφ t T u u∗ ui w x Y z z0

specific heat of air at constant pressure (J kg−1 K−1 ) drag coefficient of the vegetation first turbulent model coefficient (1.44) second turbulent model coefficient (1.92) transient and advection coefficient fitting parameter of the turbulent model (0.09) acceleration due to gravity (m s−2 ) ventilation rate (m3 s−1 ) opening height (m) von K´arm´an’s constant turbulent kinetic energy (m2 s−2 ) permeability of the porous medium (m2 ) opening length (m) leaf area index (m2 m−2 ) atmospheric pressure (Pa) horizontal distributed resistance (Pa m−1 ) source term time (s) temperature (K) horizontal air velocity (m s−1 ) friction velocity (m s−1 ) orthogonal velocities, u1 = u, u2 = w (m s−1 ) vertical air velocity (m s−1 ) horizontal distance (m) inertial factor of the screen vertical distance (m) roughness length (m)

Greek symbols α porosity of the insect-proof net (m2 m−2 ) ε turbulence dissipation (m2 s−3 ) Γ φ diffusion coefficient φ studied variable λ air thermal conductivity (W m−1 K−1 ) µ dynamic viscosity of the fluid (kg s−1 m−1 ) µe effective viscosity of the fluid (kg s−1 m−1 ) µt turbulent viscosity of the fluid (kg s−1 m−1 ) ρ air density (kg m−3 ) σ K turbulent model constant for turbulent kinetic energy (1.0) σε turbulent model constant for turbulence dissipation (1.3) Φ viscous heat generation term

the winter, the ventilation should reduce excessive humidity. In the Mediterranean region due to the high levels of radiation during the greater part of the year an effective ventilation system is essential. However, very little design information is available for naturally ventilated Almer´ıa greenhouses. The effectiveness of the ventilation may be related with the spatial distribution of cool air to maintain particular climatic conditions for the crop. The greenhouses configuration and construction, and especially the location of inlets and outlets related to the direction of the dominant local winds, are the most important factors that affect the level of ventilation. The external flows around the greenhouse are generally very complicated, involving important gradients of pressure, the bending of the air flow with whirls, separation and regrouping with increases and suppresses turbulence. The driving force of the natural ventilation is the combination of the effects of wind and buoyancy, and its relative importance depends on wind speed and the temperature differences between the inside and outside of the greenhouse. Generally, the effect of the wind prevails over buoyancy (de Jong, 1990; Fernández and Bailey, 1992). Even now, most of the studies carried out on natural ventilation have been based on estimates of a global rate of air exchange by means of the tracer gas technique (Bot, 1983; Kittas et al., 1996), simulations of a homogeneous temperature of the air by means of energy balance models (Fernández and Bailey, 1992) and wind-tunnels (Sase et al., 1984). However, these techniques only allow the prediction of a general ventilation rate in the greenhouse. Direct estimates of the airflow through the windows have also been carried out by the measurement of pressure difference in several greenhouses (Kittas et al., 1996). Even so, there is an important lack of information on the development of the airflow within the greenhouses driven by wind or by buoyancy forces. Consequently, most of the authors represent the climatic conditions in the greenhouse as uniform temperature and air velocities without differentiating between the volume occupied by the crop and the area above the plants. Moreover, some measurements of the air velocities through the windows and inside greenhouses have recently been taken using one-dimensional (Boulard et al., 1997) and three-dimensional sonic anemome-

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ters (Boulard et al., 2000) and by means of hot wire anemometry (Boulard et al., 1998; Molina-Aiz et al., 2003). An analysis of the ventilation induced by both temperature differences and wind in scale models has also been conducted (Montero et al., 2001). Given the importance of natural ventilation in the climatic control of greenhouses there have been many studies with the objective of establishing a numerical function which directly relates ventilation rate with different environmental variables, such as wind speed and direction, the solar radiation or internal/external temperatures. Until now, because of the great variability of the climatic parameters involved nobody has found a model of greenhouse ventilation for general application (Bailey, 1999). The first simulations by means of computational fluids dynamics (CFD) for the study of the ventilation in greenhouses were carried out by Okushima et al. (1989) who compared this numerical method with the experimental results obtained in a wind-tunnel (Sase et al., 1984). Although their results showed little correlation with the experimental data, probably due to the limited power of the available computer resources at that time, they provided important new information on the patterns of flow inside the greenhouses. This technique was not used for some time until the simulations of CFD were compared in a two-span greenhouse with the data obtained by means of sonic anemometry (Bot et al., 1996). Recent advances in CFD programs enable easier studies of the scalars and vector fields present within the greenhouse climate by means of the resolution of the transport equations of the air that governs the ventilation. This technique lets us consider all the climatic variables as well as the characteristics of the greenhouse, its ventilation system (geometry, location and presence of insect-proof screens) and those of the crop being cultivated. Mistriosis et al. (1997) studied Mediterranean type greenhouses using CFD in a two-dimensional grid and they concluded that CFD is a powerful tool to develop improvements in the design of greenhouses for efficient ventilation. Kacira et al. (1998) also evaluated the ventilation of a multi-span sawtooth greenhouse for several environmental conditions. Al-Helal (1998) utilised a CFD model to study natural ventilation in arid region greenhouses, and compared the simulation results with those determined from energy and mass

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balance models with good agreement. Boulard et al. (1999) studied the natural ventilation (thermal and wind driven) in a reduced-scale greenhouse in two dimensions. Al-Arifi et al. (2001) studied the air movement in greenhouses equipped with a fan. Reichrath et al. (2000) using experimental data obtained good agreement of CFD prediction of the internal climate of a commercial 60-span Venlo-type glasshouse containing tomato crops. Haxaire (1999) was the first to study the effects of the crop on the airflow inside the greenhouses, determining the drag effects of the plants. He experimented in wind-tunnels, where he studied the relationship between the crop leaf area index and the pressure drop generated for different values of air velocity. This relationship has been used in later studies of CFD to investigate the influence of the canopy on the inside climate (Haxire et al., 2000). He calculated the value of the drag coefficient of the canopy. Lee and Short (2000) also developed a model of CFD to determine the relationship between the air velocity and the pressure drop in the crop. Recently, Bartzanas et al. (2002) studied the effect on the ventilation of a tunnel greenhouse caused by the presence of insect-proof screens. The effect of very fine anti-thrips and anti-aphids nets placed over the ventilation openings has been simulated in three dimensions in commercial greenhouses (Fatnassi et al., 2003). The airflow in Almer´ıa-type greenhouses has also been analysed by means of two-dimensional (Molina-Aiz et al., 2003) and three-dimensional (Campen and Bot, 2003) simulations. Computational fluids dynamics is an advanced technique for design in engineering, it is increasingly being used in other types of agricultural studies, such as the ventilation of livestock houses (Bjerg et al., 2001) and in experiments of the aerodynamic resistance of greenhouse structures (Mistriotis and Briassoulis, 2002). The CFD technique is recognised as a powerful tool to model the climate generated inside the greenhouses and for the development of structural design improvement with regard to ventilation effectiveness. This technique has been used in several climatic regions and in the greenhouses most commonly used (multispan and Venlo) in Europe and United States, however the results achieved cannot be generalised. Consequently, it is necessary to carry out a systematic study of the Almer´ıa-type greenhouses to identify

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the ventilation systems characteristics that provide effective control of the inner climatic conditions. The main objective of this particular study was to determine by means of a CFD program the influence of the wind speed on the inner climate of the greenhouse. The natural ventilation directly affects heat and mass transfers between internal and external environment. The outside–inside air exchanges also influence the relative humidity and carbon dioxide concentration. As a consequence, the airflow affects crop development and production. Considered in this way, ventilation is one of the most important production factors, since it influences climatic control and the quality of the crop for much of the year.

2. Materials and methods 2.1. Experimental set-up 2.1.1. Site and greenhouse configuration The experimental greenhouse is a full-scale Almer´ıa-type with a “raspa y amagado” structure, the most common in the province. It is located in the University of Almer´ıa (longitude: 2◦ 24 W, latitude: 36◦ 49 N, altitude: 2 m), on the south coast of Spain. The greenhouse is located just 10 m from the beach. The surface area of the greenhouse was 1850 m2 (40–42 m long and 43–47 m wide). The five-span

greenhouse was 3.2 m high with the gutter at 2.6 m (Fig. 1). The ridge of the greenhouse was orientated northwest–southeast so it was perpendicular to the prevailing wind direction in the area. The size of the roof vent was 2 m × 30 m; it was a rollup ventilator located in the middle of the greenhouse. Each wall was equipped with a variable size continuous side opening (1.35 m × 42 m). Insect-proof screens covered all the vents with a mesh 0.4 mm ×0.8 mm. The greenhouse was covered with a 0.2 mm thick three-layer co-extruded film (composed of a layer of ethylene vinyl acetate inserted between two polyethylene films). The first set of measurements were taken on 18 and 19 April 2003, around 19:30 and 18:30 h, when exterior climatic conditions were stable (Table 1) and when there were plants inside the greenhouse. During these experiments, with a crop inside the greenhouse, the roof and side ventilation area were 1.6 and 1.5% of ground surface covered by the greenhouse, respectively. The roof opening size was 30 m × 1 m and both side openings were 0.35 m × 42 m. The crop was melon (cv. Galia) 2 m height, planted on 20 February 2003, with a density of 1.25 plants m−2 . The soil of the greenhouse was imported fine sand with drip irrigation. A second set of measurements were taken, in the empty greenhouse, on 13 and 16 July 2003, around 20:15 and 14:30 h, respectively. In this situation without a crop, the opening rates reached its maximum

Fig. 1. A sketch of the five-span commercial Almer´ıa-type greenhouse and outside weather station used in this study.

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Table 1 Statistics of the weather conditions during the measurements (mean and S.D.)

Wind speed at 4 m height (m s−1 ) Wind direction (◦ ) Global radiation (W m−2 ) Outside air temperature (◦ C)

18 April 2003, 19:15/19:45 h (yes)

19 April 2003, 18:15/18:45 h (yes)

13 July 2003, 20:00/20:30 h (no)

16 July 2003, 14:15/14:45 h (no)

Mean

S.D.

Mean

S.D.

Mean

S.D.

Mean

S.D.

1.8

0.6

7.7

1.7

5.0

0.6

1.0

0.7

208 22 17.1

17 1 0.1

195 192 18.3

12 34 1.9

187 7 24.1

11 3 0.4

222 575 28.0

11 11 0.5

Yes and no indicate the presence of a crop.

value, 3.2% of floor surface covered by the greenhouse for the roof and 6% for the side vents. 2.1.2. Instrumentation Internal air temperature and relative humidity were measured by means of a data logger HOBO® Pro RH-Temp H08-032-08 (Onset Computer Corp., Pocasset, USA), equipped with temperature and humidity probes. This measured the temperature in a range from −20 to 70 ◦ C with accuracy of ±0.3 ◦ C and of relative humidity of 0–100% with an accuracy of ±3%. The memory capacity was 65 292 data and measurements were taken every 30 s. Eighteen probes were distributed under the five ridges of the greenhouse (Fig. 2) in a cross-section at the centre of the greenhouse and at different heights (0.5, 1.5 and 2.5 m). Sensors were also located at another three heights (1, 2 and 3 m) in the centre of the greenhouse under the roof vent. Temperature sensors were protected against the direct solar radiation with a passive solar radiation shield. However, the temperature sensors were not ventilated to avoid the air mixing from a different height. It was essential that temperature measurements at different heights inside the greenhouse were made at the same time.

The outside wind speed was recorded by means of a cup anemometer DAVIS 7911 (Davis Instrument Corp., Hayward, USA) located in one of the front walls from the greenhouse at a height of 4.0 m from the ground, with a measured range of 0–78 m s−1 , an accuracy of ±5% and a resolution of 0.09 m s−1 . The wind direction was measured with a vane (accuracy ±7◦ and resolution 1.4◦ ). Solar radiation was measured with a LI-200SA pyranometer sensor (Li-Cor Inc., Lincoln, USA). This photovoltaic-based sensor cover a limited spectral range (400–1100 nm) and had an accuracy of ±5%. These three sensors were connected to a data logger HOBO® H08-006-04 for data recording. The measurement of air velocity at the same 18 points where the fixed temperature sensors were located inside the greenhouse was taken using a multifunction digital handheld instrument TESTO® 445 (Testo S.A., Cabrils, Spain) with a hot bulb probe, for the measurement of velocities of 0–10 m s−1 , with an accuracy of ±0.03 m s−1 and resolution of 0.01 m s−1 . The omni-directional hot bulb anemometer measures the magnitude of the speed vector. The equipment also contains a temperature probe (thermistor NTC) with a range of −20 to 70 ◦ C and an accuracy of ±0.4 ◦ C. We also measured temperature and air velocity with the TESTO 445 multifunction instrument at 0.5 and

Fig. 2. Temperature and humidity sensors positions in the central section of the greenhouse (⊗). Surface temperature measurements (×) and temperature measured with the TESTO 445 multifunction instrument (䊐).

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1.5 m height and at a distance of 0.5 m from the two side vents. We used smoke pencils to indicate the direction of local airflow. Production of smoke was carried out at the same points where inside air velocity and temperature measurements were made (Fig. 2). Airflow was also observed at three points (0.5, 1.5 and 2.5 m height) under each greenhouse gutter. Smoke pencils provide a quick visualisation of the path of the airstreams and thus help identify pressure differentials. Placing two small smoke incense sticks we obtained information about the velocity and direction of the air inside the greenhouse. Smoke pencils was also used for detecting air leaks in the greenhouse. For air velocities greater than 0.2 m s−1 the smoke generated by an incense stick follows the airflow direction. Although, in some points the mean air velocity was lower than this minimum value (Figs. 3 and 4), and the smoke tended to ascend toward the cover, airflow could be visualised keeping in this place the smoke pencil during some seconds. The air velocity variations at higher speeds showed the airflow direction. In places where a doubt about airflow direction existed, the smoke was placed in several points to verify the results. Using smoke pencils near vents we can determine the exit or entrance of air in the greenhouse. We applied the smoke in areas close to the doors and the front vents, which were closed at the time of the tests, to make sure no air was flowing through these

openings. This ensured that a traverse flow did not exist and that the front openings did not act as entrance or exit of air at the time of measurements. Any transverse airflow in the greenhouse section would invalidate the symmetry assumption and the validity of the two-dimensional simulations. The temperatures of the greenhouse walls, the internal soil surface and crop were measured with an infrared hand-held thermometer OMEGA® OS540 (Omega Engineering Inc., Stanford, USA) with a measurement range of −20 to 420 ◦ C, accuracy of ±2% and resolution of 1 ◦ C. The emissivity of the sensor was fixed to a value of 0.95 that corrected the temperatures using an emissivity of 0.83 for the greenhouse walls and 0.89 for the sandy floor in certain areas, for a sensor of 6–14 ␮m wavelength. The temperatures corrections were verified by means of measurements with a thermistor PY-15 (Amprobe Europe Gmbh, Mönchengladbach, Germany) with a range of −40 to +150 ◦ C (accuracy: ±1.1 ◦ C, resolution: 0.1 ◦ C). Measurements of inside air velocity and surface temperatures took about 25–30 min. With only one sampling position possible at any one time, a difficulty arises from how to deal with changing external conditions throughout the time needed to measure the 22 different measurement positions for air velocity, and 16 for surface temperatures, within the central section (Fig. 2). This problem was overcome using the average values during the experiments for wind speed and the difference in air temperature between

Fig. 3. Air velocity vector in the vertical plane in the middle of the greenhouse with a crop for a southwest wind of 1.8 m s−1 : (a) experimentally measured flow vector field with hot bulb anemometer; (b) numerically obtained flow vector field (measurements of 18 April 2003 at 19:30 h).

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Fig. 4. Air velocity vector in the vertical plane in the middle of the empty greenhouse for a southwest wind of 1.0 m s−1 : (a) experimentally measured flow vector field with hot bulb anemometer; (b) numerically obtained flow vector field (measurements of 16 July 2003 at 14:30 h).

the centre of the greenhouse and the external air, as reference (Boulard et al., 2000). Physical values can be deduced from the normalised parameters knowing the average value of the scaling parameters during the experiments (Table 1). 2.2. Simulation The CFD technique numerically solved the Navier– Stokes equations and the mass and energy conservation equations. The application of CFD for the analysis of ventilation problems in buildings and mainly in greenhouses, offers important information on the influence of wind and temperature on ventilation. In this work two-dimensional simulations have been carried out by means of a commercial CFD software packet (ANSYS/FLOTRAN v6.1) that applies the finite element (FE) method for the discretisation of the set of equations involved in ventilation processes. In general, as has already been mentioned, ventilation studies in greenhouses published until now have used CFD programs based on the finite volumes (FV) method. This method uses the integral form of the conservation equations as its starting point. The solution domain is subdivided into a finite number of contiguous control volumes. At the centroid of each CV lies a computational node at which the variable values are to be calculated. Interpolation is used to express variable values at the CV surface in terms of the nodal values. Surface and volume integral are approximated

using suitable quadrature formulae. As a result, one obtains an algebraic equation for each CV, in which a number of neighbour nodal values appear (Ferziger and Peric, 2002). The finite element procedure also begins with the division of the continuum region of interest into a number of simply shaped regions called elements, whose behaviour is specified by means of a finite number of parameters (Zienkiewicz, 1977). The given function is approximated locally over each element by continuous functions, which are uniquely defined in terms of the values of the function (and possibly its derivatives) at the corners on each element (nodes). Within each element, the dependent variables ui , P and T are interpolated by functions of compatible order, in terms of the values to be determined at a set of nodal points. The distinguishing feature of FE methods is that the equations are multiplied by a weight function before they are integrated over the entire domain. In the simplest FE methods, the solution is approximated by a linear shape function within each element in a way that guarantees continuity of the solution across element boundaries. Galerkin’s method of weighted residuals was used to form the element integrals. The weighting function for the element was also the shape function (Zienkiewicz, 1977). This approximation is then substituted into the weighted integral of the conservation law and the equations to be solved are derived by requiring the derivative of the integral with respect to each nodal value to be zero; this corresponds to selecting the best solution within the set of allowed functions (the one with minimum

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residual). The result is a set of non-linear algebraic equations (Ferziger and Peric, 2002). Once the structure type (dimensions and symmetries), the openings characteristics (location, size and opening degree) and the outside climatic parameters (temperature, speed and wind direction) are defined the CFD technique allows a systematic study of the influence of the greenhouse and its ventilation system design on the inside airflow and temperature distribution. The model size which mathematically analysed the greenhouse’s physical system, was defined by the number of nodes and elements that represent the finite element grid. 2.2.1. Numerical approach The Bernoulli relation, widely used to evaluate ventilation in greenhouses, does not allow the determination of spatial heterogeneity. To access the spatial scalars and vector fields it was necessary to solve the three-dimensional conservation equations describing the transport phenomena for steady flows in free convection. The conservation equations of the variable φ in three dimensions that describe the transport phenomena for flows in free convection are of the general form (Ferziger and Peric, 2002): ∂(ρCφ φ) ∂(ρui Cφ φ) ∂2 φ + = Γφ 2 + S φ ∂t ∂xi ∂xi

(1)

where φ represents the common variable of interest as a concentration of the transported quantity in a non-dimensional form; ρ the density of the air; Cφ the advection coefficient; ui the component of velocity vector in the direction i; Γ φ the diffusion coefficient; and Sφ the source term. These variables with their different terms are shown in Table 2 for a steady state

(first term in Eq. (1) is equal to zero) and incompressible flow. The viscous dissipation term in tensor notation is
 ∂ui ∂uk ∂ui Φ=µ + (2) ∂xk ∂xi ∂xk Numerical codes using a spatial discretisation are needed to solve the set of equations described by Eqs. (1) and (2) and Table 2. These CFD programs characterise the airflow inside a finite spatial domain constituted by the different elements of a grid. 2.2.2. Discretisation of the computational domain The software packet of modelling ANSYS/ FLOTRAN v6.1 is applied to obtain both the temperature distribution and airflow pattern. The discretisation is performed with triangular and quadrilateral elements. For the considered problem each node has 6 degrees of freedom (DOF): temperature T, pressure P, horizontal velocity u, vertical velocity w, turbulent kinetic energy K, and turbulent kinetic energy dissipation rate ε. The grid was an unstructured grid with higher density at the vent openings, where the flow was subject to strong gradients. The meshing density of areas next to the openings was greater in the case of the greenhouse with crop where the size of the elements is very small. The computational grid in this situation was denser because we refined the area between the crop and the roof opening. This refinement allows a gradual transition from quadrilateral to triangular elements. The use of only triangular elements in the model of the empty greenhouse, allowed the reduction of the grid density and the number of elements without convergence problems or lack of precision. The quality of the grid was checked carrying out two levels of modelling. A

Table 2 Reduced form of the variables, φ, advection coefficient, Cφ , diffusion coefficient, Γ φ , and source terms, Sφ , of the conservation equations defined by Eq. (1) Conservation equations

φ

Variable

Cφ

Γφ

Sφ

Mass Momentum for x direction Momentum for y direction Energy Turbulent kinematic energy Turbulent dissipation rate

1 vx vz T K ε

Density Horizontal air velocity Vertical air velocity Temperature Turbulent kinematic energy Turbulent dissipation rate

1 1 1 cp 1 1

0 µe µe λ µt /σ k µt /σε

0 −∂P/∂x + Rx ρgz − ∂P/∂z Φ µt /µΦ − ρε Cε1 µt /µΦε/K − Cε2 ρε2 /K

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number elements close to the maximum level allowed by the software used in this work (64 000 elements) and another around the half (32 000 elements). In the case of the greenhouse with crop the necessary grid refinement and the problems of convergence did not allow a reduction in the number of elements and we used a 58 300 elements grid. In the case of the empty greenhouse a diminution in the number of elements did not cause a significant variation in the accuracy of simulations (+0.2% of the measured temperature and −0.2% of the measured air velocity), neither it produce convergence problems. The relatively small accuracy increase between the different grids indicates that the grid dependency on the solution has become minimal. Finally, a grid with 28 200 elements was used because it consumes the least computational time with reasonable accuracy. It results from an empirical compromise between a dense grid, associated with a long computational time, and a less dense one, associated with a small deterioration of the simulated results. We selected a large domain including the greenhouse (95 m long and 10 m high). This domain was chosen after modelling a domain of 200 m × 20 m and not obtaining a significant improvement in the results (0% for temperature, and 1.6% for air velocity). The areas occupied by the crop and the insect-proof screens, have been simulated with rectangular elements in a mapped grid, that has a regular pattern with obvious rows of elements, while the other elements were triangular constituting a unstructured grid. The non-rectangularity of side vents was taken into account for the computation of the rectangular area used in the CFD simulations. The difference between the real opening area and the rectangular area with the same maximum width and height was 8% in the greenhouse with the crop and 10% in the empty greenhouse. The side opening vents were simulated as a rectangular surface with an area equivalent to the real window area, reducing the height of the openings from 0.38 to 0.35 m in the first case and from 1.5 to 1.35 m in the second. For the ANSYS/FLOTRAN CFD elements, the velocities are obtained from the conservation principle, the pressure is obtained from the conservation of mass principle and the temperature is obtained from the law of conservation of energy.

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2.2.3. Boundary conditions CFD involves a representation of flow, heat and mass transfer by differential forms of the conservation equations, their approximation by difference techniques and the solution of the resulting set of simultaneous algebraic equations to appropriate boundary conditions. Such boundary conditions contain the effects of external factors on the flow and temperature. A wind profile was imposed 25 m from the greenhouse as the dynamic boundary condition for ambient air and null pressure gradients in the air were assumed at the limits of the computational domain. The mean wind speed profile can be described as a logarithmic function of elevation (e.g. Rosenberg et al., 1983):
 u∗ z u(z) = ln (3) k z0 where u(z) is the horizontal wind speed as a function of the height z; u∗ the friction velocity; k the von Kármán’s constant; and z0 the surface roughness length. The surface roughness is a parameter describing the logarithmic decrease of wind speed with height due to friction with the ground, and depends on the terrain type. The value used for the roughness, z0 = 0.015, has been deduced from the fit between the experimental data and the theoretical relation expressed by Eq. (3). This value is close to the value (z0 = 0.01) given by the Eurocode for the rough open areas without obstacles (CEN, 1995). Fixed air temperature conditions were also imposed at the limits of the domain, the greenhouse cover and ground. No radiation was simulated directly, but the solar radiation has been taken into account, in an indirect way in the model. Measured surface temperatures (plastic cover and soil) depend on solar radiation and the surface absorption coefficients. The boundary conditions for temperature at all surfaces of the greenhouse are shown in Table 3. Table 1 shows the statistical values that reflect the variability of the climatic parameters during the experimental measure period. The boundary conditions prescribed a wall-type boundary condition (zero velocity) along the floor and the roof. The Boussinesq-approximation cannot be used for the temperature dependency of density in ANSYS/FLOTRAN as is possible in case of FV codes. With the usual Boussinesq-approximation the density becomes constant in all equations except for the

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Table 3 Measured boundary conditions for the experimental greenhouse

Outside temperature (K) Southwest outside surface soil temperature (K) Northeast outside surface soil temperature (K) Friction velocity (m s−1 ) Covering material temperatures (K) Span 1 Span 2 Span 3 Span 4 Span 5 Soil surface temperature inside the greenhouse (K) Southwest side area (0–4 m) Southwest area (4–22 ma ; 4–10.4 mb ) Southwest area (10.4–18.2 mb ) Centre area (22–25 ma ; 18.2–25.7 mb ) Northeast area (25–41 ma ; 25.7–33.3 mb ) Northeast area (33.3–41 mb ) Northeast side area (41–45 m) Values of the K − ε model Turbulent kinetic energy (m2 s−2 ), K = u2∗ Cµ−0.5 Turbulent dissipation (m2 s−3 ), ε = u3∗ [k(z + z0 )]−1

18 April 2003, 19:30 h (yes)

19 April 2003, 18:30 h (yes)

13 July 2003, 20:15 h (no)

16 July 2003, 14:30 h (no)

290.1 295.0 295.4 0.13

291.3 298.3 298.5 0.56

297.1 301.2 304.5 0.36

301.0 316.4 314.8 0.07

293.4 293.8 294.2 293.8 293.8

293.4 294.1 295.5 294.5 293.4

302.3 303.0 303.0 304.7 302.3

316.6 315.3 316.3 317.3 319.3

294.3 298.5 – 301.5 299.0 – 294.9

299.3 305.3 – 307.3 307.7 – 301.7

309.2 311.2 311.2 306.4 312.4 310.4 305.7

319.2 322.7 321.3 324.7 324.3 324.6 320.3

0.056 0.0055/(z + z0 )

1.045 0.4390/(z + z0 )

0.432 0.1166/(z + z0 )

0.016 0.0009/(z + z0 )

Yes and no indicate the presence of a crop. a Distance from the windward side walls with crop. b Distance from the windward side walls with an empty greenhouse.

buoyancy term in the momentum equations. However, in the ANSYS-model the temperature, which affects the density, acts as the driving force of ventilation, was simulated in all three equations (Table 4). 2.2.4. Model of the turbulent flow The presence of turbulence in a fluid flow is indicated by fluctuations of the velocity components and quantities transported by the flow, even when the boundary conditions for the problem studied are kept constant. As the airflows were highly turbulent, turTable 4 Value of the properties used to simulate the air (ANSYS, 2001) Variable

Value or model (J kg−1

K−1 )

Specific heat Thermal conductivity (W m−1 K−1 ) Dynamic viscosity (kg m−1 s−1 ) Atmospheric pressure (Pa) Density (kg m−3 )

cp = 1004 λ = 2.502 × 10−3 T 3/2 / (T + 194.44) µ = 1.4592 × 10−6 T 3/2 / (T + 110.56) P = 101 354 ρ = 101 354/(287.05T)

bulence models must be introduced in the Reynolds equations, written to separate the mean flow from its fluctuating components. The standard K − ε model (Launder and Spalding, 1974) assuming isotropic turbulence was adopted to describe turbulent transport. This model was used because their result corresponds better with experimental data for typical ventilation flows in greenhouses (Haxire et al., 2000; Kacira et al., 1998). The complete set of the equations of the K−ε model can be found in the literature (Launder and Spalding, 1974; ANSYS, 2001). 2.2.5. Simulation of the insect-proof screens In order to include the effect of the nets placed over the vents in the study, the insect-proof screens were considered as porous media. The flow of air through a porous medium can be described by means of the Darcy–Forchheimer equation:     ∂P µ Y =− |u|u (4) u+ρ 1/2 ∂x Kp Kp

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43

where µ is the dynamic viscosity of the fluid, Kp the permeability of the porous medium and Y the non-linear momentum loss coefficient or inertial factor. Eq. (4) shows how fluid velocity is related to pressure drop, through the viscous resistance force, which appears due to the momentum transfer at the fluid in1/2 terface (µ/Kp ) and the pore inertia effects (ρY/Kp ). This term was introduced as the resistance distributed term in the porous medium (Rx ) in the conservation of momentum equations (for vx ), defined by Eq. (1) and values showed in Table 2. The values of the aerodynamic properties of the porous medium used as boundary conditions were calculated using relations, which correlate permeability, Kp and the inertial factors, Y with the porosity of the screen (Miguel, 1998):

standard fluid flow equations. The drag form appearing in the source terms of momentum equations was modelled as (Yamada, 1982):

Kp = 3.44 × 10−9 α1.6

(5)

3. Results

Y = 4.36 × 10−2 α−2.12

(6)

3.1. Measured air velocities

Screen porosity was determined by magnifying one sample of 1 cm2 with a microscope equipped with a digital camera and by measuring the area filled with air and the area occupied by solid matrix and air (Valera et al., 2003), obtaining a value of α = 0.394. 2.2.6. Simulation of the vegetable cover The crop was also simulated using the porous medium approach by the addition of a momentum source term, due to the drag effect of the crop, to the

∂P = −Cd Lρu2 ∂x

(7)

where L is the crop leaf area index and Cd the total canopy drag coefficient. A drag coefficient Cd = 0.32 had been used since we did not have information about its value for a melon crop. Boulard and Wang (2002) have also successfully used this value of drag coefficient for a lettuce crop. Haxaire (1999) used wind-tunnel facilities to calculate this value of drag coefficient for a mature greenhouse tomato crop. The leaf area index was measured (L = 0.88 m2 m−2 ).

Air velocity inside the greenhouse had maximum values near the openings, whereas the air velocity was low in the middle of the greenhouse. We observed a counter flow with respect to outside wind direction in the leeward side of the greenhouse (Figs. 3a–6a). A velocity scale is also given in Figs. 3–6 to facilitate the reading of the velocity at each point. The longitudinal profile of air velocity at 1.5 m height was almost symmetrical at low wind speed, and was altered by an increase in wind speed (Fig. 7). The

Fig. 5. Air velocity vector in the vertical plane in the middle of the greenhouse with a crop for a southwest wind of 7.7 m s−1 : (a) experimentally measured flow vector field with hot bulb anemometer; (b) numerically obtained flow vector field (measurements of 19 April 2003 at 18:30 h).

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Fig. 6. Air velocity vector in the vertical plane in the middle of the empty greenhouse for a southwest wind of 5.0 m s−1 : (a) experimentally measured flow vector field with hot bulb anemometer; (b) numerically obtained flow vector field (measurements of 13 July 2003 at 20:15 h).

velocity decrease produced in the windward opening between the outside and inside of the greenhouse was 75–85% in every case. The air velocity in the leeward area remained more or less constant around 0.3 m s−1 , as result of the “chimney effect”. This air velocity seems not depend on the wind speed, since the airflow entering through the windward opening, exited through the roof vent after the air had been heated,

and airflow had not enough energy to cross the whole greenhouse. In the greenhouse with plants, the air velocity at 1.5 m height was usually lower in the central area of the greenhouse, where the two currents coming from both side vents collided. The vertical profile of air velocity in the centre of the greenhouse shows a higher value about 2.5–3 m near the exit vent. For the high-

Fig. 7. Measured (points) and CFD simulated (lines) longitudinal air velocity profile at 1.5 m high for different wind speed. Greenhouse with crop: (+) u = 7.7 m s−1 (19 April 2003), (䊐) u = 1.8 m s−1 (18 April 2003); empty greenhouse: (䊊) u = 5.0 m s−1 (13 July 2003), (×) u = 1.0 m s−1 (16 July 2003).

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Fig. 8. Measured (points) and CFD simulated (lines) longitudinal air temperature profile at 1.5 m high for different wind speed. Greenhouse with crop: (+) u = 7.7 m s−1 (19 April 2003), (䊐) u = 1.8 m s−1 (18 April 2003); empty greenhouse: (䊊) u = 5.0 m s−1 (13 July 2003), (×) u = 1.0 m s−1 (16 July 2003).

est wind speed (7.7 m s−1 ) the air velocity increased above the crop. In the empty greenhouse maximum air velocity took place near the ground since the side vent openings were at a height of 0.3–1.6 m. 3.2. Measured air temperatures A strong vertical thermal gradient was observed in first metre above the floor of the greenhouse and temperature stayed very constant between 1 and 3 m height. The horizontal profile of temperatures in both experiments with high wind speeds (empty greenhouse and with crop) shows a thermal gradient between the cooled windward and hotter leeward areas (Fig. 8). In the greenhouse with plants, a hot air accumulation was observed in the leeward area (Figs. 9 and 10), mainly below 0.5 m where the airflow was smaller. Above this height, air temperature decreased due to the entrance of outside cooled air. When wind speed was not very high (u < 2 m s−1 ) hot air accumulation was observed in the sidewall and crop areas below the level where vents were located. With a higher wind speed, this heat accumulation disappeared near the windward sidewall, but it persists near the leeward one (Fig. 9).

In the greenhouse with a crop the temperature heterogeneity was greater at high wind speeds. The maximum temperature difference, with respect to the outside temperature, was 4.9 ◦ C when the radiation reached the highest value (192 W m−2 ) in spite of the existence of a strong wind (7.7 m s−1 ). The difference decreased to 3.1 ◦ C when the wind speed was 1.8 m s−1 due to the low radiation level (22 W m−2 ), recorded on 18 April at the time the measurements were taken (Table 5). In the greenhouse with crop the maximum air temperature took place in the centre of the greenhouse where smallest values of air velocity were measured (Fig. 8). In the empty greenhouse, the higher temperatures were reached in the leeward area of the greenhouse (Fig. 8). The measurements made in the empty greenhouse showed greater temperature heterogeneity at low wind speed (1.0 m s−1 ). The maximum temperature difference was 14.5 ◦ C, when the radiation reached the highest value (575 W m−2 ), and decreased to 5.5 ◦ C when the wind speed increased to 5.0 m s−1 and the radiation decreased to 7 W m−2 at nightfall (20:15 h). In the empty greenhouse, where the air velocity increased near the floor, a smaller horizontal thermal gradient was observed. The vertical thermal gradient

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Fig. 9. CFD computed contours of air temperature and measured soil surface (between small ticks) temperatures for a southwest wind of 7.7 m s−1 , when there was a crop in the greenhouse (measurements of 19 April 2003 at 18:30 h).

Fig. 10. CFD computed contours of air temperature and measured soil surface (between small ticks) temperatures for a southwest wind of 1.8 m s−1 , when there was a crop in the greenhouse (measurements of 18 April 2003 at 19:30 h).

Table 5 Summarised results (m s−1 )

Wind speed at 4 m height Air exchanges per hour (h−1 ) Minimum inside air velocity (m s−1 ) Maximum inside air velocity (m s−1 ) Average inside–outside temperature difference (◦ C)

18 April 2003

19 April 2003

13 July 2003

16 July 2003

1.8 6.2 0.06 0.4 3.1

7.7 14.1 0.22 1.29 4.9

5.0 40.8 0.13 1.15 5.5

1.0 7.0 0.08 0.72 14.5

in the first metre above the floor was 10 ◦ C when a high solar radiation (around 575 W m−2 ) produced a very high ground temperature, 52 ◦ C. Maximum temperatures were observed in the central and leeward areas when wind speed was low (u < 1 m s−1 ). With a crop, the vertical thermal gradient was 8 ◦ C for small radiation value (192 W m−2 ). 3.3. Numerical results Fig. 8 shows CFD predicted and measured air temperature profiles. It can be seen that numerical results of CFD models and those measured in the experimental greenhouse were very close. The differences between air temperatures measured into the greenhouse and those predicted by ANSYS/FLOTRAN were 0.1–2.1 ◦ C. Average differences between the computational and the experimental data were 0.71 ◦ C for temperature and 0.07 m s−1 for velocity. The air velocity measurements inside experimental greenhouse and those predicted by CFD models are shown

in Fig. 7. It can be seen that values for the measured and simulated results run close to each other. This was necessary in order to compare inside measured air velocities simulated by CFD models. The differences between air velocities predicted by CFD models and those measured were from 0.00 to 0.36 m s−1 (0–65%). In the greenhouse with a crop the numerical results show an incoming airflow at the two side openings, that leaves the greenhouse by the central roof vent, in agreement with the experimental measurements (Figs. 3b and 5b). There was an elevated heterogeneity in the canopy on the leeward side, which may have influenced the difference between the measured and simulated temperatures. The plants’ development was more heterogeneous in the leeward area, where differences in height between plants were more apparent. A similar airflow pattern was predicted in the empty greenhouse for wind speeds greater than 1 m s−1 . Both side openings acted simultaneously as inlets and hot

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Fig. 11. CFD computed contours of air temperature and measured soil surface (between small ticks) temperatures for a southwest wind of 5.0 m s−1 , in the empty greenhouse (measurements of 13 July 2003 at 20:15 h).

Fig. 12. CFD computed contours of air temperature and measured soil surface (between small ticks) temperatures for a southwest wind of 1.0 m s−1 , in the empty greenhouse (measurements of 16 July 2003 at 14:30 h).

air left the greenhouse through the roof opening located at the top of the middle span (Fig. 6b). The maximum differences between predicted and measured air velocity were observed during a sunny day 16 July at 14:30 h, when the hottest ground temperature was recorded inside the empty greenhouse (Table 3). We observed areas inside the greenhouse, mainly in the middle of greenhouse, with very low air velocities (0.05–0.1 m s−1 ). Consequently, the temperature gradually increased between the areas near the sidewall and the roof opening (Figs. 9 and 10). However, in the empty greenhouse, the leeward area was hotter than the windward (Figs. 11 and 12), despite the reverse flow observed for the low wind speed (Fig. 4b). 3.4. Ventilation performance Integrating air speed over a complete cross-section of the greenhouse openings allows for estimation of airflow rate G, as follows:  h0 G = l0 u dz (8) 0

For four cases studied (greenhouse with or without plants, and low or high wind speed) airflow rate was estimated according to Eq. (8). For the greenhouse with plants and high wind speed (7.7 m s−1 ), airflow rate was estimated as G = 21 m3 s−1 which allows 14.1 air renewals per hour. When the wind speed was very low (1.8 m s−1 ) the airflow decreased to 9.1 m3 s−1 (6.2 air renewals per hour). For an empty greenhouse airflow

rate was estimated as G = 60 m3 s−1 (40.8 h−1 ) for a wind speed of 5.0 m s−1 , and was G = 10 m3 s−1 (7.0 h−1 ) for a wind speed of 1.0 m s−1 . 4. Discussion At low wind speed (1.8 m s−1 ), the buoyancy effect is the main driving force of the ventilation in the greenhouse with a crop. Measurements show a cool stream of air entering the side vents while the internal hotter air leaves through the roof window. This airflow pattern corresponds with the characteristic effect known as “chimney” which is produced at low wind speeds. As a result, the temperature distribution shows a side wall-greenhouse centre gradient (Fig. 8) due to the hot air movement towards the roof vent and a vertical gradient above the soil surface due to solar energy absorption at soil level. A similar temperature pattern was observed, with higher values for velocity for wind speeds of 7.7 m s−1 (Fig. 8). The air entered the greenhouse with a temperature similar to the outside one and left it 5–10 ◦ C warmer. We must remark that temperature elevation was even greater at other locations inside the greenhouse. For wind speeds greater than 1.0 m s−1 , our results show a strong current of cool air entering the greenhouse through the side ventilator, while the internal hotter air was pushed outwards through the roof opening. Similar observations were obtained by Bot et al. (1996) in a twin-span greenhouse, covered by plastic film and equipped with continuous roof and side vents. They

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observed, when only the buoyancy effect was considered, that the side ventilators were the main inlet of the cool exterior air, while the roof ventilators were expected to act as outlets of hotter air. Our results agreed with their observations. Temperature and airflow pattern in the empty greenhouse, when the wind speed was 5.0 m s−1 (Fig. 6), was similar to those observed for the greenhouse with a crop. However, for a low southwest wind speed (1.0 m s−1 ), the experimental measurements and the simulated results showed a reverse flow (Fig. 4) in the windward area (first and second span). Air enters the greenhouse through the roof vent and the lower part of both side openings, and leaves through the higher part of the side windows. This reverse flow is a response to the great importance of a local “effect chimney” in the side vent areas. Cool air comes in through lower part of the openings and the hot air exits through the upper part of the side vents. Reichrath et al. (2000) also observed a reverse flow in a Venlo-type tomato glasshouse (240 m long) for a wind speed of 3.75 m s−1 . In the empty greenhouse under low wind speed conditions (1 m s−1 ), air velocity inside the greenhouse and the ventilation rate were very small. This information is more important to us than the airflow pattern. In this case the required ventilation surface area could reach up to 9.2% of the ground surface. We observed a velocity decrease in the windward opening between the outside and inside of the greenhouse. In the windward area, the air velocity inside the greenhouse depends on the wind speed and the insect-proof screen characteristics (Valera et al., 2003). The use of an insect-proof screen resulted in a gradual temperature increase inside the greenhouse. Thus, for the cases of high wind speed, the air velocity was also lower in the leeward side of the greenhouse both with and without a crop (Fig. 7). A validating test showed similar differences, between values predicted by CFD models and those measured, to those obtained by Al-Arifi et al. (2001). The larger ventilation rate is not the only indicator of the ventilation performance of a greenhouse. The air velocity near the crop and the temperature difference that a ventilation system can achieve must be also taken into account. From the four tested situations, the situation corresponding to 13 July 2003 seems to be the best. Besides it follows the ventilation rate recom-

mended by ASAE Standards (ASAE, 2003), of 45–60 air renewals per hour; its overall performance (air velocity near the crop and temperature difference) makes this situation more suitable. The main practical result obtained in the present work was the verification of the necessity for placing roof vents in the Almer´ıa-type greenhouses. At the moment, only 35–40% of Almer´ıa-type greenhouse have roof openings. These results show the important role of roof openings area as a controlling factor for ventilation flow. The surface area of the roof openings must be similar to those placed in the sidewall. In most situations, the air leaves the greenhouse through roof vents. The placement of insect-proof screens over ventilation openings reduces the velocity of incoming air into the greenhouse. To maintain a suitable ventilation rate of 45–60 renewals per hour (ASAE, 2003), the total area of the openings should be increased. The recommended value for the ventilation surface of 15–25% of the ground surface for Mediterranean greenhouses without screens (Kittas et al., 1997), should be increased when insect-proof screens were placed in the openings. Growers and greenhouses manufacturers must take into account the need for increasing the total area of the openings and they should install roof openings in Almer´ıa-type greenhouses to improve natural ventilation. The presence of a crop had little influence on the airflow due to the great porosity of the canopy at the studied growth stage (LAI equal to 0.88 m2 m−2 ) and spacing between plants (2 m). We had observed that while air speed is greater in some areas above the crop, in another areas the air velocity increased at the ground level. The presence of insect-proof screen (39.4% porosity) has been studied in an Almer´ıa-type greenhouse (width: 16 m) by CFD simulations. We observed (Valera et al., 2003) a reduction of 50% in the incoming air velocity (and renewal rate), in agreement with results observed by Bartzanas et al. (2002). They also investigated numerically by means of a CFD package the influence of an insect-proof screen (50% porosity) on ventilation for a tunnel greenhouse with continuous side openings and their results indicated that the screen caused a 50% reduction in the airflow rate. Results obtained by Campen and Bot (2003) on ventilation with an insect-proof screen (34% porosity)

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attached to the openings, also showed a reduction of 30% in ventilation of an Almer´ıa-type greenhouse.

5. Conclusions In this work the influence of wind speed on the ventilation performance of an Almer´ıa-type greenhouse was studied numerically using a commercial fluid dynamics code based on the finite element method. The airflow field and the temperature distribution generated by a wind perpendicular to the openings of a full-scale five-span greenhouse were studied. Four different air velocities (7.7, 5.0, 1.8 and 1.0 m s−1 ) were investigated. In the case of the greenhouse with a crop, there is a similar ventilation configuration for low and high wind speeds, strongly influenced by the small vent-opening area (1.5%), the insect-proof screens placed over the ventilation openings and the crop inside the greenhouse. The results of this work show the importance of roof vents. All the Almer´ıa-type greenhouses have side openings, but only 35–40% of greenhouses have roof vents. For this reason, we emphasise the importance of this type of openings for efficient ventilation. Good overall agreement was found between the experimental and simulated data. Results show that cold outside air (corresponding to a sea breeze in all the studied cases) entered the greenhouse through the two side vent openings, both windward and leeward. In the case of strong wind, a great difference between the entrance velocities in the low side vents was observed, while they were very similar when the wind speed was lower. The wind speed seems to slightly affect the air entering through the leeward opening where the air velocity had values of 0.3–0.5 m s−1 , only increasing the air entering through the windward opening, and consequently its departure through the roof vent. The importance of sidewall openings for efficient thermally driven ventilation (‘buoyancy effect’) was confirmed. No significant influence was observed on normalised air velocity (the ratio of the internal air velocity to outside wind speed) at 1.5 m height with the presence of the crop in the greenhouse. However, we can observe a reduction of 30–50% in normalised air velocity at 0.5 m height, where most of leaf area was located during the studied growth stage, on the windward half of the greenhouse with crop.

49

The results presented in this work demonstrate the minor influence of wind velocity on internal temperature distribution when low permeability insect-proof screens were placed over small vent openings. The small opening resulted in a gradual velocity reduction and temperature increase inside the greenhouse. The presence of a crop in the greenhouse can reduce the airflow, but the low plant density studied minimised their effect. The main cause of the low air velocity inside the greenhouse is the effect of the insect-proof screen and the small vent-opening surface. The simulations suggested the need for a significant increase of the openings area to improve the climate conditions while using insect-proof screens. The results of the present study provide both, a validation of the CFD model and important information on the airflow in an Almer´ıa-type greenhouse. The wind direction was not quite perpendicular to the windward side of the greenhouse (angles from 52 to 88◦ ). Although the numerical model simulates quite well the ventilation performance of greenhouse, the three-dimensional calculation are preferable over the two-dimensional calculations when wind direction are not perpendicular, because it can play an important role in ventilation, and the accuracy of the CFD simulations can be improved using 3D models. To get a more realistic description of the flow field and temperature spatial heterogeneity within the greenhouse, heat and vapour exchanges between the crop and air, also should be applied to describe the influence of plants in microclimate in future CFD studies. Ventilation openings should be designed in such way to achieve reasonably uniform temperature and air velocity in the greenhouse and to achieve the desired temperature for the growth of the crop. The results are only valid for the specific case examined. Therefore, the conclusions, although they give a good qualitative idea about the influence of wind speed, can hardly be generalised. However, we can deduce from the results that computational fluid dynamics is a very effective tool for the study of the ventilation in greenhouses and other agricultural buildings.

Acknowledgements This research was partially supported by the projects CR-UAL-0110 and CR-UAL-0202.

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