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SOLAR RADIATION DISTRIBUTION IN A TUNNEL GREENHOUSE

2008; International Society for Horticultural Science; Issue: 801 Linguagem: Inglês

10.17660/actahortic.2008.801.100

2406-6168

Catherine Baxevanou, Thomas Bartzanas, Dimitris Fidaros, C. Kittas,

Light effects on plants

A commercial computational fluid dynamics code was used in order to investigate numerically the effect of solar radiation in an arc type tunnel greenhouse equipped with continuous side vents with a tomato crop. For the simulation’s needs a two dimensional mesh was used to render the former geometry, and the finite volume method was adopted to carry out the fully elliptic partial differential equations’ problem. Climatic data provided by the Greek Centre of Renewable Energy Sources were used in order to approach realistic conditions. Special items like the mechanical behaviour of the covering material or the climatic behaviour of the rows of the tomato crop are taken into account using external user defined functions (UDF). Optical properties of the tested covering materials were defined according to the wave-length of the incoming solar radiation and three spectral areas (UV, PAR and near infrared). Based on the meteorological data of October for the region of Volos (Greece), two parametric studies were carried out concerning different angles of the incoming solar radiation and the different optical properties of the covering materials. Results show the influence of the optical properties of the covering materials and of the incidence angle of the incoming solar radiation on the distribution of solar radiation inside the greenhouse. The flow recirculation due to buoyancy effect shows the importance of internal temperature gradients although the dominance of the forced convection resulting from natural ventilation. The diversification of the temperature patterns, mainly and secondarily of the airflow field indicates that heat transfer due to the solar radiation distribution for different covering materials in the three different spectral areas was successfully simulated. INTRODUCTION Greenhouses are used in order to provide a more favourable environment for plant growth. The most important factor affecting plant growth and development is solar radiation, and the most crucial process requiring solar radiation and governing plant growth is photosynthesis. The amount of solar radiation entering the greenhouse is highly dependent on the greenhouse design, radiative capacity of the covering material and weather conditions. One of the most important aspects in greenhouse climate conditioning is its spatial distribution. Radiative heterogeneity is particularly important in tunnel greenhouses, the most commonly used greenhouse type in the Mediterranean basin. This variability severely affects plant activity and often leads growers to over fertilize, as has been observed for lettuce crops (De Tourdonnet, 1998). Moreover, the differences on climate High Technology for Greenhouse System Management Co-operation of Protected Cultivation and greenhouse Engineering October 4-6, 2007 Naples, Italy 2 distribution not only cause non-uniform production and quality, but also problems with pests and diseases. Information not only about the quantity and quality, but also the spatial distribution of the light transmitted by the greenhouse cladding or shading materials is essential to a further evaluation of their influence on the growth and development of plants. The amount of solar energy transmitted into the greenhouse drives the physiological fluxes (mainly transpiration and photosynthesis). Rosa et al. (1989) developed an approximate model for single-span semicircular greenhouses, assuming that all incident radiation is isotropically scattered on the cladding. Critten (1993) and Kurata (1991) developed models with simple shape optimisation for single-span tunnels. These models take into account only direct-beam transmission, while failing to allow for the scattering of incident radiation by the cladding. In other words, all incident radiation is assumed to be direct and to remain so even after it has passed the cladding. These models are therefore suited only for glasshouses and not for greenhouses with plastic cladding, since such cladding scatters most of the incoming radiation towards the inner part of the greenhouse. Using this model (Kurata, 1990), he found the best orientation of the greenhouse for an EW orientation. Kurata et al. (1991) then determined the optimal shape from the point of view of radiation for the single-span greenhouse with straight cladding. Boulard and Wang (2002) simulate radiative heterogeneity at the greenhouse floor level as a function of greenhouse geometry, covering material and weather conditions. More recently, Vougioukas (2004) presented a computational algorithm, which computes the light distribution on any greenhouse surface based on a global radiation transfer model, such as the ones that have been developed for computer graphics applications. Most of the above mentioned studies for calculating greenhouse solar transmissivity are analytical and cannot handle the combined effects of light scattering due to cladding, multiple reflections of diffused light, and complex non-planar geometries, such as the ones found in multi-span tunnels of variable roof cross-sections. Moreover, no detailed information was provided about the influence of the solar radiation distribution on the energy balance of the greenhouse. In recent years the use of CFD allows easier studies determining the greenhouse microclimate with respect to its structural specifications and used equipment (Bartzanas et. al., 2004, Fatnassi et. al. 2006) In the present study a commercially available computational fluid dynamics code was used to investigate the effect on solar radiation distribution in a greenhouse microclimate. MATERIALS AND METHODS Numerical model The commercial CFD code Fluent was used as a basis (Murthy and Mathur, 1998), where the required external source code for the various sub-models and boundary conditions was embodied. The corresponding transport equations (described by the Navier-Stokes along with the energy transport equations) were solved numerically by finite volume method, using a two dimensional structured mesh consisting of 20.000 cells. In solid regions energy equation is reduced to the conduction problem. The SIMPLE (Patankar, 1980) algorithm is used for pressure-velocity coupling, yielding an elliptic differential equation in order to formulate the mass conservation equation. The discretisation of the convective terms in the RANS equations is materialized by the SOU scheme (Tamamidis and Assanis, 1993) and for the diffusive terms a central difference High Technology for Greenhouse System Management Co-operation of Protected Cultivation and greenhouse Engineering October 4-6, 2007 Naples, Italy 3 scheme is adopted. The effect of turbulence on the flow was implemented via the high Re k-e model (standard) model (Launder and Spalding, 1972). The density variation is calculated according to the Boussinesq model in order to take into account the natural convection effects. The crop was modelled using the porous medium approach (Boulard and Wang, 2002). The convergence criterion was set to 10 for the continuity, momentum and turbulence equations while for the energy and radiation equations the criterion was 10. Radiation model In order to simulate the effect of solar incident radiation on the greenhouse cover the Discrete Ordinates (DO) model is used. The DO model allows the solution of radiation on semi-transparent walls. In this model it is assumed that radiation energy is ‘convected’ through the medium at its own speed simultaneously in all directions. It is able to model a wide range of applications except gases, such as CO2 or H2O vapour which absorb and emit energy at distinct wave number, at a moderate computational cost for typical discretization. Solving a problem with a fine angular discretization may be CPU-intensive. It can be used in non-gray radiation using a gray-band model. So it is adequate to be used with the participating media with a spectral absorption coefficient αλ that varies in a stepwise fashion across the spectral bands. In this case the absorption coefficient is considered constant within the spectral bands. The discrete ordinates (DO) radiation model solves the Radiative transfer equation (RTE) for a finite number of discrete solid angles, each associated with a vector direction r s fixed in the global Cartesian system (x,y,z). It transforms the RTE equation into a transport equation for the radiation intensity in the spatial coordinates (x,y,z). The DO model solves for as many transport equations as there are directions r s (Chui and Raithby, 1993). The RTE for the spectral intensity ( ) , λ r r I r s turns to ( ) ( ) ( ) ( ) ( ) ( ) ( ) ' ' , ' , 4 , , 4 0 2 Ω Φ + = + + ∇ ∫ d s s s r I r I n s r I s s r I s b s π λ λ λ λ λ λ π σ α σ α (1) In this equation the refractive index, the scattering coefficient and phase function are assumed independent of wavelength, but in the calculation of black body emission and boundary conditions imposed by semi-transparent walls their wavelength dependency is taken into account. The phase function Φ, is assumed isotropic. The angular space 4π at any spatial location is discritized into NθxNφ solid angles of extent ωi, called control angles. The angles θ and φ are the polar and azimuthal angles, and are measured with respect to the global Cartesian system (x,y,z). In our case a 3x3 pixilation is used. This angular discretization provides us with a moderate computational cost but it may introduce discretization errors at the boundaries when the solid angles are bisected by the boundaries (Raithby 1999). The RTE equation is coupled with the energy equation through a volumetric source term given by ( ) ( ) ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ Ω − = ∫ •