ENERGY BALANCE MODEL FOR NATURAL VENTILATION OF GREENHOUSES

Abstract

Energy balance methods currently used to estimate the natural ventilation rate of greenhouses (a m ) assume that the input energy to the greenhouse is the transmitted solar radiation. An average value for the cover transmittance (c ) is usually used to estimate this energy. However, this estimate includes a large error due to the spatial variation of c  in the greenhouse. These methods also give negative values of a m  at low solar radiation levels (e.g. in the morning and afternoon). The purpose of this study was to develop a simplified energy balance model to estimate the value of a m  precisely. In this model, all modes of energy were treated at the outer surface of the cover to avoid the error caused by using an average value of c . Required environmental parameters to be used in the model were measured inside and outside a single-span glass-covered greenhouse with a floor area of 26 m 2 located in the Tokyo area, Japan during four sunny days (Sept. 29 to Oct. 2., 2005) The greenhouse was naturally ventilated using two roof ventilators (0.6 m  5 m). Diurnal variations of a m  were estimated and compared with the results of other models and showed the necessity of applying the present model. The estimated value of a m  was in the range between 0.11 kg s-1 and 2.25 kg s-1 and these results were in accordance with those measured and reported in the literature. The results also confirmed that outside wind at a speed less than 2.5 m s-1 has no significant effect on the value of a m  and the value of a m  resulting from the greenhouse thermal balance depends mainly on temperature difference of air between inside and outside the greenhouse (T ). A linear correlation between a m  and T  was provided that can be used to estimate the required ventilation rate to maintain the air temperature in the greenhouse at a desired level. 71 Ahmed M. Abdel-Ghany 72 NOMENCLATURES Alphabetic symbols A c : surface area of the greenhouse cover (m 2) A f : surface area of the greenhouse floor (m 2) C d : discharge coefficient of the vent (-) C pa : specific heat of air at constant pressure (J kg-1 o C-1) C w : wind effect coefficient (-) d: greenhouse cover thickness (m) F f-j : view factor from the floor surface to the surface j (-) F j-f : view factor from the surface j to the floor surface (-) f d : ratio of diffuse to global (direct + diffuse) solar radiation (-) g: acceleration of gravity (m s-2) H: vertical height of the vent opening (cord joining the two extremities of the vent when it is open and close) (m) h co : convective heat transfer coefficient between the cover surface and the outside ambient air (W m-2 o C-1) I i : specific enthalpy of moist air inside the greenhouse (J kg-1) I o: specific enthalpy of moist air outside the greenhouse (J kg-1) j: surface number of the greenhouse cover (1,2,…, 6) k f : equivalent thermal conductivity of the greenhouse soil (W m-1 o C-1) L: vent length (m)  : vent width (m) a m  : ventilation rate (kg s-1) N a : number of air exchange per hour (h-1) N v : number of ventilators n: refractive index of the cover material (-) Q co : convection heat rate between the cover surface and outside ambient (W) q o : heat rate conducted into the greenhouse soil surface (W) R n : net thermal radiation exchange between the outer surface of the cover and sky (W) r b : ratio of beam irradiance received by a tilted surface to that received by a horizontal surface (-) r 2 : coefficient of determination S i : global solar radiation flux transmitted into the greenhouse (W m-2) S n : net global solar energy crossing the control volume of the greenhouse (W) S o : global solar radiation flux at the greenhouse outer surface (W m-2) T c : cover outer surface temperature (o C) T di : dry bulb temperature inside the greenhouse (o C) T do : dry bulb temperature outside the greenhouse (o C) T f : floor surface temperature (o C) T sky : equivalent temperature of sky (o C) T wi : wet bulb temperature inside the greenhouse (o C) T wo : wet bulb temperature outside the greenhouse (o C) U: overall heat loss coefficient of the greenhouse cover (W m-2 o C-1) ENERGY BALANCE MODEL FOR NATURAL VENTILATION…. 73 V: wind speed outside the greenhouse (m s-1) V g : volume of the greenhouse air (m 3) Z: vertical depth under the greenhouse measured from the soil surface (m) Greek symbols c  : net absorptance of the cover to global solar radiation (-)  : slope angle of the cover surface (degree) s  : surface azimuth angle (degree) I  : specific enthalpy difference between inside and outside the greenhouse (J kg-1) T  : temperature difference between inside and outside the greenhouse (o C)  : evaporation efficiency (-) j  : fraction of the transmitted solar radiation from the surface j that transmitted back to outside the greenhouse (-)  : solar radiation heating efficiency (-)  : incidence angle of direct solar radiation (degree) r  : angle of refraction (degree) z  : solar zenith angle (degree)  : absorption coefficient of the cover material (m-1) a  : density of moist air (kg m-3) j , c  : net directional reflectance of the cover surface j to direct solar radiation (-) j , c  : net directional reflectance of the cover surface j to global solar radiation (-) ˆ:ˆ: interface reflectance on the cover surface (-) f  : net reflectance of the floor surface to global solar radiation (-) c  : average transmittance of the greenhouse cover to global solar radiation (-) j c,  : net directional transmittance of the cover surface j to direct solar radiation (-) j , c  : net directional transmittance of the cover surface j to global solar radiation (-) ˆ:ˆ: ransmittance due to absorption of solar radiation through the cover thickness (-)  : opening angle of vent (degree)  : absolute humidity (kg of water vapor/ kg of dry air)