Greenhouse climate : from physical processes to a dynamic model

In this thesis greenhouse climate has been studied as the set of environmental conditions in a greenhouse in so far as they affect crop growth and development. In chapter 2 this set has been defined in terms of temperatures and vapour pressures. Moreover we have indicated which physical processes co-operate in the greenhouse. So the dependency of the greenhouse climate on the outside weather, the physical properties of the greenhouse construction and the way ventilation and heating is performed has been described in causal relations. This description can be employed in short term as well as in long term crop growth models and it can be a powerful tool in the search for energy saving strategies. As the physical processes are at the basis of this approach, in this thesis the emphasis has been laid on a proper description of the major processes and their validation by in situ measurements.In chapter 3 natural ventilation through window openings is considered. The airflow due to wind effects through the roof openings of a large multispan greenhouse is assumed to be driven by fluctuating pressure differences over the individual openings. Static pressure differences between the openings are not expected because of the corresponding flow conditions near each span. The driving force due to wind effects together with the flow resistance of the opening determines the ventilation flux through the window opening. Parameters in this relation are the area of the opening without window, a function G(ξ) (being a function of the opening angle ξ) and the outside wind speed. In the ,function G(ξ) (called the window function) various window parameters are combined with a pressure fluctuation coefficient. From full scale ventilation experiments with a tracer gastechnique, the window function was determined for lee-side ventilation. Only one type of ventilation window was investigated experimentally under full-scale conditions. In small scale greenhouse models the window parameters of various types of ventilation windows were measured. The pressure fluctuation coefficient was calculated from the window parameters and the window function of the experimental full-scale greenhouse. This coefficient was combined with the measured window parameters of other types of ventilation windows in order to predict the window function of these windows. So we could also calculate the ventilation due to wind effects through these windows of other types.
Also in chapter 3 the ventilation due to temperature effects has been investigated. In this case the driving force is derived from the density difference over the window opening. Introduction of the resistance to flow resulted in relations for the ventilation flux due to temperature effects. These relations were derived for flow through openings at the same height and for openings with some vertical distance. Theoretically ventilation due to temperature effects has been presumed to be important at low wind speeds only. From the experiments some support was obtained for this presumption. It was also theoretically argued that the sealing of ventilation openings in the side walls substantially reduces the ventilation due to temperature effects.The fluctuative nature of the ventilation due to wind effects has been discussed in chapter 4. This fluctuative nature was concluded from the measured fluctuations of the air velocity and the air temperature in the opening. The frequency distribution of the fluctuations proved to be dependent on the window aperture; the window opening acts as a tuneable high pass filter. The measurements resulted in the calculation of the effective flux due to the fluctuating flow (represented by the RMS of the local air velocity) that may be compared with the results obtained by the tracer gas experiments. For leeside ventilation the agreement between these fluxes is reasonable. So we concluded that the RMS at windward-side ventilation indicates the ventilation flux for this type of ventilation. The superposition of a static pressure difference over the window openings may give rise to an increase of the leeside ventilation. For windward-side ventilation hardly any effect of this superposition was observed.The interaction of a multispan greenhouse cover with shortwave direct and diffuse radiation has been described in chapter 5. For direct shortwave radiation this interaction is calculated from the solar position, the optical laws for reflection and transmission, the detailed dimensions of the roof construction and the orientation of the greenhouse. The calculations were made for non-polarized light; polarization can be taken into account, however, without much difficulty. Special attention was paid to the contribution of reflected direct light and to coinciding shadows of the constructive roof parts. Calculated transmissions are presented for various data from both a north-south and an east-west oriented multispan Venlo greenhouse at 52 ^o north latitude.
Because diffuse shortwave radiation is composed of radiation from the hemisphere, the calculation procedure for direct radiation was applied to calculate the interaction with the radiation from any defined direction of the hemisphere. Integration over the hemisphere then yields the interaction with the diffuse radiation. The effect of the intensity distribution for various types of diffuse radiation is investigated in this way. The experimentally measured transmissivity for diffuse radiation indicates that the calculations are accurate.At the end of chapter 5 the interaction with the longwave sky radiation has. been discussed. Since the momentaneous interaction had to be determined, no empirical formula for the time average sky temperature or the time average sky radiation could be applied. Therefore the momentaneous sky temperature was determined by means of measurements of the net radiation above a surface with a well-defined temperature.The major convective exchange processes affecting greenhouse climate are treated in chapter 6. An experimental set-up is described to measure the convective heat transfer on the inside and the outside of the cover directly in situ. Special attention was given to minimizing the effect of the radiant exchange. Due to condensation to the inside of the cover the convective exchange at this side could not be determined accurately. On the outside reliable measurements were obtained. The measured heat transfer coefficient is lower than we expected from literature data on forced convection over a flat plate. This defect can easily be understood if we remind ourselves that the roof is saw-tooth shaped, which gives rise to secondary flows. The heat transfer between the saw tooth roof surface and the outside air is in the transition region between free and forced conevection up to a wind speed of about 3-4 ms ^-1 . The measurements at the highest wind speeds occurring during our experiments (i.e. up to 4 ms ^-1 ) actually indicate pure forced convection. The measurements at low wind speeds provided some evidence of pure free convective exchange at the outside. The exchange phenomena on the inside are expected to be similar to these latter results.From local wind speed measurements above the greenhouse, isotachen pictures were constructed for some combinations of the wind speed and the wind direction, These pictures show some characteristic flow phenomena, especially the appearance of a large eddy in the roof dale. It is precisely this secondary flow phenomenon which is responsible for the reduction of the outside beat transfer coefficient mentioned earlier.The convective heat transfer from the heating pipes is experimentally determined in the greenhouse from cool-down curves of the pipes. Corrections were made for the radiative heat losses to the environment. The heat-transfer was found to be due to free convection. The dependency of the Nusselt number on the Grashof number, however, is different from that found in literature on free convection from a horizontal cylinder. This is explained from the different experimental conditions.The transpiration was measured on a short time scale, using a sensitive weighing lysimeter. We determined the total conductivity for water transport from the vegetation to the air from the steady state transpiration during the night and the vapour pressure difference between the leaves and the air. From the response of the leaf temperature during periods with intermittent irradiation from infra red lamps, we determined the combined conductivity for transport of sensible and latent heat from the leaves to the air. The heat transfer coefficient was calculated from this combined conductivity and the conductivity for water transport. This coefficient agrees with that from the literature under the same conditions. The calculated stomatal conductivity is much higher than what was reported in the literature for transpiration in the open. By day the total conductivity for water transport from the vegetation to the air was found to be approximately in proportion with the irradiation. Some evidence was found for a "midday depression" of the conductivity.In chapter 7 the major physical processes have been combined into a physical model to simulate the momentaneous greenhouse climate as a function of the outside weather, the physical properties of the greenhouse construction and materials and the way heating and ventilation is performed. A thermal screen has been incorporated in the model. Parameter estimation techniques have been used to validate the minor physical processes. Bond graph notation is applied to obtain a transparent scheme. In the model the temperatures of the greenhouse cover, the thermal screen, the greenhouse air above and below the thermal screen, the vegetation and several horizontal soil layers have been assumed to be homogeneous. The same assumption was made for the vapour pressure of the greenhouse air compartments. The vapour pressures on the soil surface, inside the leaves, on the thermal screen and on the inside of the cover equal the local saturated vapour pressures. They were calculated from the respective temperatures. For a greenhouse with low heating pipes and a vegetation with an open structure, the vertical gradients are small, so in that case the model assumptions are valid. The agreement between the measured and simulated state variables is reasonable. Differences are due to the improper incorporation of the outside heat transfer coefficient and to the fact that the contribution of the direct and the diffuse radiation to the global radiation had to be estimated after the event. This reasonable agreement has been demonstrated for two different test periods.A final discussion and suggestions for aims of future research have been presented in chapter 8.