SIMGreen: A Simulation Tool for the Greenhouse Climate

Transcription

1 SIMGreen: A Simulation Tool for the Greenhouse Climate José Boaventura Cunha CETAV - Centro de Estudos Tecnológicos do Ambiente e Vida UTAD University, Engenharias II, Vila Real Portugal, jboavent@utad.pt Abstract This paper presents the implementation of a software tool to simulate the climate inside greenhouses, specifically for the air temperature and humidity. Simulations are computed using data related with technical specifications of the greenhouse construction, such as floor area, height, cover materials and installed actuators. The user must also provide data from the outside climate (air temperature and humidity, wind speed and solar radiation) or, for the cases that this data is not available, it must be provided relevant inputs to generate this data (such as geographical location of the greenhouse, day of the year to be used in the simulation, define boundaries for outside air temperatures, among others). The simulations can be computed and displayed using time intervals from 5 to 60 minutes for a defined day of the year. Several simulations are presented and discussed with the aim of addressing the potentials and the applicability of this software tool. Namely, it will be illustrated the potential of this tool in helping growers to design or improve their greenhouses. Key words: Agriculture, greenhouse climate, simulation models. 1 Introduction Greenhouse climate and crop models are essential to design efficient management and control systems (Weimann, G. (1989), Challa, H. (1999), Boaventura Cunha, J. et al. (1997), Van Straten et al. (2000), Critten et al. (2002), Coelho et al. (2005)), being generally used within this purpose. However, there is a lack in the use of greenhouse climate models to assist growers in choosing the greenhouse structures and equipments that are most suited to comply with their particular crop requirements. In this paper is described a greenhouse climate simulation software tool to assist the grower in defining the greenhouse technical specifications that are required in order to guarantee adequate climate conditions for the development of the plants. The climate simulations are computed for the air temperature and air relative humidity inside the greenhouse for a particular day of the year with time steps ranging from 5 to 60 minutes. The approaches used to implement the air temperature and relative humidity simulation dynamic models are based on the discretization of the physical laws involved in the heat and water vapour fluxes that take place between the air and the components inside the greenhouse and between the inside and outside air. It must be noted that the greenhouse environment is also influenced by the plants. Namely, plant transpiration processes influence the water vapour content of the air and so, it was also needed to implement response plant models. Simulations are computed using data related with technical specifications of the greenhouse construction, such as volume, covering materials, among others, and specifications of the climate actuating equipments. The user must also provide data from the outside climate (air temperature and humidity, wind speed and solar radiation) or, in the cases that this data is not available, it must be provided relevant inputs to generate this data (such as geographical location of the greenhouse, day of the year to be used in the

2 simulation, define boundaries for outside air temperatures, among others relevant parameters). Several simulations are presented and discussed with the aim of addressing the advantages of this software tool in supporting the growers to specify the technical requirements and select the greenhouse and equipments most suitable for their objectives. 2 Climate simulation models The time derivate of the air temperature (eq. 1) can be computed using heat flow equations (Boulard et al. (1993), Bot, G. (1993) ). The heat fluxes are driven by the differences between the energy content of the inside and outside air and by the controlled energy inputs provided through the actuating systems, dt dt ag 1 = ( qin, h qout, h + ph ) [º Cs ] (1) C aph In this equation, T ag is the air temperature, C aph [J.m -2.ºC -1 ] is the air thermal capacity expressed by square meter of soil, q in,h [W.m -2 ] and q out,h [W.m -2 ] are the heat inflow and outflow and p h [W.m -2 ] is another type of energy production per unit of time that can occur inside the greenhouse. The transport mechanisms for heat conduction, convection and radiation are implicit in the previous equation. Here, the heat flux from inside to outside due to ventilation and losses, q out,h, is described by: ( ) ( ) q = Φ C + C T T (2) out, h vent cap, h c, h. ag out where, C c,h [W.m -2.ºC -1 ] is the heat transfer coefficient related with the greenhouse cover losses, C cap,h [J.m -3.ºC -1 ] is the air thermal capacity per unit of volume air and Φ vent =C vent.u vent +C losses [m.s -1 ] denotes the airflow generated by the ventilation system (C vent.u vent ) and due to the air exchange losses between the inside and outside the greenhouse (C losses ). T out is the outside air temperature and the signal u vent denotes a ventilation control signal that varies in the range 0 to 100% of the actuators nominal powers. The physical constant Ccap, h = air. Ccap, h, p is computed using the heat capacity of the air at constant pressure (C cap,h,p =1000Jm -3 ºC -1 ) and the air density (ρ air =1,29kgm -3 ). There are two major components for the heat input flow, q in,h : one from the heating system (eq. 3.1) and the other from the solar radiation (eq. 3.2). ( ) q = C T T u (3.1) heat H pipe ag heat q = C Rad (3.2) rad rad The heat flux provided by the heating equipments, q heat [W.m -2 ], is computed using the actuator heat transfer coefficient (C H [W.m -2.ºC -1 ]), the water temperature in the heating pipes (T pipe ) and the heating control signal (u heat ) ranging from 0 to 100%, which corresponds to a mixing valve aperture or heat power in the radiative and convective heating systems. The heat flow term, q rad [W.m -2 ] is calculated using the solar radiation that reaches the cover, Rad [W.m -2 ], multiplied by a coefficient (C rad ) that reflects the optical and geometrical properties of the greenhouse cover transmittance to the short wave radiation. It must be noted, that other radiative exchanges and heat fluxes are present in the greenhouse, such as those that occurs between the inside air and soil. Generally, these components have much lower contributions than the previous ones, and so they will be not taken in account on the air temperature simulation model.

3 The time derivate of the inside air relative humidity RH ag (%) is computed by using equations 4.1 and 4.2. The model computes the absolute humidity, H ag, using eq. 4.1 and afterwards it is employed the eq. 4.2 to convert this value into a relative humidity. dhag dt 1 = ( qtr qw) [kg.m -3 s -1 ] Ccap, h (4.1) Cv2Tag C v1c H 2 0 T ag Cv RH ag = Hag e C ( + 273) R Tag (4.2) In these equations, C cap,h [m] is the mass capacity of the greenhouse volume air per square meter of soil, q tr [kg.m -2.s -1 ] is the contribution of the transpiration of plants, q w [kg.m -2.s -1 ] denotes the water vapour exchange between inside and outside air, C R =8314 J.K -1 Kmol -1 is the gas constant, C H2O =18Kg.Kmol -1 is the molecular mass of water and the remaining coefficients are constants that can be derived from the works of Goudriaan (1985), Stanghellini (1987) and De Jong (1990). The water vapour exchange between inside and outside air, which is originated by the ventilation system, is computed according eq. 5.1 and the plant transpiration process with eq. 5.2, C qtr = (1 e qw = Φvent.( Hag Hout ) (5.1) Cv2Tag Xs Cvo. Cv1C H T + C 2 0 ag v ). Cv, a. e Hag (5.2) C + R ( Tag 273) a, pl 3 where C a,pl is a parameter that takes into account with the effect of the soil covered by plants, X s is the dry structural matter and the other coefficients have the meaning previous explained. The models presented in equations 1 and 4.2 were discretized, by using difference equations, with the aim of being easily simulated by software. For example, for the air temperature the difference equation is: q ( k 1) + q ( k ) q ( k ) T ( k) T T ( k 1) ag heat rad out, h = + ag (6) Caph in which k denotes the sample at time kt and T is the simulation time step that can varies from 300s to 3600s. The models presented in this section were implemented using the MATLAB software package. The user has a friendly interface to input the data needed to perform the simulations. This data is related with the greenhouse structure, cover materials and equipments used, as well with the outside climate data. Table 1 shows some of the major inputs that must be entered in the simulation software tool, their allowed ranges, and the ways that users have to input relevant information whenever it is not possible to provide quantitative data. As an example, in the case that the user does not have access to climate outside data, needed to perform the simulations, it is possible to input other types of information, such as the geographical position of the greenhouse and the day of the year in order to generate the solar radiation pattern. In this case, the data is generated by using the solar radiation geometric equation (7) (Page, J., 1986). Afterwards, the atmosphere and cloud attenuations are used in eq. 8 to provide simulated solar radiation data at the ground level for a specific site.

4 Ioj = Io.( 1,03344).cos( J' 2,80º ) [W.m -2 ] (7) Rad = I oj.cos(cos (sin γ )). C cloud (8) In the previous equations, J = 360º J/ is the day angle, which expresses the day of the year as an angle, J is the number of the day measured from noon on the 31 st December, I o = 1367 Wm-2 is the solar constant, and is the solar altitude. This last variable, which denotes the angle between the centre of the solar disc and the horizontal plane, is computed with γ = sin (sinφ sinδ + cosω cosφ cos δ ), being φ the latitude of the site, the solar declination and the solar hour angle. Table 1 Examples of inputs needed for the climate simulation software model, their allowed ranges and ways to perform the data inputs. Type of input data Method(s) to provide the input Allowed ranges Outside air temperature Outside air relative humidity Wind speed Solar radiation Computed by software (user must provide the minimum and maximum temperatures for the day) Computed by software (user must enter the minimum and maximum relative humidty values for the day) Set to a constant value defined by the user Computed using the solar equations (user must provide geographical location, latitude, and cloud cover, 0 (clear sky) to 100% totally covered). -10ºC to 40ºC 20% to 100% 0 to 10ms -1 0 to 1000 Wm -2 Greenhouse floor area (GFA) Numerical value provided by the user 150 to 1000 m 2 Greenhouse height Numerical value provided by the user 2 to 4m Greenhouse windows area Numerical value of the windows area used for natural ventilation 0 to 1.7*2*sqrt(GFA) Greenhouse cover insulation Cover transmission to solar radiation Forced ventilation Heating system Plant development stage Numerical value provided by the user Typical values can be chose by specifying the type of material cover (polyethylene film, glass, etc.) and its thickness. Numerical value provided by the user. Typical values can be chose by specifying the type of material cover (polyethylene film, glass, etc.) Maximum capacity of greenhouse air volume extracted per hour and/or control ventilation signal for windows opening Numerical value of the installed power and specification of the heating type radiative and/or convective Heating pipe temperature and control signal for radiative systems Defined by the user as the crop development state, ranging from 0 (initial state) to 1 (end of the plants growing phase). The relevant model coefficients used to compute the plant transpiration are derived from this input for a tomato crop. 2 to 15 W.m -2.ºC to 95% 0 to m 3 h -1 and/or 0 to 1 0 to 100KW 20 to 85ºC and 0 to 1 0 to 1

5 3 Results and Conclusions Next figures show some of the simulation data used to compute the air temperature inside a greenhouse according to the scenario: floor area of 300m 2, 3m height, polyethylene film cover 220µm thick and geographically located at the latitude of 45ºNorth. Cooling is to be performed by natural ventilation (windows with an opening area of 52m 2 ), the heating system is convective with a maximum heat power of P max =35KW, activated during the night period to 50% of P max. A tomato crop with a development state of 0.5 was considered. The simulation data was generated using a time sample interval of 5 minutes. The outside climate data (solar radiation, outside temperatures and humidity) was generated for the 1 st day of February being the minimum and maximum values of the outside air temperature and humidity specified as 6ºC, 12ºC and 60%, 95%, respectively. The wind speed was set to a constant value of 2ms -1. Due to lack of space the figures for relative humidity are not displayed. 14 outside air temperature ºC outside solar radiation 400 W.m ventilation - window area open 0.4 (x100%) inside air temperature with natural ventilation ºC Fig. 1 Outside climate data and the windows aperture used to compute the greenhouse air temperature (bottom)

6 26 air temperature without natural ventilation ºC Fig. 2 Greenhouse air temperature computed without performing natural ventilation In Fig.2 is showed the simulated air temperature for the same conditions used in the previous figure, with exception that here no ventilation is performed during the day. As it was expected the temperature during the day increases (in this case about 2ºC). These software features give to the growers the possibility to test and compare the influences of different type of actuating systems and control actions over the greenhouse climate. Also, this tool is useful to assist the grower in specifying the actuating equipments and the greenhouse constructions more suitable for his particular needs, since it gives the possibility of testing the performance of several hardware combinations for a defined day of the year, which must be chosen for the expected extreme climate conditions of the winter and summer days. 4 References Boaventura Cunha, J., Couto J., Ruano, A.E.B Real-time parameter estimation of dynamic temperature models for greenhouse environmental control. Control Eng. Practice, Vol. 5, N.10, pp Bot, G.P.A Physical modelling of greenhouse climate. The computerized greenhouse, Academic Press Inc., 1993, pp Boulard, T., Baille, A A simple greenhouse climate control model incorporating effects on ventilation and evaporative cooling. Agricultural and Forest Meteorology, Vol.65, pp Challa, H., Integration of explanatory and empirical crop models for greenhouse management support, Acta Horticulturae 507, pp Critten, D.L. and B.J. Bailey A review of greenhouse engineering developments during the 1990s. Agricultural and Forest and Metrology 112: Coelho, J.P., Moura Oliveira, P., Boaventura Cunha J Greenhouse air temperature predictive control using the particle swarm optimisation algorithm. Computers and Electronics in Agriculture, Vol. 49, Elsevier, pp De Jong, Natural ventilation of large multi-span greenhouses. Ph.D. Thesis, Wageningen Agricultural University, Wageningen. Goudriaan, J., Van Laar, H.H., Van Keulen, H., Louwerse, W Photosynthesis, CO2, and plant production. NATO ASI Series: Life Sciences, Vol. 86, pp Page, J. K. (1986). Prediction of Solar Radiation on Inclined Surfaces. Solar Energy R&D in the European Community, Series F: Solar radiation Data, 459pp. Stanghellini, C Transpiration of greenhouse crops. Ph.D. Thesis, Wageningen Agricultural University, Wageningen. Van Straten, Challa, H., Buwalda, F Towards user accepted optimal control of greenhouse climate, Computers and Electronics in Agriculture vol. 26, pp Weimann, G The characteristics of light transmissivity, heat consumption and condensation processes in different film greenhouses. Acta Horticulturae 245: