A transient model of the interaction between crop, environment and greenhouse structure for predicting crop yield and energy consumption

J. agric. Engng Res. (1983) 28, 401-417

A Transient Model of the Interaction between Crop, Environment and Greenhouse Structure for Predicting Crop Yield and Energy Consumption P. 1. COOPER*; R. J. FULLER?

This paper describes a computer-based method of modelling the transient performance of greenhouses. The method was developed to assist in the design of low energy protected cropping structures to be used in the hot, arid inland climates of Australia. Because of the generalized form it has applicability to a wide range of climatic conditions. To facilitate the modelling procedure, a greenhouse is considered to be composed of a number These are the cover, floor, growing medium, air space of separate but interactive components. and crop. A particular feature is the use of a tomato crop model which responds to photosynthetically active radiation, leaf temperature and CO, level. Design criteria were that the greenhouses should use only a small amount of conventional energy for heating when necessary and that they must operate at all times in an essentially sealed condition for continuous CO, To satisfy the first criterion, solar air heaters, a rockpile thermal store and a moveenrichment. able thermal screen were incorporated in the simulation model, while the second condition was met by simulating the performance of a total enthalpy wheel and evaporative cooler which dehumidifies and cools without ambient venting of the greenhouse. The paper presents details of the mathematical models of each component and lists the assumptions used with each. The simulated performances of a number of different greenhouse types in winter and summer are presented and an analysis of the simulated crop yields, energy flows and temperatures indicates that the model is simulating the expected trends in greenhouses.

1.

Introduction

The primary objective of the overall project was to investigate the thermal behaviour of low energy greenhouses used in food cropping complexes situated in the remote arid regions of Australia. In these areas, fuel costs are high and fresh produce is expensive due to the significant transport costs from the centres of food production. An alternative to transport is to grow the Current greenhouse technology crops in a protected environment at their point of consumption. is capable of providing an adequate environment but at a high cost with an equally high use of conventional energy. To date, greenhouse design in Australia has been based on experience which has originated overseas, and general “rules of thumb” developed over the years. Neither of these were considered to be suitable for the task. The decision was made to develop a generalized mathematical model so that the performance of a variety of greenhouses with associated climate modifying systems could be evaluated and compared. The model should not only allow comparisons of systems to be made, but should also enable performance predictions to be made for any location where suitable long-term climatic data is available. One objective was to design a greenhouse complex which would maximize crop production, This objective could be achieved by while consuming a minimum of conventional energy. maximizing solar energy utilization for photosynthesis and heating. An important design requirement was that the greenhouse should have a minimum air exchange with ambient all the year round. An essentially sealed structure was necessary for COZ enrichment of the greenhouse air at a later date in the project. *CSIRO tCSlR0

Division of Energy Centre for Irrigation

Received

9 December

1982;

Technology, Research accepted

Highett. Griffith,

in revised

Victoria, New South

form

IO March

Australia Wales,

Australia

1983

JO1 OOZI-8634/83/050401

-i- 17 $03.00/O

@ 1983 The

British

Society

for

Research

in Apncultural

Engineermg

NOTATION horizontal crop, cover, floor and growing medium areas, respectively yield constant c COz concentration in v.p.p.m. cc02 Cpa, cpfb Cmm specific heats of air, floor and growing medium, respectively diffusion coefficient of water in air average leaf diameter net CO, uptake F convective heat transfer coefficient between crop and greenhouse h ca air convective heat transfer coefficient between cover (Mode 1) inner h coa cover (Mode 2) or screen (Mode 3) and greenhouse air convective heat transfer coefficient between cover (Modes 1 and 3) h coo or outer cover (Mode 2) and ambient air combined convective heat transfer coefficient between inner and h ct outer cover (Mode 2) or cover and screen (Mode 3) mass transfer coefficient for floor and growing medium, respectively hdf, hdgm convective heat transfer coefficient between floor and greenhouse ha air latent heat of vaporization of water 4, convective heat transfer coefficient between growing medium and h gma greenhouse air solar radiation striking the crop and the cover, respectively zc,zco solar radiation penetrating the crop canopy and striking the floor Zf photosynthetically active solar radiation IPAR crop transpiration coefficient Kt conductivities between top layer and main mass of floor and k,, k, between main mass of floor and ground sink, respectively number of air changes per hour due to infiltration i crop leaf area index LC mass transferred due to transpiration of the crop MC mass transferred due to condensation on cover (Mode 1) or inner MC0 cover (Mode 2) or screen (Mode 3) mass of floor and growing medium, respectively Mf, Mgm mass transferred due to dehumidifying device and due to infiltration Mh, Mr of ambient air, respectively mass transferred due to natural or forced venting with ambient air, Mee, Muf, Mvgm due to evaporation from floor and due to evaporation from growing medium, respectively mass of water “removed” from system MUJ mass flow rate out of cooling and/or dehumidifying device rith mass flow rate due to natural or forced venting with ambient air mu energy added by auxiliary heating energy absorbed by crop, by cover and in floor, respectively, from :a,, Qaco, Qaf solar radiation energy transferred by conduction between main mass of floor and Qbs ground sink energy transferred to cover or inner cover or screen by condensation QC energy transferred by convection between crop and floor, Qee, Qcf respectively, and greenhouse air energy transferred by convection between greenhouse air and cover Qcci, Qeco or inner cover or screen and between outside air and cover or outer cover, respectively

d”

energy transferred by convection between growing medium and greenhouse air energy transferred by convection between inner and outer cover or cover and screen energy transferred due to cooling device and due to infiltration of ambient air, respectively energy added directly into growing medium energy transferred by radiation between crop and sky surrounds, between floor and crop and from growing medium to crop, respectively energy transferred by radiation from inner and outer cover, Qri, Qro respectively energy stored in growing medium and in main mass of floor, Q sgrn,Qst respectively energy transferred by crop transpiration Qt energy transferred by conduction between top surface layer and t&b main mass of floor energy transferred due to natural or forced venting with ambient air Qve energy transferred by evaporation from floor and from growing Qvf, Qvgm medium, respectively boundary layer and stomata1 resistance, respectively Rbl, Ret ambient temperature TLZ ambient temperature adjuster to approximate sky and surroundings T ad temperature crop temperature TC cover temperature (Mode 1) inner cover temperature (Mode 2) TC i screen temperature (Mode 3) cover temperature (Modes 1 and 3) T co 1outer cover temperature (Mode 2) Tfb, Tft, Tgh,Tgm floor bulk average, floor top layer, greenhouse air and growing medium temperatures, respectively airstream temperature supplied by cooling and/or dehumidifying Th device ground sink, and sky and surroundings temperatures, respectively L Tsky floor thickness t V greenhouse volume i velocity of air moving across the crop absolute humidity ratios of ambient air and of saturated air at wlz, WC crop temperature, respectively absolute humidity ratio of saturated air of cover temperature WCC (Mode 1) or inner cover temperature (Mode 2) or screen temperature (Mode 3) Wft, Wgh, Wgm, Wh absolute humidity ratio of saturated air at floor top layer temperature, greenhouse air, saturated air at growing medium temperature and airstream supplied by cooling and/or dehumidifying device, respectively fraction of floor with free water available for evaporation W wind speed IYS crop yield Y distance from middle of main mass of floor to ground sink Y crop, cover and floor absorbances, respectively UC9~CO, af crop, cover and floor emittances, respectively EC,eco, Ef

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PREDICTION

radiation interchange factor between floor and crop and between growing medium and crop, respectively growing medium and thermal screen emittances, respectively refractive index of cover material time density of air solar transmittance of crop canopy, cover solar transmittance and cover lona-wave transmittance. resnectivelv It was decided that TRNSYS,’ an existing simulation programme, would be used as the basis for the greenhouse model, for a number of reasons. TRNSYS is used extensively for simulating the performance of solar energy systems. It is a user-oriented programme which permits the user to interlink component models normally associated with solar energy systems. Standard component models include solar collectors, rockpile thermal stores, pumps, valves, auxiliary heaters, etc. Each model is written in a generalized form. By supplying appropriate control information, a functioning system can be generated by mathematically simulating the connection of the system components and their interaction. Due to the number and complexity of the heat and mass transfer mechanisms occurring within a greenhouse, it was felt that modelling the greenhouse as a single component was too cumbersome, and that it would be more beneficial to divide a greenhouse into separate components and model them independently. Consequently, models have been developed for the growing medium, floor, crop, greenhouse air and cover. Although written as separate routines, their interaction with each other is facilitated by the organizational nature of TRNSYS.

2.

Mathematical

models

Growing medium

2.1,

2.1.1. General description The growing medium associated with plant growth may vary considerably in its properties, and may range from traditional soil to a nutrient film. This model has been written for media with different thermal capacitances and allows for the direct input of heat to the growing medium, e.g. as in root zone warming. It is assumed that moisture is freely available at the surface of the growing medium for evaporation. Condensation on the medium may also take place. 2.1.2. Mathematical description Standard equations describing the dominant heat and mass transfer mechanisms growing medium have been used to determine an energy balance at each time step : heat in -heat

affecting

the

out = heat stored.

The mechanisms modelled are as shown in Fig. 1. The contributions to an energy balance from convection, evaporation and radiation are given by the following three equations, respectively: -h -

Q cgm Q vgm

-

Q rgm

gmaA gnz (Tg, -Tsh),

hdgm =

( wgm - Wgh)

?? gmc

Hence, the energy stored in the growing medium Q sgm

The mass transfer

=

coefficient,

CAgm

Vgm4

A gm hf,,

-Tc4).

is given by

Qin - Qc,m - Qvgm - Qrgm = Mgm Cpgm dT,mldQ. hd, is obtained by using the Lewis relation,*

hagm z

heat transfer coefficient specific heat of fluid

hgma ’ 1005 ’

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COOPER;

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40.5

Fig. 1. Energy transfer mechanisms for the growing medium An approximate value for the latent heat of vaporization hf, in J kg-lK-’ is obtained following expression, which results from a curve fit to data from standard tables : hf, = [3 161.36 -(2.406

from the

T&l,

exchange, it is assumed that the growing where Tgm is in K. For the purposes of radiation medium sees an infinite expanse of crop canopy. It is also assumed that there are negligible conduction losses from the growing medium to the floor, and crop cover is complete so that no solar radiation is absorbed in the growing medium. 2.2. Floor 2.2.1. General description The floor has been modelled in two parts. The temperature of the top surface layer of the floor is assumed to respond instantaneously to energy transfer mechanisms, whilst the bulk of the floor is assumed to have thermal capacitance. Energy exchange between the top layer and the rest of the floor is by conduction. The energy transfers determining the top surface layer temperature are absorbed solar radiation, evaporation, convection and radiation to the crop and conduction to the main bulk of the floor. For thermal radiation exchange it is assumed that the floor sees an infinte crop canopy. Evaporation from the floor may take place, but only from the fraction of the floor area which has free water available. This estimated fraction is supplied as a constant for a particular simulation. The model also assumes that condensation can take place over the same fraction of the floor area. Since the emittance of water and most common flooring materials is of the same order, any change in radiant energy transfer due to the presence of free water will be small, and radiant heat transfer from the floor to the crop is based on the total floor area. The solar radiation absorbed by the floor is calculated as the product of the floor absorbance, the floor area and the solar radiation transmitted by the crop envelope. The temperature of the main floor mass is determined by conduction from the top layer and conduction to a ground sink. The temperature of this sink can be varied to correspond to seasonal differences. Edge losses are considered to be negligible compared with those through the base of the floor. 2.2.2. Mathematical description Energy transfer mechanisms determining both the floor top layer and the bulk average temperatures are shown schematically Fig. 2. Hence, the energy equations for the top layer become:

QM = adfAr, Qcf = hfaAf(Gt -Tgd

(1 - w),

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AND

ENERGY

Qvf = hczfw h,, (wft - W&) Qrf = ?? fc 0 Ar(T.t4 -Tc4), Qtb = (24 AdO (Tft -Tfb)r

CONSUMPTION

PREDICTION

Af,

and similarly for the floor bulk: Qtb = C&Ad0

Vrt -T&v

Qbs = O&&/y)

(Tfb -7’s).

\ r

C,

Cover

Floortop Floor

r,

‘G Fig. 2. Now,

Energy transfer mechanismsfor the greenhouse floor

if y = t/2 and k, = k, = k, Qbs = (2kAflt)

(Tfb -Ts)

and Qst =

Qtb

haf =

heat transfer coefficient specific heat of fluid 2’5

hf, =

[3161.36 -(2.406 T,,)],

-

Qbs

=

Mf

Cpfb

dTfb/de.

As before,

hfa

and with Tft in K. 2.3. Crop 2.3.1. General description The growth of a crop is the result of the interaction between the crop and its environment. The crop will modify the thermal conditions in a greenhouse and, as a result, the photosynthetic rate and yield of the crop will respond to these changed conditions. This model describes the thermal performance of a fully developed crop which is yielding fruit at a rate determined by the conditions within the greenhouse. Although there is a small amount of thermal capacitance in a crop, it was found that to use a crop model with capacitance required numeral integration time steps smaller than 1 h for computational stability. When compared with a crop model with no thermal capacitance, little difference was found and it was therefore assumed that the crop has negligible thermal capacitance and thermally responds instantaneously to changes in conditions. It is assumed that the yield is removed regularly so that there is no change in the crop from day to day.

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The crop absorbs solar radiation and exchanges thermal radiation with the growing medium, floor, cover and surroundings. Latent thermal energy and moisture is transferred to the greenhouse air by transpiration. Convective heat transfer takes place from the leaves, depending on the air velocity across the crop. It is assumed that no condensation takes place on the crop. The photosynthetic rate or net CO, uptake in this model is dependent on the photosynthetically active radiation (PAR), the CO, concentration and the crop temperature. It is based on a model of primary production (Enoch and Sack?) in a C-3 plant (spray carnation). Standard component models in TRNSYS are used to calculate the solar radiation striking the crop. The shape of the total crop canopy is determined and the radiation incident on each surface of that shape is multiplied by its area and the products are summed. Warning statements are printed if the crop temperature exceeds 35°C or falls below 5°C. These warning levels can be readily adjusted. 2.3.2. Mathematical description The area of the crop which interacts with the environment is the horizontal crop area (Ac) multiplied by the leaf area index (Lr), where LC is defined as the area of leaves above unit ground area taking only one side of each leaf into account. For spray carnations (Enoch*) and tomatoes (Acock et aL5), Meyer, Sale and Kriedemanr? found that the shapes of the curves of predicted photosynthate production as a function of photosynthetically active radiation, leaf temperature and COz level were similar. From Enoch,* the photosynthetic uptake of COz for spray carnations is given by - (5~673+5~1822)2(r~-20~“O]x 1O-5 kg COz F = [0.3116(IPARac)o~‘*s(Ccoz)o~241(T~)o~167 (m-2 leaf) h-l, where ln(ZPA&) during the-daylight hours, ’ = 1ln(ZPAR&) during the following night, where (Jr~aAc) is the average rate of absorption of photosynthetically active radiation over the previous day. ZPARis assumed to be 50% of the solar energy incident on the crop. This photosynthetic rate for carnations was converted to that for tomatoes by multiplying by the ratio of tomato to carnation photosynthesis at 500 w/m2, 300 v.p.p.m. and 20°C. A value of 0.66 was found by Meyer, Sale and Kriedemann.6 The crop yield Y in kg/h can be calculated from F by introducing the total horizontal crop area AC, the leaf area ratio LI, the multiplier of 0.66 and a crop-specific multiplier which relates the COz uptake to the weight of the crop-Enoch suggests a value of 7. Hence, Y = (F A, Lr 0.66)7 kg/h. It should be noted that the IPAR is calculated as 50% of the total solar radiation incident on the top and sides of the crop, divided by the horizontal crop area to reduce it to the same unit area basis as the heat transfer mechanisms. A consequence of this is that for the same horizontal area, tall crops will absorb more radiation and have a slightly increased yield compared with shorter crops. The transpiration coefficient, Kt, is based on an average minimum stomata1 resistance,’ Rst of 1.3 s/cm and the boundary layer resistance, Rbl is given by Meidner and Mansfield* Rbl = 56.16 (d)“.46 D(90.56

.

Hence Kt = l/(Rbz+Rst). Transpiration throughout a plant canopy occurs at different rates. An empirical relationship was developed based on the difference between an extrapolation of single-leaf data and the observed’ transpiration of canopies. When calculating heat and mass transfer due to crop transpiration, a

408

YIELD

AND

ENERGY

CONSUMPTION

PREDICTION

reduction factor of l/1.8 was used to allow for the above. This value was derived from data coefficient is assumed presented by Lugwig, Saeki and Evans. 9 During the night, the transpiration to be reduced to 5 46 of the normal daytime value. The energy transfer mechanisms determining the crop temperature are shown in Fig. 3. The energy equations may be written as follows: Qac = I~+&, Qcc = h,aAc Li(Tc -Tgh), Qt = Kt(Li/1.8) A( Wc - Wsd h,, Q rgm =

?? gmc ~Agm (Z-c” -Tgm4>,

Qrf = cfc OfAc (Tc4 -Tft% Qr = f(Tc4, Tci”, Tcto4,Tsky4,em), see the Appendix. Radlatlon,O,

Absorbed

Fig. 3.

solar

Energy transfer mechanismsfor rhe greenhouse crop

2.4. Greenhouse air 2.4.1, General description In this model, the air state in the greenhouse at any particular instant is defined by its temperature and absolute humidity ratio. As there are no radiant terms involved and any thermal capacitance in the air is negligible, heat and mass balances are used to give explicit solutions for the absolute humidity and temperature at each time step. Provision has been made for both the addition and subtraction of sensible heat and mass by heating, cooling and/or dehumidifying devices. Natural and forced venting with ambient air may also be accommodated in addition to the effect of the infiltration of outside air. 2.4.2. Mathematical description The equations describing the various heat additions or subtractions are :

convective

energy transfer

Qcci = hcoaAco (Tci -Tgh), Q cgm --h

ww4sm Vgm -Tgh),

Qcc = hcdc Lt (Tc -Tyh), Per = hdf (Tft -TTgh),

mechanisms

and other sensible

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409

Qi = i V Cpapa(Tgh-Ta>, Qve = finCpa (Tgh-Ta>, Qh = hh &a (Tgh-T/L). Since at any instant for Tgh. Similarly, equations

the heat gained must equal the heat lost, an explicit solution may be written as below for the mass transfer

may be found

mechanisms:

M vgm = (h,,a/1~005) Me = hzi

Agm (W,, - Wd, 1~005) Af WJ( Wft - Wgd,

Mc = (kxz/1.005) AC Kt &r/1.8) (WC Mm

=

(km/

it’fi

=

i

Mh

=

kh

Mu,

=

fi,

1 .oos>

J‘&

( Wgh

-

Wgh),

wed),

vp,(Wgh-w-a),

( Wgh( Wgh -

wh), wa).

Again at any instant, the mass gained must equal the mass lost, and hence an explicit value of Wgh may be determined. It is assumed that the air is uniformly mixed within the greenhouse. It was assumed no evaporation of the water film on the cover would occur and condensation was not permitted to take place on the crop, although there could be condensation on the floor, growing medium and cover. 2.5. Co\aer 2.5.1. General description This model can be used to simulate a cover made from any material provided the extinction coefficient-thickness product and the refractive index are known. Single or double skin structures or single skin greenhouses employing a thermal screen may be modelled. In its present form the model is only applicable to greenhouses in which the walls and roof are made of the same cladding material. In the case of a double skin, the same material must be used for both the inner and outer covers. The structure to be modelled is first reduced to a number of flat surfaces of equal area. To do this may involve some approximation particularly when curved shapes are involved, but it was found by numerical experiment that a 3 m high polyethylene tunnel could be reduced to eight surfaces (six around the curve, plus two ends) without reducing significantly the calculated amount of radiation intercepted by the structure. No coefficient has been included to account for shading due to the structural members, but allowance may be made for this by reducing the radiation incident on the cover by an appropriate amount. To calculate this radiation a component of TRNSYS is used to sum the incident radiation on each surface, calculated by taking into account the different angles of incidence for each surface. An overall average value of solar absorbance and transmittance for all the surfaces is calculated from a knowledge of the values applying to each of the flat surfaces with which the structure is modelled. If condensation is detected, it is assumed that the solar transmittance will be reduced by IS:&. It has been estimated, lo.” that in a greenhouse with a condensate film two-thirds of the covering material will have moisture deposited on it. In this situation the long-wave transmittance of the cover is assumed to be reduced to 30% of its original value. If a double cover or the single cover plus screen is used, it has been assumed that there is negligible mass transfer past the inner layer (cover or screen) to the outer material. Although condensation may take place on the cover (or screen), evaporation is not considered to take place because the small amount of water contained on the cover would not sustain this mechanism for any significant time. The cover absorbs solar radiation, and transfers heat by convection to the greenhouse and ambient air streams. The external heat transfer coefficient is calculated using wind speed data.

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Energy transfer by radiation occurs between the cover, crop and sky. With a double cover or a cover and thermal screen, radiation exchange also occurs between the covers (or cover and screen). It has been assumed that only two reflections of each incident beam take place and that a cover can be partly transparent to long wave radiation (see the Appendix). The cover does not effectively “see” the floor or growing medium for radiation exchange because of the assumed complete crop cover. The thermal screen is assumed to be a total screen, i.e. with sides and ends fully enclosing the crop, and is used only for heat retention in winter. Operation of the screen is achieved by specifying the hours of the day in which it is covering the crop. 2.5.2. Mathematical description It is assumed that the cover has negligible thermal capacitance and consequently responds instantaneously to changed conditions. In this model, the external convective heat transfer coefficient, heoo, is determined by12 h e,,o = 2.8+3,8ws.

The internal heat transfer coefficient is supplied as a constant parameter. In the case of the double skin structure, the temperature in the air space between the two covers (or cover and screen) is not calculated, and hence an overall heat transfer coefficient for the two internal surfaces may be determined by viewing the appropriate two coefficients as resistances in series, as given by the expression

hct = (l,hct ,):(l,hcr,) ’ Hence, the energy equations for a single cover are : Qcco= AC,hcoo(Tco-Ta), Qcci = Acehcoa(TB~-Tco), Qc = Ace(hcoa/ l-005)hf, ( W,it - Wcr), QOCO= ZCO ACO ace, (see the Appendix). equations are :

Qrt = fWci4, Tsky4,Tc4,Tco4,ww) For the outer cover (two covers or one cover and screen) the appropriate Qeco = Aeo hcoo V’co -Td, Qa,, = Zco AC0 ace, Qcto = AC, hct WCC-Tco),

Tc4, ~ezw) Qro = f(Tco4,Gcy4,Tct4, (see the Appendix). The models described in section 2 have been incorporated in TRNSYS following the standard rules for constructing component routines. In all component models where no explicit solution exists for the dependent variables (because of highly non-linear dependence of coefficients and potentials on temperature, for example), Newton’s method of solution has been employed. 3.

Validation of models

Initial confidence in the models’ ability to simulate accurately the thermal performance of greenhouse systems arose from a previous validation programme which had confirmed the suitability of TRNSYS to simulate the performance of a solar heat generating system.13 As the component model used of a fully-developed tomato crop resulted from empirical curve fits, there

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41 I

was little reason to doubt its ability to simulate the photosynthetic uptake for a given set of values of solar radiation, leaf temperature and carbon dioxide concentration. An area of uncertainty was modelling the heat and mass transfer processes which determined the factors affecting photosynthetic uptake. Initial confidence in the validity of the model developed in this project was gained by comparing some simulated values with published data and by examining the hourly operation over a 24 h period. In all simulations heat and mass balances were checked and found to be better than 1 “/,. The results are presented in the following sections. 3.1. Winter operation Typical information generated for a 28 d winter period at an inland location in Australia is shown in Table 1. It compares the performance of a standard polyethylene-covered tunnel (A), size 6 x 10 m and fitted with an auxiliary heater, with a similarly sized tunnel (B) with the addition of 7 mz of solar air heater, 14 m3 of rockpile thermal store and a thermal screen for covering the crop at night. In both cases, heat is supplied to the greenhouse if the greenhouse air temperature falls below 10°C. The CO, concentration in the greenhouses was assumed to be 300 v.p.p.m. at all times. TABLE 1

Greenhouse type

Yield, kg

___A B

170.7 161.8

Absorbed solar energy, GJ

Energy transpired, GJ

AUX. heat, GJ

Heat from rockpile, GJ

Solar on horizontal, GJ/m2

Yield aux. heat,

15.54 15.53

9.52 9.48

4.35 0.41

1.64

0.26 0.26

39.2 394.6

kiGJ

The winter yield of 0.71 kg tomato m-2 week-l for the conventional house can be compared with measurements by MOSS” of the yield in winter at an inland centre in Australia where the greenhouse conditions were similar to those simulated. Moss measured a yield of 0.845 kg m-2 week-l in the first two weeks of picking when the average daily radiation outside was 10.3 MJ m-2 d-l. Moss found that there was a direct relationship between radiation level and yield, so it could be reasonably expected that at 10.3 MJ m-2 d-l, the simulation would result in a yield of about (10*3/9.3)x0.71 = 0.79 kg m-2 week-l, which is comparable with the measured value of 0.845. .’ The difference of significance in Table 1 is that the conventional greenhouse A used about 10 times as much auxiliary heat as that incorporating the solar collectors, rockpile and thermal screen. The predicted yield of 39.2 kg/GJ of auxiliary energy for A is high, but acceptable in a well-sealed conventional greenhouse. Comparison of the total heat of 4.35 GJ for tunnel A with that of 2.05 GJ for B indicates a saving of about 53% resulting from using a thermal screen to limit night-time thermal radiation loss from the crop to the sky through the partly transmitting polyethylene cover. This percentage saving is typical of values found experimentally.i5 Table 1 shows that about 60% of the solar radiation absorbed by the crop is transferred by transpiration and highlights the importance of the mechanism. Garzoli and Blackwelli6 found experimentally that transpiration from a fully-developed crop varied between 48% and 75%, with an average of 57 %. 3.2. Summer operation The use of a sealed greenhouse in Australian summer conditions presents a significant cooling and dehumidification problem if ambient venting is not used. For this project the use of a rotary enthalpy wheel” has been considered. These wheels will exchange heat and moisture from one

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airstream to another with only a very small amount of carryover, and with CO, enrichment the wastage of CO, will be minimized. The following simulation results were generated for a greenhouse with vertical sides to 2.7 m and a curved roof with a maximum height of 3.28 m. The floor area was 6 x 10 m and the crop height was limited to 2.35 m above the floor. The cover material considered was profiled Tedlar covered glass reinforced polyester. The operation of the enthalpy wheel was simulated by assuming equal greenhouse and ambient air flows and equal heat and moisture effectiveness of 75%. A simple spray type evaporative cooler with an efficiency of 60% was included after the enthalpy wheel to provide additional cooling with some dehumidification should the exit temperature from the wheel be in excess of 30°C. Typical air states for ambient air of 31°C and 50’$/,r.h. and greenhouse air of 35°C and 80% r.h. are shown in Fig. 4. The results for the summer month are shown in Table 2.

0 025

0 020 z \ ? 0015

5 al ; ‘1

50 %-r h

20

25

0010

30 Dry

Fig. 4.

g

p

35

“C

bulb temperature,

Typical air states for a greenhouse

with a total enthalpy wheel and an evaporative cooler TABLE 2

Yield, kg 544.1

Absorbed energy, GJ

Energy transpired, GJ

Solar on horizontal, GJln?

49.7

38.9

0.87

The enthalpy wheel operated 35% of the month, while the evaporative cooler was on for 18yo of the time. Comparison of Tables 1 and 2 shows that the solar radiation absorbed by the crop and the yield have increased by a factor of about 3.2 from winter to summer, indicating the dominance of

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R. J. FULLER

the photosynthetically active radiation in determining the net photosynthate. The simulated value of 2.3 kg m-2 week-’ was for a very high average daily radiation level of 31 MJ m - * d-l. Moss14 measured yields of about 2 kg m-2 week-’ over the 8th to 12th weeks of picking, but the average daily radiation level over the period is not available. His data were obtained in the latter part of September-October when the average daily solar radiation though high, would have This suggests that the simulated yield is again almost certainly been below 30 MJ m-* d-l. comparable with measured values under high radiation conditions. With the greater heat stress on the crop, the energy transpired is now almost SOyA of the absorbed solar radiation, a figure only slightly above the upper value of 750,;) reported by Garzoli and Blackwell. The frequency of occurrence of greenhouse air temperatures over the month is shown in Fig. 5. In spite of there being no venting, the greenhouse air temperature did not exceed 34°C and was generally at or below 30°C. Although there was no auxiliary heating, the temperature never fell below about 15°C. 160r

0

l-lII-I

14 16 I8 20 : Greenhouse

Fig. 5.

Frequency of occurrence

24 26 20

OCRtemperature

of temperatures

32 34 36 38

lntervol endmg.“C

in a greenhouse over a month

The variation over a 24 h period of solar radiation on the horizontal, ambient temperature, greenhouse air temperature, crop temperature and net photosynthate is shown in Fig. 6. The solar radiation profile is typical of a summer day in inland Australia, with little or no cloud, peak radiation levels of around 1100 W/m2 and total radiation in excess of 30 MJ m-2 d-‘. Maximum ambient temperature was over 37°C at 1500 h. From 2400 h to about 0500 h, the greenhouse air and crop temperature are actually below ambient. This is a result of night-time radiant cooling of the cover to a sink which was assumed to be 9 K below ambient. Normally, this would not be a noticeable temperature difference between the cover (and hence air and crop) and ambient because convective exchange of heat from ambient would balance the radiant loss. For the case illustrated in Fig. 6, the wind velocity was very low until 1000 h and thus the crop and greenhouse air temperature are depressed below ambient. This apparent difference is also due to the assumed instantaneous response of the crop and structure. In a real situation, capacitance of the crop and structure would minimize the difference in temperature.

YIELD

414

AND

ENERGY

CONSUMPTION

PREDICTION

06 05

___*--2 I 0

I I 4

, I‘./ I

I 8

I

I 12

I

I I I 16 20

04

1”

03

g

02

5

01

g ra f =

0 _--I

-0

,

24O 2

Hour of day

Fig. 6.

Variation of solar radiation on the horizontal, ambient temperature, greenhouse air temperature, crop temperature and net photosynthate over a 24 h period

Until sunrise, at about 0500 h, there is a net loss of photosynthate as the crop gives out CO,, in accordance with Enoch’s expression. After sunrise, there is a very rapid rise in solar intensity, crop temperature, greenhouse air temperature and photosynthate production. When the greenhouse air reaches 30°C between 0700 and 0800 h, the enthalpy wheel begins to operate and there is a drop in temperature of the air until the increasing radiation intensity causes the air to climb to almost 32°C at about 1200 h. At this stage, because the air exiting from the enthalpy wheel is in excess of 30°C the evaporative cooler after the wheel is energized and the crop and air temperatures level out. The wheel and evaporative cooler remain on until about 1900 h, when the greenhouse air temperature has fallen sufficiently far to turn them off. This is followed by a brief rise in crop temperature, but because the solar radiation level has now almost fallen to zero, the crop temperature again drops. The crop temperature is slightly below the greenhouse temperature between 1700 and 2000 h. This is because the greenhouse air has a lower absolute humidity than the air in contact with the leaf (assumed to be saturated) and the crop is evaporatively cooling itself below the greenhouse air temperature. This effect can also be due to radiant cooling of the crop, particularly if the cover is partly transparent to thermal radiation.18 From 2000 h until 2400 h all temperatures fall, but because of higher wind speeds than the previous night the greenhouse air and crop temperatures rapidly approach ambient air temperature. The shape of the net photosynthate curve closely follows that of the solar radiation, because of the dominant influence of photosynthetically active radiation in Enoch’s expression.4 The hourly examination of the system performance on a typical summer day indicates that the model shows qualitative agreement with expected trends.

P.

I.

COOPER;

R.

J.

415

FULLER

4.

Conclusions

Mathematical models have been formulated for the component parts of a greenhouse, namely the cover, the crop, the growing medium, the floor and the greenhouse air. These models have been incorporated into TRNSYS for use as a design tool for greenhouse systems. A particular feature of this modular approach to system simulation has been the use of an interactive C-3 plant model based on empirical correlations. Typical predicted values of crop yield and thermal performance have been presented for selected greenhouses for winter and summer operation. Significant energy savings with a modified greenhouse were demonstrated for winter operation. Simulation of the performance of a sealed greenhouse using an enthalpy wheel and evaporative cooler for dehumidification and cooling indicated that the predicted results would be acceptable if achieved in practice. Reference to published experimental data and trends measured under conditions which were similar to those simulated shows that the models are predicting the experimental values satisfactorily, indicating that a full-scale validation programme is justified. Future work should be directed at validating the absolute values of predicted greenhouse energy consumptions and crop yields. Acknowledgement Support for this project was provided under the National Energy Research, Development and Demonstration Programme, administered by the (Australian) Department of National Development and Energy. REFERENCES ’

Klein, S. A.; Cooper, P. I. ; Freeman, T. L.; Beekman, D. M. ; Beckman, W. A.; Duiiie, J. A. A method of simulation of solar processes and its application. Solar Energy, 1975 17 (3) 29-37

1 Kusuda, T. Calculation of the temperature of a flat plate wet surface under adiabatic conditions with respect to the Lewis Relation. In Humidity and Moisture, Vol. 1 Principles and Methods of Measuring Humidity in Gases (Wexler, A., Ed.). New York: Reinhold Publishing Corporation, 1965 16-32 ’ Enoch, H. Z.; Sacks, J. M. An empirical model of CO9 exchange of a C3 plane in relation to light, CO, concentration and temperature. Photosynthetica, 1978 12 (2) 150-l 57 ’ Enoch, H. Z. A theory for optimalisation of primary production in protected cultivation. Acta Hort., 19787645-57 * Acock, A.; Charles-Edwards, D. A.; Fitter, D. J.; Hand, D. W.; Ludwig, L. J.; Wilson, W. J.; Withers, A. C. The contribution of leaves from dtyerent levels within a tomato crop to canopy nett photosynthesis. An experimental examination of two crop models. J. exp. Bot., 1978 19 (Ill) 815-827 b Meyer, C. P.; Sale, P. J. M.; Kriedemann, P. E. Comparativephotosyntheticperformance in horticultural species based on simulation using functional versus empirical models. 9th Int. Bot. Congr., Sydney,

21-28 August 1981 ’ Korner, C. H.; Scheel, J. A.; Batter, H. Maximum leaf di&ive conductance in vascularplants. Photosynthetica, 1979 13 (1) 45-82 a Meidner, H.; Mansfield, T. A. The Physiology of Stomata. New York: McGraw-Hill, 1969 p Ludwig, L. J,; Saeki, T.; Evans, L. T. Photosynthesis in artificial communities of cotton plants in relation to leaf area I. Experiments with progressive defoliation of mature plants, Aust. J. biol. Sci., 1965 18 1103-1118 lo Walker, J. N.; Walton, L. R. Effect of condensate on greenhouse heat requirements. Trans. Am. Sot. agric. Engrs, 1971 14 282-284 ” Garzoli, K. V.; Blackwell, J. An analysis of the nocturnal heat loss from a single skin plastic greenhouse. J. agric. Engng Res., 198126 203-214 ‘* Watmuff, J. H.; Charters, W. W. S.; Proctor, D. Solar and wind induced external coeflicients-solar collectors. Int. Rev. d’Heliotech., 2nd Semester 1977, 56 ” Cooper, P. I. ; Sheridan, J. C. The simulated and experimental performance of a solar heat generating system. Am. Sot. Mech. Engrs J. Solar Energy Engng, 1982 104 (November) 317-325 ” Moss, G. I. Root-zone warming of tomatoes in nutrient-film as means of reducing heating requirements. J. Hort. Sci. 1983 58 (1) 103-109

416

YIELD

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CONSUMPTION

I5 Hanan, J. J.; Holley, W. D.; Goldsberry, K. L. Greenhouse Management.

PREDICTION

New York: Springer-Verlag,

1978 172-175 lb Garzoli, K.; Blackwell, J. The response of a glasshouse to high solar radiation and ambient temperature. J. agric. Engng Res., 1973 18 205-216 ” Dunkle, R. V.; Banks, P. J.; Ellul, W. M. J. Regenerator research, development and applications in Australia-1978 status. Int. J. Refrig. 1978 l(3) 143-l 50 ’’Seemann, J. Climate under glass. World Meteorological Organization, Tech. Note No. 131, 1974 Appendix Thermal

radiation

exchange

between

the environment, two partly opaque surface

transmitting

surfaces

and an

Some of the cover materials commonly used on greenhouses will partially transmit thermal radiation, e.g. polyethylene cladding. To model the radiant interchange between the crop, the covers and the surrounding environment, it is necessary to derive a mathematical relationship which adequately describes the radiation transfer. Because of the problems involved in developing a general relationship which takes into account all inter-reflections, the following analysis has been restricted to only two reflections of each beam. This approximation will not result in any significant errors, as the product of three or more reflectances each of which are not normally greater than 0.1, is a very small number. A general schematic diagram of the emission, absorption and reflection of thermal radiation between the sky, two covers and an opaque surface is shown in Fig. Al. The sky is assumed to be a black body at temperature TS. For each surface a radiation balance of the following form can be written: Net radiation

loss from surface = (radiation emitted) -(incoming (absorbance of surface).

radiation)

x

Referring to Fig. Al, let the subscripts 1, 2, 0 and s apply to the outer cover, the inner cover, the opaque surface and the sky. p, T, a and E are the reflectance, transmittance, absorbance and emittance of each surface to thermal radiation.

Surface

I

Surface

2

Surface 0 (opaque)

Fig. Al.

Schematic

diagram of the emission, absorption and rejection of thermal radiation between the sky, two covers and an opaque surface

Surface 0

The incoming radiation to the opaque surface which originates from the sky, surface 2, surface 1 and itself and allowing only two reflections is shown schematically in Figs AZ. Radiation

from sky = ~~~~~~~~(1+plp,+p,p,+p,p,7,2),

Radiation

from 2 = •,uT,~ (1 +p0p2+po~22p1),

P.

I.

COOPER;

R.

J.

FULLER

417

Radiation

from 1 = T~E~cJT~~ (1 +popz+pIp2+pop1~22),

Radiation

from 0 = QuT,,~ (pz+ ~~~p~),

Radiation

emitted from 0 = E,uT,~.

Then, net radiation

loss from opaque surface =

‘o~~,4-ao[(l+PoP2+P~P2+PoP~T22)(~~72~~4+T2E~~.T~4) +E~uT~~(~+PoPB+Po~:!~P~)+Eo~~~~(P~-~~~~P~)~ x c”uT”4 [1 -a0b2+722dl

-4l

fPoPefP1P2tPoP1722)

(T172UTs4+T2E1uT~4)+~2u~24 (~+PoP2+P0~2~f~)l. In a similar net radiation

manner,

radiation

balances

on the two covers yield the following

loss from cover (1) = <,uT14 [2-al(p2+T2’p0)]

-aI

results:

[uTS4 (1 fT1f2~T1foT22)

+E2u~24(~+f1f2+f1T22f~+f0T2)

+Eou~04(T2+f~f2T2+fof2T2+T23fof~I~

net radiation

loss from cover (2) = E,uT,~ [2 -a2(p,tP,,+2P,,P1T2)] -a2tT,~~s4(1+f~f2+foT2+fof~T22)

+W’~04(~+f2fo+f~T2+T22f~fo)

+E~u~,4(~+T2f~+P~foT22+f~f2)1~

Fig. A2. (Top left) Radiation from sky which reaches the opaque surface after no more than two reflections; (top right) radiation from surface 2 which reaches the opaque surface after no more than two reflections; (bottom left) radiarion from surface I which reaches the opaque surface after no more than two reflections; (bottom right) radiation .from the opaque surface which is rejected back on itself after no more than two reflections