Validation of a dynamic model for predicting energy use in greenhouses

J. agric. Engng Res. (1987) 38, l-14

Validation

of a Dynamic Model for Predicting Energy Use in Greenhouses

R. J. FULLER*; C. P. MEYER*; P. J. M.

SALE*

This paper describes the measurements made in a polyethylene-covered unventilated greenhouse containing a growing crop and their use to validate a previously reported predictive model of transient energy use. Over a 40 h period of intensive measurement and a 5-day period in winter, the measured and predicted energy use differed by no more than 10%. Prediction of maximum day-time temperature was satisfactory, the greatest error being 2.2” at 27.6”C. The following parameters are examined in relation to the sensitivity of the model to variations

in their magnitude: sky temperature, air infiltration, ground sink temperature, thermostat setting, internal and external heat transfer coefficients, incident solar radiation, cover transmittance and plant transpiration. Some areas where further work is necessary are suggested.

1. Introduction A generalized mathematical model of a greenhouse structure containing a mature tomato crop has been previously reported by Cooper and Fuller.’ It was developed first to assess the design options for a small experimental low energy greenhouse system, intended as a possible prototype for a larger commercial unit to produce fresh food in remote areas of inland Australia. Secondly, the model was intended for wider application as a design tool for non-specialist users in the field, such as consulting engineers and agricultural extension officers, who might be called upon to design and evaluate various greenhouse options. To meet this objective a model was required which broadly could be described to be: (a) (b) (c) (d)

user orientated; readily available; capable of allowing simulation of the full engineering system; able to use available climatic data.

The model would also be required to evaluate greenhouses using active solar components, since such systems have already met with some commercial acceptance in Australia. For these reasons, it was decided that an existing solar simulation program, TRNSYS, would be used as the basis for the greenhouse model. The program is already used by several public and private institutions in Australia, and as described previously,’ it is used extensively for simulating the performance of solar energy systems because of the ease with which a user can interlink component models. In our work, five new subroutines were developed-crop, floor, growing medium, cover and airspace-to describe the main component parts of a greenhouse, and these were compatible with the existing program. Its main disadvantage was that at the time of the original formulation of the model, it was only available for use on mainframe computers. Its current availability in Microsoft Fortran for the IBM-PC and XT will enable it to be used more easily at commercial levels. * CSIRO Centre for Irrigation and Freshwater Research, Griffith,

NSW

2680,

Australia

Received 17 September 1985; accepted in revised form I1 October 1986

0021~8634/87/090001+

14 %03.00/O

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1987 The British Society for Research in Agricultural

Engineering

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A comparative study using data reported by other researchers justified the use of Cooper and Fuller’s model’ to make relative judgements about the effect of various solar and conservation strategies on energy consumption and crop yield.* This in turn led to the design and construction of an experimental facility, of which one purpose was to provide data for the validation of the model in an absolute sense. In general, the models and validation data reported by previous workers in this field have been concerned largely with comparisons of measured and predicted temperatures rather than energy quantities. While accurate temperature prediction is of prime importance during the daytime for determining energy levels in excess of greenhouse requirements, during the night it is the accurate prediction of energy consumption which is the ultimate requirement of a model. Those researchers who have considered energy consumption have obtained variable results. Kimball,3 using the most comprehensive of his models, only compared measured energy consumption with predictions made using average climatic data derived from 10 years of meteorological records. He did not make predictions using the actual climatic forcing functions of the days when energy measurements were made. While measured and predicted values were of the same general order, discrepancies of up to 50% were common. Duncan et ~1.~developed a greenhouse energy balance simulation model and calibrated it over a 3-day period. In a validation run made over a subsequent 3 days the model predicted temperatures satisfactorily but over-predicted energy consumption by 56x, which they attributed to faulty logic in thermostat modelling. While Arinze et al.’ reported agreement within 2% between measured energy consumption and that predicted by a thermal model, their results were for only a single night and the following morning; a comparison over a longer period is essential before confidence can be placed in simulated performance. They also found that a time step of 300 to 600 s was necessary to achieve sufficient accuracy of prediction, which makes longer runs expensive in computer time. Other researchers, e.g. Chandra et a/.,6 Rotz et al.,’ have considered predictions of energy use by their models but only in general terms and without specific comparisons. One of the most important requirements of our own model’ was that it should be able to predict greenhouse energy requirements over extended periods, and this aspect is therefore emphasized in this validation paper. In addition, there is discussion on changes made in some of the original model assumptions and their effect on the model performance, and the current shortcomings of the model are identified as potential areas for future work. It is anticipated that this will provide a sound basis for further development of the model by future users. 2. Experimental procedure The greenhouses constructed for the purpose of model validation have been described elsewhere.* An experimental greenhouse with a solar air heater, rock pile storage and thermal screen was built alongside a more conventional polyethylene-covered structure equipped with an electrical resistance heater and evaporative cooling. The daily energy consumption values for both greenhouses were measured over an entire growing season and have been published as monthly totals.’ The original intention had been to validate the model primarily by comparison of predicted performance with the measurements taken in the experimental greenhouse, and some preliminary results using this data have been reported by Fuller et ~1.” However, the complexity of modelling the operation of this greenhouse, 10 operating modes being possible, proved to have two disdavantages. First, almost all of the routines permissible (50) in a TRNSYS simulation were required to describe the engineering system adequately, leaving barely enough output routines (printers, integrators, etc.) for analysis.

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Secondly, analysis of the response of the greenhouse model itself was made more difficult by the complex operation of the logic and engineering hardware routines (controllers, thermostats, etc.). It was therefore decided that initial validation would be carried out using data collected from the simpler control greenhouse. The test period used for the validation was 40 h from 1700 hours on 8 June to 0800 hours on 10 June 1983. Data logging was nominally every 15 min when greenhouse dry and wet bulb air temperatures were recorded using solid state temperature sensors (AD590, Analog Devices, USA), two pairs of sensors being located in and above the crop rows. Plant water use and electrical energy consumption were read hourly from sight gauges and kWh meters, respectively. Climatic data was recorded continuously by the standard meteorological facility of the Centre on an area adjacent to the greenhouses, and Fig. 1 shows the ambient conditions for the 40 h test period; they were quite typical conditions for Griffith. The first night was cold with clear skies and a gentle wind. The following morning was clear until midday when scattered cloud presaged the approach of a change. The first half of the second night was also clear and still, but then cloud cover gradually built up until, by 0800 hours. there was full cover and light rain. Consequently, the second night was warmer than the first. 3. Model parameters The predictions of a model of any description will be dependent on (a) the general assumptions built into the model, (b) the specific parameters supplied to the generalized model to describe the particular system under scrutiny, and (c) the quality of the data used for the forcing functions. To eliminate areas of uncertainty, as many parameters as possible were measured. Tables 1, 2 and 3 list the parameters used in the simulations. Table 1 shows those measured by the authors, Table 2 those derived from other sources and Table 3 those for which only estimates could be made. The model includes a submodel which considers the effects of the growing medium, but since our crop was grown by nutrient film technique the growing medium area was set to zero and consideration of growing medium is therefore irrelevant in this instance.

Time,

h

Fig. 1. Ambient conditions for 40 h period. ~, horizontal radiation intensity; temperature; ., wind speed

- -

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ambient dry bulb

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Table 1 Parameters measured by authors Value

Parameter Emittance of polyethylene cover (dry)* Longwave transmittance of polyethylene Cover area Floor area Greenhouse volume Leaf area index Thermostat setting Auxiliary heater size Floor mass Floor thickness Projected area of crop

cover (dry)*

0.35 0.57 122.5 60 141.4 2.7 11.5 54000 14400 0.1 42.2

Uniis

mz $ “C kJ h-’ kg ,“z

* If condensation formed on inner surface of cover, model reduces longwave transmittance to 17%. and emittance increases to 75% as discussed by Cooper and Fuller’

4. Results

The measured energy use in the polyethylene tunnel on the two nights, 8-9 June was 322.9 MJ and 177.8 MJ respectively. Model predictions for the corresponding periods were 272.1 MJ and 189.7 MJ, giving a 16% underprediction on the first and a 7% overprediction the second night. An hourly comparison of measured and predicted energy use is given in Fig. 2. The apparently big fluctuations in hourly measured energy consumption, particularly on the first night, are likely to have been caused by the method of recording. The power meters were read by the operator nominally every hour, and a difference in meter reading time of 10 min, for example, would result in a 9 MJ addition or subtraction to the apparent energy used over that hour. However, even allowing for this, the model did underpredict in the coldest part of the night. Hourly values of measured and predicted greenhouse dry bulb air temperatures are shown in Fig. 3 for the 40 h experimental period. While there was acceptable agreement at most intervals, the figure illustrates a small problem that was experienced with the radiation processor in TRNSYS. This standard routine takes hourly horizontal radiation data and calculates the radiation falling on defined planes. It occasionally has problems at the end of the day, around 1700 hours or 1800 hours when angles of incidence are low, and overpredicts the radiation levels. Thus, at 1800 hours on both days differences of up to 5°C resulted between the prediction and the recorded temperature. The results of testing the model over a 7-day period (5-12 June) are shown in Fig. 4. Because of temporary failures in the data collection system, sky temperature data for the Table 2 Parameters and inputs derived from other sources

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Table 3 Parameters and inputs for

which estimates were made T

Value

Parameter Convective heat transfer crop to air Convective heat transfer floor to air Convective heat transfer inside cover to air Average absorptance of greenhouse surfaces Average leaf width Velocity of air in crop

Units

coefficient 12.5 coefficient 14.1 coefficient 10.1 internal 0.9 0.025 0.05

0100-0900 hours on the second night and 1900-0900 hours on the third night had to be estimated, and assumed either full cloud or clear sky conditions. Over the 5 nights for which full climatic data was known 1132 MJ of energy was used and the model predicted 1213 MJ, i.e. an overprediction of 7.2%. As outlined earlier, accurate prediction of daytime temperatures in a greenhouse is important not only for use in determining ventilation requirements, but also in assessing excess energy available in the structure. There is growing interest from the Australian nursery industry in using this energy to offset conventional heating requirements, and the economic viability of this strategy will be largely determined by the quantities of excess energy available. While the model appears to have a general tendency to underpredict maximum daytime temperatures, this is usually only by a small amount as indicated in Table 4. periods

5. Discussion The comparisons given above use data from the best simulation runs achieved within the time available, which is normal practice when reporting model validation. However, in the course of the validation, several parameters and mechanisms were scrutinized in detail to establish that predictions of the magnitudes of these mechanisms were within acceptable limits. The purpose of this was to proceed with some logic through the validation process (rather than merely manipulating parameters to achieve satisfactory results). This would, in turn, mean that if unacceptable differences still existed, then the heat and mass transfer mechanisms worthy of further study could be profitably identified.

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Fig. 2. Hourly

measured

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measured

3.

and predicted

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h

greenhouse dry bulb air temperatures. - - , predicted

__,

measured:

Validation process

The mechanisms and parameters studied in more depth can be conveniently divided into those which have a significant effect during the daytime, defined as the solar irradiated period, and the night-time or non-solar period. The following mechanisms or parameters are important in determining the energy losses from a greenhouse at night: (a) (b) (c) (d) (e)

sky temperature; infiltration; ground “sink” temperature; thermostat setting; internal and external heat transfer coefficients;

while during the daytime the important factors are: (a) incident solar radiation; (b) cover transmittance; (c) plant transpiration; and it is these which will largely determine the daytime temperature structure.

regimes within the

Table 4 Measured and predicted daytime maximum greenhouse air temperatures Predicted

Date 6 7 8 9 10 11 12

June June June June June June June

Temperature, “C

Time, h

Temperature, “C

Time, h

26.9 N.A. 23.3 27.6 23.2 25.9 26.1

1145 N.A. 1345 1404 1315 1404 1415

26.0 24.6 23.0 25.4 21.3 25.4 24.8

1200 1300 1400 1400 1300 1500 1500

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300 -

-i 250H .E 200 E zl 2 1508 2 tJ IOOI; 50-

I

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5-6

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6-7

7-0

t

I

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1

9-10 IO-11 II-12

8-9 June

Fig. 4. Daily measured and predicted energy consumption. ?? , measured energy use; 0, prediction made , prediction made using fill cloud cover; A, prediction made using clear using known sky temperatures; ? ? sky conditions

The section below discusses the investigations into each of the above and the conclusions to be drawn at this stage of the validation. 5.2. Dominant factors in night-time energy balance 5.2.1.

Sky temperature

In the original model, an average sky temperature was used. This was defined by a constant parameter and determined by the user from the prevailing conditions likely to be

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measured: - - - , predicted using Fig. 5. Hourly measured and predicted sky temperatures. -, observers’ estimate of cloud cover; ., outside ambient dry bulb temperature

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encountered in the area. In inland Australia, for example, sky temperatures of 20°C below ambient are not uncommon on cloudless nights.14 Due to the sensitivity to this parameter, this approach was found to be inadequate. The effect of sky temperature on energy use at night is illustrated by Fig. 4 when simulation runs were made on the third night, assuming either full cloud cover or clear sky conditions. Predicted energy use was 171.4 MJ and 252.5 MJ respectively-an increase of over 40% for the clear sky compared with full cloud conditions. Sky temperatures had been generated using the expression proposed for clear sky conditions by Idso and Jackson15 and the modifier for cloudy conditions developed by Cole.” These expressions were found to give an acceptable prediction of sky temperature when compared to measurements made with an Epply Pyrgeometer (Fig. 5). Climatic data tapes available in Australia contain hourly estimates of cloud cover and the above expressions have now been incorporated into the model to improve the prediction of sky temperature. 5.2.2. Infiltration Actual infiltration rates in both greenhouses were determined by the equilibrium method and found to be represented by the relationships AER = 0.7 +0*19 V for the tunnel,

(1)

AER = 0.1 1 + 0.0244 V for the solar greenhouse,

(2)

where AER = air exchange rate per hour and V = wind speed (km h- ‘). Conservation measures in the experimental greenhouse, i.e. a thermal screen and reduced air infiltration were shown by Fuller et al.’ to be responsible for a 46% reduction in total energy consumption in the winter growing season of 1983. The effect of reducing the infiltration in the polyethylene tunnel over the 40 h period to the level of the experimental greenhouse was determined by substituting Eqn (2) for Eqn (1) in the tunnel simulation runs. An average reduction in energy requirement of 12.4% was achieved. The thermal screen had been estimated experimentally to reduce9 the energy consumption in the experimental greenhouse by approximately 24%. The predicted reduction of over 12% from reduced infiltration therefore agrees satisfactorily with overall energy saving achieved by conservation. 5.2.3. Ground sink temperature The floor subroutine used in the greenhouse model is simpler than that proposed by many other modellers, having only an instantaneously responding top layer and a main floor mass responding with time. Actual ground temperature was not measured below the polyethylene greenhouse during this experiment and so for the present purpose, the sink temperature to which losses from the concrete slab occur has been taken as 10*2”C, which is the average soil temperature for June at 20 cm depth calculated from readings taken on an adjacent meteorological station at 0900 hours and 1500 hours each day over a 9-year period. However, the model is sensitive to this temperature. Increasing its value by 2”C, decreases energy consumption by 12.5% for the two nights, while a decrease of 2°C in the same parameter produces an increase in energy use of a similar amount. It was also found that when a sink temperature of ll.l”C, i.e. only 0.9”C greater than the long-term average was used in the week-long simulation, that daily predictions improved noticeably with f 15% being the greatest variation from the measured result. Over the 5 days this resulted only in a 1 MJ difference between the measured and predicted use. Again, this highlights the sensitivity to this parameter, and it is an area suggested later as requiring further work.

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Thermostat setting

The setting on the thermostat dial in the control greenhouse was 12°C but the mean of all the temperature measurements recorded during the heating period of the two nights was 11~5°C. As previously stated, this was used in the simulation runs. The effect of using 12C, i.e. 0.5”C higher was to increase the energy consumption prediction by 7.2%, indicating the sensitivity and benefits of achieving a good level of thermostat response. 5.2.5. Heat transfer coeficients There would be no area of greenhouse modelling in which greater variation of opinion exists than in the correct choice of external and internal convective heat transfer coefficients. Some of this variation is graphically shown by Kimball.” Some more recent investigations7*‘8 have followed the relationships suggested by ASHRAE” for flow past a vertical plate which used McAdams*’ expression h, = 5.7+3.8 V, where h, is the convective heat transfer coefficient in Wm- 2 Cm 1 and V is the air velocity measured in m s- I. Kimball” also uses these coefficients for a similar linear expression in an example of the use of his model. It has been suggested by Watmuff et al.** that this expression contains a radiation term and since this mechanism has been considered separately in this model, it is inappropriate. Excluding the radiation term reduces the intercept in the expression from 5.7 to 2.8 and this lower value has been used in our greenhouse model. For the calculation of the internal convective heat transfer coefficient, it has been assumed that the air velocity in the closed greenhouse is zero. The sensitivity to these parameters is demonstrated through a comparison with the expression advocated by Garzoli and Blackwell. 23 They found from a study on a single layer plastic greenhouse that the equation h, = 7.2+ 3-8 V

was the best fit to their experimental data. Similarly, the first term of the right-hand side of the equation is used for the value of internal convective heat transfer coefficient. Only a small increase in predicted energy usage (less than 1%) resulted from changing only the external coefficient, but an increase of over 50% resulted from the use of both internal and external values of the magnitude suggested by Garzoli and Blackwell. 5.3. Dominant factors in daytime energy balance 5.3.1.

Solar radiation

Some investigators4*24*26have used the horizontal global radiation falling on a surface equal to the size of the greenhouse floor attenuated by some transmittance factor to calculate the amount of solar radiation penetrating the greenhouse. While this technique may be acceptable for structures covering a large area, where the roof is the dominant surface, this approach is inadequate when dealing with smaller greenhouses. The influence of the side walls increases in importance as the structure decreases in size and it is often data from small structures that has been used to validate models. If the 6 m x 10 m hemispherical tunnel is reduced to eight flat surfaces of approximately equal area, the total solar radiation falling on the structure can be calculated using the standard radiation processor routine in TRNSYS. This is shown in Fig. 6 for 9 June 1983, a midwinter day, and is compared with the amount of solar radiation that would be predicted incident on the cover if only horizontal radiation and the floor area are used. Even allowing for the overestimate that the processor makes late in the day at 1800 hours, mentioned in Section 4, the differences in estimated solar radiation striking a small structure

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\ \ \ \

1’

.g

ENERGY

\ t

0 * 40-

0

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14

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Fig. 6. Comparison of estimates of hourly solar radiation intercepted by a 60 m2 polyethylene-covered tunnel greenhouse in midwinter. - - -, summation of radiation falling on eight inclined surfbces, , using horizontal radiation only

in midwinter are considerable. At midday, for example, the simpler method underestimates by approximately 37%. 5.3.2. Solar transmittance of covering material The solar transmittance of the glazing material is often supplied as a fixed parameter, its value being based on experience for a certain structure24 or an average value for various angles of incidence. 26 For small structures subject to winter radiation where angles of incidence may be high, the correct approach is to calculate the transmittance for each surface of the greenhouse based on the angle of incidence on that surface. The radiation penetrating the structure is then the sum of the products of the transmittance and incident radiation on each surface. TALF, a standard routine within TRNSYS, has been used to calculate the transmittance of each surface. Parameters supplied for this calculation are the thickness extinction coefficient product and refractive index of the particular glazing material. Predictions of the transmittance of polyethylene for various angles of incidence (O-60“) are compared against those measured on an integrating sphere*’ (Fig. 7). An averaged weighted transmittance for the structure is obtained by dividing the summed transmittance-incident radiation products by the summed incident radiation. Hourly values of this value of transmittance are shown in Fig. 8. They compare well with the measured daily ratio of internal to external horizontal solar radiation of 0.69. The amount of energy actually entering the greenhouse is therefore calculated as the product of the total quantity striking the cover and the average weighted transmittance on each hour. Although it is assumed that no radiation passes straight out of the greenhouse without striking some surface, the above product is reduced by approximately 9% to allow for the radiation which is lost by internal reflection. This is determined using the analysis described by Duffie and Bechman. ** Finally the captured radiation is partitioned between the crop and floor using the ratio of projecied crop to floor area (0.7) as the partitioning factor. 5.3.3. Plant transpiration The production of latent heat through crop transpiration is a powerful mechanism operating during the day, accountable for up to three-quarters of the absorbed solar radiation.*” Measured hourly water use by the crop is compared with that predicted (Fig. 9). While predicted water use at night compared well with the quantities measured, serious

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Angle

of incidence,

’

Fig. 7. Solar transmittance of 150 m UV stabilized polvethylene cover (thickness-extinction product = 0.05 refractive index = I-41). , measured; - - - , predicted

overprediction section.

co@icient

occurred in the daytime. The reasons for this are discussed in the next

5.4. Areas for future work 5.4.1.

Crop and air temperature differential

Measurements taken in the experimental greenhouse showed that the crop and surrounding air temperatures were close together ( f l.S’C) for most of the test period. The model, however, predicted a greater divergence, crop temperatures being up to 44°C greater than air during the day, and up to 2.7”C below greenhouse air temperature at night. Measurements taken at a later date confirm that night-time leaf temperatures can be below their surrounding air temperatures in a polyethylene tunnel, presumably because of the effect of the partial transmittance of the material to longwave radiation. The daytime crop temperature predictions are unsatisfactory and are responsible for the overprediction of transpiration during the day. This in turn led to predicted saturated air conditions during the day when in reality the water vapour content of the air was lower than this.

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Fig. 8. Hourly values of weighted transmittance ( ) used in simulation compared with measured daily mean ratio of internal to external horizontal radiation ( - - - )

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Fig. 9. Hourly measured and predicted crop water. ___,

measured; - - -, predicted

The incorporation of some mass in the crop model, estimated in this instance to have been 700 kg, may have helped, but this would have led to unacceptably small time steps being required to maintain computational stability, a problem also experienced by other workers.5 5.4.2. Floor model The greenhouses described in this paper were constructed on concrete slabs, and while the existing floor model may be satisfactory for this or similar constructions, it is felt that the model requires further development so that other types of floor, e.g. earth or gravel, may be simulated. 6. Conclusion A mathematical model has been tested against data gathered from a small unventilated plastic greenhouse. Predictions of energy consumption are within 10% over a 5-day period. Predicted maximum daytime temperatures generated in the greenhouse are close to measured temperatures, the greatest error margin being 2.2”C at 276°C. Some of the important parameters and mechanisms which dominate an unventilated greenhouse have been identified separately to ascertain whether their individual magnitudes are also within acceptable limits. However, the authors are conscious that while acceptable results have been achieved in temperature and energy predictions over both short and extended periods, it is possible that the model is “calibrated” only against a particular experimental facility. Further testing of the model is required against other structures to prove its generality. The present model shows considerable promise for development into a generalized greenhouse design tool and areas of further work which will enable this to be done have been identified. Acknowledgements Although no longer directly involved in the project, the advice from Dr P. I. Cooper is gratefully acknowledged. Thanks are also due to J. C. Sheridan for the assistance he gave on several occasions

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relating to the operation of TRNSYS. Many people in the Centre for Irrigation and Freshwater Research assisted in the running of the experiments and data collection, especially R. Dalgleish, R. D. Sides, G. I. Moss, G. S. G. Shell, R. E. Speed and A. Ceresa. Dr P. I. Cary checked the typescript.

References 1 Cooper,

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3 4

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P. I.; Fuller, R. J. A transient model of the interaction between crop, environment and greenhouse structure for predicting crop yield and energy consumption. Journal of Agricultural Engineering Research 1983, 28(S): 401-417 Fuller, R. J.; Cooper, P. I. Computer simulation and design of a low energy greenhouse suitable for food production in a hot dry climate. Proceedings International Workshop ‘The Solar Greenhouse-Architecture and Agriculture’, Perpignan 1982, Vol. 3, pp. 199-219 Kimball, B. A. Energy storage for greenhouses in an arid climate. American Society of Agricultural Engineers 1980, Paper No. 804029, San Antonio, Texas Duncan, G. A.; Loewer, 0. J.; Colliver, D. G. Simulation of energy flows in a greenhouse: magnitudes and conservation potential. Transactions of the American Society of Agricultural Engineers 1981, 24(4): 1014-1021 Arinze, E. A.; Schoenau, G. J.; Besant, R. W. A dynamic thermal performance simulation model of an energy conserving greenhouse with thermal storage. Transactions of the American Society of Agricultural Engineers 1984, 27(2): 508.-5 19 Chandra, P.; Albright, L. D.; Scott, N. R. A time dependent model of the greenhouse thermal environment. Transactions of the American Society of Agricultural Engineers 1979, 24(2): 442-449 Rotz, C. A.; Aldrich, R. A.; White, J. W. Computer predicted energy savings through fuel conservation systems in greenhouses. Transactions of the American Society of Agricultural Engineers 1979, 2(2): 362-369 Fuller, R. J.; Sale, P. J. M. A solar heated greenhouse for maximum crop yield and low energy usage. CSIRO Centre for Irrigation Research Information Leaflet No. 22-3, 1983 Fuller. R. J.: Meyer, C. P.: Sale, P. J. M. Energy use and conservation in a solar heated greenhouse. Transactions bf the’ Institution of Engineers, Australia, Mechanical Engineering 1985, lO(4): 241-245 Fuller, R. J.; Cooper, P. I.; Sale, P. J. M.; Speed, R. E. W. Crop yield and energy use in a solar greenhouse. Proceedings International Solar Energy Society Solar World Congress, Perth, 1983. Vol. 2, pp. 1222-1226 AIRAH Design Data Manual, Section 3, Parts 1 and 2, Australian Institute of Refrigeration, Air Conditioning and Heating. Parkville, 1978 Monteith, J. L. Principles of Environmental Physics, 3rd ed. London: Arnold, 1973 Garzoli, K. V. Ph.D. Thesis. Melbourne University, 1984, pp. 398-403 Dunkle, R. V.; Christie, E. A.; Cooper, P. I. A method of measuring sky temperature. Proceedings of International Solar Energy Society Silver Jubilee Congress, Atlanta, Georgia, 1979, Vol. 3, pp. 2222-2226 from the atmosphere. Journal of Geophysical Idso, S. B.; Jackson, R. D. Thermal radiation Research 1968,74: 5397-5403 Cole, R. J. The longwave radiation incident upon the external surface of buildings. Building Service Engineer 1976, 44: 195-206 Kimball, B. A. Simulation of the energy balance of a greenhouse. Agricultural Meteorology 1973, 1 I(2): 243-260 Froelich, D. P.; Albright, L. D.; Scott, N. R.; Chandra, P. Steady periodic analysis of glasshouse thermal environment. Transactions of the American Society of Agricultural Engineers 1979, 22(2): 387-399 ASHRAE Handbook of Fundamentals. American Society of Heating, Refrigerating and Airconditioning Engineers, New York, 1972 McAdams, W. H. Heat Transmission, 3rd ed. McGraw Hill, New York, 1954 Kimball, B. A. A modular energy balance program including subroutines for greenhouses and other latent heat devices. Agricultural Research Service, Phoenix, Arizona, 1983 Watmuff, J. H.; Charters, W. W. S.; Proctor, D. Solar and wind induced external coefficientssolar collectors. Comples 1977, 56: 6

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23 Garzoli, K. V.; Blackwell, J. An analysis of the nocturnal heat loss from a single skin plastic greenhouse. Journal of Agricultural Engineering Research 1981, 26: 203-214 24 Garzoli, K. V.; Blackwell, J. The response of a glasshouse to high solar radiation and ambient temperature. Journal of Agricultural Engineering Research 1973, lS(3): 205-216 *5 Maher, M. J.; O’Flaherty, T. An analysis of greenhouse climate. Journal of Agricultural Engineering Research 1973, 18: 197-203 26 Walker, J. N. Predicting temperatures in ventilated greenhouses. Transactions American Society of Agricultural Engineers 1965, 8(3): 445-448 27 Fuller, R. J.; Cooper, P. I. Solar transmittance of Australian greenhouse cladding materials. Agricultural Engineering Australia 1983, 12(l): 25-33 28 Duffie, J. A.; Beckman, W. A. Solar Engineering of Thermal Processes. Wiley, New York, 1980