Application of a model for calculating glasshouse energy requirements

Energy in Agriculture, 3 (1984) 99--108 Elsevier Science Publishers B.V., Amsterdam -- Printed in The Netherlands

99

APPLICATION OF A MODEL FOR CALCULATING GLASSHOUSE ENERGY REQUIREMENTS

S.N. WASS' and I.A. BARRIE 2

Meteorological Office, Ministry of Agriculture, Fisheries and Food, 'Bristol BS10 6NJ (Great Britain) 2Wolverhampton WV6 8TQ (Great Britain) (Accepted 3 January 1984)

ABSTRACT Wass, S.N. and Barrie, I.A., 1984. Application of a model for calculating glasshouse energy requirements. Energy Agric., 3: 99--108. A model to calculate glasshouse energy requirements from meteorological data is described. The model uses a heat balance equation relating transmission losses, ground heat flux, solar contribution, input from the heating system and CO 2 production in order to quantify the effects of variations in weather, glasshouse temperature regimes and glasshouse dimensions. Model estimates are compared with fuel-use figures supplied by four growers in the South West of England. These comparisons demonstrate how the model can be used for measuring the efficiency of glasshouse heating systems and for the costing of fungal disease control procedures which involve heating the air. An example is also given of how the model can be used for planning purposes by showing the spatial variability in energy requirements over Great Britain.

INTRODUCTION A s s e s s m e n t o f glasshouse h e a t i n g e f f i c i e n c y is usually limited to the boiler alone b y m e a s u r i n g t h e t e m p e r a t u r e and CO2 c o n t e n t o f the flue gases. T y p i c a l glasshouses have low t h e r m a l inertia c o m b i n e d w i t h high transmission losses w h e n c o m p a r e d w i t h m o s t buildings. T h e s e features, c o u p l e d w i t h t h e high t e m p e r a t u r e s required for y e a r - r o u n d m o n o c r o p p i n g , m a k e glassh o u s e e n e r g y r e q u i r e m e n t s in t h e U.K. very d e p e n d e n t o n m e t e o r o l o g i c a l c o n d i t i o n s . H e a t loss increases with the t e m p e r a t u r e d i f f e r e n c e across the glass; increasing w i n d increases transmission losses f r o m all surfaces and increases t h e a d v e n t i t i o u s v e n t i l a t i o n rate, whilst irradiance m a y m a k e a useful positive c o n t r i b u t i o n t o t h e e n e r g y r e q u i r e m e n t s . E s t i m a t e s o f w e e k l y fueluse, derived f r o m m e t e o r o l o g i c a l d a t a averaged over m a n y years, m a y well be in e r r o r in a n y p a r t i c u l a r w e e k b y m o r e t h a n 100%. T h e r e are several c o m p r e h e n s i v e m o d e l s t o simulate the e n e r g y balance o f a glasshouse (e.g. Kimball, 1 9 7 3 , 1 9 8 1 ) b u t t h e y require m o r e detailed infor-

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© 1984 Elsevier Science Publishers B.V.

100

mation than is usually available for commercial houses. Moreover the quality and resolution of site representative meteorological data does n o t justify their use in practical advisory work. This paper describes a simple model for calculating energy requirements and presents results which demonstrate how it can be used to enable a grower to quickly assess the probable cost of any changes in his operating procedure without having to wait for many months or even years to distinguish between effects attributable to the new procedures and effects due to the weather. It will be shown that such a model is capable of producing fuel use estimates comparable to weekly measurements made on a commercial nursery. MODEL DESCRIPTION

Data collected during an investigation into thermal screening (Bailey, 1979) were used to develop the model. The model is described in detail b y Wass (1980), b u t may be summarised briefly as follows: The p o w e r required to maintain a glasshouse at a target temperature is given by: Q = A(UF(Ti-

T a ) - K * - Q g - Qf)

(1)

where A is the ground area; U a heat transmission coefficient; F the glass to floor ratio; T i the internal temperature; T a the outside air temperature; K* the net short-wave radiation; Qg the flux from the structure, ground and contents, hereafter called the ground flux; and Qf the heat flux density due to combustion in the CO2 production process. Glasshouses are usually vented at a temperature above their target temperature b u t we are only concerned with the energy required to achieve the target temperature. Equation 1 is evaluated for every hour and a daily or weekly summary of each term is produced. TRANSMISSION COEFFICIENT

The heat transmission coefficient (U) is usally related to windspeed and typical values have been reported by a number of workers (e.g. Kimball, 1973). The coefficient shows considerable variation depending on the age, type, condition and exposure of the glasshouse under investigation b u t as will be shown later a precise expression is not essential when the model is used for comparison purposes. We chose to use that obtained by Bailey in his experiments. He found that the transmission coefficient at night was: U = 5.25 + 0.375 Ur

(W m -2 K -1)

for the glass

(2)

where Ur is the windspeed (m s-1) measured away from the glasshouse and corrected to ridge height. This expression implicitly includes long-wave radiation loss and transfer of heat from the soft. The relationship m a y n o t be true

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for houses with a large plan area. In the calculations of our model, outside air temperatures are assumed to follow sinusoidal functions between maxim u m and minimum temperatures whilst internal temperatures achieve their day or night values immediately at dawn and dusk, respectively. RADIATION

Daily short-wave irradiance is calculated from hours of bright sunshine (Cowley, 1978) and its distribution through the day is assumed to follow a half-cycle cosine curve. To ascertain h o w much of the solar energy can be utilised for heating, a regression analysis of estimated daytime heat requirements against solar energy was carried o u t on Bailey's data. Using days when the vents remained closed (Fig. 1) this empirical technique gave: K~ = 0.46 K, - 1.066

(MJ m -2)

for the ground area

(3)

where K ~ is the daily net short-wave radiation contribution to space (and soft} heating and K~ the daily incoming short-wave radiation estimated for an area outside the glasshouse. 6 O Non venting days V

4

Venting days %z 'T

2

".=

0

.c. o

1

I

I

1

I

1

I

I

2

4

6

8

10

12

14

16

Solar radiation [MJ m-2)

Fig. 1. D i f f e r e n c e s b e t w e e n c a l c u l a t e d d a y t i m e h e a t losses using e q u a t i o n 2 a n d g e n e r a t e d h e a t against solar r a d i a t i o n d u r i n g F e b r u a r y a n d M a r c h 1979.

The intercept of - 1 . 0 6 6 M J m -~ results from neglect of the ground flux term Qg in both the derivation of equation 2 and in the calculation of the available energy plotted in Fig. 1. Making use of the fact that the heat flux into the soil in the morning as the air temperature is raised to its target value, must broadly equal the heat flow o u t of the soil in the evening, when the air temperature falls to its target night time value, it was calculated that a more appropriate expression for the heat transmission coefficient was:

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U -- 5.82 + 0.375 Ur

(W m -2 K-~ )

(4)

and that an average value for the heat flow into the soil during the day was 0.532 MJ m -2. In equation 3 the intercept has 95% confidence limits o f - 0 . 5 2 a n d - 1 . 6 1 and the slope has limits of 0.37 and 0.55, also at the 95% probability level. Assuming a mean transmissivity for solar radiation of 0.65 for the glass (Edwards and Lake, 1965) and an albedo of 0.2 for the crop (Van Wijk, 1963) then a coefficient of 0.46 for K~ suggests that 88% of the incoming solar energy was utilised. Investigations of the variation in the rate of water loss from tomatoes (Rothwell and Jones, 1959) have shown that about 65% of the total radiation entering the glasshouse is used for transpiration. Our results suggest that much of this energy is recovered when latent heat is released during condensation, though some is inevitably lost through leakage of water vapour out of the building. In the model, equation 1, the solar contribution is limited to that which is needed to achieve a balance; any excess is assumed to be vented to atmosphere. GROUNDFLUX

From measurements made in a nursery glasshouse (Bailey, 1979) the assumed average value for ground flux of 0.532 MJ m -2 corresponded to a mean diurnal variation of internal temperature o f 3.5 K. This gives a mean daily value for heat flow from the ground and structure of 0.152 MJ m -2 K -1. At sunset, when the internal temperature is allowed to fall to the night time value, the inverse power law deduced from experiments in unheated glasshouses is applied to permit the slow release of the stored heat (Whittle and Lawrence, 1960) : Qg = Qs/2 t

where Qs is the total heat stored in the soil and structure; and t is the number of hours from sunset. A similar expression is used for the supply of heat in the morning when the temperature is raised to its daytime value. Although only strictly applicable to glasshouses with a soil-based system, recent results from growers using nutrient fluid techniques indicate no loss of overall accuracy. COMBUSTION

It is c o m m o n practice to burn hydrocarbon fuel during the day to generate carbon dioxide. The model assumes t h a t fuel is burnt during daylight hours when transmission and ground heat flux losses exceed the solar input. For tomatoes fuel is burnt at a recommended rate that produces 55 kg h -1 ha -1 of CO2. For propane as fuel Qf in equation 1 is set to 24.38 J m -2 h -1, whereas for paraffin Qf is set to 17.35 J m -2 h -1. Although the fuel burners

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are usually controlled by the vents opening or closing, the model only sums contributions from CO2 production during daylight hours when there is a n energy deficit. RESULTS

Results demonstrate how the model can be used for the analysis of individual nurseries energy use and for long term planning purposes. During the first 6 months of 1981 four tomato growers in the South West of England supplied weekly fuel readings and target temperatures. There was considerable variation in glasshouse design and temperature regimes but all four used a central boiler house and single oil supply. The area under glass varied between 0.59 ha and 2.11 ha. Energy requirements were calculated by the model, using data recorded at the nearest meteorological station, corrected where necessary for exposure and altitude (Smith, 1976). Total calculated energy requirements were then expressed as a fraction of the total net calorific value of the fuel burnt to give a weighting factor which was subsequently used to scale individual weekly model estimates (Wass, 1981). Figure 2 shows the comparison between estimated and recorded fuel use, expressed in energy units, for site B which was 3 km from the nearest meteorological station. The conversion factor of 0.76, in this case, provides a standard which can be used to compare the results with other sites and also a 0

80

0 0

70

O

60

i

50

%

E 0 ---

0

40

0 0 0

3o

0

0

0 0 0

20 0 10

I

I

I

I

I

1

I

I

I

10

20

30

40

50

60

70

80

90

Energy I~rom fuel (MJ m-21

Fig. 2. Comparison

of model

estimates

and weekly

fuel use figures

for site B.

104

m e a n s o f investigating the effects o f any change o n the same site. Results f o r all f o u r sites are s h o w n in Table I. A m o r e detailed e x a m i n a t i o n o f site C will serve t o d e m o n s t r a t e a n o t h e r application o f the model. Weekly m o d e l estimates c o m p a r e well with fuel readings b e t w e e n weeks 2 and 13 as s h o w n in Fig. 3. It should be n o t e d t h a t fuel was m e a s u r e d b y a dipstick and r e c o r d e d t o the nearest 2 5 0 0 l which w o u l d c o n t r i b u t e t o t h e r o o f m e a n square (rms) e r r o r o f 3 2 8 7 1. A f t e r week TABLE I Comparison b e t w e e n estimated and actual energy requirements Glasshouse site

A B C D

Area (ha)

2.12 1.82 1.29 0.59

Distance f r o m Correlation meteorological coefficient station (kin)

Number of weeks

7 3 10 21

19 19 12 19

0.97 0.97 0.92 0.93

rms error

Conversion factor

(GJ) (1) 169 83 104 68

7150 2810 3290 2350

0.61 0.76 0.81 0.75

X

t

80

6C I E

I I

i.u

4O

From fuel records number 2C Model estimates Excess due to forced venting

I 5

I 10

I 15 Week number

Fig. 3. Comparison of m o d e l estimates and weekly fuel use figures for site C.

l 20

105

13, forced ventilation was used for disease c o n t r o l and the effect can be seen as the difference b e t w e e n actual and estimated energy use from calculations w h i c h assume a c o n t i n u a n c e o f earlier normal procedures. The 9-week excess is equivalent to over 56 0 0 0 1 o f oil. The usefulness o f m o d e l s like the o n e described is that o n c e d e v e l o p e d and verified t h e y can easily be run with either different data sets or with different c o n t r o l parameters. Figure 4 s h o w s the spatial variability over Great

3000

?

2200 '2000

Fig. 4. Average annual energy required ( M J m -2) to maintain 20°C by day and 16°C by night in a glasshouse with glass to floor ratio = 1.6 (lowland sites only). Standardised 20-year period 1961--1980.

106 Britain of the mean annual energy required to maintain glasshouses of similar dimensions at 20°C by day and 16°C by night based on meteorological records for 34 stations. After verification of the technique a similar analysis could be made for most regions because of the simplicity and availability of the input variables. Table II shows the annual mean energy balance components calculated by the model from 20 years meteorological data for Birmingham assuming a day/night regime of 20°C/16°C and F ratio of 1.6 (see equation 1). It can be seen that over an average year the heat supplied to the ground during the day is n o t fully recovered as useful heat during the night; thus, following the resetting of the thermostats in the abrupt changeover from daytime to night time target air temperatures, there may be a period when the system cannot in practice recover the heat flux coming from the ground. Such situations will occur when internal temperatures remain above the night time target temperatures for sometime after the changeover, because external temperatures are close to target temperatures. TABLE II Calculated mean annual energy budget for a glasshouse sited near Birmingham, 1961-1980 (for hours when boiler was assumed operative)

Day Night Total

Losses (MJ m-2)

Gains (MJ m-s)

To ground

Transmission

From ground

COs production

Solar contribution

Boiler

323 0 323

1703 1702 3405

0 200 200

178 0 178

880 0 880

968 1502 2470

The reverse situation in the morning changeover does not occur since the solar contribution is insufficient to meet the heating requirements and over a season the heating system has to compensate for this imbalance. Another application is demonstrated in Fig. 5 which shows the mean annual energy required to maintain a glasshouse at various day and night target temperatures. From such a diagram it is possible to estimate the likely energy demands set by various temperature combinations as an aid to economic planning. Reducing growing temperatures reduces fuel costs but carries a penalty of delayed growth. The pecked isopleths in Fig. 5 show the effect of different temperature regimes on just one growth stage of tomatoes, the number of days between flowering and ripening of the fruit (Hurd and Sheard, 1981). Such types of analysis, based on several years of meteorological records, are now possible with the advent of computers and access to large climatological data banks.

107 Night-time temperature (°C) 0

2

4

8

10 12 14 16 18 20 22 I

22-

\

21 2000 20 -

~

\\

~\

\

19 \\

\

\

17

\

"~ 16 E

\\

15 looo

60

\\\~

= a

\ 12

I

\\

\ \

18 1500

I

~

~,

. c°~ o~

500

11 10

\\ g

90

J

O°

Fig. 5. Average annual heat requirement (MJ m -2) for combinations of day/night temperature regimes calculated from Birmingham meteorological records, 1961--1980.

ACKNOWLEDGEMENT

The authors would like to acknowledge the help given to them by the growers who supplied fuel-use data.

REFERENCES Bailey, B.J., 1979. Glasshouse thermal screen development farm project. First season: heat consumption and environment. NIAE Dep. Note DN/G/981/04013, National Institute of Agricultural Engineering, Silsoe, Great Britain, 36 pp. Cowley, J.P., 1978. The distribution over Great Britain of global solar irradiation on a horizontal surface. Meteorol. Mag., 107 (1277): 357--373. Edwards, R.I. and Lake, J.V., 1965. Transmission of solar radiation in a large-span eastwest glasshouse. II. Distinction between the direct and diffuse components of the incident radiation. J. Agric. Eng. Res., 10 (2): 125--131. Hurd, R.G. and Sheard, G.F., 1981. Fuel saving in greenhouses. Grower Guide, 20: 29--46. Kimball, B.A., 1973. Simulation of the energy balance of a greenhouse. Agric. Meteorol., 2(2): 243--260. Kimball, B.A., 1981. A versatile model for simulating many types of solar greenhouses. Pap. 81-4038. American Society of Agricultural Engineers, St. Joseph, MI, 46 pp.

108 Rothwell, J.B. and Jones, D.A., 1959. The water requirement of tomatoes in relation to solar radiation. Exp. Hortic., 5: 25--30. Smith, L.P., 1976. The agricultural climate of England and Wales. In: Tech. Bull. 35, HMSO, London, pp. 3--18. Van Wijk, W.R. and Scholte Ubing, D.W., 1963. Physics of Plant Environment. NorthHolland Publishing Co. Wass, S.N., 1980. The solar contribution to glasshouse heating. Agric. Memor. 903, an unpublished paper available from National Meteorological Library, London Road, Bracknell, Berks., 11 pp. Wass, $.N., 1981. Estimating glasshouse heating efficiency. Agric. Memor. 924, an unpublished paper available from National Meteorological Library, London Road, Bracknell, Berks., 5 pp. Whittle, R.M. and Lawrence, W.J.C., 1960. The climatology of glasshouses. J. Agric. Res., 5(2): 165--178.