The application of heat pumps to glasshouses

Building and Environment, Vol. 12, pp. 165 174. Pergamon Press 1977. Printed in Great Britain

I

1 I

I

The Application of Heat Pumps to Glasshouses S. K. NISBET K. K. CHEE A theoretical analysis is undertaken oJthe application o/the heat pump to glassh¢mse heating. An introductory description q['glasshouses and heat pumps is given and an expressionjor the heat load is derived. The optimum heat pump capacity isJbund to be essentially independent of the heat source or drive and is about 100 k W /103 m 2 ground area. An economic'analysis shows that substantial savings would resultfrom using engine driven heat pumps. A n air to air electric drive heat pump becomes attractive if oil prices rise to 34p/gallon against an eleetricity tariff q( 1.76p/k Wh.

sections with fairly large panes of glass, typically 1.65 m × 0.73 m x 4 mm thick, clipped over p.v.c, bedding strips. The extruded sections are so shaped to provide strength, interior and exterior water drainage channels, and glazing surfaces. The gable ends are more substantial and costly than those intermediate, and cost can be reduced by having a fairly long glasshouse. This is modified in practice by the site topography coupled with the desire for an East/West orientation to maximise light and the need to work machinery within the structure. There is a wide variation in size from the small to those in excess of l hectare (21 acres). However, the most common size by numbers being installed at present is about 103m2 (¼ acre). Because heat pumps may be installed in multiple units of varying cost per unit output size effects were reduced by basing the analysis on a Venlo type glasshouse having a nominal ground area of 103m2 (¼ acre). This form of construction is the most popular for the ground size chosen. It was assumed to have three bays dimensioned as indicated in Fig. 1.

1. I N T R O D U C T I O N AT PRESENT 90 % of the glasshouse industry uses some form ofoil heating[l]. When this is coupled with the fact that fuel costs represent about 20To of the crop cash return, the vulnerability of the industry to the recent rapid rise in oil prices is readily apparent and any practical means of reducing heating costs deserves consideration. In the following analysis the economics of heating glasshouses by replacing part of the heating system by a heat pump is examined. The method adopted has been to consider a typical glasshouse growing early tomatoes/winter lettuce located in the West of Scotland, and to compare, by calculation, the capital and running costs of a conventional oil fired air heating system with heat pumps using various combinations of drives and sources. The optimum size of heat pump is determined for each case. The results presented should be of interest both to horticulturalists and to proponents of the heat pump. Because the former may have little acquaintance with heat pumps and the latter with glasshouses (greenhouses) brief descriptions of relevant aspects of both are included. Much of the data used in the analysis was presented in f.p.s, units and calculations were completed in these units before conversion to the S.I. system. Since the former system appears still to be well entrenched in practical horticulture a dual presentation of units is given where appropriate.

Heating and temperature control

Most modern glasshouses have automatic temperature control. When the solar radiation gain is too high to give the required temperature, cooling is applied by opening ventilation panels in the roof. It should be noted that the so-called "grc,_'nhouseeffect' is less of a radiation trap and more of a convection suppressor in the ratio of one part to two[2]. In conditions when the solar gain is absent, or insufficient, heating must be supplied, usually in the form of an oil fired boiler/calorifier system or by oil fired fan assisted air heaters in smaller houses. Relatively few glasshouses now use coal fired heating and a lesser number run on gas owing to remoteness from the gas main. The heat load depends upon heat transfer parameters

2. THE GLASSHOUSE The function of the glasshouse is to provide the optimum environment for plant growth. This is achieved basically by providing temperature and ventilation control, wind shelter, sometimes extra light, CO2 enrichment, etc. T h e structure

In order to maximise entry of light, the present trend is to make the structure of fine extruded aluminium alloy

t

Department of Mechanical Engineering, The University of Glasgow, Glasgow.

,9.2m Fig. 1. Glasshouse dimensions.

165

I

S.K. Nisbet mid K. K. C/tee

166

without and within the glasshouse. The lormer is essentially weather dependent, rather difficuh to average for the U.K. as a whole. As a consequence this analysis assumes the glasshouse to be located in the West of Scotland, whose climate is characterised by moderate temperatures and by sonaewhat greater cloud cover compared to most other parts of the U.K. The interior temperature required in the glasshouse depends upon the crops grown and what is considered to be the optimum growing conditions. It was assumed that the crops were early tomatoes, from December to September, followed by a crop of winter lettuce from September to December. The glasshouse temperatures are shown in Table I and are those suggested by the West of Scotland Agricultural College Advisory ServiceD].

whose area is about 20",i of thai of the ground in modern houses. The majority of ventilation systems arc manually controlled, but there is an increasing trend to inslal automatic ventilation equipment[l]. A few glasshouses use side fans to assist air movement and sometimes spray cooling is used with this system. The "natural" air infiltration rate depends upon the "lightness" of the glasshouse, gaps a n d ' o r cracks in the structure, and upon the wind speed. When the ventilation system is closed down the air change rate is about one half per hour for modern glass under cahn conditions rising to three per hour under windy conditions[4]. 3. T H E H E A T P U M P Heat pumping devices form one of the most common

Table 1. Glasshouse temperatures Night

Day Crop

Tomatoes

Lettuce

Period

1½weeks December Mid December end January February- Mid April Mid April Octob,:r September December

C

F

C

20

68 64 68 64 60

18.3 15 15 16.7 8.3

17.8 20 17.8 15.5

65 59 59 62 47{min

Yearly time averaged interior temperature = 16.4 C (61.6 F).

Humidity The humidity level in the glasshouse can rise to near saturation conditions if left unchecked by the operation of the ventilation system, the more advanced of which incorporate psychrometers into their controls. Although the level of humidity does not appear to be critical, high levels are detrimental to plant growth since condensation on the plant surface produces conditions favourable for fungoid growth. In the heat transfer analysis an average value of 70 % was assumed for the relative humidity. Carbon dioxide It has been demonstrated that CO2 enrichment of the air promotes improved photosynthesis and growth, and it is normal practice to increase the CO2 content of the air to about 0.1%, about three times normal, during daylight hours provided the ventilation system is not open substantially. The CO2 is provided from bulk storage, liquid or solid, or by burning propane. Carbon dioxide is one of the gases which will absorb and emit radiation and its presence is considered in estimating the heat load. bentilation An environmental factor which has a substantial bearing on the heating, or cooling, load is the ventilation rate. Some small air infiltration equivalent to an air change rate of one or two per hour is necessary for photosynthesis, but a higher rate merely serves to increase the heat load. However, during periods of high solar gain the temperature will tend to rise well above that desired and the ventilation rate is increased accordingly to sometimes over 60 changes per hour. Ventilation is achieved by opening ridge hinged panels or windows

classes of thermodynamic machines in common use. They are most likely to be encountered as refrigerators in which heat is pumped from a cold compartment and discharged to waste. When the utilization of the heat is changed, that is the discharged heat is utilized, the device is termed a heat pump. Naturally the cold compartment is replaced by a much warmer heat source, often ambient air. The semantics become confusing when it is realised that most heat pumps can reverse the heat flow and operate as cooling devices. There has been a steady, but relatively small, demand for heat pumps over the last three decades, the principal market being found in wealthy regions where the heat pump can capitalise on its cooling ability to overcome its higher initial cost. When fuel prices were relatively low the heat pump could not compete effectively in the U.K. when required principally for heating duty. The situation is now changing because the recent substantial rises in fuel prices have increased the running cost advantages sufficiently Dr heat pump manufacturers to claim a 25 "~;,saving t 1974

Outdoor coil

clltH C

%

Indoor coi~

H

Compressor

IIIIIP C ~b,<3

I

Fig. 2. Simple heat pump circuit.

The Application of Heat Pumps to Glasshouses prices) over oil fired systems[5], and a reduction in the capital cost differential. A diagrammatic representation of a simple basic air to air, split heat pump is shown in Fig. 2. In the heating cycle the working fluid in the vapour state is compressed and passes to the indoor coil in which it condenses, transferring its latent heat to air forced over the coil. This heated air flow is the useful output of the pump. The working fluid, now liquid, passes to a throttling device where it drops in pressure to a very wet vapour. It then enters the outdoor coil in which it evaporates back to a dry vapour by abstracting heat from an outdoor air flow. This is the heat source. The vapour is now returned to the compressor and the cycle is repeated. When cooling is required the reversing valve redirects the flow as shown. In practice the cycle is necessarily more complex and usually incorporates an accumulator heat exchanger placed after the evaporator, a subcooling control valve, metering devices, heat exchangers, drier filters, etc., and in the larger units multi-stage compression is often advantageous. Such details, and further references, are readily available in the literature and are not treated here[6-8]. However, certain factors require further elaboration.

Coefficient of performance The energy utilization of the heat pump is usually expressed by manufacturers as the Coefficient of Performance, C.O.P., and defined by them as the useful heat output per unit of energy input. The relationship between the idealised C.O.P. and the Carnot cycle, and the more realistic Rankine cycle, can be found in Thermodynamic texts. Despite the fact that in practice the highly irreversible heat transfer reduces the measured C.O.P. to less than half that predicted by the Rankine cycle, the idealised cycle analysis is valuable because it shows that the C.O.P. is a function of the ratio of the fluid condenser temperature to the difference between the fluid temperatures in the condenser and evaporator. In effect this means that the C.O.P. falls with increasing output air temperature and rises with increasing input (source) air temperature. The output also decreases with decreasing source temperature. These effects are shown in Figs. 3 and 4. The curves are averaged from manufacturers' literature. Care is required in the interpretation of manufacturers' data because the coefficient of performance may be defined for the compressor alone, thereby excluding the power requirement of the condenser and evaporator air fans and the power requirements of the control system. The power consumption of the air fans can be substantial, taken in this analysis as 25 ~o of the compressor power input. If the fan power is incorporated into the C.O.P. the effect is to move the curve to the left as shown in Fig. 3. It will be seen that the C.O.P. so modified agrees fairly well with the measured values, inclusive of fan power, quoted by Heap[9] for a small heat pump. It should be noted, of course, that some of the fan power will be recovered as useful heat. This recovery has been ignored in this study.

Compressor drives The great majority of heat pumps have electric motors to drive the compressor because of general convenience, ease of control, long life, freedom from vibration and their

167

'

il'l

,'/ /

/'/ / //

////

~;o -5

2 Coefficient

3 of p e r f o r m a n c e

4

Fig. 3. Effect of source temperature on C.O.P. (a) compressor coefficient of performance (bj reduction in C.O.P. due to fan power consumption (c) measurements by Heap[9]. ability to be readily incorporated into sealed units. But they suffer from the major disadvantage that electricity costs are high. By replacing the electric motor with some form of engine fitted with heat recovery plant the running costs can be substantially reduced. The practical choice of engine for glasshouse use is at present limited to the Diesel owing to the absence of mains gas supply. Of the fuel energy received by the engine about 33 ~o is converted into the compressor input, virtually all of the jacket heat, 30 ~o is recoverable, and 10 ~o of the fuel energy as exhaust, has been successfully recovered[10]. Thus for an average C.O.P. of 2.6 it is seen that 1.27 kW of useful heat output is obtained per 1 kW of fuel energy consumed. A conventional oil fired heating system will do well to supply 0.8 kW per 1 kW fuel input, giving an advantage to the engine driven heat pump of some 60 ~o improvement in energy utilisation. The figure of 1.27 kW is conservative. The Festival Hall heat pump[ 113 had an equivalent figure of 1.4kW, using a water source and complex heat

~1°1~ Eol ~1

I0

m o

-5

50

Nominal

I00

heat pump capacity,

150

kW

Fig. 4. Heat pump output variation with source temperature.

168

S. K. N i,shet and K. K. (+hee

recovery plant. Engine driven heat pumps are available in the U.K. as "custom-built' units but not yet apparently as "off-the-shelF packaged units+ ()n a cautionary note it should be stated that engine driven units tire uncommon, probably because of higher capital costs and complexity, reliability problems, vibration and noise, and just msulTicient development.

Heat sources The heat pump requires a cheap, reliable heat source in order to function. Figures 3 and 4 show that ideally this should be at as high a temperature as possible. A wide variety of heat sources are used but only those available to horticulturalists are considered. A iv Atmospheric air has the advantages of convenience, abundance, cheapness, cleanliness, and has two major drawbacks. Firstly, the demand for heat is greatest when air temperature is lowest, and Figs. 3 and 4 show that the heat pump is at its worst at the time of maximum need. Secondly, cold humid air is liable to freeze on the evaporator coil requiring flequent operation of the defrost system. Despite these disadvantages air source heat pumps are by far the most common and should be fairly well suited to the West of Scotland's moderate climate. Water By incorporating the outdoor coil in a heat exchanger water can be used as a heat source. It has the advantage of not suffering from defrost problems and is often at a higher temperature than air. But it is not always available particularly in the form of higher temperature waste water. However, interest is currently being shown in the U.K. and in France in using power station cooling water, possibly at 15 C ( 6 0 F), as a heat pump source for horticulture established adjacent to power stations. It has been claimed[12] that glasshouse heating by a heat pump using well water as a sourcc would be economic. Well water has the advantage of being fairly uniform in temperature throughout the year, thus maintaining a steady and high annual average C.O.P., but again it is not always available and drilling costs can be high. River and loch water may vary in temperature too much to justify the piping costs, and legal restrictions often abound.

Soil Various attempts have been made to use the ground as a heat source by burying a pipe grid, of 1 2 m pitch, some 1 2 m below the surface. At these depths daily and seasonal temperature cycles are much reduced. Although this source remains theoretically attractive, the actual performance is reduced progressively by insulating air spaces appearing around the pipe as a result of pipe working[13]. Problems are also encountered in maintenance and leak detection. The ground area involved can be large, a rough extraction rate of l kW per 30m of 2 0 m m pipe[14] indicates a ground area requirement about twice that of the ghlsshouse it serves. While crops have been grown above a collecting grid without deletereous effect[ 14], the

prospects are unlikely to be attractive to a horticulturist and consequently have not been inchlded in this analysis

Sizing aml additional heutiJ~g The relatively high capital cost of the heat pump does not permit it to be sized equal to the maximum heating load. In domestic practice a unit is installed which will give a condenser coil output equal to about 4 0 " , of the maximum heat load. The remaining 60 ?, load is provided by banks of electrical resistance heating elements incorporated into the packaged unit. The running cost is high, of course, at near maximum demand but this condition occurs for only a small fraction of tile heating season. The situation is different tor glasshouse applications. Relatively high temperatures have to be maintained tit night, and heat pump capacities are much greater so thai electrical resistance heating is uneconomic. In this study tile additional heating is provided by oil fired air heaters which are aheady well established in the glasshouse industry. Their choice also simplifies the optimisation procedure and the comparison between the heal pump end conventional heating plant. 4. T H E HEAl" L O A D

It is important to ditTerentiate between the heat load for sizing the heating plant and the heat load to determine rtmning costs. In the former case the heat load is estimated for extreme adverse weather conditions while for the latter case it is found for statistically averaged conditions. The nominal capacity of heating plant suitable for early tomatoes was taken at its common value of 290kW/103m 2 ~4×10 ~'Btu:h acre)[3]. If tile overall structural heat loss coefficient, t' value, is taken as 7 . 9 W m e C < l . 4 B t u / h f t 2 F)[3,15], the corresponding sizing temperature difference is 25 C. This is equivalent to a minimum outside night temperature of 10C113 F),a conservative figure for the West of Scotland considering that a temperature lower t h a n - 5 ('{21 F ) is likely to occur lbr only 26 h/yr. When running loads tire calculated with a t l value of 7.9W/m2 C (l.4Btu/hft 2 Fi it is found that the predicted oil consumption is some 16% higher than that measured in practice. While this is not an excessive error it was found that running loads dominated the comparison between heating options, and a more accurate U value reflecting the West of Scotland climate was required. This was obtained as follows. The steady state heat balance for a glasshouse can be expressed in the folh)wing equation :

Qh+Q,+Qr<,,+Q<,=Q<.+Q~+Q, +Q~±Q,,-t-Q, I l l where Qj, is the heat supplied by beating system: Q~ is the solar heat gain; Qr~,.
169

The Application of Heat Pumps to Glasshouses The terms Q.... Qe, Qp are usually small in relation to other terms and are neglected. The equation can be further simplified by noting that the evapotranspiration rate is approximately a fixed fraction, t, of the solar heat gain rate[16], and that the heat loss to the ground can be expressed as a fraction of the total heat load[15, 17], averaged at 5 ~ in this case. Thus equation (1) reduces to:

Qh={Qc+Qr+Q~,-(1-t)Q~}I.05.

(2)

The estimation of the running cost of a heat pump is particularly difficult because, as already seen, its C.O.P. and output vary substantially with source temperature. Therefore recourse is made to climatological tables which give the percentage time during which given temperature bands (usually 2°F) occur in any region. The tables do not distinguish between day and night and consequently it becomes necessary to reduce equation (21 by averaging to the simple temperature function:

Qh=l.O5A(h~+h,+h,.-h~)(ti-to)

(3)

where the h terms are overall heat transfer coefficients averaged over the year and related to the glass surface area, A, and the inside/outside temperature difference (ti - to), the subscripts remain as before.

Convective heat transfer coefficient, h¢ The convective heat loss from the glasshouse structure cannot be quantified accurately. It is dependent crucially on the boundary layer form, which in turn depends on the wind, local topography, roof angles, general size, etc. Care must be exercised in the choice of a convective heat transfer correlation because the large dimensions involved can easily push the Grashof and Reynolds numbers beyond their limiting values. The one chosen representative of forced convection from the glasshouse surface to the ambient air is the Colburn correlation given by McAdams[18] :

h (Cpp~2/3

Cpv;\ k Jl

0.036

(LvP/~) °2

(4)

where the symbols have their usual connotation. A forced convection correlation is unsuitable for use at low velocities where the mechanism of convective heat transfer is characterised by free convection. The free convection correlation was again chosen from McAdams[ 18] :

measured at a height of 40ft (not 10m). This can be reduced to a mean glasshouse roof height of 4 m (12 ft) by multiplying by the height ratio raised to the power 0.17. The corrected average windspeed is therefore 7 m.p.h. The glass temperature is generally unknown and it becomes necessary to eliminate it by considering the heat transfer from the air within the glasshouse to the exterior air. Although an air heating system will produce localised high velocities which may scour a small fraction of the glass, the mean air velocity will be well below 0.3 m/s (1 ft/s) and the interior convective heat transfer coefficient will be characterised by free convection. Using equation (5) gave a convective heat transfer coefficient interior air to glass of 3.08W/m 2 °C (0.54Btu/hft 2 °F). This will underestimate the heat transfer because it ignores mass transfer arising from condensation on the glass.

Radiation heat transfer coefficient, h r In evaluating thermal radiation effects due attention should be paid to the fact that the air within the glasshouse contains both water vapour and carbon dioxide, both of which absorb and emit radiation in depth. Although gas radiation at moderate temperatures is often neglected, in the glasshouse path lengths are long and humidity is high. The complexity of this facet of heat transfer was reduced by assuming that the glass roof and the soil and crop formed two infinite parallel planes, the side walls reducing the edge effect. It was further assumed that the air and crop were roughly at the same temperature and the glass some 5.5°C (10°F) lower. An approximation suggested by Hottel as given by Wiebelt[19] was used to evaluate the radiant heat flux striking the glass: [ e ~ + l "~

GzA2=~o "A 1 "Eb(To)+ ( 1 - % ) " A 1 "~-~--)"Eb(Tw) (7t where G is the radiant heat flux, A is the area, eg and % the gas emissivity and absorptivity, E(T) the emissive power as a temperature function, and subscripts g and w refer to the gas and wall respectively. As previously stated a humidity of 70 ~o and a COz concentration of 0.1 Vo were assumed, together with a glass emissivity of 0.94 and an averaged soil/crop emissivity of 0.9. The net internal radiation flux striking the glass was then expressed for convenience in the form of a heat transfer coefficient; namely

Q,.i,, = h,.i,tA (ti - tw) = 7.10 A(ti-tw) W

hL

~f=O.14 { (No,)(Np,)} 1/3.

(5)

The convective heat transfer coefficients obtained from equations (3 and 4) can be related to the windspeed, w, in m.p.h, by a linear relationship without serious error.

(8)

The external radiation from the glass to assumed black surroundings was evaluated as: Q..... =4.83 A(t,~- to) W = 0.85 A (t,~ - to) Btu/h.

h = 3.08 +0.62 w where h is in W/m 2 °C

(9)

(6)

Combined convective and radiation heat transfer coefficients

The time averaged wind velocity at Renfrew is 9 m.p.h.

The external and internal convective and radiation heat

h=0.54+0.11 w where h is in Btu/h ft 2 °F.

C

= 1.25 A ( t i - tw) Btu/h.

170

S.K..'\/.she/and K. K. Chee

transfer coeMcients from equations 161, 18). (9) added to give

can

°l

be

--

- 1.39 +0.11 w

Btu,'h ft 2 F

Internal hi,,, =10.18 = 1.79

I

I

I

m U~ o 2::

W,, m 2 C

External h,.,, = 7.91 + 0.62 w

80O

g

600

W:nY" ('

_o

Blu h 1"1" k.

a

2o

The glass, or wall, temperature t w can be eliminated by the standard technique of applying the principle of the continuity of heat flow across the glass. The glass was assumed to be opaque to the long wavelengths emanating fi'om the glasshouse interior. The thermal resistance of the glass was included. The overall combined convective and radiative heat transfer coefficielU, air to air, was found to be

400

ila m

:5 2OO

0~

0

o h,.... 4.31 +0.136w : 0 . 7 6 +0.024 w

6a

W/m -~ C Btu/h fl -~ F

m

9

12

3

6pro

Time of day

Fig. 5. Variation of solar radiation with lime.

(10)

where w is the windspeed in m.p.h.

h!/71tratioH coqfficient, h, The assumption is made that the ventilation system will be open substantially only when the heating plant is closed down. The ventilation rate therefore will be that of air infiltration which is wind velocity dependent. The air change rate at a wind speed of 7 m.p.h, varies between 1 and 3[4] depending on the glasshouse structure. Taking a mean value of 2, and a base of 0.5 changes per hour, the air infiltration coefficient is expressible as h r =;)(~p{[/'/A } Ii0.5 4- 12/7 )w{

(11 )

where p and C~, are the density and specific heat capacity of the air, Vand A are the volume and surface area of the glasshouse. On substitution h, becomes h,. =0.358 +0.204 w =0.063 +0.036 w

of this 70 '!,., only 40'>o[ 16] on average will go to raise the temperature, the remainder being absorbed by evapotranspiration effects. It is recognised that this is a crude assumption but it is justified by the relatively small size of the solar component. The direct plus diffuse solar radiation per unit horizontal area is shown for latitude 56~N (mid Scotland) in Fig. 5. The average direct plus diffuse radiation per unit horizontal area time averaged sunrise to sunset is shown in Table 2.

W/m 2 C Btu/h ft 2 F.

Solar heat tran,~lbr coeOicient, 1< It is not easy to obtain a meaningful average for the solar radiation throughout the year because the period May to August in the West of Scotland provides 78 %,i of thc solar heat gain but only 18!I,i of the heat load. A common practice is to ignore the solar gain arguing that the low thermal capacity of the glasshouse results in minimal heat storage and any excess solar heat gain is dumped by increased ventilation. But this is not the case throughout the year and the following analysis is an attempt to quantify a solar heat transfer coefficient. The problem of the summer excess solar gain can be partially solved by averaging the solar gain over the months September to April inclusive, a period in which the solar gain is moderate but which requires 82 %,, of the annual heat load. Of the solar energy striking the glasshouse, part strikes the opaque structure, frames, etc., and part will be reflected or absorbed by the glass. The remainder, 70 '!S[20], will enter the glasshouse. However,

Table 2

Date

Daily average hours of sun at Renfrew

Average radiation Wi'm 2 horizontal sunrise to sunset

21 January 21 February 21 March 21 April 21 May 21 June 21 July 21 August 21 September 21 October 21 November "~1 Decem her

1.12 2.11 2.94 4.72 5.97 6.09 5.14 4.43 3.69 2.34 1.41 0 .q~

139 249 372 463 50l 498 501 463 372 24'J 139 S~,

The average hours of direct sunlight, September to April in the Clyde Valley is 2.39121], and the average radiation sunrise to sunset in that period is 258 W/m z horizontal. The solar heat transfer coefficient, h~, can now be found from

h~A"(ti-t°)=t258xO'7xO'4)

x 2.39 24 x/l°'

(12)

where A~, is the area of glass, A,o, is the equivalent horizontal ground area, and (ti-h~t

is the average

171

The Application of Heat Pumps to Glasshouses

rate. The cost of heat pumps will vary according to type, supplier, etc. but it is thought that the figures given in Table 4 reflect a conservative average for mid 1976. Units built in the U.K. may have somewhat lower prices.

temperature difference inside/outside over the period September to April, calculated from the number of degree days[21] to be 11.5C (20.8 F). The ground area has to be increased to Aor to account for the solar radiation intercepted by the vertical wall of the glasshouse and produces a solar 'shadow' equal to 0.3 of the ground area in this case. Substituting these values in equation (12) gives a value for hs of 0.5 ~ W/m 2 C (0.08 s Btu/h ft 2 F ) .

Table 4. Cost of split air/air heat pumps, mid 1976

Combined heat transfer equation If the various heat transfer coefficients are now substituted in equation (3) noting that h~ and h~ are now combined in equation (10), then Qh=A(4.36+O.36wl(ti--to)

25

30

36

Output capacity at 7.3C in kW

57

74

90

105

4750

5850

6440

7110

83

79

72

67

Cost £

Btu/hft 2 E

Cosl "kW t2

(13)

When the average wind speed is substituted these equations further reduce to

=l.21A(ti-t o)

20

W/m 2 ' C

=AlO.77+O.O63w)(t~-to)

Qh = 6.88 A (ti - to)

Nominal capacity tons

The capital cost of a water source heat pump was taken as 1017oabove the basic air to air heat pump. These units are available in the U.K. as packaged units, at least up to 30 kW, and as custom-built units. Engine driven units can be obtained in the U.K. as custom-built units only, but for comparative purposes a package unit price was estimated. Replacing the electric motor and its ancillaries, costing about £16/kW, with a Diesel engine costing about £32/kW will increase the unit cost by around 12 }o. However, the engine driven unit will require in addition heat exchangers, probably a more substantial frame to take the increased vibration, possibly more substantial compressor seals, possible noise sup; pression, etc. Consideration of these factors suggests that the basic price should be increased by 25 IV,,for the air source and by 35/~ for a water source engine driven heat pump. The capital cost of the oil fired air heaters was taken as £9.2/kW output (£2700/106 Btu/h) which includes ducting and a storage tank. The output for which the capital cost was estimated was found by deducting the heat pump output a t - 5 . 5 ° C from the maximum heat load of 290 kW/103 m 2 (10 b Btu/h/¼ acre).

W/m 2 rC Btu/h ft 2 -'F.

(14)

If equation (14) is used with the degree days appropriate to an early tomato crop the predicted oil consumption of 1600 gallons/103ft 2 agrees well with the quoted value[3] of 1550 gallons/103 ft 2. The conventional v value of 1.4 Btu/h ft 2 F therefore appears to be around 161to too high for the West of Scotland. Equation (13) shows that the heat load is doubled by a 13 m.p.h, wind and demonstrates the importance of wind shielding. The wind effect appears to be shared equally between increased convective cooling and air infiltration. 5. COST E V A L U A T I O N O F HEAT P U M P OPTIONS The dependence of the heat pump performance on its source temperature requires that its annual running cost be found by dividing the year into periods of equal temperature bands of 3 . 3 C (6'-F) spread as shown in Table 3. The annual heating load was determined for a ground area of 103 m 2 (¼ acre) using equation (14) and a mean internal glasshouse temperature of 16.4~'C (61.6 F).

Running costs The tariff adopted for the electric driven heat pumps is that applied by the South of Scotland Electricity Board with effect from April 1976 to ' F a r m and other miscellaneous premises'. The tariff is given as

Capital cost Although indigenous heat pumps are available, the bulk of units sold in the U.K. appear to be imported from the U.S.A. and reflect the adverse Sterling/U.S. dollar

6.099p for each of the first 238 k Wh 2.051p for each of the next 3762 k Wh 1.762p for each additional k Wh.

T'nhle

Temperature band 'C

<(-5.5t

Temperature band F

<22

22 28

52

149

Hours per year

( 5.5) I 2.21 4 2.2H.1

1.1 4.4

4.4 7.8

7.8.11.1

11.1-14.4

14.4-17.8

28 34

34-40

40-46

46-52

52-58

58 64

569

1235

1629

204l

17l 7

1007

172

S.K. Nishet and K. K. Chee

The demand of the heat pumps in all but the stunmer months quickly exhausts the first two prices and consequently all electrical costing has been based on the charge of 1.762p/kWh. No advantage was found m using an off-peak tariff, but lower charges might be obtained from some of the "Maximum Demand Tariffs'. These require knowledge of the maximum monthly kVA demand, and since this reformation could not be predicted with sufficient accuracy investigation of these tarifl; was abandoned. The power required for the air circulation f:ans was averaged at 25'!o of the heat pump compressor input and therefore the tariff based on the heat pump output is given by

3000

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2000

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output (k Wh) cost,& Wh output =compress0r c.O.P, x 2.20p, The cost of 35 second oil (gas oil) suitable both for use in air heaters and Diesel engines was taken as 26p/gallon. However, oil costs continue to escalate and figures are also given for oil at 30p/gallon. Other values can be obtained by ihterpolation, and doubtless by extrapolation. The useful output of the air heaters was given as 80 % of the fuel energy input, and the fan power taken as 2z2"~o of the output. The costs were thus calculated as 0.692p/kWh output at 26p/gallon and 0.799p/kWh at 30p/gallon. The running cost of a D i e s e l driven heat pump was based on the performance of the Nuffield College Heat Pump[10], already detailed, in which the engine thermal efficiency is 1/3 and there is 40 % heat recovery. If Qhp is the heat pump output in kW and Qs the fuel energy input, then

Also total heat output

Qhp

Qf

C.O.P.

3

= Qhp + 0.4 QI = (1 R

1.2 " +(~:O.p.) Qh'"

The H.C.V. for gas oil is 45800kJ/kg (19,700Btu/lb) and its specific gravity is 0.835. The running cost exclusive of fan power therefore reduces to Running cost, pence = 1.62 Qnp at 26p/gat C.O.P.

-,ooc

I

I

I00 200 Nominal heat pump capacity,

200 kW

Fig. 6. "]ariation of annual running costs saving per 103m2 with heat pump capacity for various drives and sources. Key: drive (electricity or Diesel), source (air or water), oil price: (a) e, a, 26 (e) e, w15,26 (i) D, w7.26 (b) e, a, 30 (f) e, wl 5, 30 (j) D, w7, 30 (c) e, w7, 26 (g) D,a, 26 (k/D, wl5, 26 (d) e, w7, 30 (h) D, a, 30 (1) D, wl 5. 30. heat pump provides only 20 3; of the maximum (conservative) heat load but it covers the total heat demand for over 75 3; of the running time. The corresponding figures for the electric drive water source at 15.5~'C (60' F} and the engine drive air source are respectively, 45 % of full load and 90 % of the time, and 31 g;, of full load and again , • 90 °4, of the time. The saving in annual running costs rises with increasing capital expenditure. A simple method of introducing a capital cost element is to estimate the likely life of the plant, typically 10 years for refrigeration equipment, and to consider the total expenditure over that period. This is shown in Fig. 7, which demonstrates that cost saving cannot be achieved by the introduction of any size of 2OOO

f

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I

o 'E~ Io,oo0

1.87 Qhp at 30p/gal. C.O.P.

8 gain

The power to drive the heat pump fans is taken to be supplied by the Diesel engine and represents roughly a 103~, contribution to total oil costs. By using a Diesel drive for the fans part of the fuel energy so expended is recovered from the engine jacket and exhaust. The cost of water has not been included in the running costs of the water source units.

Cost presentation The saving in annual running cost per 103m a (¼ acre} over a conventional oil fired air heating system is shown in Fig. 6 for various heat pump options. Irrespective of the drive or source the optimum size of unit is around 100 kW output (35 ton nom.) per 103m =. Atthis size an air source

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20,000 Nominal

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dO0 200 heat pump c a p a c i t y ,

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300

kW

Fig. 7. Variation in savings in running and capital cost over 10 years against heat pump capacity for various drives and sources. Key as in Fig. 6.

The Application of Heat Pumps to Glasshouses electric drive air source heat pump while oil prices remain at 26p/gallon. This also holds true for the electric drive water source at 7.2~C (45°F). However, some saving can be achieved when the oil price rises to 30p/gallon and the electricity tariff remains constant. This is a dubious proposition in view of the leap-frogging nature of fuel prices. The method represented by Fig. 7 oversimplifies the situation because money is interest and therefore time dependent. A more realistic appraisal can be made by the concept of present values or present worth. This method assumes that the capital is spent at the start of the 10yr period and each constant annual running cost reduced by a factor to a value which, if invested at a predetermined rate of interest, would yield that running cost in that period of time. An interest rate of 10% was chosen as the minimum return which would be attractive, When the annual running costs are summed the present value of the difference in costs is given by Present value difference (10 %, 10 yr) = { Co (Chp + C,o)} + 6.145 {R o -

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Nominol heat pump copacity,

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20

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I00 200 Nominal hegt pumpcapocity,

500 kW

Fig. 9. Variation of interest rate with heat pump capacity for -

where C is capital cost, R constant annual running costs, and the subscripts, hp, ao, o refer to the heat pump, additional oil heating, conventional oil heating alone, respectively. The variation of the present value difference with heat pump size is shown in Fig. 8. The ordinate axis is reduced by half, but too much attention should not be paid to the monetary value. It is sufficient that where a curve intersects the abscissa the return is 10%, and above the abscissa the return is in excess of this. These curves show again that the optimum size of heat pump is about 100kW/103m 2, that the air and ground water source electric drive options are financially unattractive even with an oil price of 30p/gallon. In fact oil prices would need to rise to 34p/gallon against a steady electricity tariff of 1.76p/kWh to give a 10 'Yoreturn. The situation is better for the electric drive water source at 15.5°C (60QF) with oil at 30p/gallon, and all engine driven units show a good return. ~qooo,

40

173

300 kW

Fig. 8. Variation of present value difference with heat pump capacity for various drives and sources. Key as in Fig. 6.

various drives and sources. Key as in Fig. 6. A weakness of the present value method is that it is difficult to interpret without annuity tables. An alternative method is to use the time adjusted rate of return (T.A.R.). To those unfamiliar with this concept it can be visualised as follows. The excess in capital expenditure of the heat pump, plus its oil fired additional heating over a convelational system using oil fired air heating alone, will yield a 'profit' equal to the saving in annual running cost. The crop return is, of course, assumed independent of the heating system. The return on this capital can be compared to that which could be obtained from the money market. The interest rate, i, is then expressible as function of capital and running costs. Interest rate i = ~ (C~p + C,o) - Co In practice the interest rate is found from present value tables. The variation of the T.A.R. interest rate against unit size is shown in Fig. 9. Care is required in the interpretation of Fig. 9 as the unit size becomes small, because in the limit as Chp and Rhv tend to zero, C,o and R,o tend to C Oand R o respectively, and the function thus becomes an indeterminate. Consequently the curves should not be extrapolated below the 50 kW size. The curves for the electric drive air source and water source at 7.2°C (45°F) have been omitted from Fig. 9 because they show only a loss. Considering the optimum size of the heat pump, 100kW, it is seen that returns of better than 15% compound interest are achieved by all engine drive units, and the electric drive with a water source at 15.5°C (60°F) when the oil price is 30p/gallon. The remaining options can be described as marginally attractive only. It may be that the interest rate is not a linear function of capacity for heat pumps below 100 kW, and the straight lines shown could have a small downwards curvature. The uncertainty arises because cost, output, etc. are not a continuous function of size and so produce a small scatter of points. The scatter is aggravated by the form of the table of interest rates at high values.

S, Ix, Nishel aml K. K. ('hue

174

6. C O O I J N G A heat p u m p coines with a built-in bonus in the form of a cooling capacity a little in excess of its heating capacity. That is, a unit having a nominal 100 k W heating capacity is capable of providing a b o u t l l 5 k W of cooling with entry air at 25 C (77 Fi. This does not, of course, mean that complete air conditioning can be installed economically because the m a x i m u m cooling load can easily exceed the m a x i m u m healing load in value. In fact the o p t i m u m sized pump for heating, 100 kW/10Sm 2, has a cooling capacity equivalent to a b o u t 20 :.tit" changes per h o u r for a 5 C (9 F) inside/outside temperature difference, and o n l y 10 changes per h o u r for a 10 C difference. Ne,~ertheless these equivalent ventilation rates are sufficient to provide complete air conditioning for a moderate solar gain, or alternatively complete air conditioning for a partitioned section if desired. Additionally the indoor fan capacity of a 100kW unit is a b o u t 20mS/s (13000 cfm) which could provide a useful c o n t r i b u t i o n lo air circulation. 7. C O N C L U S I O N S

when using a temperature source abo'~e 10 (. (18 F ). The economic adwmtage will depend on the long term inter-relationship betwecn oil and electricity prices. 3.

The optimuln size of heat p u m p is a b o u t 100kW per 10Sm ' g r o u n d area and is independent of source, drive or fuel costs. This sizing provides 20 ,,, of the m a x i m u m heat d e m a n d and supplies lhe total d e m a n d for m e r 75 ",, of the running time.

4.

The o p t i m u m sizc of heat pump l\~r heating duty provides a useful c o n t r i b u t i o n to air cooling equivalent to l0 -fir changes per hour for a 10 ( ' 118 F) temperature difference. This factor should be considcrcd with item 2 above.

O n a final note the authors believe there is a future t\)r heat p u m p s in glasshouse heating within the above constraints. But heal pumps, particularly in their more complex forrns, are not immune to teething troubles and it would be prudent as a first step to instal a heat p u m p in an experimental unit. The theoretical advantages appear sufficiently great to warrant such a step.

The economic analysis indicates the following: 1.

Heat p u m p s with an engine drive and backed by oil fired air heaters could show substantial savings in glasshouse heating costs. This applies irrespective of the source or fuel cost.

2.

C o n v e n t i o n a l electric drive air to air heat p u m p s are attractive when oil prices are 34p/gallon and the corresponding electricity tariff is 1.76p/kWh, or

Acknowledgements The authors wish to thank the West of Scotland Agricultural College Advisor} Service and the Glasshouse Investigation Unit, Auchincruive, for their kindness and help, and the authors accept full responsibility for any misinterpretation of their information. Due acknowledgment is made to manufacturers and agents in the glasshouse and heat pump industries for information received. Our thanks are also due to Miss J. W. Martin for typing the script.

REFERENCES I. K. W. Winspear & A. E. Canham. Glasshouse construction and environmental control, Outlook/or ,1 grieulture ( I.C.I. ) N o. 4 (1974). 2. F. Hiller, Heat balance and climatic factors in the greenhouse. H.L.H. 8 11957). 3. West of Scotland Agricultural College Advisory Service: Management Notes, Horticulture, August (1973). 4. R. M. Whittle & W. J. C. Lawrence, The climatology of glasshouses. II. Ventilation, ./. cig#*ic. Engtlg Res. 5, 1 (1960). 5. Domestic Heating Nines, May (1974). 6. S. Lloyd & C. Starling, The heat pump. B.S.R.I.4. Bihtiograph.!' 103 (1975). 7. A.S.H.R.A.E.: Systems (1973). 8. A.S.H.R.A.E.. Heat pumps improved design and perfl~rmance. Semi-Annual Meeting, January (1970). 9. R. D. Heap, Heat pumps and housing, Building Services Engineer, July (1976). I 0. J.R. Kell & P. L. Martin, The N uffield College heat pump. ,I. Inst. [teat. l,k'm. Engrs 30, [ 1963). 1I. P.E. Montagnon & A. L. Ruckley. The Festival Hall heat pump, J. lnst. Flw127 (1954). 12. J.B. Reeker& H. Marsmann, The use of heat pumps in greenhouses. WarmeKlima und Sanitarteehnik, 26 (5), May (19741. Electricity Council Translation OA 983. 13. E. R. Ambrose, The fteat Pump and Electric Heating. Wiley, N.Y. 11966). 14. M.V. Griffith, Some aspects of heat pump operation in Great Britain. E.R.A. Tedl. Report YT22 ( 19581. 15. E.R. Hoare & L. G. Morris, The heating and ventilation of glasshouses. J. Inst. Heat. Vent. Engrs 24, 1 {1956}. 16. J. N. Walker & D. J. Cotter, Influences of structural features and plant growth on temperatures in greenhouse structures. Acta ftnrtieultural, Symposium on Phmt Enrironment in Glasshouses. Silsou 47 (1965). 17. E. R. Smith, Application of heating and ventilating to glasshouses. J. Inst. Heat. Vent. Engrs 125 (1963}. 18. W. tt. McAdams, Heat Transmission. McGraw-Hill (1954). 19. J.A. Wiebelt, Engineering Radiation Heat Transfer. Holt Rinehart & Winston {1966i. 20. R. 1. Edwards, Transmission of solar radiation in glasshouses. Acta Horticultural, Symposium on Phmt Environment in Glasshouses, Silsoe, 47 (1965). 21. Meteorological Office, Climatologieal Memorandum No. 60.