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PERFORMANCE OF HOUSEHOLD HEAT PUMPS FOR NIGHTTIME COOLING OF A TOMATO GREENHOUSE DURING THE SUMMER Y. Tong, T. Kozai, K. Ohyama

ABSTRACT. To produce high-quality greenhouse crops year round, a cooling method to decrease the air temperature is required in summer. In the present experiment, multiple small-capacity (2.8 kW) household heat pumps were used for cooling a greenhouse in Chiba, Japan, during summer nights. The environmental conditions inside the greenhouse, average coefficient of performance (COP) of eight heat pumps, and amount of water drained from the heat pumps were investigated. The results showed that when the heat pumps were used in the greenhouse, the air temperature, CO2 concentration, and water vapor pressure deficit were more suitable for crop growth than when the heat pumps were not used. Average COP for cooling ranged from 5.8 to 10.7, which was 1.3 to 2.4 times greater than the value obtained under Japanese Industrial Standard conditions, due to the smaller difference in air temperature between inside and outside the greenhouse during the nighttime(20:00-05:00) from20June 20 July 2010. The amount of water drained from the heat pumps accounted for 15% to 25% of the amount of irrigated water. These results indicate that the environmental conditions inside a greenhouse can be improved by using heat pumps during summer nights achieving high COP and low net water consumption. Keywords. Air temperature, CO2 concentration, Vapor pressure deficit, Sensible heat factor.

T

he investment required for constructing a greenhouse and appropriate environmental control system can be quite high. To shorten the investment recovery period, year-round production of high-quality crops is required. However, in temperate and tropical regions, high air temperatures inside greenhouses during summer nights and days are obstacles to high-yield, high-quality crops. For example, high daytime air temperatures reduce fruit set and inhibit development of normal fruit color (Jones, 1999). High nighttime air temperatures may cause excessively high rates of dark respiration and inhibit carbohydrates accumulation (van de Dijk and van Keulen, 1986; Salisbury and Ross, 1992). To overcome these problems, an

Submitted for review in October 2012 as manuscript number SE 9984; approved for publication by the Structures & Environment Division of ASABE in April2013. The authors are Yuxin Tong, Assistant Professor, Institute of Environment and Sustainable Development in Agriculture, Chinese Academy of Agricultural Sciences, Beijing, China, and Key Lab of Energy Conservation and Water Treatment of Agricutural Structures, Ministry of Agriculture, Beijing, China; Toyoki Kozai, Professor Emeritus, Center for Environment, Health and Field Sciences, Chiba University, Kashiwanoha, Kashiwa, Chiba, Japan; and Katsumi Ohyama, Associate Professor, Center for Environment, Health and Field Sciences, Chiba University, Kashiwanoha, Kashiwa, Chiba, Japan and Graduate School of Horticulture, Chiba University, Matsudo, Chiba, Japan. Corresponding author: Yuxin Tong, Institute of Environment and Sustainable Development in Agriculture, Chinese Academy of Agricultural Sciences, Beijing 100081, China; phone: +86-108210-6015;e-mail: [email protected] hotmail.com.

effective cooling method is needed to lower the air temperature inside greenhouses during the summer. For lowering the daytime air temperature in greenhouses in summer, ventilation and shading are commonly used due to their low cost and simplicity (Beytes, 2003; Short, 2003; Kim et al., 2008; Kittas et al., 2009). However, lowering the air temperature inside the greenhouses by increasing the ventilation rate only works when the air temperature outside is lower than that inside. Although the use of shade can decrease the air temperature inside the greenhouses, this method limits the entry of photosynthetically active radiation (Kittas et al., 2009). Evaporative cooling (e.g., pad and fan or fog system) is also used for cooling greenhouses (e.g., Arbel et al., 2003; Ball, 2003; Ohyama et al., 2008). However, evaporative cooling is associated with an increase in humidity inside the greenhouses, which is desirable in dry regions but not in humid regions (e.g., Kumar et al., 2009). Another approach would be the use of heat pumps, which have recently become popular for heating greenhouses, especially household heat pumps with a high coefficient of performance (e.g., Tong et al., 2010; Aye et al., 2010). Thus, using the same heat pumps for cooling the greenhouses on summer nights may be a potential solution for obtaining the optimum environmental conditions for greenhouse crop growth without any further capital costs. Using the heat pumps for cooling greenhouses on summer days is technically feasible only when the solar radiation is relatively low (e.g., less than 300 W m-2), since a large portion of the solar radiation entering the greenhouse is

Applied Engineering in Agriculture Vol. 29(3): 414-421

© 2013 American Society of Agricultural and Biological Engineers ISSN 0883-8542

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converted to heat energy, which increases the cooling load (Baille, 1999). Despite the economic difficulty of cooling a greenhouse on summer days, it has been demonstrated that the crop quality increases by lowering the nighttime air temperature in summer (Willits and Peet, 1998). For greenhouse cooling on summer nights, less energy consumption by the heat pumps is expected because there is no solar radiation entering the greenhouse and there is a smaller difference in air temperature between inside and outside the greenhouse. However, little information is available on the use of recently developed household heat pumps for cooling greenhouses. The objectives of this study were to investigate: 1) the nighttime environmental conditions inside the greenhouse cooled by the heat pumps; 2) the average coefficient of performance (COP) of the heat pumps; and 3) the amount of water drained from the heat pumps.

MATERIALS AND METHODS EXPERIMENTAL PERIOD AND SETUP This experiment was carried out during the nighttime (20:00-05:00) from 20 June to 20 July 2010. Two singlespan greenhouses each with an A-frame roof (north-south orientation) located in Chiba, Japan (35°87’ N and 139°58’ E) were used for this study. Each greenhouse had one roof ventilator and two side ventilators. The roof slope of the greenhouses was 21.8°. The greenhouses were 21 m long, 7.2 m wide, and 3.7 m high, each with a volume of 420 m3. The roofs of the greenhouses were covered with a single layer of polyethylene terephthalate (PET) film with a thickness of 0.8 mm. The side walls of the greenhouses were covered with a single layer of polyvinyl chloride (PVC) film with a thickness of 0.8 mm. The soil surface in the greenhouses was covered with black polyester film, which is typically used in Japan. In one greenhouse, eight (number based on expected cooling load) household air-source heat pumps each with the cooling capacity of 2.8 kW (MSZ-SV288-W, Mitsubishi, Electric Co., Tokyo, Japan) driven by electricity were

installed to maintain the inside air temperature at 18°C and to circulate the air during the nighttime (fig. 1). On-off operation of the heat pumps was controlled by their own timers. The internal units of the heat pumps were installed inside the greenhouse along both side walls at a height of 1.5 m above the ground. Each external unit was installed near the internal unit but outside the greenhouse. During the experiment, the roof and side ventilators were fully closed in the greenhouse. The other identical greenhouse (without the heat pumps) at a distance of 1.0 m away from the greenhouse with the heat pumps was also used in the present experiment. In this greenhouse, the roof ventilator opened automatically when the air temperature inside the greenhouse rose above 25°C. The side ventilators were operated during the experiment to decrease the air temperature. GREENHOUSE PLANTS Tomato (Solanum lycopersicum cv. Momotaro York) plants were grown in both greenhouses. Seedlings (height: 31-43 cm; number of leaves: 8-9) were transplanted with a planting density of 2.0 plants m-2 in the greenhouses on 1 March 2010. Slow release fertilizer was applied in the soil at an N:P:K ratio of 1:1:1 before transplanting. Drip irrigation was manually implemented as needed using the drip tapes placed between the black polyester film and the soil surface. High-wire was used to support the tomato plants. The average height of the tomato plants in both greenhouses was approximately 170.5 cm when the experiment was started on 20 June 2010. Plant growth and yield data were not collected during the experiment. MEASUREMENTS AND ESTIMATIONS

Measurements

The air temperature and relative humidity in the greenhouses were measured using sensors (SHT-71, Sensirion AG, Switzerland; precision: air temperature ±0.4°C, relative humidity ±3%). Nine measuring points, each with three sensors at heights of 0.6, 1.2, and 1.8 m above the ground, were placed uniformly across the

External unit

Greenhouse

Internal unit Refrigerant piping T and RH measurement point

3.7

2.5 1.8 7.2

1.8

1.5 1.8

1.8

21

(Unit: m)

Figure 1. Schematic diagram of the heat pumps installed in the greenhouse. Dotted lines indicate internal parts hidden from view.

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greenhouses (fig. 1). The air temperature outside the greenhouses was measured using another sensor (MT-060, EKO Instruments, Co., Ltd., Tokyo, Japan; precision: temperature ±0.3°C) placed at a height of 1.8 m above the ground in the northwest direction at a distance of 30 m from the greenhouses. CO2 concentration in the greenhouses was measured at a height of 2 m above the ground in the middle of the greenhouses using infrared-type CO2 analyzers (GMP 220, Vaisala Oyj, Helsinki, Finland). CO2 concentration outside the greenhouses was also measured by placing the CO2 analyzer between the two greenhouses at a height of 2.0 m above the ground and at a distance of 0.5 m away from the greenhouse with the heat pumps. Inside the greenhouses, the vapor pressure deficit (VPD) was determined from the measurements of the air temperature and relative humidity. The data of air temperature, relative humidity, and CO2 concentration from the sensors was automatically recorded every minute with custom-made wireless data collection systems. SENSOR CALIBRATIONS The air temperature and relative humidity sensors were calibrated by using an Assmann aspirated psychrometer (Y5011, Yoshino, Co., Tokyo, Japan) at air temperatures of 10°C, 0°C, 10°C, and 20°C. The infrared-type CO2 analyzers were calibrated using CO2 calibration gasses with concentrations of 100, 400, and 1000μmol mol-1. The wattmeters (Clamp on Power Hitester 3169/3168, Hioki, Co., Nagano, Japan; resolution: 0.01 W) were calibrated by using a standard calibration unit (Clamp on Power Hitester 9796, Hioki, Co., Nagano, Japan). The electric balance was calibrated by using a standard calibration weight (60 kg).

Coefficient of Performance Average COP of eight heat pumps for cooling the greenhouse can be estimated by the following formula (ASHRAE, 2001):

COP =

Q P

(1)

where Q is cooling load (W), P is electricity consumption rate of eight heat pumps (W). The electricity consumption rate of each heat pump was measured using a wattmeter and recorded every minute.

Cooling Load The cooling load of a greenhouse is typically determined by analyzing the heat energy balance of the greenhouse. In the present experiment, the air temperature inside the greenhouse with the heat pumps was maintained at 18°C during the nighttime, thus, the cooling load of the greenhouse can also be estimated by:

Q = q ⋅ρ⋅

n

 ( is,k − id ,k )

(2)

k =1

where q is air flow rate (m3s-1); ρ is density of dry air (kg m-3of dry air); n is the number of heat pumps used in the greenhouse, 8; is, id are enthalpy at the air suction and discharge ports of the internal unit of the heat pump (kJ kg-1 of dry air).

416

The air flow rate at the air discharge port of the internal unit was measured manually once every hour using an anemometer (Testo, 405-V1, Japan; resolution: 0.01 m3 s-1). The enthalpy was determined from the measurements of the air temperature and relative humidity at the air suction and air discharge ports of the internal unit. The latent heat load can be estimated by: n

Ql = λ ⋅ q ⋅ρ ⋅  ( xs,k − xd ,k )

(3)

k =1

where λ: latent heat of water vaporization (2.5 MJ kg-1 at 20°C; ASHRAE, 2001); xs, xd: absolute humidity at the air suction and discharge ports of the internal unit of the heat pump (kg kg-1 (D.A.)).

Sensible Heat Factor The sensible heat factor (SHF) can be estimated by: SHF = 1 −

Ql Q

(4)

Electricity Cost The electricity cost per unit heat energy discharged from the greenhouse can be estimated by: A=

P⋅a a = Q COP

(5)

where A is electricity cost per unit heat energy discharged from the greenhouse ($ MJ-1); a is electricity cost ($ MJ-1, IEA, 2011). The amount of water drained from the heat pumps can be estimated from equation 3. It can also be determined by collecting the drained water using a plastic bucket and measuring its weight every day using an electronic balance (Loadcellscale 60H, Shimadzu, Co., Japan; resolution: 0.01 kg). In the present experiment, both estimation and measurement were conducted.

RESULTS AND DISCUSSION ENVIRONMENTAL CONDITIONS The nighttime air temperature was 2.8°C to 5.9°C (on a relatively cool day, 24-25 June 2010) and 6.3°C to 7.6°C (on a relatively hot day, 19-20 July 2010) lower inside the greenhouse with the heat pumps compared to the greenhouse without the heat pumps (fig. 2a). The nighttime air temperature differences between the two greenhouses were in the range of 2.8°C to 7.6°C during this study. Willits and Peet (1998) reported a strong dependence of yield on nighttime air temperature after analyzing data from six seasons of nighttime cooling of greenhouse grown tomatoes. When nighttime air temperatures during the warm treatment(s) approached 24°C (differences of 4°C with that during the cooling treatment), nighttime cooling was found to increase yield by as much as 40% to 50%, and quality was even more enhanced. In a growth chamber experiment conducted by Peet and Bartholomew (1996), a decrease in fruit number and fruit set with increasing nighttime air

APPLIED ENGINEERING IN AGRICULTURE

T (oC)

28

June 24 – 25, 2010

June 26 – 27, 2010

July 19 – 20, 2010

a(a)

22

CO2 concentration (μmol mol-1)

16 850

b(b)

600

350

VPD (kPa)

1.5 c(c) 1.0 0.5 0 20

23

2

5 20

23

2

5 20

23

2

5

Time of day (h) Figure 2. Time courses of (a) air temperature, (b) CO2 concentration, and (c) water vapor pressure deficit (VPD) of the air inside and outside the greenhouses with and without the heat pumps. The data were obtained on 24-25 June (relatively cool day), 26–27 June (average day), 19-20 July (relatively hot day), 2010 and are shown as examples. : inside the greenhouse with the heat pumps; : inside the greenhouse without the heat pumps; : outside the greenhouses. The temperature set point for the greenhouse with heat pump was 18°C.

temperature (18°C, 22°C, 24°C) was observed. Van de Dijk and van Keulen (1986) reported that under low light intensity (24 W m-2), growth of tomato plants was limited under relatively warm nights because carbohydrate accumulation in the plants decreased with an increase in nighttime air temperature. Thus, lowering nighttime air temperature inside the greenhouse by using the heat pumps can increase yield and quality of tomato plants. As a result of the low ventilation rate of the greenhouse and the dark respiration of plants, the CO2 concentration inside the greenhouse with the heat pumps reached around 820μmol mol-1 at 05:00, while it was approximately 500μmol mol-1 inside the greenhouse without the heat pumps where the side ventilators were fully opened on June 24-25, 2010 (fig. 2b). Hence, the net photosynthetic rate of the plants in the greenhouse with the heat pumps could be approximately 1.5 times higher than in the greenhouse without the heat pumps during the first half hour after sunrise due to the higher CO2 concentration. The VPD in the greenhouse with the heat pumps decreased with time at night, but maintained higher than 0.2 kPa (fig. 2c). In the greenhouse without the heat pumps,

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the VPD decreased linearly and reached 0.2 kPa at around 03:00 on 19-20 July. A VPD in the range of 0.2 to 1.0 kPa has little effect on the growth and development of tomato plants (Grange and Hand, 1987). Bakker (1984), Amor and Marcelis (2006), and Max et al. (2009), reported that low VPD may lead to loss of crop quality due to fungal diseases and physiological disorders (e.g., blossom end rot, leaf necrosis). Therefore, decreasing the VPD on summer nights can reduce the occurrence of disease and/or physiological disorders in tomato plants in the greenhouse, but this was not specifically evaluated during this study. COEFFICIENT OF PERFORMANCE FOR COOLING THE GREENHOUSE In the present experiment, the average COP of eight heat pumps for cooling the greenhouse ranged from 5.8 to 10.7 with an average of 8.9 (fig. 3), and was 1.3 to 2.4 times greater than that of the heat pumps under Japanese Industrial Standard (JIS) conditions (dry bulb temperature of 27°C indoors and 35°C outdoors; Japanese Standards Association, 2005). The high COP for cooling the greenhouse was obtained in the present experiment

417

12

10

10

Average COP

Average COP

12

8

6 4

2

4

6

8

Tout-Tin (ºC) Figure 3. Average coefficient of performance (COP) of the heat pumps for cooling as affected by the difference in air temperature between inside and outside the greenhouse (Tin and Tout, respectively), when the air temperature inside the greenhouse was maintained at around 18°C. The data were obtained on 23-25 June, 26-27 June, and 19-20 July 2010 and are shown as examples. Each data point represents a 10-min average.

probably because the air temperature difference of 2.8°C to 7.6°C between inside and outside the greenhouse was smaller than the difference of 8°C under the JIS conditions. The high COP indicates that heat pumps can use electricity efficiently for cooling the greenhouse that was evaluated. The COP for cooling decreases with the decrease in air temperature outside the greenhouse and/or increase in air temperature inside the greenhouse. In the present experiment, the air temperature inside the greenhouse was maintained at approximately18°C during the nighttime, so the average COP should decrease with the increase in the air temperature difference between inside and outside the greenhouse if the COP was only affected by the air temperature difference as shown in figure 3. However, the COP reached a maximum value when the air temperature difference was around 5°C, and then decreased with the decrease/increase in the air temperature difference. This is because other factors in addition to the air temperature inside and outside the greenhouse affect the COP for cooling a greenhouse, such as the ratio of the cooling load to the cooling capacity of the heat pumps, and/or the sensible heat factor. It has been reported that most heat pumps are designed to reach the maximum COP for cooling a greenhouse when the ratio of the cooling load to the cooling capacity of the heat pumps is in the range of 0.6 to 0.8 (Mitsubishi Electric Co. Ltd., personal communication). In the present experiment, the ratio was sometimes below this range, resulting in a decrease in the COP (fig. 4). Under low cooling load, the operation of each heat pump will be intermittent, which may cause fluctuations in the air temperature and VPD inside the greenhouse and reduce the COP of the heat pumps. To maintain a high COP and stabilize the environmental conditions inside the

418

8 6 4 0

0.5

1

1.5

R Figure 4. Average coefficient of performance (COP) of the heat pumps for cooling as affected by the ratio (R) of the cooling load estimated by equation 2 to the cooling capacity of the heat pumps (22.4 kW under JIS conditions). The data were obtained on 23-25 June, 26-27 June, and 19-20 July 2010 and are shown as examples. Each data point represents a 10-min average.

greenhouse, consideration should be given to varying the number of heat pumps operated for cooling the greenhouse according to the cooling load. The household heat pumps used in this experiment are designed to operate effectively when the sensible heat factor ranges between 0.65 and 0.75 (performance characteristic of the household heat pump reported by Mitsubishi Electric Co. Ltd.). If the sensible heat factor is beyond this range, a change in the number of heat pumps operated for cooling the greenhouse, or modification of the coil design and/or the air flow rate is required to avoid the decrease in the COP. In this experiment, the sensible heat factor was in the range of 0.59 to 0.80 with the average of 0.73 (fig. 5). Although the sensible heat factor obtained during the present study was generally within the acceptable range of the operation of the heat pumps, careful attention should be paid to the sensible heat factor to maintain a high COP for cooling greenhouses. COST FOR COOLING A GREENHOUSE USING MULTIPLE HOUSEHOLD HEAT PUMPS As shown in figure 6, the electricity cost per hour increased with an increase in the air temperature difference between inside and outside the greenhouse and a decrease in the COP of the heat pumps. In this experiment, the average electricity cost per hour was approximately $2.50. Electricity costs per unit heat energy discharged from the greenhouse were analyzed by using the lowest COP of 5.8, the average COP of 8.9 and the highest COP of 10.7 attained during the present study (table 1). Electricity costs in different countries were used for the calculations. For example, in Japan, the electricity costs per unit heat energy discharged from the greenhouse were $7.6×10-3 MJ-1, $4.9×10-3 MJ-1,and $4.1×10-3 MJ-1 when the COP for cooling a greenhouse was 5.8, 8.9, and10.7, respectively.

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Table 1. Electricity costs (IEA, 2011) per unit heat energy discharged from the greenhouse under the lowest coefficient of performance (COP) of 5.8, the average COP of 8.9, and the highest COP of 10.7 in different countries.[a] Cost per Unit HeatEnergy (×10-3 $MJ-1) COP=5.8 COP=8.9 COP=10.7 Country Japan 7.6 4.9 4.1 Taiwan 2.8 1.8 1.5 Korea 3.6 2.3 1.9 USA 3.3 2.1 1.8 UK 6.5 4.2 3.5 France 5.1 3.3 2.8 Italy 13.2 8.6 7.2 [a] Source: IEA (International Energy Agency), Key World Energy Statistics 2011.

10 8 6 4 0.5

0.9

0.6 0.7 0.8 Sensible heat factor

Figure 5. Average coefficient of performance (COP) of the heat pumps for cooling as affected by the sensible heat factor. The data were obtained on 23-35 June, 26-27 June, and 19-20 July 2010 and are shown as examples. Each data point represents a 10-min average.

The household heat pumps employed in this experiment were inexpensive (e.g., the ratio of price to cooling capacity: $0.20W-1) compared with heat pumps for industrial use. If the heat pumps are used for integrated greenhouse environment control all year round, such as for cooling, heating, circulating air, and distributing CO2 in the greenhouse, the investment for installing the heat pumps would be lower than that for introducing equipment independently (Kozai et al., 2009). Moreover, the use of multiple heat pumps for cooling a greenhouse decreases the risk of an interruption in cooling due to the possible malfunction of a single heat pump. The distributed installation of internal units of the heat pumps can also provide uniform environmental conditions inside the greenhouse (Tong et al., 2010).

Electricity cost ($h-1)

12

0.1

COP-4

y = 0.35 x R 2 = 0.62

8

COP-2 COP

4 0

AMOUNT OF WATER DRAINED FROM THE HEAT PUMPS The measured and the estimated amount of water drained per night from each heat pump used in this experiment are shown in figure 7. The amount of water drained from the heat pumps can be used to estimate the latent heat load, because the amount of water that condenses on the evaporator coil is related to the latent heat exchange in the heat pumps. The difference between the measured and estimated amount of water was probably because the water drained from the heat pumps was measured over longer time intervals, thus the changes in the amount of water drained during the nighttime cannot be accurately reflected. During the present experiment, the measured amount of water drained from the heat pumps was 0.3 to 0.5 kg m-2 per night. Tomato plants generally consume about 2 kg m-2 of water per day during full fruit production in a greenhouse (e.g., Jones, 1999). Hence, the amount of water used for irrigation may be reduced by 15% to 25% if the drained water from the heat pumps is used for irrigation. While the reduction in water use presented here is a rough estimation, further investigation on harvesting water as a byproduct of using the heat pumps for cooling the greenhouse is needed, especially in semi-arid and arid regions.

COP+2

0

2

6 4 Tout-Tin (ºC)

8

10

Figure 6. Electricity cost per hour as affected by the air temperature difference between inside and outside the greenhouse and the COP of the heat pumps. COP+2, COP-2 and COP-4 represent +2, -2, and -4 points different compared to the average COP of eight heat pumps obtained during the current experiment.

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Wm (kg m-2)

Average COP

12

0.05

0

0

0.05 We (kg

0.1

0.15

m-2)

Figure 7. Amount of drain water, measured and estimated (Wm and We, respectively), per night from each heat pump used for cooling the greenhouse. The data were obtained on 21-27 June 2010 and are shown as examples. Each data point represents daily averages.

419

CONCLUSION In the present experiment, eight household heat pumps were used to cool a greenhouse at night in summer. The results showed that more suitable environmental conditions for crop production were obtained in the greenhouse with the heat pumps compared to the greenhouse without the heat pumps. The average coefficient of performance (COP) of eight heat pumps for cooling ranged from 5.8 to 10.7, which was 1.3 to 2.4 times greater than the value obtained under Japanese Industrial Standard conditions, indicating that the heat pumps can use the electricity efficiently. Possible collection of water using the heat pumps can be determined by analyzing latent heat load or collecting and measuring the drained water. In this experiment, the amount of water drained from the heat pumps, 0.3 to 0.5 kg m-2 per night, accounted for 15% to 25% of the amount of irrigation water. Therefore, the use of the heat pumps for cooling the greenhouse at night during the summer can improve the environmental conditions inside greenhouses for crop production achieving high COP and lower net water consumption. ACKNOWLEDGEMENTS We express our appreciation to Associate Professor M. Hojo, Mr. Y. Nakamura, and Mr. H. Enomoto, from the Center for Environment, Health and Field Sciences, Chiba University, for their technical assistance. We thank Mr. Masao Ohyama for his technical assistance. We also gratefully acknowledge Mitsubishi Electric Co., Ltd. for supplying and installing the heat pumps and for incidental electric engineering work. We are grateful for the financial support from the National High Technology Research and Development Plan of China (863 Project, grant No. 2013AA103007).

NOMENCLATURE ABBREVIATIONS COP coefficient of performance DA dry air RH relative humidity (%) SHF sensible heat factor VPD vapor pressure deficit (kPa) CONSTANTS n number of heat pumps λ latent heat of water vaporization (MJ kg-1) VARIABLES A electricity cost per unit heat energy discharged from the greenhouse ($MJ-1) a electricity cost ($MJ-1) i enthalpy [kJ kg-1 (D.A.)] q air flow rate (m3 h-1) ρ density of dry air (kg (D.A.) m-3) P consumption rate of electricity (W) Q cooling load (W)

420

R

ratio of the estimated (eq. 2) cooling load to the cooling capacity of the heat pumps (22.4 kW for all eight pumps) T air temperature (°C) W amount of water drained from each heat pump per unit floor area (kg m-2) SUBSCRIPTS e estimated data d air discharge port m measured data s air suction port

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