Evaporation characteristics in a naturally ventilated, fog-cooled greenhouse

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Renewable Energy 31 (2006) 2207–2226 www.elsevier.com/locate/renene

Evaporation characteristics in a naturally ventilated, fog-cooled greenhouse Ahmed M. Abdel-Ghany, Eiji Goto, Toyoki Kozai Laboratory of Environmental Control Engineering, Faculty of Horticulture, Chiba University, Matsudo Chiba, 271-8510, Japan Received 12 October 2005; accepted 13 November 2005 Available online 27 December 2005

Abstract In a greenhouse cooled by a fogging system, the fraction of fog that evaporates by absorbing sensible heat from the greenhouse air, b, is an essential parameter to be determined for evaluating the system performance. Recent studies estimated b under indoor conditions by collecting the nonevaporated fog that fell on a plastic sheet during a specified time and b was the difference between the amount of sprayed fog and the non-evaporated fog divided by the amount of sprayed fog. Using this method in the greenhouses causes an overestimation of b due to the evaporation of the fog that fell on the plant leaf/floor surfaces affected by solar and thermal radiation and the difficulty of collecting the non-evaporated fog that falls on the plant leaf surfaces. This paper presents a method for simulating b and for analyzing the fog evaporation based on the heat and water vapor balance of the greenhouse air. The conditions of the un-cooled air in the greenhouse were investigated to be used essentially in the simulation. An experiment to determine parameters for the simulation was conducted on a hot sunny day (August 9, 2004) in the Tokyo area to measure the environments inside and outside a naturally ventilated greenhouse with a floor area of 26 m2. The greenhouse was cooled intermittently at a fogging rate of 10 g s
1 for five different fogging durations (i.e., fogging time–interval time) of 1–3, 0.5–1.5, 1.5–4.5 , 0.5–1 and 1–2 min, respectively. Evapo-transpiration rate of 150 potted tomato plants was estimated using reported correlations and the resulting values could be corrected based on the water vapor balance of the greenhouse air. The results showed that b had a certain pattern along with the fogging and interval time. The values of b estimated from the heat balance were identical to those estimated from the water vapor balance. The fogging duration of 1–3 min showed relatively high evaporation rate, in which, the integrated value of b over a working time of 41 min was 0.36. r 2005 Elsevier Ltd. All rights reserved. Keywords: Fogging; Evaporation; Heat; Water vapor; Natural ventilation; Greenhouse Corresponding author. Tel./fax: +81 047 308 8843.

E-mail address: [email protected] (A.M. Abdel-Ghany). 0960-1481/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2005.11.004

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Nomenclature Af Cp Ec Ef ETr ET e Fx Go Gi hc–i hc–o hp–i hf–i hs–i Hc Hf Ii Io LAI _a m _ DA m _f m mf _v m _w m mw _p m _s m Qc
i Qc
o Qf
i QL Qp
i Qs Rc Rf Tc Tdi Tdo Tf Tu

surface area of the greenhouse floor (m2) specific heat (J kg
1 1C
1) emissive power of the cover (W m
2) emissive power of the floor (W m
2) evapo-transpiration rate of plant and pot’s soil surfaces (kg m
2 s
1) total amount of the evapo-transpiration (kg m
2) partial pressure of water vapor in the air (kPa) conductive soil heat flux (W m
2) solar radiation flux outside the greenhouse (W m
2) solar radiation flux inside the greenhouse (W m
2) convective coefficient between the cover and the inside air (W m
2 1C
1) convective coefficient between the cover and the outside air convective coefficient between the plant leaves and the inside air (W m
2 1C
1) convective coefficient between the floor surface and the inside air (W m
2 1C
1) convective coefficient between the pot’s soil and the inside air (W m
2 1C
1) thermal radiation absorbed by the cover (W m
2) thermal radiation absorbed by the floor (W m
2) enthalpy of the moist air inside the greenhouse (kJ kg
1) enthalpy of the moist air outside the greenhouse (kJ kg
1) leaf area index (Ap/Af) (dimensionless) ventilation rate of moist air in the greenhouse (kg m
2 s
1) ventilation rate of dry air in the greenhouse (kg m
2 s
1) evaporation rate of the non-evaporated fog (kg m
2 s
1) total amount of the non-evaporated fog (kg m
2) rate of water vapor associated with ventilation (kg m
2 s
1) fogging rate (kg m
2 s
1) total amount of sprayed water (kg m
2) transpiration rate (kg m
2 s
1) pot’s soil evaporation rate (kg m
2 s
1) convective heat rate from the cover to the inside air (W m
2) convective heat rate from the cover to the outside ambient (W m
2) convective heat rate from the floor surface to the inside air (W m
2) latent heat rate added to the greenhouse air (W m
2) convective heat rate from the plant leaves to the inside air (W m
2) sensible heat rate added to the greenhouse air (W m
2) solar radiation energy absorbed by the cover (W m
2) solar radiation energy absorbed by the floor (W m
2) cover surface temperature (1C) dry bulb temperature inside the greenhouse (1C) dry bulb temperature outside the greenhouse (1C) floor surface temperature (1C) dry bulb temperature of the un-cooled air in the greenhouse (1C)

ARTICLE IN PRESS A.M. Abdel-Ghany et al. / Renewable Energy 31 (2006) 2207–2226

Twi TN t ttot U V v¯ VPD Z

2209

wet bulb temperature inside the greenhouse (1C) soil temperature at a soil depth, Z (1C) time (s) total working time (s) overall heat transmission coefficient (W m
2 1C
1) wind speed outside the greenhouse (m s
1) air current speed estimated inside the greenhouse (m s
1) vapor pressure deficit (kPa) soil depth (m)

Greek letters b Dt j k la ls p oET oi oo osi ou

fraction of fog that evaporates in the greenhouse air (dimensionless) time interval (s) relative humidity (%) latent heat of vaporization of water (J kg
1) thermal conductivity of air (W m
1 1C
1) thermal conductivity of soil (W m
1 1C
1) cover to floor surface area ratio (dimensionless) absolute humidity due to evapo-transpiration rate (kgv/kgDA) absolute humidity of the greenhouse air after fogging (kgv/kgDA) absolute humidity of the outside air (kgv/kgDA) absolute humidity of the saturated greenhouse air (kgv/kgDA) absolute humidity of the un-cooled air in the greenhouse (kgv/kgDA)

1. Introduction Fogging systems which use high-pressure nozzles to generate fog droplets have been examined for cooling greenhouses under hot summer seasons [1–4] and have been used for commercial greenhouses in many areas in the world [5–7]. The popularity of fogging systems is due to their ability to economically maintain the desired growth conditions in the greenhouses (i.e., temperature and relative humidity). Fogging systems are based on spraying water as small drops in the fog range (p60 mm in diameters) in order to increase the water surface in contact with the air. The drops are easily carried by the air stream in the greenhouse and evaporate by absorbing sensible heat from the air, resulting in a decreased dry bulb temperature and increased air humidity. Evaporation of water drops depends on the design parameters of the fogging system and on the environmental factors in the greenhouse, which are essentially air temperature, air current speed and air humidity. However, not all the drops evaporate completely before reaching the floor. A portion of these drops, which depends on their descending velocities, fall on the floor and foliage surfaces. This portion is referred to as non-evaporated fog. The fraction of fog which evaporates in the greenhouse air b is an essential parameter to be determined for evaluating the fogging system performance and the cooling efficiency. Increasing the b factor increases the cooling efficiency of the system and decreases the wetting of the foliage. A recent experimental study [8] estimated the b factor by collecting

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the non-evaporated fog on a plastic sheet that was mounted on the floor under the fogging nozzle. Fogging at a certain rate was supplied for a certain time; the non-evaporated fog was collected on the plastic sheet during this time and can be weighed. The b factor was the difference between the amount of supplied fog and the collected (non-evaporated) fog divided by the amount of supplied fog. This experiment was carried out under indoor and dark conditions to avoid the effects of radiation in evaporating the fog from the plastic sheet during the time of collection. Evaporation of drops under indoor and dark conditions is different from evaporation under outdoor conditions. Using this method in the greenhouse conditions results, of course, in an overestimation of b due mainly to: (i) the difficulty of collecting all the non-evaporated fog falling on the floor and foliage surfaces and (ii) the evaporation of the fog fell on the plant leaf/floor surfaces, which is affected by the solar and thermal radiation in the greenhouse. A search of the literature revealed that there is no measuring method to determine b factor in the greenhouse correctly and the simulation approach is the unique solution. The objective of this study is to provide a simulation method aided by simple experimental measurements to estimate the b factor correctly under greenhouse conditions and to investigate the evaporation characteristics of the evaporated and the nonevaporated fog during the fogging and interval times. This method is based on investigating the conditions of the un-cooled air in a greenhouse during the operation of a fogging system. The heat and water vapor balances of the cooling process (i.e., the conditions of air from the un-cooled state to the cooled state) were used to estimate b. The concept of the un-cooled air in the greenhouse will be explained later. Enhancing the b factor to obtain efficient cooling and the desired conditions for plant growth is beyond the scope of this study. 2. Measuring the required parameters Experiment to measure the required environmental parameters to be used in the simulation was conducted in a 26 m2 glass-covered greenhouse (Fig. 1(a)). The greenhouse oriented in a N–S direction on the Matsudo campus, Chiba University (Tokyo area, Japan, 139.461E, longitude and 35.411N, latitude). Layout dimensions and locations of the instruments used to measure different parameters are illustrated, not to scale, in Fig. 1(a). The greenhouse was naturally ventilated using one roof ventilator and intermittently cooled by spraying water-fog at five different fogging durations (fogging time–interval time) of 1–3; 0.5–1.5; 1.5–4.5; 0.5–1.0 and 1.0–2.0 min, respectively. Water at 32–35 1C and a rate of 10 g s
1 was pumped through 6 mm diameter vinyl tube (KIT 64, Maruyama Mfg. Co., Japan) using a 3.2 MPa water pump (MS027, Maruyama Mfg. Co., Japan) and controlled by an on/off timer switch (TM55, Maruyama Mfg. Co., Japan). Fog was supplied to the greenhouse using 6-spray nozzles (Type-P: +0.3 mm, Maruyama Mfg. Co., Japan) connected to the water tubes and installed at 2 m above the greenhouse floor. The floor was covered with a black sheet (polyvinyl chloride) to prevent the evaporation of soil and the greenhouse contained 150 potted tomato plants with total leaf area index, LAI, of 0.25. The measurements were carried out at around noon (12:19–14:30) on a sunny, hot summer day (August 9, 2004). Required parameters to be used in the simulation were measured at the locations shown in Fig. 1(a) and recorded at every 5-s in a data logger (CR23X Micrologger, Campbell Scientific, Inc.). Measured environmental

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5.5 m

4m

0.7 m

0.5 m 1.8 m

(5)

(1)

(2)

0.5 m

(4)

Water supply line (3)

3.4 m

N

(7) 0.7 m

2.2 m

3.4 m

(6)

1m

2.4 m

2m

4.8 m

3m

(1) Filter, (2) water tank, (3) pump,(4) flow control valve, (5) pressure relief valve, (6) nozzles, (7) end cap,

(a)

solarmeters,

wind speed anemometer,

00

Φ

aspirated psychrometers and

albedo meter,

%

I

ωsi ωi

Fog

ging

=1

Infra-red thermometer.

U

ωu

Qs S

ωo

QL O (b)

Two

Twi Tdi

Tdo

Tu

Fig. 1. (a) Layout dimensions and measuring locations in the naturally ventilated, fog-cooled greenhouse used in the experiment and simulation (not to scale). (b) Psychrometric chart showing the processes of: sensible heating (O–S), latent heating (S–U) and fogging (U–I) in the naturally ventilated, fog-cooled greenhouse.

factors are: (i) the outside and the mean value of the inside dry and wet bulb temperatures (Tdo, Two and Tdi, Twi) using aspirated psychrometers in each, two thermocouples type-T, copper constantan of 0.1 and 0.3 mm in diameters to measure dry and wet bulb temperatures, respectively, (ii) the outside and inside downward solar radiation flux (Go and Gi) using MS-100 solarmeters (accuracy of 75% EKO- Instruments Trading Co. Ltd., Japan), (iii) the outside wind speed (V) using PGWS-100 wind sonic anemometer (accuracy of 72%/12 m s
1, Gill England), (iv) the inside net solar radiation flux (down–upward) recorded at 0.5 m over the greenhouse floor using an albedometer (accuracy of 73%, PCR-01, Prede Co. Ltd., Italy) and (v) un-shaded plant leaf temperature (Tp) using an infra-red radiation thermometer (accuracy of 71% IT2-01, Keyence Co., Osaka, Japan).

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3. Estimating the relative and absolute humidities Relative and absolute humidities inside and outside the greenhouse (ji, oi, jo and oo) were estimated using correlations reported in [9] as follows: (i) Saturation vapor pressure (es) at certain temperature (T) in kPa:   16:78T
116:9 . (1) es;T ¼ exp T þ 237:3 (ii) Vapor pressure (i.e., partial pressure of water vapor) (e) in kPa: e ¼ es;w
LPðT d
T w Þ,

(2)

where es,w is the saturation vapor pressure estimated at the wet bulb temperature (Tw), P is the total pressure (i.e., P ¼ 101:325 kPa), Td is the dry bulb temperature and L is defined by L ¼ 0:00066ð1:0 þ 0:00115T w Þ. The relative and absolute humidities are respectively, given by e e , and o ¼ 0:623 f¼ es;d ð101:325
eÞ

(3)

(4)

where es,d is the saturation vapor pressure estimated at the dry bulb temperature. Substituting the measured dry and wet bulb temperatures into Eqs. (1)–(4), values of j and o can be calculated for the air inside and outside the greenhouse. 4. Estimating the cover and floor temperatures Over small time intervals (e.g., 5 s), heating and cooling processes of the greenhouse components (i.e., cover, floor surface, plants, pot’s soil and inside air) were assumed to be quasi-steady-state processes. To investigate the cover and floor surface temperatures, (Tc and Tf), an energy balance was applied to the greenhouse cover and floor surface assuming: (i) the floor is a black surface and the cover is gray in terms of long wave radiation, i.e., its radiative properties are independent of the wavelength and both are characterized by an equivalent temperature, Tc and Tf, (ii) the energy stored in these components is negligible, (iii) the surfaces reflect solar and thermal radiation diffusively, (iv) the cover is opaque to incident thermal radiation and the solar radiation transmitted into the greenhouse is multiply reflected between the floor, cover and plants and (v) because the plants were at a low growth stage (LAI ¼ 0.25), all the non-evaporated fog, _ f , falls on the floor surface. Parameters in present analysis are time dependent and to m simplify the expressions, the functional relationship of t is omitted from all the symbols hereafter (e.g., Tc(t) is replaced by Tc). The energy balance equations of the cover and floor surface are as follows: Rc þ H c
Qc2i
Qc2o
2E c ¼ 0:0,

(5)

_ f ¼ 0:0, Rf þ H f
Qf2i
E f
F x
km

(6)

where Rc and Hc are the solar and thermal radiation absorbed in the unit area of cover, Rf and Hf are the net solar and thermal radiation on the unit area of floor surface (positive downward). Values of Rc, Rf, Hc and Hf are mathematically formulated in the current

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study [10] as functions of the radiative properties of cover, floor and plant leaf surfaces and of the LAI. Ec and Ef are the emissive power of the cover and floor (i.e., esT 4 , e is the surface emittance of the cover or floor surfaces and s is the Stefan–Boltzmann constant). Fx is the conductive heat rate into the unit area of floor (i.e., F x ¼ ls ðT f
T 1 Þ=Z). Values of soil thermal conductivity, ls, soil depth, Z, and the soil temperature at the soil depth Z _ f is the latent heat rate released from the (i.e., TN) are discussed and reported in [10]. km _ f ; and k is the latent heat of unit area of floor to the inside air due to the evaporation of m vaporization of water. Qc– i, Qc–o and Qf–i are the convective heat rates from the cover to the inside air, from the cover to the outside air and from the floor to the inside air, respectively. These convective rates in addition to the convective heat rate from the plants to the inside air (Qp–i) were estimated using Newton’s law of cooling (Q1–2 ¼ h1–2(T1
T2)). Appropriate correlations for the heat transfer coefficients, h, were selected from the literature derived for a mixed convection mechanism in the greenhouses at day time conditions: (i) Between the cover surface and outside air [11]: hc2o ¼ 0:95 þ 6:76V 0:49 ;

T c 4T do

and

V p6:3 m s
1 ,

(7)

where V is the wind speed outside the greenhouse. (ii) Between the cover surface and inside air [11]: hc2i ¼ 1:95ðT c
T di Þ0:3 ;

ðT c
T di Þp11:1  C.

(8)

Eq. (7) is valid for V p6:3 m s and Eq. (8) for ðT c
T di Þp11:11C. However, during carrying out the experiment under the hot summer daytime conditions the temperature difference and the wind speed outside the greenhouse did not exceed these limitations. (iii) Between the floor and the inside greenhouse air [12]:  0:5 v¯ 0:33 hf2i ¼ 1:52ðT f
T di Þ þ 5:2 , (9) Lf
1

where Lf is the characteristic length of the greenhouse floor (Lf ¼ 4 m) and v¯ is the mean velocity of air in the greenhouse approximated as the volume flow rate of the ventilated air divided by the frontal surface area of the greenhouse. (iv) Between the plant leaf and inside air [13]: Nu ¼

hp2i Lp ¼ 0:37ðGr þ 6:92Re2 Þ0:25 , la

(10)

where Nu is the Nusselt number, Gr is the Grashof number, Re is the Reynolds number, Lp is the characteristic length of the plant leaf (Lp ¼ 5 cm) and la is the thermal conductivity of air. By solving Eqs. (5) and (6) simultaneously using FORTRAN-based program constructed and linked to IMSL Math Library subroutines [14], the values of the unknowns Tc, Tf and Fx could be obtained at each time step. Also the values of the heat transfer coefficients, in Eqs. (7)–(10), could be obtained. 5. Estimating the ventilation rate _ a (i.e., m _a ¼ m _ DA þ m _ v, m _ DA is The ventilation rate of moist air per unit area of floor m _ v is the rate of water vapor) can be estimated from the heat balance the rate of dry air and m

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equation of a greenhouse as follows: _a ¼ m

Gi
pUðT di
T do Þ
F x . ðI i
I o Þ

(11)

Under hot summer conditions, the average overall heat transmission coefficient U was estimated to be 4.5 W m
2 1C
1 [15] and the enthalpy of the moist air, in kJ kg
1, inside and outside the greenhouse (Ii and Io) as a function of the dry bulb temperature and the absolute humidity is given by [9] I ¼ ð1:007T
0:026Þ þ oð2501 þ 1:84TÞ;

T in  C:

(12)

6. Estimating the conditions of the un-cooled air At a certain time t in a greenhouse cooled by intermittent water fogging, the outside ambient air characterized by Tdo and Two enters the greenhouse during the natural ventilation process (the point O in Fig. 1(b)). This air exchanges a sensible heat with the cover, floor, plant leaf and pot’s soil surfaces. This exchange, under hot sunny summer conditions, contributes by adding sensible heat Qs to the air and increases its dry bulb temperature from Tdo to Tu (the line O–S in Fig. 1(b), S is an imaginary point). _ p ), the pot’s soil evaporation rate (m _ s ) and evaporation rate of the Transpiration rate (m _ f ) add a latent heat QL to the air and non-evaporated fog that fell on the floor surface (m increase its absolute and relative humidities (the line S–U in Fig. 1(b)). The resulting condition of adding sensible and latent heat to the air is the un-cooled air condition represented by the imaginary point U in Fig. 1(b). The line O–U represents the heating process of the air in the greenhouse. Then, at the point U, the air is characterized by dry and wet bulb temperatures (Tu and Twi) and absolute humidity (ou). Evaporation of fog cools the air from the un-cooled state (Tu and ou) to the cooled state (Tdi and oi) at a constant Twi. Values of Tdi and oi could be obtained from measurements at each time step and the corresponding values of Tu and ou need to be determined. Tu was formulated based on the sensible heat balance of the inside air at the absence of fogging effect and is given by [16] Qs _ DA C pa m _ DA C pa ÞT do þ ðphc2i ÞT c þ ð2LAI hp2i ÞT p þ ðhf2i ÞT f Þ ððm , ¼ _ DA C pa þ phc2i þ 2LAI hp2i þ hf2i Þ ðm

T u ¼ T do þ

ð13Þ

where p is the area ratio of cover to floor and C pa is the specific heat of dry air. The absolute humidity of the un-cooled air (ou) can be estimated from the heat balance of the fogging process as follows: ou ¼ osi


C pa ½T u
T wi , k

(14)

where osi is the absolute humidity of saturated air estimated at Twi using Eqs. (1)–(4).

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7. Estimating the evapo-transpiration rate _ s) (i) Evaporation rate of pot’s soil: Evaporation of the moisture in a pot’s soil (m was treated as a mass flux of water vapor and was assumed to take the form of free convection and could be characterized by the mass transfer coefficient km (m s
1) in the form [17] _ s ¼ km As ra ðoss
oi Þ=Af . m

(15)

Here oss and oi are the absolute humidities of saturated air estimated at the temperature of the pot’s soil surface (i.e., assumed to be equal Tf) and of the inside air, respectively. The mass transfer coefficient km can be estimated correctly from the heat transfer coefficient hs–i by assuming Pr ¼ 0:71 and Sc ¼ 0:63 in the free convection region, assumed between the pot’s soil surface and the surrounding air [18] km ¼ hs2i =ðra C pa ÞðSc=PrÞ0:67 , l hs2i ¼ ð0:12Gr0:33 Pr0:33 Þ, L

ð16Þ

in which L ¼ 0.12 m is the diameter of pot surface as a characteristic length. Sc, Pr and Gr are the Schmidt, Prandtl and Grashof numbers, respectively. (ii) Transpiration rate: Most of the reported transpiration models are similar to the Penman–Monteith equation and have the following pattern [19]: _ p ¼ LAI½aRn þ bðVPDÞ, m

(17)

where Rn is the net radiation exchange between the plant and the environment (W m
2) and VPD is the air vapor pressure deficit (kPa). However, a and b are no longer adjusted constants; they are estimated as a function of the LAI and the aerodynamic and stomata resistances. Transpiration models differ mainly in the values of a and b which depend on the way used to estimate the aerodynamic and stomata resistances. Jolliet and Bailey [19] compared five transpiration models for tomato crops in a greenhouse. They suggested a ¼ 0:141 and b ¼ 28:1 with R2 ¼ 0:87 for the summer seasons (June–July) and they considered Rn as the solar radiation measured above the plant _ p in (mg m
2 s
1) from Eq. (17). The coefficients, a and b, depend on the canopy to give m conditions of the experimental measurements for which the correlation was made. _ p in a fog-cooled greenhouse using Eq. (17) may include an error, Therefore, estimating m _ s using Eq. (15) may also include an error and we are not sure how much and estimating m _ p and m _ s are considered as one term as the error in each of them. Accordingly, both m _p þ m _ s Þ. Then, water vapor balance of the evapo-transpiration rate ETr ðETr ¼ m greenhouse air is given by _ f þ bm _ w ¼ 0, _ DA ðoo
oi Þ þ ETr þ m m

(18)

_ w is the rate of fog evaporate in the greenhouse air and m _ w is the fogging where the term bm rate supplied to the greenhouse. By carrying out the integration over the working time (ttot), the total amount of the non-evaporated fog (mf) should equal ð1
bÞmw if the total amount of the evapo-transpiration (ET) estimated from Eqs. (15) and (17) is correct. The difference between mf and ð1
bÞmw represents the amount of error that should be added to or subtracted from the value of ET.

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The absolute humidity of the un-cooled air, Eq. (14) can also be estimated from the water vapor balance of the inside air: ou ¼ oo þ oET þ of ,

(19)

where oo is the absolute humidity of the outside air, oET is the absolute humidity due to the evapo-transpiration rate (ETr) and of is the absolute humidity due to the evaporation _ f from the floor. Values of oET, and of are given by of m _p þm _ s Þ=m _ DA oET ¼ ðm

and

_ f =m _ DA . of ¼ m

(20)

8. Fog evaporation _ w can be estimated either from heat or water vapor balance of the In Eq. (18), bm greenhouse air during the fogging process as follows: _ DA C pa ðT u
T di Þ=k, _w ¼ m bH m _ DA ðoi
ou Þ, _w ¼ m bL m

ð21Þ

.

start

mf = 0.0 βHmw=0.0

t=t+t

t=0

. Read: U, mw, Tdi, Twi, Tdo, Two, Tp Go, Gi, V, physical, ttot and radiative properties of air, cover, plant and floor Compute ωi ωo Solve Eqs. (5, 6)

Tf, Tc, Fx, hc-o, hc-i, hf-i, hp-i, hs-i

Compute: Ii, Io, Eq. (12)

.

Compute: ma, Eq. (11) Compute: ETr, Eqs. (15, 17) Compute: Tu, ωu, Eqs. (13,14, 19)

.

.

Compute: βHmw, βLmw, Eq. (21)

.

Compute: mf, Eq. (18)

YES er1> 0.01, NO er2> 0.01

ER= mf-(1-βH)mw

Compute er1,er2

.

.

mf, βHmw

t < ttot

Yes

No Compute mf, βHmw

YES ER≈0.0 NO

Compute the correction factor of ETr Store the required results

Stop

Fig. 2. Flowchart showing the computation procedures.

.

.

er1= (mf)new-(mf)old

.

.

er2= (βHmw)new-(βHmw)old)

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where bH and bL are the fractions of the evaporated fog estimated based on the heat and water vapor balance, respectively. _ w is determined, the corresponding m _ f can be estimated Once the value of bm from Eq. (18). The computation procedures of the previous analysis are illustrated in Fig. 2. 9. Results and discussion Dry bulb temperature of the un-cooled air (Tu) is the essential parameter used to analyze the fog evaporation. Time courses of the dry bulb temperatures measured inside and outside the greenhouse (Tdi and Tdo) and the simulated Tu are illustrated in Figs. 3(a)–(e). Fig. 3(a) is for fogging duration of 1.0–3.0 min; Fig. 3(b) for 0.5–1.5 min; Fig. 3(c) for 1.5–4.5 min; Fig. 3(d) for 0.5–1.0 min and Fig. 3(e) for 1.0–2.0 min, respectively. In Figs. 3(a)–(c) and (e), the values of Tu are very close or equal to the values of Tdi at the end of each interval time and just before the beginning of each fogging time. However, at these instants the fog-cooling has little or no effect on cooling the inside air or reducing Tdi. While in Fig. 3(d) Tdi is lower than Tu most of the time due to the effect of the repetition of fogging after a short interval time (i.e. 0.5–1.0 min) in reducing Tdi. Eqs. (15) and (17) are for estimating the evapo-transpiration rate (ETr) in the greenhouses without fog cooling. Using these equations to estimate ETr in a fog-cooled greenhouse is expected to result in an overestimation of ETr. This is because these equations are derived based on relatively high vapor pressure deficits (VPD) in greenhouses without fog cooling. Therefore, the iteration technique was used to estimate _ f . In the computation procedure, Fig. 2, the first estimate of ETr was made by assuming m _ f in Eq. (6) is equal to zero. Then, ETr could be corrected based on the water vapor that m balance of the greenhouse air, Eq. (18). Time courses of the first estimate of ETr from Eqs. (15) and (17) and the final corrected values are illustrated in Figs. 4(a)–(e) for the five fogging durations. No difference was seen in Fig. 4(a) between the first estimate and the corrected values of ETr for the fogging duration of 1.0–3.0 min. Overestimations of ETr are shown in Fig. 4(b)–(e). However, the corrected values of ETr are lower than the first estimate of ETr from Eqs. (15) and (17) as we expected due to the effect of fogging in reducing the VPD as well as ETr in the greenhouse. _ w , the evaporation of fog (bH m _w Using the corrected values of ETr, the time courses of m _ w Þ are _ w ) and the evaporation of the non-evaporated fog from the floor ðð1
bH Þm and bL m illustrated in Figs. 5(a)–(e) or the five fogging durations, respectively. In this figure, values _ w was _ w and bL m _ w are almost the same, and therefore, the fog evaporation rate bm of bH m _ w in Eq. (18). Also it is worth noting that the evaporation rate of fog considered as bH m _ w ) is low and most of the fog falls on the floor surface (i.e., ð1
bÞm _ w ). This is because (bm one roof ventilator was open during the experiment and the ventilation rate was low (the number of air exchanges was estimated to be from 15 to 30 h
1). However, this experiment was conducted mainly for the present analysis, the purpose of which was to develop a simulation method to estimate the fog evaporation under the greenhouse conditions instead of measuring methods which include errors and was not for enhancing the fog evaporation or cooling efficiency of the fogging system. In previous studies of fogging systems, the amount of fog which evaporates in the _ w ) was supposed to evaporate during the fogging time at a constant greenhouse air (bm

ARTICLE IN PRESS A.M. Abdel-Ghany et al. / Renewable Energy 31 (2006) 2207–2226

2218 Temperatures, (°C)

45 Tdo

Tu

1 min on, 3 min off

Tdi

40 35

(a)

9 12

:5

9 12

:4

9 :3 12

12

12

:2

:1

9

9

30

Time of the day

Temperatures, (°C)

45 Tu

0.5 min on, 1.5 min off

Tdi

Tdo

40 35

4 13

:2

9 13

:1 13

(b)

Time of the day 45

Temperatures, (°C)

:1

4

9 :0 13

13

:0

4

30

1.5 min on, 4.5 min off

Tu

Tdi

Tdo

40 35

45

05 13

:5

0:

05 13

:4

5:

05 :4

0.5 min on,1 min off

Tu

Tdi

Tdo

40 35

:1 1: 3

0

05 9:

05

14

14

14 :0

:0

4:

9: :5 13

13

:5

4:

05

30

(d) Temperatures, (°C)

13

Time of the day

05

Temperatures, (°C)

(c)

0:

05 13

:3

5:

05 0: :3 13

13

:2

5:

05

30

Time of the day 45 Tu

Tdo

1 min on, 2 min off

Tdi

40 35

(e)

0

14

:3

9 14

:2

4 14

:2

9 :1 14

14

:1

4

30

Time of the day

Fig. 3. Time courses of the dry bulb temperatures measured inside and outside the greenhouse (Tdi, Tdo) and the simulated dry bulb temperature of the un-cooled air (Tu) in the greenhouse for the five different fogging durations.

ARTICLE IN PRESS A.M. Abdel-Ghany et al. / Renewable Energy 31 (2006) 2207–2226

1 min on, 3 min off

0.10 0.08 0.06 0.04 0.02 0.00

9 12

Time of the day

(a)

0.5 min on, 1.5 min off

0.10 0.08 0.06 0.04 0.02 0.00

(b)

4 13

:2

9 13

:1

4 :1 13

:0 13

13

:0

9

First estimate using Eqs. (15,17) Final corrected value 4

ETr, (g m-2 s-1)

0.12

Time of the day 0.12

1.5 min on, 4.5 min off

0.10 0.08 0.06 0.04 0.02 0.00

(c)

05 13

:5

0:

05 13

:4

5:

05 13

:4

0:

05 5: 13

:3

0: 13

:3

5: :2 13

05

First estimate using Eqs. (15,17) Final corrected value 05

ETr, (g m-2 s-1)

:5

9 12

:4

9 :3 12

:2 12

12

:1

9

First estimate using Eqs. (15,17) Final corrected value

9

ETr, (g m-2 s-1)

0.12

2219

Time of the day

0.5 min on, 1 min off

0.10 0.08

(d)

1 min on, 2 min off

0.10 0.08 0.06 0.04 0.02

0 14 :3

9 14 :2

4 14 :2

4 14 :1

9

First estimate using Eqs.(15,17) Final corrected value

0.00

14 :1

ETr, (g m-2 s-1)

14 :

05 14 :0 9:

05

Time of the day

0.12

(e)

11 :3 0

First estimate using Eqs. (15,17) Final corrected value 14 :0 4:

14 :5

4:

05

0.00

05

0.06 0.04 0.02

13 :5 9:

ETr, (g m-2 s-1)

0.12

Time of the day

Fig. 4. Time courses of the first estimate of the evapo-transpiration rate (ETr) from Eqs. (15) and (17) and the final corrected values for the five different fogging durations.

ARTICLE IN PRESS A.M. Abdel-Ghany et al. / Renewable Energy 31 (2006) 2207–2226

2220 Evaporation rate (g m-2 s-1)

0.40 0.35 0.10

1 min on , 3 min off

0.05

0.5 min on , 1.5 min off

0.05

13 :1 9

13 :1 4

13 :0 9

13 :2 4

0.00

(b)

Time of the day

Evaporation rate (g m-2 s-1)

0.40 0.35 0.10

1.5 min on , 4.5 min off

0.05

0:

05

:5 13

:4 13

:4 13

:3 13

:3 13

5:

05 0:

05 5:

05 0:

05 5: :2 13

Time of the day 0.40 0.35 0.10

0.5 min on , 1 min off

0.05

05

:1 1 14

:0 14

14

13

9:

:0 5 :0 4

05 :5

9:

4: :5 14

(d)

:3 0

0.00 05

Time of the day 0.40 0.35

1 min on , 2 min off

0.10 0.05

(e) . βHmw

Time of the day . . (1-βH) mw βLmw

14 : 14 29 :3 0

:2 4

:1 14

14

:1

4

9

0.00 14

Evaporation rate (g m-2 s-1)

05

0.00

(c)

Evaporation rate (g m-2 s-1)

12 :4 9

12 :3 9

12 :2 9

12 :1 9

Time of the day 0.40 0.35 0.10

13 .0 4

Evaporation rate (g m-2 s-1)

(a)

12 :5 9

0.00

. mw

_ w ; bL m _ w ), the non-evaporated fog ðð1
bH Þm _ wÞ Fig. 5. Evaporation characteristics of the evaporated fog (bH m and the fogging rate supplied in the greenhouse for the five different fogging durations.

ARTICLE IN PRESS A.M. Abdel-Ghany et al. / Renewable Energy 31 (2006) 2207–2226

12 :5 9

Time of the day

(b)

:2 4 13

:1 9 13

13

13

13

:0 9

:1 4

0.25 0.5 min on, 1.5 min off 0.20 0.15 0.10 0.05 0.00 :0 4

Time of the day 0.30 0.25 0.20 0.15 0.10 0.05 0.00

(c)

0: 13

13

:5

:4

:4

5:

05

05

05 0:

05 5: :3 13

13

13

:3

:2

0:

5:

05

05

1.5 min on, 4.5 min off

13

β

12 :4 9

12 :3 9

12 :2 9

12 :1 9

β

0.25 1 min on, 3 min off 0.20 0.15 0.10 0.05 0.00

(a)

β

2221

Time of the day 0.25

0.5 min on, 1 min off

0.20 β

0.15 0.10 0.05

(d)

:0 5 14 :1 1: 30

09 14 :

Time of the day 0.25 0.20

β

05

:0 59

14 :0 4:

13 :

13 :

54

:0

5

5

0.00

1 min on, 2 min off

0.15 0.10 0.05

(e)

0

14

:3

9 :2 14

:2 4 14

9 :1 14

14

:1 4

0.00

Time of the day

Fig. 6. Time course of the fraction of fog that evaporates in the greenhouse air (b) for the five different fogging durations.

ARTICLE IN PRESS A.M. Abdel-Ghany et al. / Renewable Energy 31 (2006) 2207–2226

2222

0.40 0.35 0.30

β

0.25 0.20 0.15 0.10 0.05 0.00 )

3.0

0(1.

5)

-1.

5 (0.

5(1.

4.5

) 5 (0.

0) -1.

0 (1.

0) -2.

Fogging duration, (on, min - off, min) Fig 7. Time integral of the b factor for the five different fogging durations.

rate, which means that b is constant during the fogging time and equal to zero during the interval time. According to Figs. 5(a)–(e), this assumption is not true because b has a certain profile during both the fogging and interval times which could be investigated and illustrated in Figs. 6(a)–(e) for the five different fogging durations, respectively. In Figs. 5 _ w ) and evaporation of the nonand 6, evaporation of fog in the greenhouse air (bm _ evaporated fog ðð1
bÞmw Þ could be characterized during both the fogging and the interval times. The integrated values of b over the whole time (fogging and interval times) of the five fogging durations are illustrated in Fig. 7. This figure shows that using a fogging duration of 1.0–3.0 min resulted relatively high evaporation rate ðb ¼ 0:36Þ followed by 1.5–4.5 min ðb ¼ 0:33Þ: However, under the weather and experimental conditions mentioned in Section 1, the optimal fogging duration is 1.0 min (on)–3.0 min (off) and this cannot be generalized for any weather and greenhouse design conditions. Integrated mass balance was applied to the greenhouse for the five fogging durations based on the estimated and corrected values of ET (i.e., total amount of evapotranspiration in kg) and is illustrated in Figs. 8(a) and (b). In this figure, the total amount of water vapor that entered and exited the greenhouse with ventilation (mvi, mvo) and the total amount of water supplied for fogging (mw) were estimated based on measurements. The total amount of evaporated fog bmw was estimated from the measured Tdi and the predicted Tu which depends on the predicted Tc, Tf and the measured Tp. However, the Fig. 8. Integrated water vapor balances of the greenhouse for the five fogging durations (in kg of vapor) (a) based on the first estimate of ET using Eqs. (15) and (17) and (b) based on the corrected values of ET. ET is the evapotranspired vapor, mw is the amount of fog supplied to the greenhouse, bmw is the amount of fog that evaporates, mf is the amount of fog that fell on the floor surface, mvi and mvo are the amount of water vapor entering and exiting the greenhouse with ventilation.

ARTICLE IN PRESS A.M. Abdel-Ghany et al. / Renewable Energy 31 (2006) 2207–2226 mw 3.0

mw 6

mw 3.6 19.17

16.3

34.96

mvi

m w βm 3.884

mvo

0.72

2.12 2.12

mvo

mvi

βmw 1.97

5.636 6

ET

ET 0.35

0.31 (0.5 min on,1.5 min off)

Fogging duration: (1 min on, 3 min off) (41 min)

(1.5 min on, 4.5 min off)

(21 min)

(25 min)

mw 3.3

mw 3.0 12.1

mvi

14.54

mvo mvi

βm m w

1.93

0.76

10.5

0.57

7.76 7.

mvo m w βm

1.7

1.87

mf

1.62

mff ET

ET

0.8 Fogging duration: Working time:

3.159

mf

ET 0.004 4 Working time:

mvo m w βm

2.048

2.83

mf

mf m

1.202 1.202

12.81

10.83

23.287 mvi

2223

0.54 (0.5minon, 1.0 min off) (17 min, 25 sec)

(1.0 min on, 2.0 min off) (16 min)

(a) mw 3.0

mw 6

mw 3.6 16.31

mvi

βmw 3.88

5.64

2.428

2.478

mf

mf

ET

(1.0 min on, 3.0 min off) (41 min) mw 3.3

mw 3.0

mf

(b)

0.73

mvo mvi

βmw 1.05

2.27 mf

ET Fogging duration: Working time:

14.54 10.5

0.54 2.76

(0.5 min on, 1.0 min off) (17 min, 25 sec)

2.78

(1.5 min on, 4.5 min off) (25 min)

12.1

mvi

βmw

ET

(0.5 min on, 1.5 min off) (21 min)

7.76

mvo

mf

ET Fogging duration: Working time:

mvi

βmw 2.32

19.17 12.81

mvo

0.68

2.12 mvi

10.83

mvo

1.172

34.96 23.28

mvo βmw 1.05

ET (1.0min on, 2.0 min off) (16 min)

ARTICLE IN PRESS A.M. Abdel-Ghany et al. / Renewable Energy 31 (2006) 2207–2226 0.04

ωo

1 min on, 3 min off

0.01

0.04

ωo

0.03

ωf ωu

ωET

9 :5 12

:4

0.5 min on, 1.5 min off

0.01

4 13

:2

9 13

13

:1

4 :1

:0 13

13

:0

9

0.00 Time of the day 0.04

ωo

ωET ωsi

ωi ωu

ωf

0.03 0.02 0.01

1.5 min on, 4.5 min off

05

05 13

13

:5

:4

0:

5:

05 0: 13

:4

5: :3 13

13

13

:3

:2

0:

5:

05

05

0.00 05

Time of the day 0.04

ωo

ωET

ωf

ωu

ωsi

ωi

0.03 0.02 0.5 min on, 1 min off

0.01

(d)

1: 30 :1 14

9: 05 14

:0

4: 05 14

13

13

:5

:5

4:

9: 05

05

0.00 :0

Time of the day 0.04 0.03

ωo

ωET

ωf ωu

ωi ωsi

0.02 1 min on, 2 min off

0.01

:2 14 9 :3 0

14

:2 4

:1 9 14

14

:1 4

0.00 14

Absolut humidity, (kgv / kgDA)

12

ωi ωsi

0.02

4

Absolute humidity, (kgv / kgDA)

Time of the day

(c) Absolute humidity, (kgv / kgDA)

9

9 :3 12

:2 12

12

:1

9

0.00

(b)

Absolute humidity, (kgv / kgDA)

ωsi

ωi

0.02

(a)

(e)

ωu

ωf

ωET

0.03

9

Absolut humidity, (kgv / kgDA)

2224

Time of the day

Fig. 9. Time courses of the absolute humidities in the greenhouse due to ventilation (oo), evaporation of the nonevaporated fog (of) and evapo-transpiration (oET) of the un-cooled air (ou), the cooled air (oi) and the saturated air (osi) for the five different fogging durations.

ARTICLE IN PRESS A.M. Abdel-Ghany et al. / Renewable Energy 31 (2006) 2207–2226

2225

value of bmw is not directly affected by the error in ET. Also, the summation of bmw and mf (i.e., the total amount of the evaporated and the non-evaporated fog) should be equal to mw. The difference, if any, between mw and (mf þ bmw ) represents the error in ET. Fig. 8(a) shows the overestimation of ET and the amount of vapor that should be subtracted and added to mf to adjust the balance for all the fogging durations except for the 1.0–3.0 min which gives an accurate estimate of ET. The integrated mass balances using the corrected values of ET are illustrated in Fig. 8(b). The absolute humidity of the greenhouse air oi is a result of different contributions of water vapor sources that increase the humidity in the greenhouse such as: outside air enters the greenhouse with ventilation causes oo, ETr causes oET , and evaporation of the nonevaporated fog from the floor causes of. The three contributions together cause the _ w ) in absolute humidity of the un-cooled air ou in Eq. (19). Finally, evaporation of fog (bm the un-cooled air causes the absolute humidity of the inside air oi. The time courses of these absolute humidities in addition to the absolute humidity of the saturated greenhouse air osi are illustrated in Fig. 9. This figure shows the humidity of the outside greenhouse air oo makes a major contribution to the humidity of the greenhouse air oi and the fog evaporation rate as well as the b factor is expected to increase efficiently if oo was low. 10. Conclusion In this study, a simulation method to investigate the evaporation characteristics of water fog supplied to the greenhouse air is presented. Evaporation of fog in the greenhouse air _ w as well as the b factor could be simulated correctly in the greenhouse conditions bm instead of measurements which definitely include error. Under the experimental conditions described above, a fogging duration of 1–3 min provided relatively high evaporation rate of fog compared to other fogging durations. Fog evaporation was low because of the low ventilation rate. Therefore, the fogging systems are expected to work well in a well ventilated greenhouse under dry weather conditions. However, in humid areas the fogging systems need to be modified to enhance the evaporation rate of fog. References [1] Giacomelli GA, Gininger MS, Krass AE, Mears DR. Improved methods of greenhouse evaporative cooling. Acta Hortic 1985;174:49–55. [2] Giacomelli GA, Roberts W. Try alternative methods of evaporative cooling. Acta Hortic 1989;257:29–32. [3] Montero JI, Anton A, Biel C, Franquet A. Cooling of greenhouse with compressed air fogging nozzles. Acta Hortic 1990;281:199–209. [4] Arbel A, Yekutieli O, Barak M. Performance of a fog system for cooling Greenhouses. J Agric Eng Res 1999;72:129–36. [5] Hayashi M, Sughara T, Nakajima H. Temperature and humidity environments inside a naturally ventilated greenhouse with the evaporative fog cooling system. Environ Control Biol 1998;36(2):97–104 (in Japanese with English summary). [6] Arbel A, Barak M, Shklyar A. Combination of forced ventilation and fogging systems for cooling greenhouses. Biosyst Eng 2003;48(1):45–55. [7] Hasan Hu¨seyin O¨ztu¨rk. Evaporative cooling efficiency of a fogging system for greenhouses. Turk J Agric For 2003;27:49–57. [8] Toida H, Kozai T, Ohyama K, Handarto H. Enhancing fog evaporation rate using an upward air stream: an Indoor experiment to improve the performance of a fogging system used for cooling greenhouses. Biosyst Eng 2005, in press.

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[9] Equation describing the physical properties of moist air at: http://www.natmus.dk/cons/tp/atmcal/ ATMOCLC1.HTM and http://members.nuvox.net/on.jwclymer/wet.html [10] Abdel-Ghany AM, Kozai T. Dynamic modeling of the environment in a naturally ventilated, fog-cooled greenhouse. Int J Renewable Energy 2005, in press. [11] Papadakis G, Frangoudakis A, Kyritsis S. Mixed, forced and free convection heat transfer at the greenhouse cove. J Agric Eng Res 1992;51:191–205. [12] Kindelan M. Dynamic modeling of greenhouse environment. Trans ASAE 1980:1232–9. [13] Stanghellini C. Mixed convection above greenhouse crop canopies. Agric For Meteorol 1993;66:111–7. [14] Compaq Visual FORTRAN. Professional Edition, Software Package; 1999. [15] Abdel-Ghany AM, Kozai T. On the determination of the overall heat transmission coefficient and soil heat flux for a fog-cooled, naturally ventilated greenhouse: analysis of radiation and convection heat transfer. Int J Energy Conversion Manag 2005, in press. [16] Abdel-Ghany AM, Kozai T. Cooling efficiency of fogging systems for greenhouses. Biosyst Eng 2005, in press. [17] Bakker JC. Measurement of canopy transpiration or evapo-transpiration in greenhouses by means of a simple vapor balance model. Agric For Meteorol 1986;37:133–41. [18] Bot GPA. Greenhouse climate: from physical process to a dynamic model. PhD thesis, Agriculture University of Wageningen, The Netherlands, 1983. [19] Jolliet O, Bailey BJ. The effect of climate on tomato transpiration in greenhouses: Measurements and models comparison. Agric For Meteorol 1992;58:43–62.