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Modified thermal model to predict the natural ventilation of greenhouses
Accepted Manuscript Title: Modified thermal model to predict the natural ventilation of greenhouses Author: I.M. Al-Helal S.A. Waheeb A.A. Ibrahim M.R. Shady A.M. Abdel-Ghany PII: DOI: Reference:
S0378-7788(15)00312-6 http://dx.doi.org/doi:10.1016/j.enbuild.2015.04.013 ENB 5805
To appear in:
ENB
Received date: Accepted date:
11-3-2015 11-4-2015
Please cite this article as: I.M. Al-Helal, S.A. Waheeb, A.A. Ibrahim, M.R. Shady, A.M. Abdel-Ghany, Modified thermal model to predict the natural ventilation of greenhouses, Energy and Buildings (2015), http://dx.doi.org/10.1016/j.enbuild.2015.04.013 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Highlights A model was developed to predict the natural ventilation of greenhouses. The model is able to predict ventilation rate at low or zero solar radiation intensity.
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Wind at a speed < 2.5 m s-1 has no significant effect on the ventilation rate and the temperature difference do the main effect.
A correlation between the ventilation rate and temperature difference was
Ac ce p
te
d
M
an
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cr
provided.
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Modified thermal model to predict the natural ventilation of greenhouses I. M. Al-Helala, S. A. Waheebb, A. A. Ibrahimc, M. R. Shadya, A. M. Abdel-Ghany*,a a
us
cr
ip t
Department of Agricultural Engineering, College of Food and Agriculture Sciences, King Saud University, PO Box 2460, Riyadh 11451, Saudi Arabia. b Department of Engineering Sciences, Community College, Umm Al Qura University, PO Box 715, Makkah 21955, Saudi Arabia. c Department of Plant Production, College of Food and Agriculture Sciences, King Saud University, PO Box 2460, Riyadh 11451, Saudi Arabia.
ABSTRACT
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Most of thermal models used to estimate the natural ventilation of greenhouses ( m a ) use an average value for the cover transmittance ( c ) to estimate the input solar energy to the greenhouse. These models failed to predict m a at low solar radiation flux
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due to the spatial variation of c in the greenhouse and the thermal inertia of soil. This study is to develop and validate a thermal model predict m a precisely. All modes
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of energy were treated, under the unsteady state conditions, at the outer surface of the
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cover to avoid the sources of error. The required parameters were measured for a naturally ventilated glasshouse. The predicted values of m a were in the range between
Ac ce p
0.36 kg s-1 and 1.65 kg s-1 and showed good accordance with measured and simulated values in the literature. The results also confirmed that outside wind at a speed < 2.5 m s-1 has no significant effect on the value of m a and the temperature difference of air
between inside and outside the greenhouse ( T ) is the main driving force of
ventilation. A correlation between m a and T was provided, it can be used to estimate m a that required to maintain the air temperature in the greenhouse at a desired level.
Keywords: Greenhouse; natural ventilation; energy balance, solar radiation *Corresponding author: (Tel & fax: +966 (011) 4678352) E-mail addresses: [email protected] ; [email protected] (A. M. Abdel-Ghany)
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Nomenclatures surface area of the greenhouse cover (m2)
Af
surface area of the greenhouse floor (m2)
Cpa
specific heat of air at constant pressure (J kg-1 oC-1)
d
greenhouse cover thickness (m)
fd
ratio of diffuse to global solar radiation (-)
hc-o
convective heat transfer coefficient between the cover surface and the outside
ip t
Ac
cr
ambient air (W m-2 oC-1)
specific enthalpy of moist air inside the greenhouse (J kg-1)
Io
specific enthalpy of moist air outside the greenhouse (J kg-1)
j
surface number of the greenhouse cover (1,2,…, 6)
kf
equivalent thermal conductivity of the greenhouse soil (W m-1 oC-1)
m a
ventilation rate of the greenhouse (kg s-1)
Na
number of air exchange per hour (h-1)
n
refractive index of the covering material (-)
Qc-o
convection heat rate between the cover surface and outside ambient (W)
qo
heat rate conducted into the greenhouse soil surface (W)
Rn
net thermal radiation exchange between the cover and sky (W)
rb
ratio of beam irradiance received by a tilted surface to that received by a
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Ii
horizontal surface (-)
global solar radiation flux transmitted into the greenhouse (W m-2)
SL
solar radiation loss to outside the greenhouse (W m-2)
Sn
net global solar energy crossing the control volume of the greenhouse (W)
So
global solar radiation flux at the greenhouse outer surface (W m-2)
Tc
cover outer surface temperature (oC)
Ti
air temperature inside the greenhouse (oC)
To
air temperature outside the greenhouse (oC)
Tf
floor surface temperature (oC)
Tsky
equivalent temperature of sky (oC)
U
overall heat loss coefficient of the greenhouse cover (W m-2 oC-1)
V
wind speed outside the greenhouse (m s-1)
Vg
volume of the greenhouse air (m3)
z
vertical depth under the greenhouse measured from the soil surface (m)
Ac ce p Si
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Greek symbols absorptance of the cover to global solar radiation (-)
slope angle of the cover surface (degree)
I
specific enthalpy difference (Ii-Io) (J kg-1)
T
temperature difference (Ti-To) (oC)
evaporation efficiency (-)
s
surface azimuth angle (degree)
solar radiation heating efficiency (-)
absorption coefficient of the cover material (m-1)
incidence angle of direct solar radiation (degree)
r
angle of refraction (degree)
z
solar zenith angle (degree)
a
density of moist air (kg m-3)
c, j
directional reflectance of the cover surface j to direct beam solar radiation (-)
c, j
directional reflectance of the cover surface j to global solar radiation (-)
ˆ
interface reflectance between the cover surface and air (-)
f
reflectance of the floor surface to global solar radiation (-)
c
average transmittance of the greenhouse cover to global solar radiation (-)
c, j
directional transmittance of the cover surface j to direct solar radiation (-)
ˆ
transmittance due to absorption of solar radiation in the cover material (-)
absolute humidity (kg of water vapor/ kg of dry air)
Ac ce p
te
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cr
ip t
c
1. Introduction
Ventilation of greenhouses plays a major role in providing a suitable environment for plant growth. In summer, ventilation is for cooling the greenhouse air, and in winter ventilation can remove excess humidity from the greenhouse. Recently, most greenhouse ventilation studies have been focusing on the use of natural ventilation to reduce electric energy consumption by greenhouses. Although investigation of natural
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ventilation in the greenhouses started since 50 years ago, there is still no adequate method to precisely predict the amount of natural ventilation [1]. Based on the survey of the previous researches performed in this area, the main methods that have been
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used to estimate the natural ventilation rate of greenhouses and the problems associated with each method can be summarized as follows:
cr
(i) Measuring methods, in which, a tracer gas such as N2O or CO2 is injected in the
greenhouse and the decay rate of the gas concentration is measured [2-8]. These
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methods can measure the ventilation rates during the time of experiments only.
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However, the ventilation rate strongly depends on the environmental conditions and on the greenhouse design parameters. Therefore, developing theoretical models to
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estimate the ventilation rate of greenhouses was essential need. (ii) Air dynamic models, in which, ventilation was assumed to be driven by two
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forces, namely, the wind force and the buoyancy force and such models is used only
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for greenhouses with roof vents [9]. The resulted ventilation rate from these models depends on two critical dimensionless coefficients, (i.e., the discharge coefficient and
Ac ce p
the wind coefficient). However, these coefficients are usually determined by in situ measurements and differ from greenhouse to greenhouse, and depend on the design configuration of the vents, greenhouse location, orientation and environmental conditions. Several values for the wind coefficient (0.006-0.28) and for the discharge coefficient (0.4-0.848) were reported in the literature [9-11]. (iii) Energy balance models, in which, energy balances are applied to the
greenhouse air. A simple design formula was suggested by [12] to estimate m a based on the fundamental heat balance of the greenhouse. This formula assumed the air is completely mixed in the greenhouse and is given by:
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m a
S o c Af UAc T , I
(I 0.0)
(1)
This equation has been modified, based on the sensible heat balance of the greenhouse air and used as ASAE-STD and reported in [9] in the form: (1 ) c S o Af UAc T C pa T
ip t
m a
(2)
cr
In equations (1) and (2), So is the global solar radiation flux on a horizontal surface
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outside the greenhouse; c is the average transmittance of the greenhouse cover to solar radiation; Af and Ac are the surface areas of the greenhouse floor and cover; U is
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the overall heat loss coefficient of the cover; I is the moist air specific enthalpy difference between inside and outside the greenhouse (Ii-Io); Cpa is the specific heat
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of air at constant pressure and is an “evaporation coefficient”, which estimates the fraction of total solar radiation load taken up by evaporation in the greenhouse. No
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details are given in the literature for the proper selection of , and standard examples
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often use = 0.5. The term (1 ) c in Eq. (2) is also defined as the solar radiation
Ac ce p
heating factor , (i.e. the fraction of So that was converted into sensible heat and used to warm up the greenhouse air). Several values of are reported in the range between
0.3 and 0.7 [13-15]. Determination of as well as value is quite difficult,
especially if the greenhouse includes a crop canopy and associated with an evaporative cooling in summer. Limitations of using Eq. (1) as reported in [12] are: So > 230 W m-2; I > 8.368 kJ kg-1 and the time interval should be higher than 20 min.
In summer, values of I and T in Eq. (1) and Eq. (2) are always positive during the daytime, even though, these equations resulted in negative values of m a at low solar radiation levels.
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Several previous studies estimated the natural ventilation rate of greenhouses by using energy balance methods. All of these studies assumed that solar radiation transmitted into the greenhouse was the only input energy and used an average value of the cover
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transmittance ( c ). However, c depends on the spatial location within the greenhouse and on the altitude of the greenhouse. The maximum longitudinal variation of c over
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the floor surface in a venlo-type N-S glasshouse (4 mm thick of cover) was measured
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by [16] at the location 52o 20’ N to be 0.4. In addition, the maximum spatial variation of c was measured by [17] in a scale model of a glasshouse (4 mm thick of cover) at
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the location 37o 58’ N to be 0.8. Accordingly, using an average value of c will cause a large error in the estimation of the transmitted solar radiation into the greenhouse
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and in the estimation of m a as well. This error is expected to be high in small greenhouses because the cover to floor surface area ratio is usually high (e.g., 3~5),
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and unfortunately most of the ventilation studies using an energy balance method or
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any other method were based on experimental greenhouses.
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The objectives of this study were to: (i) develop a simplified energy balance model to estimate the natural ventilation of greenhouses precisely, and (ii) check the validity of the model by comparing its results with results of theoretical models and experimental measurements reported in the literature. Uncertain parameters such as the thermal inertia of the greenhouse soil, and using an average value of c were avoided in the
proposed model. The proposed energy balance was applied to a control volume for the greenhouse suggested to be between the outer surface of the cover and the floor surface.
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2. The Proposed model The greenhouse used for this study is a single-span, its frame was constructed from aluminum bars and covered with a glass sheet of 4-mm thick (Fig. 1). It was
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considered as a thermodynamic system, enclosed by a control volume (cv). The different modes of energy crossing the boundary (i.e. the cv) of the system were
cr
illustrated in Fig. 1. During the daytime, the cover surfaces (i.e. surface 1 to surface 6)
were found to have almost the same temperature because the absorptance of
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transparent materials is not strongly affected by the incident angle of solar beam
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radiation or the surface orientation [18]. Therefore, measuring Tc of one or two surfaces is sufficient to represent the temperature of the whole cover surfaces. Energy
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balance was applied to the cv under the un-steady state condition assuming: (i) The moist air inside or outside the greenhouse is well mixed and characterized by average
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temperatures and relative humidity (Ti, RHi, To, RHo) and average thermo-physical
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properties. (ii) The cover and floor are gray surfaces in terms of long wave radiation and characterized by an equivalent temperatures (Tc and Tf). (iii) The cover is opaque
Ac ce p
to transmit thermal radiation and is a diffuse emitter and diffuse reflector; and the floor surface reflects solar and thermal radiation diffusively. (iv) Parameters in the upcoming analysis are time dependent. For simplification, the functional relationship of time is omitted from all the symbols hereafter. Energy terms are crossing the cv of
the system (Fig. 1), in and out, are: sensible and latent heat associated with the ventilation process ( I o m a and I i m a ); net solar radiation (Sn); convection exchange between the outer surface of the cover and the outside ambient air (Qc-o); thermal radiation exchange between the outer surface of cover and sky (Rn); and the conducted heat into the floor (qo). Determinations of these terms are as follows:
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2.1. The net solar radiation (Sn) The different surfaces of the greenhouse cover were designated with the numbers 1 to 6 (Fig. 1), and all the surfaces were supposed to be facing outward. The slope and
received by a tilted surface j, St,j (j=1,2,..6) is given by [19] as:
cr
S t, j ( S b, t S d, t S gr, t ) j
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azimuth angles of these surfaces ( o , so ) were determined. The total solar irradiance
(3)
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where Sb,t is the beam irradiance; Sd,t is the sky diffuse irradiance and Sgr,t is the global irradiance which is received by the tilted surface j from that reflected from the ground
can be rewritten in the form [19]
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outside the greenhouse. Assuming the sky diffuse irradiance is anisotropic, Eq. (3)
St, j So (1 f d )rb f d cos2 ( )1 F sin3 ( ) 1 F cos2 sin3 z gr sin2 ( ) 2 2 2 j
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cos , cos z ,
(5)
if 90 o
Ac ce p
0
if 0 o 90 o
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rb
(4)
d
with F = 1-(fd)2 and
In Eq. (5), rb is the ratio of beam irradiance received by a tilted surface j to that
received by a horizontal surface; fd is the diffuse fraction (ratio of diffuse to global solar radiation). Diurnal variation of fd in sunny days was estimated for Riyadh area to
be 0.8 in the early morning and before sunset; and it was 0.1 most of the day time. Therefore, a precise value of fd was taken to be 0.13 on average. and z are the incident and azimuth angles of the solar beam radiation on the surface j; So is the
outside global solar radiation received by a horizontal surface; and gr is the reflectance of the ground to solar beam radiation and was taken to be 0.2 for sandy soil [15]. Values of and z were estimated during the day using the well-known
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relations reported in [19]. The net solar energy entering the cv at the outer surfaces of the cover (Fig. 1) as a function of time, or , is given by: 6
S n A j S t, j (1 c, j ) S L
(6)
j 1
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where c, j is the reflectance, to the outside, of the cover surface j to global solar
cr
radiation and Aj is the area of the surface j. The transmitted solar radiation from each
surface j into the greenhouse is assumed to be suffering multiple reflections between
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the cover and floor surfaces. Part of the transmitted radiation is transmitted again to outside the greenhouse (solar radiation loss, SL). The diffuse solar radiation that
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incident on the inside and outside surfaces of the cover was treated as direct beam incident at an incidence angle of 60o [19]. For the greenhouse without crop canopy,
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used in this study, the diurnal variation of SL was estimated to be 0.1-0.3 of the incident solar radiation outside the greenhouse with a maximum error less than 1%
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[15]. The floor reflectance to the global solar radiation f was taken to be 0.2 on average [20].
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Value of c, j was estimated according to [21] as:
c , j f d c, j
θ 60
(1 f d ) c , j
(7)
In Eq. (7), c , j is the directional reflectance of the cover surface j to direct beam solar
radiation. The radiative properties of the glass cover (values of c, j and c , j ) at a specified incidence angle are given, respectively by [21] as:
c, j
2 ˆ1 ˆ 1 (ˆ ˆ ) 2
(8)
c, j ˆ 1 ˆ c, j
(9)
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In Eqs. (8) and (9), the directional transmittance due to absorption ( ˆ ) and the interface reflectance ( ˆ ) of a cover sheet having a thickness d and an absorption coefficient are given by [21] as: r
(10)
ip t
1 sin 2 ( r ) tan 2 ( r ) 2 sin 2 ( r ) tan 2 ( r )
ˆ e (d / cos ) and ˆ
the refractive index (n) of the cover material is defined by:
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r sin 1 sin / n
cr
The angle of refraction ( r ) of a solar beam passing through the cover sheet related to
(11)
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Values of n and were taken to be 1.526 and 0.3 cm-1, respectively [21]
2.2. The net thermal radiation (Rn)
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For single-span greenhouses such as in Fig. 1, the view factor between the outer surface of the cover and the sky dome is assumed to be equal one. The net thermal
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radiation exchange between the outer surface of the cover having an emittance c and
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an average temperature Tc and the assumed black sky dome at an equivalent
Ac ce p
temperature Tsky is given by [19] as:
4 Rn c Ac Tc4 Tsky
(12)
with Tsky is in Kelvin and is given by [19] as:
Tsky 0.0559(To )1.5
(13)
where To is the outside air temperature in Kelvin.
2.3. The convective heat (Qc-o)
The convective heat exchange between the outer surfaces of the cover and the outside ambient air Qc-o can be estimated using Newton’s law of cooling with a convective heat transfer coefficient hc-o reported in [21] for the forced convection condition over buildings as:
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8.6V 0.6 hc o max 5, 0.4 Lc
Qc-o= Ac hc-o (Tc-Tdo),
,
L c 3 Vg
(14)
where V is the wind speed outside the greenhouse and Vg is the greenhouse volume.
ip t
2.4. Conduction into the soil (qo) The nature of heat conduction into the greenhouse soil depends on the soil
cr
composition, the soil thermo-physical properties and the soil water contents. For simplicity, the floor soil was assumed to behave as a homogeneous layer having a
us
thickness z, an equivalent thermal conductivity kf, an upper surface temperature Tf and
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a lower constant subsoil temperature T (i.e. unaffected by the daily variation of Tf). The heat flux qo crossing the cv downward and conducted into the floor soil, assuming
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quasi-steady state conditions at small time intervals (dt = 10 second), was approximated as [13] by:
k f Af Tf T z
d
qo
(15)
te
In Eq. (15), Af is the floor surface area; values of kf, z and T were taken to be 2.0 W
Ac ce p
m-1 C-1, 0.5 m, and 20 oC, respectively [13]. 2.5. The model equation
Energy balance was applied to the cv of the greenhouse (Fig. 1) under the un-steady
state condition according to the following equation:
dT ( S n m a I o ) ( Rn Qc o q o m a I i ) mC p dt cv
(16)
The energy terms on the left hand side of Eq. (16) are: Sn is estimated from Eq. (6) by measuring So on a horizontal plane outside the greenhouse; Rn and Qc-o are estimated from Eq. (12) and Eq. (14), respectively, by measuring Tc and To; qo is estimated from Eq. (15) by measuring Tf; and the specific enthalpy of the moist air (kJ kg-1) inside
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and outside the greenhouse (Ii and Io) was estimated based on the air temperature and its absolute humidity as: I (1.007T 0.026) (2501 1.84T ), T in oC
(17)
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The right hand side of Eq. (16) is the rate of stored energy of the masses enclosed in the cv, in which the mass m, the specific heat Cp and the change of temperature
cr
history (i.e. dT /dt) were counted for the glass cover, the aluminum frame, (assuming
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its temperature is the same as Tc ), and the greenhouse air. The unknown in Eq. (16) is the ventilation rate of air ( m a ), which can be determined by solving this equation at
changes per hour (Na) can be determined as:
(18)
M
N a m a 3600 /(Vg a )
an
each time interval. Once the value of m a is determined, the number of greenhouse air
where a is the density of moist air in the greenhouse.
d
3. Measuring the required parameters
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An experiment to measure the required environmental parameters to be used for
Ac ce p
solving Eq. (16) was conducted in a 32 m2 glass-covered greenhouse without crop canopy (Fig. 1). The greenhouse was oriented in a N-S direction on the Agricultural Research and Experiment Station, Agriculture Engineering Department, King Saud University (Riyadh, Saudi Arabia, 46o 47` E, longitude and 24o 39` N, latitude). The
floor was covered with black plastic mulch; the greenhouse was naturally ventilated using two roof openings (0.65 m x 6 m for each), automatically closed at 6:0 pm and opened at 6:0 am in the winter season. In winter seasons, the air temperature drop drastically below 10 oC (desert climate) during the night times; therefore, farmers used to close the ventilators at night to protect plants. The measurements were carried out on three consecutive winter sunny days (Dec 22-24, 2014). The measurements were conducted from 6:00 to 18:00; the measured parameters were: (i) the air 13
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temperatures and its relative humidity inside and outside the greenhouse (Ti, RHi, and To, RHo) using Thermohygrometers DMA033 (LSI-Lastem, Italy), (ii) the outside wind speed (V) at 3.5 m above the floor using 2-D wind sonic anemometer (RS-232)
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having an accuracy of ±2% @12 m s-1, range of 0 to 60 m s-1, and a resolution of 0.01 m s-1., (iii) the downward solar radiation flux outside and inside the greenhouse (So
cr
and Si) using CMP3 solarmeters (Kipp & Zonen B.V. Inc., USA), (iv) the cover
surface temperature (Tc) using four thermocouple junctions (copper constantan type-
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T) of 0.3 mm in diameter were smoothly attached to the outside of the cover surfaces
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1, 2, 3 and 4 and the average value of Tc was obtained and (v) the floor surface temperature (Tf) at three locations using three thermocouple junctions (0.3 mm in
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diameter) smoothly attached to the floor surface and average value was obtained. The measuring technique for Tc and Tf was reported in [18], in which, the thermocouple
d
junctions on the cover and floor surfaces were kept exposed to radiation and all the
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thermocouples were calibrated before use. The effect of radiation on these junctions was excluded by using a correction factor reported in [18], however, the effect of the
Ac ce p
air current (for V < 5 m s-1) on the junction reading can be neglected [18]. The parameters were measured at 5-second, intervals, averaged at each 5-minute and recorded in a data logger (CR3000 Micrologger®, Campbell Scientific, Inc.). The
average value of the cover transmittance ( c ) was estimated to be 0.65 during the period of the experiment to be used for Eq. (1) and Eq. (2). 4. Results and discussion
4.1. The environmental parameters The environmental parameters were measured in three consecutive sunny days; no significant differences were observed in the values of each parameter among these days. Therefore, for each parameter, the measured data were averaged to be presented
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in one day. Values of each parameter were averaged for every 30 min and illustrated in Fig. 2 and Fig. 3. Figure 2 depicts the time courses of Ti, To, Tc and Tf. Values of Tf are the highest because the greenhouse was without crop canopy under a sunny
ip t
weather. Values of Tc are relatively lower than Ti because the measurements were carried out in winter and because of the greenhouse effect. However, in hot summer
cr
seasons, Tc is always higher than Ti due to the large amount of solar radiation absorbed by the cover material. In Fig. 3, the solar radiation flux outside the
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greenhouse (So) and inside and outside relative humidity (RHi and RHo) were
an
illustrated. Values of RHi > RHo in the afternoon because of the heat accumulated in the greenhouse that enhanced evaporation of water that may condensed at night when
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the greenhouse vents were closed and Ti was low. The night time condensation on the inner surface of the cover makes RHi < RHo before noon.
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4.2. Energy exchange with the cv of the greenhouse
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The rates of energy gained and lost by the greenhouse system (i.e. input and output energy crossing the cv in Fig. 1) are illustrated in Fig. 4 and Fig. 5. Figure 4 illustrated
Ac ce p
the time courses of the net solar energy input to the cv (Sn) estimated by using Eq. (6),
per unit area of floor, and the transmitted solar energy into the greenhouse (Si) estimated by using the approximated value of the greenhouse cover transmittance ( c ),
i.e., (Si = 0.65 S o ). If the absorbed solar radiation in the glass cover ( c 0.15) was
subtracted from Sn, one can recognize the difference between the transmitted solar radiations into the greenhouse in each case. It is clear that assuming an average value for c would lead to large error in the estimation of the transmitted solar radiation and the greenhouse energy balance as well. In the proposed model, use of c was avoided by treating the solar radiation at the outside of the cover surface. Figure 5 illustrated the time courses of the different modes of energy losses leaving the cv. These modes 15
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are: conduction into the soil (qo) per unit area of floor, convection from the outer surface of the cover to the outside air (Qc-o) per unit area of cover, and net thermal radiation exchanges between the outer surface of the cover and sky, (Rn) per unit area
ip t
of cover. In the early morning and late afternoon both the conductive and the convective heat (qo and Qc-o) are input to the cv. Because, at that time the soil releases
cr
heat into the greenhouse air and the cover temperature Tc is lower than To. However,
under daytime conditions, the greenhouse cover always loses thermal radiation to the
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cold sky dome (Tsky< To). 4.3. Estimating the ventilation rate
an
Previous studies had concluded that for wind speeds (V) higher than 2 m s-1, the
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natural ventilation is mainly driven by the wind effect, and the buoyancy effect can be neglected. The effects of wind speed and the design configuration of vents opening on
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the natural ventilation have been examined by many studies. However, at low wind
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speeds such as in the present study (V was from 0 m s-1 to 2.5 m s-1), the daily behaviors of the natural ventilation as affected by the environment inside and outside
Ac ce p
the greenhouses received little attention in the previous studies. At low wind speeds, natural ventilation is driven by the combined wind and buoyancy effects and strongly affected by the enthalpy difference I between inside and outside the greenhouse. The enthalpy difference I depends on the combined T and the absolute humidity
difference. Figure 6(a) illustrates the time courses of the ventilation rate ( m a ) and I during the period of measurements when the ventilators are open. Figure 6(a) shows that the variations of m a are inversely related to the variations of I (see Eq. 1) when the wind speed is low. The estimated value of m a was in the range between 0.36 kg s-1 and 1.65 kg s-1. The number of greenhouse air changes per hour (Na) is sometimes
used, as a general unit, to express the ventilation rate. In Fig. 6(b), the time course of
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the value of Na based on the value of m a was illustrated. The value of Na was in the range between 11 h-1 and 58 h-1. These values are in the same order of magnitude of the values reported in [22], which were in the range between 20 h-1 and 60 h-1, for a
ip t
single-span greenhouse with roof and side wall ventilators and V was less than 3 m s-1. 4.4. Comparison with other models
cr
The values of m a estimated using the proposed model were compared with those
us
estimated using Eq. (1) and Eq. (2) (i.e. fundamental energy and sensible heat balance). In Eqs. (1) and (2), values of U and were taken to be 0.47 and 5 (W m-2 o -1
an
C ) according to [9, 10. The results of this comparison were illustrated in Fig. 7 and
showed how the fundamental heat balances (Eqs. (1) and (2)) failed to predict the
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correct value of m a at low solar radiation levels and the applicability of the proposed model to predict m a precisely at low or even zero solar radiation intensity. The
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negative values of m a are attributed to the fact that at low solar radiation levels (in the
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early morning and late afternoon) the inside air is warm ( I > 0) and the heat loss
Ac ce p
from the greenhouse is much higher than the input solar energy. In the proposed model, this problem was avoided by: (i) applying the heat balance in the unsteady state condition, (ii) dealing with the energy terms at the outer surface of the cover, and (iii) excluding the effect of thermal inertia of the greenhouse soil (i.e. source of error due to several uncertain parameters and assumptions usually used to estimate this term) by selecting the cv over the floor surface. 4.5. Validation of the model The rate of ventilation depends on the design configuration of the greenhouse and its ventilators and on the environmental conditions inside and outside the greenhouse (i.e. Ti, To, RHi, RHo, and V). Therefore, it was not possible to directly compare the results
17
Page 17 of 27
of the proposed model with those measured in different greenhouses under different conditions. The main purpose of this comparison is to present the results of the present model beside other measured results to show the order of magnitude. The
ip t
hourly average values of m a were calculated per unit area of vent opening during the three day of experiment and plotted in Fig. 8 against the wind speed (V) outside the
cr
greenhouse. In this figure, values of m a (per unit area of vent opening) measured by
us
using the decay tracer N2O gas technique [5] are also presented. The measurements in Ref. [5] were carried out by using two types of ventilators (i.e., roof and both roof and
an
side walls) in a multi-span greenhouse. The measured values of m a in Ref. [5] are lower than those predicted using the proposed model because the greenhouse used in
M
the present study was small (Af = 32 m2), with two roof ventilators compared to the large greenhouse of Ref. [5] (Af = 882 m2) that had one roof ventilator per span.
d
Moreover, the two side wall ventilators in the large greenhouse of Ref. [5] did not
te
significantly enhance the ventilation rate. Also the environmental conditions inside
Ac ce p
and outside the greenhouses are different between the present study and Ref. [5]. 4.6. Parameters affecting the ventilation rate The main parameters affecting the natural ventilation rate of greenhouses are the outside wind speed (V) and the temperature difference between inside and outside T .
The values of m a were calculated, per unit area of floor, and plotted in Fig. 9 against the measured values of V and plotted in Fig 10 against the measured values of T .
Winds with speeds less than 2.5 m s-1 have no significant effect on the value of m a (Fig. 9); whereas m a is strongly affected by T (Fig. 10) in an inverse relation. Also Eq. (1) and Eq.(2) show the inverse relation between m a and I as well as T . The regression line for the data in Fig. 10 is given by:
18
Page 18 of 27
m a 0.0993 7.35 10 3 ( T )
(19)
with value for the coefficient of determination (R2) of 0.77. This correlation can be used to estimate the required ventilation rate to maintain the
ip t
air in a single-span greenhouse at a certain temperature stipulating that the outside wind speed is less than 2.5 m s-1. Based on Fig. 10, in the greenhouses Ti is always
cr
higher than To, however, an outside air at a rate of about 0.1 kg s-1 is required (per unit
us
area of greenhouse floor) for ventilating the greenhouse to maintain Ti equal to To. On the other hand, closing the greenhouse ventilators (i.e., m a = 0) increases Ti to about
an
13.6 oC higher than To.
M
5. Conclusion and recommendation
A thermal model was proposed based on a simple energy balance applied to a control
d
volume containing the greenhouse. This model can be used to predict the natural
te
ventilation rate of any greenhouse having: any transparent (in term of solar radiation) cover, and any shape and size at any location. The model is capable of predicting the
Ac ce p
natural ventilation rate precisely at low, even zero, solar radiation intensity because the uncertain parameters that cause errors were avoided such as the average transmittance of the cover and the thermal inertia of the floor soil. The predicted ventilation rate using the present model showed a reasonable accordance with those measured and reported in the literature. The wind outside the greenhouse at a speed less than 2.5 m s-1 has no significant effect on the ventilation rate. However, the
difference between the inside and outside air temperature ( T ) is the main parameter controlling the ventilation rate. A linear correlation was provided that can be used to estimate the natural ventilation rate of greenhouses as a function of T at low wind speed conditions. Further experiments will be conducted in summer to predict the
19
Page 19 of 27
ventilation rate for greenhouses during 24-h period; the model is able to work well at zero solar radiation intensity (night time). Acknowledgement
ip t
The authors extend their sincere appreciation to the Deanship of Scientific Research at King Saud University for its funding of this research through the Research Group no.
cr
RG-1435-074.
us
References
an
[1] D. Etheridge, A perspective on fifty years of natural ventilation research, Building and Environment, doi: 10.1016/j.buildenv.2015.02.033 (in press). [2] E. M. Nederhoff, J. Van de Vooren, A. J. Udink ten Cate, A practical tracer gas method to determine ventilation in greenhouses, J. Agric. Eng. Res. 31(1985) 309-319.
M
[3] F. J. Baptista, B. J. Bailey, J. M. Randall, J. F. Meneses, Greenhouse ventilation rate: Theory and measurement with tracer gas techniques, J. Agric. Eng. Res. 72(1999) 363-374.
te
d
[4] J. E. Fernandez, B. J. Bailey, Measurement and prediction of greenhouse ventilation rates, Agric. For. Meteorol. 58(1992) 229-245.
Ac ce p
[5] J. P. Parra, E. Baeza, J. I. Montero, B. J. Bailey, Natural ventilation of Parral greenhouses, Boisyst. Eng. 87(2004) 355-366. [6] N. Katsoulas, T. Bartzanas, T. Boulard, M. Mermier, C. Kittas, Effect of vent openings and insect screens on greenhouse ventilation, Biosyst. Eng. 93(2006) 427436. [7] M. Samer, C. Ammon, C. Loebsin, M. Fiedler, W. Berg, P. Sanftleben, R. Brunsch, Moisture balance and tracer gas technique for ventilation rates measurements and greenhouse gases and ammonia emissions quantification in naturally ventilated buildings, Building and Environment 50(2012) 10-20.
[8] S. Cui, M. Cohen, P. Stabat, D. Marchio, CO2 tracer gas concentration decay method for measuring air change rate, Building and Environment 84(2015) 162-169. [9] T. Boulard, A. Baille, Modelling of air exchange rate in a greenhouse equipped with continuous roof vents, J. Agric. Eng. Res. 61(1995) 37-48. [10] T. Boulard, J. F. Meneses, M. Mermier, G. Papadakis, The mechanisms involved in the natural ventilation of greenhouses, Agric. For. Meteorol. 79(1996) 61-77. 20
Page 20 of 27
[11] T. Boulard, B. Draoui, Natural ventilation of a greenhouse with continuous roof vents: Measurements and data analysis. J. Agric. Eng. Res. 61 (1995) 27-36.
ip t
[12] Y. Mihara, Fundamental and Practice of Greenhouse Design (in Japanese), Yokendo Inc. Tokyo,160-169, 1983.
cr
[13] I. M. Al-Helal, A. M. Abdel-Ghany, Energy partition and conversion of solar and thermal radiation into sensible and latent heat in a greenhouse under arid conditions, Energy & Buildings 43(2011) 1740-1747.
us
[14] A. M. Abdel-Ghany, Solar energy conversions in the greenhouses, Sustainable Cities and Society 1(2011) 219-226.
an
[15] A. M. Abdel-Ghany, I. M. Al-Helal, Solar energy utilization by a greenhouse: General relations, Renewable Energy 36(2011) 189-196.
M
[16] T. Kozai, Direct solar light transmission into single-span greenhouses, Agric. Meteorol. 18(1977) 327-338.
d
[17] G. Papadakis, D. Manolakos, S. Kyritsis, Solar radiation transmissivity of a single-span greenhouse through measurements on scale models, J. Agric. Eng. Res. 71(1998) 331-338.
te
[18] A. M. Abdel-Ghany, Y. Ishigami, E. Goto, T. Kozai, A method for measuring greenhouse cover temperature using a thermocouple, Biosyst. Eng. 95(2006) 99-109.
Ac ce p
[19] M. M. Elsayed, I. S. Taha, J. A. Sabbag, Design of Solar Thermal Systems, 1st ed. Seientifc Publishing Centre, King Abdulaziz University, Jeddah, Saudi Arabia, 1994.
[20] J. L. Monteith, M. H. Unsworth, Principals of Environmental Physics, 2nd ed., London, Arnold, 1990. [21] J. A. Duffie, W. A. Beckman, Solar Engineering of Thermal Processes, New York, John Wiley& Sons Inc, 1991. [22] T. Kozai, S. Sase, M. Nara, A modeling approach to greenhouse ventilation control, Acta Hort. 106(1980)125-136.
21
Page 21 of 27
ip t
S
Sky thermal radiation
1 Ventilation of air
25o
us
2
cr
N
an
Sn
5 South side
Qc-o
6 North side
Control volume (cv)
M
3
Floor cover
Qc-o 4
d
qo
Ac ce p
te
Fig. 1 Schematic diagram for the greenhouse and the suggested control volume (cv), and the different modes of energy exchange.
22
Page 22 of 27
55
To
50
Ti
45
Tc
Jan. 22-24, 2014
Tf
40
ip t
35 30 25 20
cr
Temperatures (oC)
60
15
us
10 5 0 6
8
9
10 11 12
13 14 15 16
17 18
an
7
Local time (h)
RHo RHi
45
900
d
So
40
800 700
te
35 30 25
Ac ce p
Relative humidity (%)
1000
Jan. 22-24, 2014
600 500
20
400
15
300
10
200
5
100
0
6
7
8
9
Outside solar radiation So (W m-2)
50
M
Fig. 2 Time courses of the measured values of the air temperatures outside and inside the greenhouse (To, Ti), the cover surface temperature (Tc) and the floor surface temperature (Tf).
0 10
11 12 13 14 15 16 17
18
Local time (h)
Fig. 3 Time courses of the solar radiation flux measured outside the greenhouse (So) and the relative humidity inside and outside the greenhouse (RHi, RHo).
23
Page 23 of 27
1200 Jan. 22-24, 2014
1000 900 800
ip t
700 600 500
300
cr
400 Sn
200
Si
100 0 6
7
10
9
8
11 12
13
us
Solar radiation flux (W m-2[floor])
1100
14 15 16 17 18
an
Local time (h)
M
Fig. 4 Time courses of the net solar radiation flux (Sn) crossing the control volume at the outer surface of the cover and estimated by using the present model, and the transmitted solar radiation flux into the greenhouse (Si), estimated by using an average value of c .
Jan. 22-24, 2014
Energy loss (W m-2)
Ac ce p
150
qo Qc-o Rn
te
175
d
200
125 100 75 50 25 0
6
7
8
9
10 11
12 13 14
15 16
17 18
Local time (h)
Fig. 5 Time courses of the different modes of energy crossing the control volume: conducted into the soil (qo), convected to the outside air (Qc-o) and emitted to the sky (Rn).
24
Page 24 of 27
4.0
25 20 15
2.5
10 2.0 5 1.5
0
cr
Ventilation rate (kg s-1)
3.0
1.0
us
0.5 0.0 6
7
8
10 11 12 13
9
(b)
Jan. 22-24, 2014
60
M
55 50 45 40
d
35 30 25 20 15
Ac ce p
10
te
Number of air exchanges, Na (h )
17 18
an
65
15 16
14
Local time (h)
70
-1
ip t
30
3.5
Enthalpy difference I, (kJ kg-1)
35
(a)
5 0
6
7
8
9
10 11 12 13 14
Local time (h)
15 16 17 18
Fig. 6 Time courses of: (a) the natural ventilation rate ( m a ) and the enthalpy difference of air between inside and outside the greenhouse ( I ); and (b) the number of the greenhouse air exchanges (Na) per hour.
25
Page 25 of 27
Jan. 22-24, 2014 1.5
ip t
1.0
cr
0.5
0.0 Present model Eq. (1) Eq. (2)
-0.5
us
The greenhouse ventilation rate, (kg s-1)
2.0
-1.0 8
10
12
14
16
18
an
6
Local time (h)
M
Fig. 7 Time courses of the natural ventilation rate ( m a ) estimated by using the proposed model comparing to those estimated by using Eq. (1) and Eq. (2).
d
Proposed model, roof ventilators Measured by N2O gas method, roof ventilators, Ref. [5] Measured by N2O gas method, roof &side wall ventilators, Ref. [5]
te
0.3
Ac ce p
Ventilation rate (m3 s-1 m-2[opening])
0.4
0.2
0.1
0.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
-1
Wind speed V, (m s )
Fig. 8 The ventilation rate ( m a ), per unit area of vent opening, estimated by using the proposed model in comparison with the measured values of Ref. [5] as affected by the wind speed (V) outside the greenhouse.
26
Page 26 of 27
Proposed model Regression line
0.08
0.06
ip t
Ventilation rate ma, (kg s-1m-2 [floor])
0.10
.
0.04
0.00 0.0
0.5
1.0
1.5
us
cr
0.02
2.0
2.5
3.0
Wind speed V, (m s-1)
M
an
Fig. 9 The ventilation rate ( m a ) estimated per unit area of floor using the proposed model as affected by the wind speed (V) outside the greenhouse.
d
0.08
0.06
Y=0.0993 -7.35(10)-3X,
(R2=0.77)
te
Ventilation rate ma, (kg s-1m-2[floor])
0.10
.
Ac ce p
0.04
0.02
Proposed model Regression line
0.00
0
2
4 6 8 10 Temperature difference T, (C)
12
14
Fig. 10 The ventilation rate ( m a ) estimated per unit area of floor using the proposed model as affected by the difference between the inside and outside air temperature ( T ).
27
Page 27 of 27
S0378-7788(15)00312-6 http://dx.doi.org/doi:10.1016/j.enbuild.2015.04.013 ENB 5805
To appear in:
ENB
Received date: Accepted date:
11-3-2015 11-4-2015
Please cite this article as: I.M. Al-Helal, S.A. Waheeb, A.A. Ibrahim, M.R. Shady, A.M. Abdel-Ghany, Modified thermal model to predict the natural ventilation of greenhouses, Energy and Buildings (2015), http://dx.doi.org/10.1016/j.enbuild.2015.04.013 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Highlights A model was developed to predict the natural ventilation of greenhouses. The model is able to predict ventilation rate at low or zero solar radiation intensity.
ip t
Wind at a speed < 2.5 m s-1 has no significant effect on the ventilation rate and the temperature difference do the main effect.
A correlation between the ventilation rate and temperature difference was
Ac ce p
te
d
M
an
us
cr
provided.
1
Page 1 of 27
Modified thermal model to predict the natural ventilation of greenhouses I. M. Al-Helala, S. A. Waheebb, A. A. Ibrahimc, M. R. Shadya, A. M. Abdel-Ghany*,a a
us
cr
ip t
Department of Agricultural Engineering, College of Food and Agriculture Sciences, King Saud University, PO Box 2460, Riyadh 11451, Saudi Arabia. b Department of Engineering Sciences, Community College, Umm Al Qura University, PO Box 715, Makkah 21955, Saudi Arabia. c Department of Plant Production, College of Food and Agriculture Sciences, King Saud University, PO Box 2460, Riyadh 11451, Saudi Arabia.
ABSTRACT
an
Most of thermal models used to estimate the natural ventilation of greenhouses ( m a ) use an average value for the cover transmittance ( c ) to estimate the input solar energy to the greenhouse. These models failed to predict m a at low solar radiation flux
M
due to the spatial variation of c in the greenhouse and the thermal inertia of soil. This study is to develop and validate a thermal model predict m a precisely. All modes
d
of energy were treated, under the unsteady state conditions, at the outer surface of the
te
cover to avoid the sources of error. The required parameters were measured for a naturally ventilated glasshouse. The predicted values of m a were in the range between
Ac ce p
0.36 kg s-1 and 1.65 kg s-1 and showed good accordance with measured and simulated values in the literature. The results also confirmed that outside wind at a speed < 2.5 m s-1 has no significant effect on the value of m a and the temperature difference of air
between inside and outside the greenhouse ( T ) is the main driving force of
ventilation. A correlation between m a and T was provided, it can be used to estimate m a that required to maintain the air temperature in the greenhouse at a desired level.
Keywords: Greenhouse; natural ventilation; energy balance, solar radiation *Corresponding author: (Tel & fax: +966 (011) 4678352) E-mail addresses: [email protected] ; [email protected] (A. M. Abdel-Ghany)
2
Page 2 of 27
Nomenclatures surface area of the greenhouse cover (m2)
Af
surface area of the greenhouse floor (m2)
Cpa
specific heat of air at constant pressure (J kg-1 oC-1)
d
greenhouse cover thickness (m)
fd
ratio of diffuse to global solar radiation (-)
hc-o
convective heat transfer coefficient between the cover surface and the outside
ip t
Ac
cr
ambient air (W m-2 oC-1)
specific enthalpy of moist air inside the greenhouse (J kg-1)
Io
specific enthalpy of moist air outside the greenhouse (J kg-1)
j
surface number of the greenhouse cover (1,2,…, 6)
kf
equivalent thermal conductivity of the greenhouse soil (W m-1 oC-1)
m a
ventilation rate of the greenhouse (kg s-1)
Na
number of air exchange per hour (h-1)
n
refractive index of the covering material (-)
Qc-o
convection heat rate between the cover surface and outside ambient (W)
qo
heat rate conducted into the greenhouse soil surface (W)
Rn
net thermal radiation exchange between the cover and sky (W)
rb
ratio of beam irradiance received by a tilted surface to that received by a
te
d
M
an
us
Ii
horizontal surface (-)
global solar radiation flux transmitted into the greenhouse (W m-2)
SL
solar radiation loss to outside the greenhouse (W m-2)
Sn
net global solar energy crossing the control volume of the greenhouse (W)
So
global solar radiation flux at the greenhouse outer surface (W m-2)
Tc
cover outer surface temperature (oC)
Ti
air temperature inside the greenhouse (oC)
To
air temperature outside the greenhouse (oC)
Tf
floor surface temperature (oC)
Tsky
equivalent temperature of sky (oC)
U
overall heat loss coefficient of the greenhouse cover (W m-2 oC-1)
V
wind speed outside the greenhouse (m s-1)
Vg
volume of the greenhouse air (m3)
z
vertical depth under the greenhouse measured from the soil surface (m)
Ac ce p Si
3
Page 3 of 27
Greek symbols absorptance of the cover to global solar radiation (-)
slope angle of the cover surface (degree)
I
specific enthalpy difference (Ii-Io) (J kg-1)
T
temperature difference (Ti-To) (oC)
evaporation efficiency (-)
s
surface azimuth angle (degree)
solar radiation heating efficiency (-)
absorption coefficient of the cover material (m-1)
incidence angle of direct solar radiation (degree)
r
angle of refraction (degree)
z
solar zenith angle (degree)
a
density of moist air (kg m-3)
c, j
directional reflectance of the cover surface j to direct beam solar radiation (-)
c, j
directional reflectance of the cover surface j to global solar radiation (-)
ˆ
interface reflectance between the cover surface and air (-)
f
reflectance of the floor surface to global solar radiation (-)
c
average transmittance of the greenhouse cover to global solar radiation (-)
c, j
directional transmittance of the cover surface j to direct solar radiation (-)
ˆ
transmittance due to absorption of solar radiation in the cover material (-)
absolute humidity (kg of water vapor/ kg of dry air)
Ac ce p
te
d
M
an
us
cr
ip t
c
1. Introduction
Ventilation of greenhouses plays a major role in providing a suitable environment for plant growth. In summer, ventilation is for cooling the greenhouse air, and in winter ventilation can remove excess humidity from the greenhouse. Recently, most greenhouse ventilation studies have been focusing on the use of natural ventilation to reduce electric energy consumption by greenhouses. Although investigation of natural
4
Page 4 of 27
ventilation in the greenhouses started since 50 years ago, there is still no adequate method to precisely predict the amount of natural ventilation [1]. Based on the survey of the previous researches performed in this area, the main methods that have been
ip t
used to estimate the natural ventilation rate of greenhouses and the problems associated with each method can be summarized as follows:
cr
(i) Measuring methods, in which, a tracer gas such as N2O or CO2 is injected in the
greenhouse and the decay rate of the gas concentration is measured [2-8]. These
us
methods can measure the ventilation rates during the time of experiments only.
an
However, the ventilation rate strongly depends on the environmental conditions and on the greenhouse design parameters. Therefore, developing theoretical models to
M
estimate the ventilation rate of greenhouses was essential need. (ii) Air dynamic models, in which, ventilation was assumed to be driven by two
d
forces, namely, the wind force and the buoyancy force and such models is used only
te
for greenhouses with roof vents [9]. The resulted ventilation rate from these models depends on two critical dimensionless coefficients, (i.e., the discharge coefficient and
Ac ce p
the wind coefficient). However, these coefficients are usually determined by in situ measurements and differ from greenhouse to greenhouse, and depend on the design configuration of the vents, greenhouse location, orientation and environmental conditions. Several values for the wind coefficient (0.006-0.28) and for the discharge coefficient (0.4-0.848) were reported in the literature [9-11]. (iii) Energy balance models, in which, energy balances are applied to the
greenhouse air. A simple design formula was suggested by [12] to estimate m a based on the fundamental heat balance of the greenhouse. This formula assumed the air is completely mixed in the greenhouse and is given by:
5
Page 5 of 27
m a
S o c Af UAc T , I
(I 0.0)
(1)
This equation has been modified, based on the sensible heat balance of the greenhouse air and used as ASAE-STD and reported in [9] in the form: (1 ) c S o Af UAc T C pa T
ip t
m a
(2)
cr
In equations (1) and (2), So is the global solar radiation flux on a horizontal surface
us
outside the greenhouse; c is the average transmittance of the greenhouse cover to solar radiation; Af and Ac are the surface areas of the greenhouse floor and cover; U is
an
the overall heat loss coefficient of the cover; I is the moist air specific enthalpy difference between inside and outside the greenhouse (Ii-Io); Cpa is the specific heat
M
of air at constant pressure and is an “evaporation coefficient”, which estimates the fraction of total solar radiation load taken up by evaporation in the greenhouse. No
d
details are given in the literature for the proper selection of , and standard examples
te
often use = 0.5. The term (1 ) c in Eq. (2) is also defined as the solar radiation
Ac ce p
heating factor , (i.e. the fraction of So that was converted into sensible heat and used to warm up the greenhouse air). Several values of are reported in the range between
0.3 and 0.7 [13-15]. Determination of as well as value is quite difficult,
especially if the greenhouse includes a crop canopy and associated with an evaporative cooling in summer. Limitations of using Eq. (1) as reported in [12] are: So > 230 W m-2; I > 8.368 kJ kg-1 and the time interval should be higher than 20 min.
In summer, values of I and T in Eq. (1) and Eq. (2) are always positive during the daytime, even though, these equations resulted in negative values of m a at low solar radiation levels.
6
Page 6 of 27
Several previous studies estimated the natural ventilation rate of greenhouses by using energy balance methods. All of these studies assumed that solar radiation transmitted into the greenhouse was the only input energy and used an average value of the cover
ip t
transmittance ( c ). However, c depends on the spatial location within the greenhouse and on the altitude of the greenhouse. The maximum longitudinal variation of c over
cr
the floor surface in a venlo-type N-S glasshouse (4 mm thick of cover) was measured
us
by [16] at the location 52o 20’ N to be 0.4. In addition, the maximum spatial variation of c was measured by [17] in a scale model of a glasshouse (4 mm thick of cover) at
an
the location 37o 58’ N to be 0.8. Accordingly, using an average value of c will cause a large error in the estimation of the transmitted solar radiation into the greenhouse
M
and in the estimation of m a as well. This error is expected to be high in small greenhouses because the cover to floor surface area ratio is usually high (e.g., 3~5),
d
and unfortunately most of the ventilation studies using an energy balance method or
te
any other method were based on experimental greenhouses.
Ac ce p
The objectives of this study were to: (i) develop a simplified energy balance model to estimate the natural ventilation of greenhouses precisely, and (ii) check the validity of the model by comparing its results with results of theoretical models and experimental measurements reported in the literature. Uncertain parameters such as the thermal inertia of the greenhouse soil, and using an average value of c were avoided in the
proposed model. The proposed energy balance was applied to a control volume for the greenhouse suggested to be between the outer surface of the cover and the floor surface.
7
Page 7 of 27
2. The Proposed model The greenhouse used for this study is a single-span, its frame was constructed from aluminum bars and covered with a glass sheet of 4-mm thick (Fig. 1). It was
ip t
considered as a thermodynamic system, enclosed by a control volume (cv). The different modes of energy crossing the boundary (i.e. the cv) of the system were
cr
illustrated in Fig. 1. During the daytime, the cover surfaces (i.e. surface 1 to surface 6)
were found to have almost the same temperature because the absorptance of
us
transparent materials is not strongly affected by the incident angle of solar beam
an
radiation or the surface orientation [18]. Therefore, measuring Tc of one or two surfaces is sufficient to represent the temperature of the whole cover surfaces. Energy
M
balance was applied to the cv under the un-steady state condition assuming: (i) The moist air inside or outside the greenhouse is well mixed and characterized by average
d
temperatures and relative humidity (Ti, RHi, To, RHo) and average thermo-physical
te
properties. (ii) The cover and floor are gray surfaces in terms of long wave radiation and characterized by an equivalent temperatures (Tc and Tf). (iii) The cover is opaque
Ac ce p
to transmit thermal radiation and is a diffuse emitter and diffuse reflector; and the floor surface reflects solar and thermal radiation diffusively. (iv) Parameters in the upcoming analysis are time dependent. For simplification, the functional relationship of time is omitted from all the symbols hereafter. Energy terms are crossing the cv of
the system (Fig. 1), in and out, are: sensible and latent heat associated with the ventilation process ( I o m a and I i m a ); net solar radiation (Sn); convection exchange between the outer surface of the cover and the outside ambient air (Qc-o); thermal radiation exchange between the outer surface of cover and sky (Rn); and the conducted heat into the floor (qo). Determinations of these terms are as follows:
8
Page 8 of 27
2.1. The net solar radiation (Sn) The different surfaces of the greenhouse cover were designated with the numbers 1 to 6 (Fig. 1), and all the surfaces were supposed to be facing outward. The slope and
received by a tilted surface j, St,j (j=1,2,..6) is given by [19] as:
cr
S t, j ( S b, t S d, t S gr, t ) j
ip t
azimuth angles of these surfaces ( o , so ) were determined. The total solar irradiance
(3)
us
where Sb,t is the beam irradiance; Sd,t is the sky diffuse irradiance and Sgr,t is the global irradiance which is received by the tilted surface j from that reflected from the ground
can be rewritten in the form [19]
an
outside the greenhouse. Assuming the sky diffuse irradiance is anisotropic, Eq. (3)
St, j So (1 f d )rb f d cos2 ( )1 F sin3 ( ) 1 F cos2 sin3 z gr sin2 ( ) 2 2 2 j
M
cos , cos z ,
(5)
if 90 o
Ac ce p
0
if 0 o 90 o
te
rb
(4)
d
with F = 1-(fd)2 and
In Eq. (5), rb is the ratio of beam irradiance received by a tilted surface j to that
received by a horizontal surface; fd is the diffuse fraction (ratio of diffuse to global solar radiation). Diurnal variation of fd in sunny days was estimated for Riyadh area to
be 0.8 in the early morning and before sunset; and it was 0.1 most of the day time. Therefore, a precise value of fd was taken to be 0.13 on average. and z are the incident and azimuth angles of the solar beam radiation on the surface j; So is the
outside global solar radiation received by a horizontal surface; and gr is the reflectance of the ground to solar beam radiation and was taken to be 0.2 for sandy soil [15]. Values of and z were estimated during the day using the well-known
9
Page 9 of 27
relations reported in [19]. The net solar energy entering the cv at the outer surfaces of the cover (Fig. 1) as a function of time, or , is given by: 6
S n A j S t, j (1 c, j ) S L
(6)
j 1
ip t
where c, j is the reflectance, to the outside, of the cover surface j to global solar
cr
radiation and Aj is the area of the surface j. The transmitted solar radiation from each
surface j into the greenhouse is assumed to be suffering multiple reflections between
us
the cover and floor surfaces. Part of the transmitted radiation is transmitted again to outside the greenhouse (solar radiation loss, SL). The diffuse solar radiation that
an
incident on the inside and outside surfaces of the cover was treated as direct beam incident at an incidence angle of 60o [19]. For the greenhouse without crop canopy,
M
used in this study, the diurnal variation of SL was estimated to be 0.1-0.3 of the incident solar radiation outside the greenhouse with a maximum error less than 1%
te
d
[15]. The floor reflectance to the global solar radiation f was taken to be 0.2 on average [20].
Ac ce p
Value of c, j was estimated according to [21] as:
c , j f d c, j
θ 60
(1 f d ) c , j
(7)
In Eq. (7), c , j is the directional reflectance of the cover surface j to direct beam solar
radiation. The radiative properties of the glass cover (values of c, j and c , j ) at a specified incidence angle are given, respectively by [21] as:
c, j
2 ˆ1 ˆ 1 (ˆ ˆ ) 2
(8)
c, j ˆ 1 ˆ c, j
(9)
10
Page 10 of 27
In Eqs. (8) and (9), the directional transmittance due to absorption ( ˆ ) and the interface reflectance ( ˆ ) of a cover sheet having a thickness d and an absorption coefficient are given by [21] as: r
(10)
ip t
1 sin 2 ( r ) tan 2 ( r ) 2 sin 2 ( r ) tan 2 ( r )
ˆ e (d / cos ) and ˆ
the refractive index (n) of the cover material is defined by:
us
r sin 1 sin / n
cr
The angle of refraction ( r ) of a solar beam passing through the cover sheet related to
(11)
an
Values of n and were taken to be 1.526 and 0.3 cm-1, respectively [21]
2.2. The net thermal radiation (Rn)
M
For single-span greenhouses such as in Fig. 1, the view factor between the outer surface of the cover and the sky dome is assumed to be equal one. The net thermal
d
radiation exchange between the outer surface of the cover having an emittance c and
te
an average temperature Tc and the assumed black sky dome at an equivalent
Ac ce p
temperature Tsky is given by [19] as:
4 Rn c Ac Tc4 Tsky
(12)
with Tsky is in Kelvin and is given by [19] as:
Tsky 0.0559(To )1.5
(13)
where To is the outside air temperature in Kelvin.
2.3. The convective heat (Qc-o)
The convective heat exchange between the outer surfaces of the cover and the outside ambient air Qc-o can be estimated using Newton’s law of cooling with a convective heat transfer coefficient hc-o reported in [21] for the forced convection condition over buildings as:
11
Page 11 of 27
8.6V 0.6 hc o max 5, 0.4 Lc
Qc-o= Ac hc-o (Tc-Tdo),
,
L c 3 Vg
(14)
where V is the wind speed outside the greenhouse and Vg is the greenhouse volume.
ip t
2.4. Conduction into the soil (qo) The nature of heat conduction into the greenhouse soil depends on the soil
cr
composition, the soil thermo-physical properties and the soil water contents. For simplicity, the floor soil was assumed to behave as a homogeneous layer having a
us
thickness z, an equivalent thermal conductivity kf, an upper surface temperature Tf and
an
a lower constant subsoil temperature T (i.e. unaffected by the daily variation of Tf). The heat flux qo crossing the cv downward and conducted into the floor soil, assuming
M
quasi-steady state conditions at small time intervals (dt = 10 second), was approximated as [13] by:
k f Af Tf T z
d
qo
(15)
te
In Eq. (15), Af is the floor surface area; values of kf, z and T were taken to be 2.0 W
Ac ce p
m-1 C-1, 0.5 m, and 20 oC, respectively [13]. 2.5. The model equation
Energy balance was applied to the cv of the greenhouse (Fig. 1) under the un-steady
state condition according to the following equation:
dT ( S n m a I o ) ( Rn Qc o q o m a I i ) mC p dt cv
(16)
The energy terms on the left hand side of Eq. (16) are: Sn is estimated from Eq. (6) by measuring So on a horizontal plane outside the greenhouse; Rn and Qc-o are estimated from Eq. (12) and Eq. (14), respectively, by measuring Tc and To; qo is estimated from Eq. (15) by measuring Tf; and the specific enthalpy of the moist air (kJ kg-1) inside
12
Page 12 of 27
and outside the greenhouse (Ii and Io) was estimated based on the air temperature and its absolute humidity as: I (1.007T 0.026) (2501 1.84T ), T in oC
(17)
ip t
The right hand side of Eq. (16) is the rate of stored energy of the masses enclosed in the cv, in which the mass m, the specific heat Cp and the change of temperature
cr
history (i.e. dT /dt) were counted for the glass cover, the aluminum frame, (assuming
us
its temperature is the same as Tc ), and the greenhouse air. The unknown in Eq. (16) is the ventilation rate of air ( m a ), which can be determined by solving this equation at
changes per hour (Na) can be determined as:
(18)
M
N a m a 3600 /(Vg a )
an
each time interval. Once the value of m a is determined, the number of greenhouse air
where a is the density of moist air in the greenhouse.
d
3. Measuring the required parameters
te
An experiment to measure the required environmental parameters to be used for
Ac ce p
solving Eq. (16) was conducted in a 32 m2 glass-covered greenhouse without crop canopy (Fig. 1). The greenhouse was oriented in a N-S direction on the Agricultural Research and Experiment Station, Agriculture Engineering Department, King Saud University (Riyadh, Saudi Arabia, 46o 47` E, longitude and 24o 39` N, latitude). The
floor was covered with black plastic mulch; the greenhouse was naturally ventilated using two roof openings (0.65 m x 6 m for each), automatically closed at 6:0 pm and opened at 6:0 am in the winter season. In winter seasons, the air temperature drop drastically below 10 oC (desert climate) during the night times; therefore, farmers used to close the ventilators at night to protect plants. The measurements were carried out on three consecutive winter sunny days (Dec 22-24, 2014). The measurements were conducted from 6:00 to 18:00; the measured parameters were: (i) the air 13
Page 13 of 27
temperatures and its relative humidity inside and outside the greenhouse (Ti, RHi, and To, RHo) using Thermohygrometers DMA033 (LSI-Lastem, Italy), (ii) the outside wind speed (V) at 3.5 m above the floor using 2-D wind sonic anemometer (RS-232)
ip t
having an accuracy of ±2% @12 m s-1, range of 0 to 60 m s-1, and a resolution of 0.01 m s-1., (iii) the downward solar radiation flux outside and inside the greenhouse (So
cr
and Si) using CMP3 solarmeters (Kipp & Zonen B.V. Inc., USA), (iv) the cover
surface temperature (Tc) using four thermocouple junctions (copper constantan type-
us
T) of 0.3 mm in diameter were smoothly attached to the outside of the cover surfaces
an
1, 2, 3 and 4 and the average value of Tc was obtained and (v) the floor surface temperature (Tf) at three locations using three thermocouple junctions (0.3 mm in
M
diameter) smoothly attached to the floor surface and average value was obtained. The measuring technique for Tc and Tf was reported in [18], in which, the thermocouple
d
junctions on the cover and floor surfaces were kept exposed to radiation and all the
te
thermocouples were calibrated before use. The effect of radiation on these junctions was excluded by using a correction factor reported in [18], however, the effect of the
Ac ce p
air current (for V < 5 m s-1) on the junction reading can be neglected [18]. The parameters were measured at 5-second, intervals, averaged at each 5-minute and recorded in a data logger (CR3000 Micrologger®, Campbell Scientific, Inc.). The
average value of the cover transmittance ( c ) was estimated to be 0.65 during the period of the experiment to be used for Eq. (1) and Eq. (2). 4. Results and discussion
4.1. The environmental parameters The environmental parameters were measured in three consecutive sunny days; no significant differences were observed in the values of each parameter among these days. Therefore, for each parameter, the measured data were averaged to be presented
14
Page 14 of 27
in one day. Values of each parameter were averaged for every 30 min and illustrated in Fig. 2 and Fig. 3. Figure 2 depicts the time courses of Ti, To, Tc and Tf. Values of Tf are the highest because the greenhouse was without crop canopy under a sunny
ip t
weather. Values of Tc are relatively lower than Ti because the measurements were carried out in winter and because of the greenhouse effect. However, in hot summer
cr
seasons, Tc is always higher than Ti due to the large amount of solar radiation absorbed by the cover material. In Fig. 3, the solar radiation flux outside the
us
greenhouse (So) and inside and outside relative humidity (RHi and RHo) were
an
illustrated. Values of RHi > RHo in the afternoon because of the heat accumulated in the greenhouse that enhanced evaporation of water that may condensed at night when
M
the greenhouse vents were closed and Ti was low. The night time condensation on the inner surface of the cover makes RHi < RHo before noon.
d
4.2. Energy exchange with the cv of the greenhouse
te
The rates of energy gained and lost by the greenhouse system (i.e. input and output energy crossing the cv in Fig. 1) are illustrated in Fig. 4 and Fig. 5. Figure 4 illustrated
Ac ce p
the time courses of the net solar energy input to the cv (Sn) estimated by using Eq. (6),
per unit area of floor, and the transmitted solar energy into the greenhouse (Si) estimated by using the approximated value of the greenhouse cover transmittance ( c ),
i.e., (Si = 0.65 S o ). If the absorbed solar radiation in the glass cover ( c 0.15) was
subtracted from Sn, one can recognize the difference between the transmitted solar radiations into the greenhouse in each case. It is clear that assuming an average value for c would lead to large error in the estimation of the transmitted solar radiation and the greenhouse energy balance as well. In the proposed model, use of c was avoided by treating the solar radiation at the outside of the cover surface. Figure 5 illustrated the time courses of the different modes of energy losses leaving the cv. These modes 15
Page 15 of 27
are: conduction into the soil (qo) per unit area of floor, convection from the outer surface of the cover to the outside air (Qc-o) per unit area of cover, and net thermal radiation exchanges between the outer surface of the cover and sky, (Rn) per unit area
ip t
of cover. In the early morning and late afternoon both the conductive and the convective heat (qo and Qc-o) are input to the cv. Because, at that time the soil releases
cr
heat into the greenhouse air and the cover temperature Tc is lower than To. However,
under daytime conditions, the greenhouse cover always loses thermal radiation to the
us
cold sky dome (Tsky< To). 4.3. Estimating the ventilation rate
an
Previous studies had concluded that for wind speeds (V) higher than 2 m s-1, the
M
natural ventilation is mainly driven by the wind effect, and the buoyancy effect can be neglected. The effects of wind speed and the design configuration of vents opening on
d
the natural ventilation have been examined by many studies. However, at low wind
te
speeds such as in the present study (V was from 0 m s-1 to 2.5 m s-1), the daily behaviors of the natural ventilation as affected by the environment inside and outside
Ac ce p
the greenhouses received little attention in the previous studies. At low wind speeds, natural ventilation is driven by the combined wind and buoyancy effects and strongly affected by the enthalpy difference I between inside and outside the greenhouse. The enthalpy difference I depends on the combined T and the absolute humidity
difference. Figure 6(a) illustrates the time courses of the ventilation rate ( m a ) and I during the period of measurements when the ventilators are open. Figure 6(a) shows that the variations of m a are inversely related to the variations of I (see Eq. 1) when the wind speed is low. The estimated value of m a was in the range between 0.36 kg s-1 and 1.65 kg s-1. The number of greenhouse air changes per hour (Na) is sometimes
used, as a general unit, to express the ventilation rate. In Fig. 6(b), the time course of
16
Page 16 of 27
the value of Na based on the value of m a was illustrated. The value of Na was in the range between 11 h-1 and 58 h-1. These values are in the same order of magnitude of the values reported in [22], which were in the range between 20 h-1 and 60 h-1, for a
ip t
single-span greenhouse with roof and side wall ventilators and V was less than 3 m s-1. 4.4. Comparison with other models
cr
The values of m a estimated using the proposed model were compared with those
us
estimated using Eq. (1) and Eq. (2) (i.e. fundamental energy and sensible heat balance). In Eqs. (1) and (2), values of U and were taken to be 0.47 and 5 (W m-2 o -1
an
C ) according to [9, 10. The results of this comparison were illustrated in Fig. 7 and
showed how the fundamental heat balances (Eqs. (1) and (2)) failed to predict the
M
correct value of m a at low solar radiation levels and the applicability of the proposed model to predict m a precisely at low or even zero solar radiation intensity. The
d
negative values of m a are attributed to the fact that at low solar radiation levels (in the
te
early morning and late afternoon) the inside air is warm ( I > 0) and the heat loss
Ac ce p
from the greenhouse is much higher than the input solar energy. In the proposed model, this problem was avoided by: (i) applying the heat balance in the unsteady state condition, (ii) dealing with the energy terms at the outer surface of the cover, and (iii) excluding the effect of thermal inertia of the greenhouse soil (i.e. source of error due to several uncertain parameters and assumptions usually used to estimate this term) by selecting the cv over the floor surface. 4.5. Validation of the model The rate of ventilation depends on the design configuration of the greenhouse and its ventilators and on the environmental conditions inside and outside the greenhouse (i.e. Ti, To, RHi, RHo, and V). Therefore, it was not possible to directly compare the results
17
Page 17 of 27
of the proposed model with those measured in different greenhouses under different conditions. The main purpose of this comparison is to present the results of the present model beside other measured results to show the order of magnitude. The
ip t
hourly average values of m a were calculated per unit area of vent opening during the three day of experiment and plotted in Fig. 8 against the wind speed (V) outside the
cr
greenhouse. In this figure, values of m a (per unit area of vent opening) measured by
us
using the decay tracer N2O gas technique [5] are also presented. The measurements in Ref. [5] were carried out by using two types of ventilators (i.e., roof and both roof and
an
side walls) in a multi-span greenhouse. The measured values of m a in Ref. [5] are lower than those predicted using the proposed model because the greenhouse used in
M
the present study was small (Af = 32 m2), with two roof ventilators compared to the large greenhouse of Ref. [5] (Af = 882 m2) that had one roof ventilator per span.
d
Moreover, the two side wall ventilators in the large greenhouse of Ref. [5] did not
te
significantly enhance the ventilation rate. Also the environmental conditions inside
Ac ce p
and outside the greenhouses are different between the present study and Ref. [5]. 4.6. Parameters affecting the ventilation rate The main parameters affecting the natural ventilation rate of greenhouses are the outside wind speed (V) and the temperature difference between inside and outside T .
The values of m a were calculated, per unit area of floor, and plotted in Fig. 9 against the measured values of V and plotted in Fig 10 against the measured values of T .
Winds with speeds less than 2.5 m s-1 have no significant effect on the value of m a (Fig. 9); whereas m a is strongly affected by T (Fig. 10) in an inverse relation. Also Eq. (1) and Eq.(2) show the inverse relation between m a and I as well as T . The regression line for the data in Fig. 10 is given by:
18
Page 18 of 27
m a 0.0993 7.35 10 3 ( T )
(19)
with value for the coefficient of determination (R2) of 0.77. This correlation can be used to estimate the required ventilation rate to maintain the
ip t
air in a single-span greenhouse at a certain temperature stipulating that the outside wind speed is less than 2.5 m s-1. Based on Fig. 10, in the greenhouses Ti is always
cr
higher than To, however, an outside air at a rate of about 0.1 kg s-1 is required (per unit
us
area of greenhouse floor) for ventilating the greenhouse to maintain Ti equal to To. On the other hand, closing the greenhouse ventilators (i.e., m a = 0) increases Ti to about
an
13.6 oC higher than To.
M
5. Conclusion and recommendation
A thermal model was proposed based on a simple energy balance applied to a control
d
volume containing the greenhouse. This model can be used to predict the natural
te
ventilation rate of any greenhouse having: any transparent (in term of solar radiation) cover, and any shape and size at any location. The model is capable of predicting the
Ac ce p
natural ventilation rate precisely at low, even zero, solar radiation intensity because the uncertain parameters that cause errors were avoided such as the average transmittance of the cover and the thermal inertia of the floor soil. The predicted ventilation rate using the present model showed a reasonable accordance with those measured and reported in the literature. The wind outside the greenhouse at a speed less than 2.5 m s-1 has no significant effect on the ventilation rate. However, the
difference between the inside and outside air temperature ( T ) is the main parameter controlling the ventilation rate. A linear correlation was provided that can be used to estimate the natural ventilation rate of greenhouses as a function of T at low wind speed conditions. Further experiments will be conducted in summer to predict the
19
Page 19 of 27
ventilation rate for greenhouses during 24-h period; the model is able to work well at zero solar radiation intensity (night time). Acknowledgement
ip t
The authors extend their sincere appreciation to the Deanship of Scientific Research at King Saud University for its funding of this research through the Research Group no.
cr
RG-1435-074.
us
References
an
[1] D. Etheridge, A perspective on fifty years of natural ventilation research, Building and Environment, doi: 10.1016/j.buildenv.2015.02.033 (in press). [2] E. M. Nederhoff, J. Van de Vooren, A. J. Udink ten Cate, A practical tracer gas method to determine ventilation in greenhouses, J. Agric. Eng. Res. 31(1985) 309-319.
M
[3] F. J. Baptista, B. J. Bailey, J. M. Randall, J. F. Meneses, Greenhouse ventilation rate: Theory and measurement with tracer gas techniques, J. Agric. Eng. Res. 72(1999) 363-374.
te
d
[4] J. E. Fernandez, B. J. Bailey, Measurement and prediction of greenhouse ventilation rates, Agric. For. Meteorol. 58(1992) 229-245.
Ac ce p
[5] J. P. Parra, E. Baeza, J. I. Montero, B. J. Bailey, Natural ventilation of Parral greenhouses, Boisyst. Eng. 87(2004) 355-366. [6] N. Katsoulas, T. Bartzanas, T. Boulard, M. Mermier, C. Kittas, Effect of vent openings and insect screens on greenhouse ventilation, Biosyst. Eng. 93(2006) 427436. [7] M. Samer, C. Ammon, C. Loebsin, M. Fiedler, W. Berg, P. Sanftleben, R. Brunsch, Moisture balance and tracer gas technique for ventilation rates measurements and greenhouse gases and ammonia emissions quantification in naturally ventilated buildings, Building and Environment 50(2012) 10-20.
[8] S. Cui, M. Cohen, P. Stabat, D. Marchio, CO2 tracer gas concentration decay method for measuring air change rate, Building and Environment 84(2015) 162-169. [9] T. Boulard, A. Baille, Modelling of air exchange rate in a greenhouse equipped with continuous roof vents, J. Agric. Eng. Res. 61(1995) 37-48. [10] T. Boulard, J. F. Meneses, M. Mermier, G. Papadakis, The mechanisms involved in the natural ventilation of greenhouses, Agric. For. Meteorol. 79(1996) 61-77. 20
Page 20 of 27
[11] T. Boulard, B. Draoui, Natural ventilation of a greenhouse with continuous roof vents: Measurements and data analysis. J. Agric. Eng. Res. 61 (1995) 27-36.
ip t
[12] Y. Mihara, Fundamental and Practice of Greenhouse Design (in Japanese), Yokendo Inc. Tokyo,160-169, 1983.
cr
[13] I. M. Al-Helal, A. M. Abdel-Ghany, Energy partition and conversion of solar and thermal radiation into sensible and latent heat in a greenhouse under arid conditions, Energy & Buildings 43(2011) 1740-1747.
us
[14] A. M. Abdel-Ghany, Solar energy conversions in the greenhouses, Sustainable Cities and Society 1(2011) 219-226.
an
[15] A. M. Abdel-Ghany, I. M. Al-Helal, Solar energy utilization by a greenhouse: General relations, Renewable Energy 36(2011) 189-196.
M
[16] T. Kozai, Direct solar light transmission into single-span greenhouses, Agric. Meteorol. 18(1977) 327-338.
d
[17] G. Papadakis, D. Manolakos, S. Kyritsis, Solar radiation transmissivity of a single-span greenhouse through measurements on scale models, J. Agric. Eng. Res. 71(1998) 331-338.
te
[18] A. M. Abdel-Ghany, Y. Ishigami, E. Goto, T. Kozai, A method for measuring greenhouse cover temperature using a thermocouple, Biosyst. Eng. 95(2006) 99-109.
Ac ce p
[19] M. M. Elsayed, I. S. Taha, J. A. Sabbag, Design of Solar Thermal Systems, 1st ed. Seientifc Publishing Centre, King Abdulaziz University, Jeddah, Saudi Arabia, 1994.
[20] J. L. Monteith, M. H. Unsworth, Principals of Environmental Physics, 2nd ed., London, Arnold, 1990. [21] J. A. Duffie, W. A. Beckman, Solar Engineering of Thermal Processes, New York, John Wiley& Sons Inc, 1991. [22] T. Kozai, S. Sase, M. Nara, A modeling approach to greenhouse ventilation control, Acta Hort. 106(1980)125-136.
21
Page 21 of 27
ip t
S
Sky thermal radiation
1 Ventilation of air
25o
us
2
cr
N
an
Sn
5 South side
Qc-o
6 North side
Control volume (cv)
M
3
Floor cover
Qc-o 4
d
qo
Ac ce p
te
Fig. 1 Schematic diagram for the greenhouse and the suggested control volume (cv), and the different modes of energy exchange.
22
Page 22 of 27
55
To
50
Ti
45
Tc
Jan. 22-24, 2014
Tf
40
ip t
35 30 25 20
cr
Temperatures (oC)
60
15
us
10 5 0 6
8
9
10 11 12
13 14 15 16
17 18
an
7
Local time (h)
RHo RHi
45
900
d
So
40
800 700
te
35 30 25
Ac ce p
Relative humidity (%)
1000
Jan. 22-24, 2014
600 500
20
400
15
300
10
200
5
100
0
6
7
8
9
Outside solar radiation So (W m-2)
50
M
Fig. 2 Time courses of the measured values of the air temperatures outside and inside the greenhouse (To, Ti), the cover surface temperature (Tc) and the floor surface temperature (Tf).
0 10
11 12 13 14 15 16 17
18
Local time (h)
Fig. 3 Time courses of the solar radiation flux measured outside the greenhouse (So) and the relative humidity inside and outside the greenhouse (RHi, RHo).
23
Page 23 of 27
1200 Jan. 22-24, 2014
1000 900 800
ip t
700 600 500
300
cr
400 Sn
200
Si
100 0 6
7
10
9
8
11 12
13
us
Solar radiation flux (W m-2[floor])
1100
14 15 16 17 18
an
Local time (h)
M
Fig. 4 Time courses of the net solar radiation flux (Sn) crossing the control volume at the outer surface of the cover and estimated by using the present model, and the transmitted solar radiation flux into the greenhouse (Si), estimated by using an average value of c .
Jan. 22-24, 2014
Energy loss (W m-2)
Ac ce p
150
qo Qc-o Rn
te
175
d
200
125 100 75 50 25 0
6
7
8
9
10 11
12 13 14
15 16
17 18
Local time (h)
Fig. 5 Time courses of the different modes of energy crossing the control volume: conducted into the soil (qo), convected to the outside air (Qc-o) and emitted to the sky (Rn).
24
Page 24 of 27
4.0
25 20 15
2.5
10 2.0 5 1.5
0
cr
Ventilation rate (kg s-1)
3.0
1.0
us
0.5 0.0 6
7
8
10 11 12 13
9
(b)
Jan. 22-24, 2014
60
M
55 50 45 40
d
35 30 25 20 15
Ac ce p
10
te
Number of air exchanges, Na (h )
17 18
an
65
15 16
14
Local time (h)
70
-1
ip t
30
3.5
Enthalpy difference I, (kJ kg-1)
35
(a)
5 0
6
7
8
9
10 11 12 13 14
Local time (h)
15 16 17 18
Fig. 6 Time courses of: (a) the natural ventilation rate ( m a ) and the enthalpy difference of air between inside and outside the greenhouse ( I ); and (b) the number of the greenhouse air exchanges (Na) per hour.
25
Page 25 of 27
Jan. 22-24, 2014 1.5
ip t
1.0
cr
0.5
0.0 Present model Eq. (1) Eq. (2)
-0.5
us
The greenhouse ventilation rate, (kg s-1)
2.0
-1.0 8
10
12
14
16
18
an
6
Local time (h)
M
Fig. 7 Time courses of the natural ventilation rate ( m a ) estimated by using the proposed model comparing to those estimated by using Eq. (1) and Eq. (2).
d
Proposed model, roof ventilators Measured by N2O gas method, roof ventilators, Ref. [5] Measured by N2O gas method, roof &side wall ventilators, Ref. [5]
te
0.3
Ac ce p
Ventilation rate (m3 s-1 m-2[opening])
0.4
0.2
0.1
0.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
-1
Wind speed V, (m s )
Fig. 8 The ventilation rate ( m a ), per unit area of vent opening, estimated by using the proposed model in comparison with the measured values of Ref. [5] as affected by the wind speed (V) outside the greenhouse.
26
Page 26 of 27
Proposed model Regression line
0.08
0.06
ip t
Ventilation rate ma, (kg s-1m-2 [floor])
0.10
.
0.04
0.00 0.0
0.5
1.0
1.5
us
cr
0.02
2.0
2.5
3.0
Wind speed V, (m s-1)
M
an
Fig. 9 The ventilation rate ( m a ) estimated per unit area of floor using the proposed model as affected by the wind speed (V) outside the greenhouse.
d
0.08
0.06
Y=0.0993 -7.35(10)-3X,
(R2=0.77)
te
Ventilation rate ma, (kg s-1m-2[floor])
0.10
.
Ac ce p
0.04
0.02
Proposed model Regression line
0.00
0
2
4 6 8 10 Temperature difference T, (C)
12
14
Fig. 10 The ventilation rate ( m a ) estimated per unit area of floor using the proposed model as affected by the difference between the inside and outside air temperature ( T ).
27
Page 27 of 27