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1. Effect of Roof Slope Variations on the Simple Structure Greenhouse
1School of Energy, Environment and Materials; 2School of Bioresources and Technology,
King Mongkut's University of Technology, Thonburi
*Corresponding author, Division of Energy Technology, School of Energy, Environment and Materials
126 King Mongkut’s University of Technology Thonburi,
Thungkru, Bangmod, Bangkok, 10140, Thailand. Fax: +662
Abstract
The natural ventilation system for a Simple Structure Greenhouse (SSG) with gable roof and
roof vent, each column of which is < 2.5 m high and average roof slope of which is < 15°
causes the air temperature inside the greenhouse to be higher than the ambient air temperature
for 6-8 Celsius degrees. This phenomenon occurs to the greenhouse that is covered by nets.
The study by the consideration of the routine and form of the air flow in an unoccupied 6x8
m2 greenhouse with the Computational Fluid Dynamics (CFD) demonstrates that the wakeof
the hot air inside the greenhouse is in the form of the air flow under the canopy in the routine
of Thermal Driven, bringing the hot air back to the greenhouse. The rest of the hot air is vent-
ed out by the Wind Driven routine though the side wall opening of the greenhouse. The study
by varying the roof slope, at the 15°, 30° and 42° slopes, with the wind speed of <2.0 m s-1 to
lower the air temperature inside the greenhouse to be equivalent to the ambient air tempera-
ture in the environment. In addition, the wind load on the roof slope on the outside of the
greenhouse is considered. The result from the calculation of the equation between ventilation
rate and the wind pressure coefficient indicates that the 30° slope is appropriate for a green
house. The ventilation system inside the greenhouse is the mixed convection where Gr/Re2 <
1. The difference of the temperature is (Ti – To) at the <2.5 m height from the ground and the
<2 Celsius degrees temperature.
Keywords: Greenhouse, Air ventilation, Computational Fluids Dynamics, Roof slope,
Temperature difference
1. Introduction
In Thailand, the high temperature inside the greenhouse causes the problem of the hot air ac-
cumulation within the greenhouse. This phenomenon occurs in the greenhouse with the open
side walls, which makes the temperature inside different from the temperature outside (Ti –
To) different for 6–8 Celsius degrees depending on the ambient air temperature in the environ-
ment.
The solution to this problem is the application of natural ventilation which is a practical
method for controlling greenhouse microclimate because of its economic advantages. The
75% of Thailand farmers have too low incomes and unable to afford equipments and materi-
als to reduce hot air within their greenhouses. Most of these greenhouses are the Simple
Structure Greenhouses (SSG), as shown in Fig. 1. This type of greenhouses is appropriate for
Thailand climate because it protects the crops contained therein from rain and insects. Gener-
ally, greenhouses that can reduce the hot air under their ceilings should have 3–4 m high
columns [1, 2]. For a Simple Structure Greenhouse (SSG), this requirement is difficult to ac-
complish due to the roof structure and the damage from strong winds. Thus, the air ventilation
system that can reduce the hot air relies on the side wall opening. This method leads to the
loss of humidity caused from the plant transpiration due to the high level of the velocity of the
wind inside, and the decrease of carbon dioxide absorption. Kalma and Kuiper [3] proposed
that the optimal wind velocity within a greenhouse should be less than 1 m s-1 and be within
the range of 0.1–0.6 m s-1 [4]. Thus, the control the internal wind speed depends on the side
wall opening. Kittas et al. [5] had applied a math model to calculate the size of the open parts
of the side walls and concluded that the open parts of a side wall should be 15–25% of the en-

2. tire floor area of a greenhouse, which is suitable for ventilation rate in a Mediterranean green-
house (where the irradiation intensity is 1000 W m-2 and ΔT ≅ 5°C).
Connellan [6] reported that, in a region with high temperature, a naturally ventilated green-
house, the minimum ventilation opening area of 20% of the greenhouse floor area should be
maintained so that greenhouse temperature will be as equivalent as possible to the tempera-
tures of the external environment.
Albright [7] reported that the temperature inside a greenhouse will not begin to be transmitted
to the ambient air temperatures until the ridge and side area is more than 10% of the floor
area. At the same time, Brugger et al. [8] who had studied on the ventilation in the Parral
Style greenhouse, when the external wind speed was > 2 m s-1, in the Computational Fluids
Dynamics (CFD) system and could achieve the results stating that the air exchange rate in-
creased respectively with the roof slope. In other words, when the roof slope is higher than
27°, there will be a minimal additional air exchange rate.
As for this research, the natural ventilation is applied to the Simple Structure Greenhouse.
Concerning the natural ventilation and the wind-induced ventilation systems in Thailand, the
factor that needs to be considered is the wind velocity. As for Thailand, the wind velocity data
show that the average external wind speed is inferior to 2 m s-1 [9], which makes the ventila-
tion system inside the greenhouse become the mix convection. Around 50% of the ventilation
systems in a greenhouse are thermal driven ventilations (free convection). This effect has in-
fluences on the air temperature under the ceiling of the greenhouse. Thus, the greenhouse with
low roof slope and low ceiling tend to face the problem concerning the increase of the inside
air temperature.
Therefore, this research focuses on lowering the air temperature inside the Simple Structure
Greenhouse (SSG) with gable roof and roof vent, the columns of which are not high as 3 me-
ters, so as that the temperature inside the greenhouse will be equivalent to the ambient air.
This study examines the flow pattern and the temperature distribution inside the greenhouse
with variable roof slopes and the CFD technique is utilized as the tool for the study. Further-
more, this study also concentrates on the angles of roofs and the wind pressure applied to the
roof structure outside the greenhouse by analyzing the ventilation performance with wind
pressure coefficient. The results from the study will specify the roof slope appropriate for the
greenhouse.
2. Simple Structure Greenhouse, SSG
The Simple Structure Greenhouse (SSG) is constructed with the materials that are available in
the local area, e.g., wood and bamboo. This type of greenhouse can last for 1–2 years depend-
ing on the treatment process. In constructing this type of greenhouse, the constructor will
clump the wood or bamboo sticks together with screws or ropes so as to build the greenhouse.
This construction scheme facilitates the repair or the relocation of the greenhouse. In addition
to wood or bamboo sticks, soil or cement will be used for building the foundation of columns,
each of which is 2.5 meters high.
The typical roof style of this type of greenhouse is the gable roof. However, this roof style al-
ways leads to the problems concerning the air temperature and heat under the canopy. The so-
lution to such problems is to design the roof top with the additional 0.5 meter height for the
roof vent and the side wall opening. The side wall opening needs to be open on the basis of
the air temperature inside greenhouse.
In Thailand, a greenhouse of this type is called a ‘flat-roof style greenhouse’ [1]. In general,
the sidewalls and roof of the greenhouse are covered by PVC or PE film, and the gable roof
slope ranks from 15° to 20° depending on the greenhouse span and the number of the wood or

3. bamboo sticks that are clumped together. The SSG greenhouse has 6 meters width and 4 me-
ters sectional depth, which is considered to be the normal span for an SSG.
3. Theoretical Basis
3.1 Theory on Ventilation System
The discussion on the ventilation system for a greenhouse that concerns the formation of free
convection implies that, even in forced convection, the temperature gradients in the fluid may
give rise to free convection. Therefore, it is useful to have some criteria for the relative impor-
tance of free convection in forced convection. It has been shown that the parameter
สูตร คำำนวณ (1)
is a mean to measure the relative importance of free convection in relation to forced convec-
tion. When Gr/Re2 < 1, the ventilation system is considered to be primarily by force convec-
tion (wind driven ventilation). On the contrary, when Gr/Re2 > 1, free convection is dominant
(thermal driven ventilation). Furthermore, when Gr/Re2 ≅ 1, the ventilation system is consid-
ered as mixed convection [10].
In the Equation 9(1), β is the volume coefficient of thermal expansion, ΔT is the difference
between internal and external air temperatures (°C), g is the gravitation acceleration (m s-2), h
is the vertical distance between the midpoints of the side wall vent and roof vent (m), and u is
the outside wind speed (m s-1).
3.2 Theory of greenhouse ventilation
Natural ventilation is caused by two physical factors known as stack and wind effects. The
formula for calculating ventilation that is caused by stack and wind effects was proposed by
Kittas et al. [5]. The assumption of this formula is that the air flows through ventilators at the
roof or the side walls of a greenhouse, and the equation is as the follow:
สูตรคำำนวณ (2)
where Q is the ventilation rate (m3 s-1); AR and AS are the areas of the ventilating roof and
sidewall openings (m2), AT is total area of vents (m2), respectively; and Cd is the discharge co-
efficient of the ventilation opening; T is the mean of absolute temperature (°C); Cw is the
globalwind pressure coefficient; and u is the wind speed (m s-1).
When the contribution of stack effect is negligible, the ventilation rate from Equation (2) can
be expressed by the following equation:
สูตรคำำนวณ (3)
To compare ventilation results obtained in the different greenhouse, the modification of the
non-dimension parameter of ventilation function, G(α), proposed by Bot [12] has been used
by a number of authors [13, 14]:
สูตรคำำนวณ (4)
where A is the area of the ventilation opening in the greenhouse surface (m-2). Under the Q is
the air ventilation output (m3 s-1), which is agreeable to that from equations (2) and (3).
3.3 Wind pressure coefficient
Wind loads on the greenhouse cover are the results from external and internal pressures in-
duced by the external wind on the cover. The aerodynamic or pressure coefficients, Cp, de-

4. scribes the corresponding pressure distribution on the external or the internal surface of a
greenhouse normalized by the dynamic wind pressure:
สูตรคำำนวณ (5)
where PG is the pressure on the greenhouse roof (Pa), Pref is the pressure reference (Pa), uref is
the wind velocity at a reference height (m s-1) and ρ is the air density (kg m-3).
4. Method of study
4.1 Problem definition
The Simple Structure Greenhouse with the dimension of 6 m width × 8 m depth is construct-
ed on the flat ground without impediment to the air flow, as shown in Fig. 1(b). The height of
the greenhouse, from the ground level to gable roof top is 3.6 m, and each of the columns or
sidewall is 2.5 m high. The greenhouse lies itself perpendicularly, in the north-south direction
and across the wind direction.
The sidewall and roof of the greenhouse in the east-west direction are covered by PVC film
whilst the other side wall has an opening vent with the height of 0.4 m from the ground or
15% of sidewall height. Likewise, the gable also has a vent the size of which is 0.5 m × 8 m.
Thus, the total area of ventilation opening is 22% of the greenhouse floor area [6, 7].
As for the roof slope variation, the average roof slopes studied in this research are 15°, 30°
and 42°. The geometry is the roof slope as shown in Fig. 2 (a-c).
4.2 Measurements of the air ventilation in the greenhouse
In this research, the simulation results from the database measurement by Tuntiwaranruk [15],
who had studied on the SSG-greenhouse, are compared with the results from this study. The
air temperature is measured by 4 thermistor probe temperature sensors (XTI108-39+122,
StowAway™ XTI Temp Temperature Data Logger), with the +0.5 Celsius degrees accuracy
and 0.35 Celsius degrees resolution, placed at the height of 0.90 m, 1.5 m, 2.0 m and 2.50 m
from the ground. The air ventilation is investigated by using air velocity transmitter (HVAC,
EE65, Elektronik, Engerwitzdorf, Austria) with the accuracy of ±0.3 m s-1 which is according
to ASHRAE standard, 2001. The transmitters are placed at the 25 point parallel to the length
of side wall vent and at the gable. As a result the routines of the ventilation and temperature
distribution inside the greenhouse are discovered and the guideline of the greenhouse ventila-
tion is improved.
5. Numerical methods
5.1 Computational fluid dynamics method
Concerning the air flow in the steady condition which is related to the continuity equation of
mass conservation, it is practical to apply the Navier–Stokes’ momentum equation that con-
siders the gravity body force, together with the energy equation with air physical property.
In this ventilation prediction, the viscosity is included. In addition, the thermal driven refer-
ence from ambient temperature in the form of Boussinesq’s approximation with standard
Kepsilon (turbulent kinetic energy and dissipation rate) model can represent the turbulent
transport within the greenhouse [16,17].
To achieve accurate results, a second-order upwind discretization scheme is applied in the
momentum, heat and turbulence transport equations. The convergence criterion for all vari-
ables is 1×10-4.

5. 5.2 Computational meshes
The CFD simulation for this research relies on a general three-dimensional model and a sys-
tem of equations built with variables, which is numerically solved with finite volume method.
The computational mesh is a model which is similar to the experimental configuration (Fig. 1)
on the basis of unstructured mesh. The area around of the greenhouse is extended in order to
prevent blockage effects. However, it needs to be confirmed that extending the area will not
significantly affect the accuracy of the simulations but will substantially increase the
computing time and memory requirements. To obtain the accurate results and less comput-
ing time, the simulations are run at three different grid resolutions, namely, 712,029, 852,550
and 1,192,514 elements.
5.3 Boundary conditions
To determine the flow inlet boundary, an atmospheric wind velocity profiles is imposed. The
mean velocity boundary condition prevailing windward is assumed to be incompressible, with
a logarithmic relation between the height and the wind speed. Inlet velocity profile was de-
fined by Richards and Hoxey [18].
The outlet boundary specified with relative static pressure is zero; the normal gradient of oth-
er variables is zero, i.e. ∂/∂x = 0. No-slip walls are used along the solid parts of the green-
house (ground and greenhouse wall), where a classical logarithmic wall functions is imposed.
The top and side boundaries of the computational domain-a symmetry-type boundary condi-
tion, are used to describe both zero normal velocity and gradients of all variables at a symme-
try plane.
The inlet boundary of atmospheric wind velocity profile at 6 m is defined with initial velocity
of 0.5, 1.5 and 2 m s-1, with the average ambient temperature of 32 °C. The inside boundary
conditions of greenhouse are based on the maximum temperature (ΔT = 8 °C), which is the
result from the outside solar radiation of 800 W m-2. The given heat flux of greenhouse roof
boundary is 112 W m-2 [15]. The boundary details value and empirical formulae are used for
the simulations as shown in tables 1.
6. Results and discussion
6.1 Validation of predicted results against experimental results
Fig. 3 shows the comparison between the ventilation rate resulted from the data measurement
and the simulated results the three different grid resolutions. The outcomes from the compari-
son show that, where the sidewall opening that is 0.4 m high from the ground (or 15% of side-
wall high), the outside wind speed ranks between 0.5 and 2.0 m s-1 and the roof of the green-
house has low slope, the prediction on the coarse grid has the error of < 15%. This grid, com-
pared with the result calculated from the Gr/Re2, with the data measurement on the vertical
axis in the middle of greenhouse as shown in Fig. 4, shows a high level of agreement to the
simulated results. Thus, as for the investigation on roof slope variations for the
SSG-greenhouse, the computational grid should be the low resolution ranking between
729,170 and 731,116 elements. These results will be used for analyzing the ventilation routine
in the latter parts.
6.2 The problems of low slope roof for the SSG
Fig. 5 shows the air flow pattern and air temperature distributions inside the greenhouse when
the external wind speed is 1.6 m s-1. It is found that the external wind speed at the ventilation
opening that is at the 0.4 m height from the ground causes the wake of air inside the green-
house. This effect induces the air ventilation movement to roof vent and the other sidewall.
However, when the inside air has a low pressure, the air ventilation at the roof vent is ob-
structed by the external wind speed in the form of the backward wind on the roof top with a
high pressure. As the result, the ventilation performance on roof vent drops. This also affects

6. the heat storage under the greenhouse roof as shown in Fig. 5(b). The averaged air tempera-
ture at the height of 1.5 m from ground is 35 °C which makes the air temperature difference
rank between 6–8 °C.
The investigation on the ventilation system in the greenhouse is performed by using the Gr/
Re2, whereby the vertical line in the center of greenhouse at the height of 0.5 m to 2.5 m
above the ground is considered. The results calculated from the Gr/Re2 formula vary in the
range of 0.3–0.8, and show that the ventilation system inside greenhouse is the wind driven
type [10].
This case, as shown in Fig. 5(a), reveals that the wind induces the wake of air and reduces the
hot air at the height of < 0.7 m from the ground. At the height of > 0.7 m, the hot air inside the
greenhouse remains. In addition, when the Gr/Re2 ≥ 1 formula is used, the vertical line is >
2.5 m high. Thus, the ventilation system trend in this zone is free convection or thermal driv-
en ventilation, which influences the heat storage under the roof. Furthermore, the temperature
of the hot air inside the greenhouse needs to be lowered so as that it will be similar to the ex-
ternal ambient air temperature.
The results from the simulation of the temperature distribution in the SSG, as shown in Fig.
5(b), reveal that the air temperature inside the greenhouse, at the height of 0.4 m from the
ground, is higher than the ambient air temperature for 2–3 °C where the external wind speed
at the ventilation opening varies from 1.6 to 1.8 m s-1. In this case, the averaged value of the
internal wind speed inside the greenhouse is 0.638 ≤ ui ≤ 1.0 m s-1. This concurs with the re-
sults reported by Kalma and Kuiper [3]. However, the internal wind speed that is suitable for
maintaining the favorable environment for crop growth is in the range of 0.1–0.6 m s-1 [4].
Fig. 5 (a) and (b) show that, at the wind speed of 0.6 m s-1, the air temperature inside is higher
than ambient air temperature for 5 °C. This is caused from the air ventilation inefficiency.
Thus, in case of natural ventilation with roof and sidewall vent in the tropical climatic condi-
tion where the external wind speed is less than 2 m s-1, the ventilation opening on the sidewall
at the 0.4 m height from the ground is appropriate for controlling the wind speed [3,4], the
failure is caused from the incident where the air temperature inside is higher than the external
air temperature. To solve this problem, various roof slopes for reducing the air temperature in-
side the greenhouse at the < 2.5 m height from the ground are examined.
6.3 Effect of ventilation performance on roof slope variations
The heat storage in the SSG depends on the low roof slope. Thus, when investigating on the
roof slope variations for lowering the hot air inside the greenhouse at the height of < 2.5 m
where the space under the gable roof is used as the zone for storing the heat before the hot air
is transmitted through the roof vent.
Fig. 6 shows the results from the calculation for ventilation rate in term of average ventilation
function, G(α), as the function of the external wind speed for comparing various roof slopes.
The results indicate that, when the wind speed is < 1.5 m s-1, the roof slope variation can vary
the performances. At the wind speed of > 1.5 m s-1, the ventilation system is wind-influenced,
and the roof slope variation is not influential. When the wind speed is < 1.5 m s-1, the incline
of roof reduces the drag force on thermal driven force, as shown in Fig. 7. This figure shows
the flow pattern and vector field of air inside the greenhouse.
In addition, it is discovered that the ceiling of the roof slopes of 30° and 42° (Fig. 7, b-c) fa-
cilitate the air movement under the roof to flow out through the roof vent with the speed high-
er than the speed of the air flow in the center of the greenhouse.
The results from the comparison between this finding and the results from the case of the 15°
roof slope indicate that most of the air is waked inside the greenhouse and some of the air at-

7. tempts to flow out off the greenhouse. Therefore, at the roof slope of 15°, the ventilation func-
tion, G(α), decreases when the external wind speed is less than 1.5 m s-1.
In other investigations, the ventilation function can be considered in term of ventilation resis-
tance or ventilation requirement. For the example, in case of the roof slope of 42° with the ex-
ternal wind speed of 0.5 m s-1, the ventilation resistance or ventilation requirement is 0.3 of
inlet air volume. When the wind speed is 2 m s-1, the ventilation resistance or ventilation re-
quirement is less than 0.15 of inlet air volume. Thus, the higher the external of air wind speed
is the lower the ventilation resistance or ventilation requirement is. However, the results from
the investigation also show that the ventilation performance is dependent on the influences
from external wind whilst the roof slope is the feature of the greenhouse which can reduce the
heat existing under the roof.
The results from the examinations of the air temperature in term of temperature function,
(ΔT/To), as shown in Fig. 8, show that the air temperature inside the greenhouse at various
roof slopes is affected by the external wind speed in the range of 0.5–2 m s-1. It is also found
that the air temperature decreases and depends on the external wind speed.
The results from the comparison among the roof slopes of 15°, 30° and 42° show that the air
temperature inside increases by 10–20% when the roof slope is 15°. This shows that the low
roof slope facilitates the increase of air temperature. In other words, the low roof slope does
not provide the heat storage zone. As a result, the heat on the ceiling convection is transmit-
ted, in the manner of the wake of air, into the greenhouse.
Furthermore, Fig. 8 shows that when the slope of roof is higher than 30°, the air temperature
inside the greenhouse will not decrease much more. This phenomenon is emphasized on in
Fig. 9, which shows the simulated results on the air temperature distributions of the air inside
the greenhouse at each roof slope. When the external wind speed is 0.5 m s-1 and the roof
slope is 42° (Fig. 9(c)), which provide more space (point b) near the gable roof, the air tem-
perature inside the greenhouse is not much different from the air temperature inside the green-
house that has 30° roof slope. In addition, the heat storage in both cases occurrs inside the
greenhouse at the height of > 2.5 m from the ground.
This case, compared with the results from case of the 15°roof slope, shows that the air tem-
perature inside the greenhouse decreases (ΔT) for 1–2°C at the height of < 2.5 m from the
ground. According to a number of studies on the inside air temperature at various roof slopes,
this air temperature difference correlates to the external wind speed. The results are shown in
table 2, and indicate that when the roof slope varies between of 10°–15°, it can lower the in-
side air temperature (ΔT) around 1–1.5 °C. This is based on the average of air temperature
data on different external wind speeds.
Since the inside of air temperature increases in accordance to the effects from the heat stored
under the roof, the entire ventilation system inside the greenhouse is affected by the stored
heat as well. Thus, the data that can be applied to the creation of a guideline for the ventilation
system inside the greenhouse for lowering the hot air temperature are shown in Fig, showing
the ventilation system under various roof slopes, on the bases of Gr/Re2 and the external wind
speed, at the 2.5 m height from the ground.
When the external wind speed is 0.5 m s-1 and the Gr/Re2 value at the roof slopes of 30° and
42° is < 1, the dominating ventilation system inside the greenhouse is wind-induced one.
When the Gr/Re2 is 1 and the roof slope is 15°, the ventilation system inside the greenhouse is
mixed convection [10].
However, when the external wind speed is < 0.5 m s-1 and the value of Gr/Re2 is > 1, the ven-
tilation system in side the greenhouse will shift from the mixed convection to the free convec-

8. tion or thermal driven ventilation. Thus, the air temperature inside the greenhouse will be
high.
Likewise, Papadakis et al. [20], having studied on the ventilation system inside the green-
house, discovered that, when the Gr/Re2 was < 1, the ventilation system was wind-induced.
When the Gr/Re2 was higher than 0.1 and lower than 16 (0.1 < Gr/Re2 < 16), the dominating
ventilation system would be the mixed convection.
Fig. 10 shows that the ventilation system is the mixed convection when the external wind
speed is < 1 m s-1; and the ventilation system in wind driven ventilation when the external
wind speed is > 1.5 m s-1. When the wind speed is 0.5 m s-1 and the Gr/Re2 is higher than 0.6
and lower than 1 (0.6 < Gr/Re2 < 1), the ventilation system inside greenhouse will be the
mixed convection. Thus, to avoid the ventilation system of the free or mixed convection type
when the external wind speed is < 1 m s-1, the greenhouse roof slope should be > 15° so as to
generate the wind-induced ventilation system inside the greenhouse.
6.4 Effect of wind loads on roof slope variations
The height of roof slope can be damaged by wind loads. Thus, it is essential to simulate the
air flow on the outside so as to determine the effects from wind loads in term of wind pressure
coefficient which is applied to the outside of the roof.
The results shown in Fig. 11, in this figure shows the wind pressure coefficient as the simulat-
ed data on X axis to the span of greenhouse, S, which is presented by the comparison between
the results simulated by the CFD technique and the data measured by Oliveira and Younis
[21] and Gingera and Holmes [22] who had studied on the effects from wind loads on the roof
slopes of 27° and 35°, respectively.
As for this study, the comparison is between the wind pressure coefficient on the roofs the av-
erage slope of which is 15° (wind loads applied to the roof slope of 20°) and that on the roof
the average slope of which is 30° (wind loads applied to the roof slope of 33°). The results
from the comparison indicate that the simulated results are not significantly different from the
results from the previous studied.
From Fig. 11, concerning the wind pressure coefficient, Cp, when the roof slopes are 15°,
30°and 42°, it is found that the value of Cp at the roof slopes of 30° is close to zero. However,
when the roof slopes are 15° and 42°, the Cp values become -0.5 and 0.6, respectively.
Theoretically, when the roof slope is 30°and the dp/dx ≅ 0, the air flow is regarded as a transi-
tion. In this study, when the roof slope is 15°, the dp/dx is found to be < 0, so the air flow is a
favorable pressure gradient, where the gutter and the small incline of roof are induced to the
wind velocity increase and the flow direction change, which generates the wake of air on the
roof. This creates the high pressure in the leeward wind floe applied to the roof. On the con-
trary, when the roof slope is 42°, the dp/dx will be > 0; hence, the air flow is an adverse pres-
sure gradient, where flow separation can never occur on the roof, and the windward flow has
the high pressure on the roof side.
6.5 The correlation between the air ventilation and wind load at various roof slopes
In this research, the ventilation performance is depends on the greenhouse geometry and the
vent opening. Thus, the results from the study on roof slope and wind speed variations are
calculated so as to obtain the ventilation drag coefficient, Cd, at the roof slopes of 15°, 30°
and 42°. The outcomes from the calculation are the Cd values of 0.641, 0.650 and 0.650, re-
spectively. The average Cd is 0.636, which is close to the value obtained by Parra et al. [14]
who had studied on the greenhouse with roof and side ventilation.

9. However, the Cd values for greenhouses with roof and side vent are in the range of 0.6–0.8,
where the average value of Cd is 0.66 [19].
The roof slope variations, thus, can be said to have influences on the air temperature and ven-
tilation performance: the high gable is vulnerable to the wind loads.
In addition, the ventilation rate and the pressure coefficient on wind force applied to the out-
side structure of the greenhouses with different roof slopes are investigated by combining the
ventilation estimates in equation (2) with the pressure coefficient in equation (5), where the
stack effect in equation (2) is negligible. The result from the combination of the two equations
can be expressed by the equation Cd 2 = (Cp / Cw)(ρ2/ΔP)(Q/ AT)2.
The correlation between Cd 2 and (ρ2/ΔP)(Q/ AT)2, is shown in Fig. 12, and indicates that the
results from the combination between equations (2) and (5) shows the performance, when the
roof the slope of which is 15°–30°, in terms of the ventilation efficiency and the loading effi-
ciency when the wind force is applied to the structure on roof side. A roof slope the angle of
which is greater than 30° does not influence to the air ventilation rate increase or the inside air
temperature decrease. Thus, the 30° gable roof is best suitable for a greenhouse.
7. Conclusions
This research investigates the problem of air ventilation in a Simple Structure Greenhouse
(SSG) with gable roof and roof vent via the Computational Fluid Dynamics (CFD) technique.
The results from the study on an empty 6m width x 8 m depth greenhouse indicate that the
problem of air temperature increase for 6–8 C° inside the greenhouse the roof slope of which
is ≅ 15° is caused from the stored heat.
This problem also occurs to the greenhouse each column of which is not high as 2.5 m. As the
results, the ventilation system appears to be the thermal-driven one on heat convection. In ad-
dition, the heat transmission between the roof top and the center of the greenhouse is induced.
Furthermore, the 0.4 side opening is found to generate the wake of air and the wind-induced
ventilation so as to lower the air temperature inside the greenhouse. This is possible when the
inside wind speed ranks from 0.638 to 1.0 m s-1. Otherwise, it will not succeed in lowering the
air temperature inside greenhouse. Thus, in this study, the researchers consider the effects
from roof slope variation, where the averaged roof slopes are 15°, 30° and 42°, with the ob-
jective to lower the air temperature inside the greenhouse so as that it will be similar to the
ambient temperature.
In this study, the ceiling of greenhouse is the heat storage zone where the hot air remains be-
fore being ventilated out through the roof vent. The performance of roof slope is considered
in terms of ventilation function: G(α), temperature function: (ΔT/To), and Gr/Re2.
This results from this study show that the 30° is the maximum degree of roof slope that facili-
tates the justification of the air temperature inside the greenhouse to the outside ambient tem-
perature.
It is also found that the air temperature inside the greenhouse is different from that outside the
greenhouse (ΔT) for 2°C.
When the Gr/Re2 is < 1, at the height of 2.5 m from the ground, the dominating ventilation
system appears to be the wind-induced one.
Since the height of roof slope causes the problem to the greenhouse structure, the ventilation
performance is considered to be related to the wind pressure applied to the greenhouse roof.

10. The equation for calculating the output is the combination between the ventilation rate equa-
tion and the pressure coefficient of the wind force at various roof slopes. The results from the
calculation, excluding the dimension, reveal that the roof slope that can influence the ventila-
tion performance in justifying the air temperature to the ambient temperature under the wind
pressure on the greenhouse roof is < 30°. Thus, the suitable roof slope for a Simple Structure
Greenhouse in a hot and humid region is 30°.
Acknowledgements
The authors would like to express their sincere appreciation to the Energy Policy and Plan-
ning Office (EPPO) for the financial support to this research project.
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คำำบรรยำยภำพ
Fig. 1 Prototype of a Simple Structure Greenhouse (SSG-greenhouse), built with a bamboo
structure (a) and Schematic view of the empty SSG-greenhouse, with different sidewall open-
ings (b)
Fig. 2 Greenhouse configuration for roof slope difference (a) Average roof slope of 15° (b)
Average roof slope of 30°; (c) Average roof slope of 42°

12. Fig. 3 Comparison, in term of the ventilation rate as the function of wind speed outside the
greenhouse, between the results from the experiment by Tuntiwaranruk et al. [15] and the nu-
merical results obtained from the examinations on the three different grid resolutions
Fig. 4 Comparison, from the calculation of the measurement data in the middle distance of the
greenhouse by the Gr/Re2formula, from results from the experiment by Tuntiwaranruk et al.
[15] and the results obtained from the simulation of the coarse grid resolution
Fig. 5 Flow pattern (a) and temperature distributions (b) of air inside the SSG-greenhouse,
where the side opening is 15% or 0.4 m from ground and the outside wind velocity is 1.6 m s-1
with the wind direct of 0°
Fig. 6 Comparison of the ventilation performance in term of ventilation function, G(α) for the
roof slope variations, at the external wind speed of 0.5, 1.5 and 2.0 m s-1
Fig. 7 Comparison of the velocity vector inside the greenhouse at different the roof slopes
with the wind speed of 0.5 m s-1: for the roof slopes of (a) 15°, (b) 30° and (c) 42°
Fig. 8 Comparison of the different roof slopes for the variable the wind speeds resulted from
the temperature function, (ΔT/To)
Fig. 9 Comparison of the temperature distribution inside the greenhouse at different the roof
slopes with the wind speed of 0.5 m s-1: for the roof slopes of (a) 15°, (b) 30° and (c) 42°
Fig. 10 Comparison of the ventilation system with different roof slopes calculated from the
Gr/Re2, at the height of 2.5 m from the ground, as functional wind speeds
Fig. 11 Prediction resulted from roof slope variations, compared with measured pressure coef-
ficients for roof pitch greenhouse, generated by Oliveira and Younis [21], and Gingera and
Holmes [22] when the roof slopes are 27° and 35°, respectively
Fig. 12 Effects from the roof slope variation on the ventilation performance and wind pressure
coefficient, presented in the form of Cd 2 to (ρ2/ΔP)(Q/AT)2
Table 1 Parameter values of boundary conditions used for the simulations
Table 2 Linear regression equations of temperature difference ΔT on wind speed uα