Computers and Electronics in Agriculture

34 (2002) 191 – 205

www.elsevier.com/locate/compag

Numerical estimation of the internal and

external aerodynamic coefficients of a tunnel

greenhouse structure with openings

A. Mistriotis *, D. Briassoulis

Department of Agricultural Engineering, Agricultural Uni

6ersity of Athens, Iera Odos

75

,

11855

Athens, Greece

Abstract

The external and internal aerodynamic coefficients on a tunnel (vaulted-roof) structure

with openings are numerically calculated in the case of a transverse wind, using the Finite
Element method. Ventilation configurations involving (a) both side symmetrical openings;
and (b) only a leeward opening have been studied. The numerical results show that the
external aerodynamic coefficients are only weakly influenced by the position or the size of the
openings. On the contrary, the internal aerodynamic coefficients, and so the total wind
pressures on the structure, strongly depend on the ventilation opening configuration. These
results are compared with the relevant provisions of prEN13031-1 European standard and
the Eurocode-1 and may provide support to future revisions of the codes within the normal
standardisation activities. © 2002 Elsevier Science B.V. All rights reserved.

Keywords

:

Aerodynamic coefficients; CFD; Greenhouses

Nomenclature

wind pressure (aerodynamic) coefficient

c

p

fitting parameter of the k –

m model, 0.09

C

m

turbulent kinetic energy (m

2

s

− 2

)

k
K

Von Karman constant, 0.4

* Corresponding author. Tel: + 30-1-5294022; fax: + 30-1-5294023.
E-mail address

:

[e-mail] (A. Mistriotis).

0168-1699/02/$ - see front matter © 2002 Elsevier Science B.V. All rights reserved.

PII: S 0 1 6 8 - 1 6 9 9 ( 0 1 ) 0 0 1 8 7 - 9

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34 (2002) 191 – 205

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pressure (kg m

− 1

s

− 2

)

P

Symbols

air velocity (m s

− 1

)

6

6

f

friction velocity (m s

− 1

)

height above the ground level (m)

z
z

o

surface roughness length (m)
turbulence dissipation rate (m

2

s

− 3

)

m

density (kg m

− 3

)

z

Subscripts

external

e
i

internal
at reference height

ref
x

at position x

1. Introduction

Plastic greenhouses are light structures designed with relatively low safety coeffi-

cients in order to reduce cost and optimise the functionality of the cover as a mean
for protecting the indoor cultivation. Unfortunately, in many cases reliable design
procedures are not followed or the data required for a reliable design are missing
or not well justified. A well-documented knowledge of the design loads is necessary
for developing not only efficient but also safe greenhouse structures. Since wind is
the most usual cause of failure of plastic greenhouses, it dominates the design of
these structures. For this reason, the best possible estimation of wind loads is
essential for the optimal design of greenhouse structures.

Greenhouses are included in the general category of low-rise buildings. The

estimation of the wind loads for greenhouse structures is based on measurements
obtained by full-scale or wind-tunnel experiments which have been performed on
greenhouses or other low-rise buildings with similar geometrical characteristics
(Wells and Hoxey, 1980; Hoxey and Richardson, 1983; Hoxey et al., 1993;
Richardson et al., 1997). Several of these results are incorporated in the systematic
standardisation activities, which are in progress in Europe, and have led to the
establishment of the European standard for commercial production greenhouses,
prEN13031-1 (CEN, 1999). This standard aims at supporting the system of the
structural Eurocodes (CEN, 1995) with respect to greenhouse design. The design of
steel, timber or other types of greenhouses has to comply with the relevant
provisions of the Eurocodes.

Designing a greenhouse according to Eurocode-1 implies that the corresponding

wind loads are calculated in the same way as for any other conventional building

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of the same geometry under the same local climatic conditions (CEN, 1995). The
question whether this is an appropriate design approach for greenhouses has been
widely discussed. The determination of specific design loads for greenhouses is one
of the reasons for the development of a European standard for greenhouse design.
The final version of the European standard for commercial production greenhouses,
prEN13031-1 (CEN, 1999), which has been recently completed, represents the first
attempt to provide such specific design loads through standardising the greenhouse
design methodology at a European level.

In spite of this standardisation effort, several scientific and technical questions

remain open due to the particular structural and functional characteristics of
greenhouses. For example particular configurations of ventilation openings may
influence positively or negatively the wind loads on the greenhouse structure. Such
influence may be critical for the stability of the structure not only under specific
extreme circumstances, but also under certain critical combinations of load and
greenhouse geometry/openings configurations. Answering these questions would
require a wide range of full scale and wind-tunnel experiments to determine the
corresponding aerodynamic coefficients. Alternatively, Computational Fluid Dy-
namics (CFD) simulations can be used as a more flexible and cheaper tool replacing
wind-tunnel experiments for the estimation of wind loads. Numerically obtained
external aerodynamic coefficients for various low-rise buildings, as well as numeri-
cal simulation of the ventilation process in greenhouses show a satisfactory agree-
ment with full scale or wind-tunnel measurements (Hoxey et al., 1993; Mistriotis et
al., 1997b). Moreover, CFD simulations of the wind induced ventilation flow in
greenhouses have shown good agreement with experimental data (Mistriotis et al.,
1997a; Kacira et al., 1998; Boulard et al., 1999; Lee and Short, 2000). Therefore,
not only the outdoor but also the indoor air flow can be modelled efficiently.

The current work aims at presenting the complexity of the air flow in green-

houses with ventilation openings. The pressure distribution on both the external
and the internal surfaces of the cover is calculated. The interaction between external
and internal flows is investigated. The corresponding external and internal aerody-
namic coefficients are calculated for a tunnel greenhouse and compared with the
corresponding provisions of relevant codes. The results obtained are expected to
contribute to a more realistic determination of wind loads for greenhouse design
and subsequently contribute to the corresponding pre-normative research in sup-
port of the new European Standard for greenhouse design.

2. Finite element method (FEM) in computational fluid dynamics simulations

The CFD method allows the explicit calculation of all physical variables of a flow

(pressure, velocity, temperature, etc.) by numerically solving the corresponding
transport equations.

In a flow field, the continuity equation and the three momentum equations

describe the velocity components and the pressure as functions of time and space.
When energy is transported, an extra equation describes the temperature field.

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Solving analytically the set of continuity, momentum and energy equations is only
possible for limited cases such as the laminar flow. The use of numerical techniques
is indispensable for problems with more complex nature involving turbulence.

In the present work, the Finite Element Method (FEM) has been used, rather

than the most commonly used Finite Volume Method (FVM). FEM allows easier
modelling of objects of arbitrary shape (Anderson et al., 1992). Furthermore, if
tetrahedral elements are used, a rapid but smooth and consistent transition from
fine to coarse elements is possible. However, the solution is more sensitive to the
selected mesh than the one obtained by the FVM and the convergence of the
solution with respect to mesh refinement should be investigated before the results
are acceptable (see Section 4).

In the present CFD simulations, turbulence is described by the most widely used

standard k –

m model (e.g. Awbi, 1991). The weakness of the k–m model in describing

large eddies due to the false assumption of spectral equilibrium, is cured by high
refinement of the mesh at the locations where circulating flow is expected. In this
way, the flow corresponding to large eddies is treated explicitly, while only
small-scale turbulence is described by the k –

m model.

In the present work, a commercial software package implementing

FEM

is used

(

ANSYS-FLOTRAN

v5.6). For the two-dimensional elements used, the velocity com-

ponents are obtained from the conservation of momentum principle, and the
pressure is obtained from the mass conservation law. The solution of the nonlinear
set of partial differential equations is obtained through a self-consistent iterative
scheme in each step of which all governing equations are sequentially solved
(

ANSYS

, 2000).

3. Boundary conditions

In CFD numerical experiments, external factors such as the wind, the solar

radiation etc., influencing the flow are simulated by boundary conditions. There-
fore, the definition of realistic boundary conditions is crucial for correctly reproduc-
ing the flow characteristics. Wind-tunnel experiments for calculating the air flow
around and through low-rise buildings should model correctly the wind in the
lowest atmospheric surface layer. The wind velocity profile, namely the height
dependence of the wind velocity, and the turbulent characteristics of the wind
within the surface layer should be simulated as boundary conditions at the inlet.

The wind characteristics depend on the terrain type around the studied building.

It is known that the wind velocity profile is described by a logarithmic function of
the form (e.g. Kaimal and Finnigan, 1994):

6(z)=

6

f

K

ln

z + z

o

z

o

(1)

where

6(z) is the wind velocity as a function of the height z, 6

f

is the friction

velocity, K is the von Karman constant and z

o

is the surface roughness length. The

constant K has been determined to be approximately 0.4 (e.g. Kaimal and Finni-

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gan, 1994). The surface roughness length is a parameter describing the logarithmic
decrease of the wind velocity with the height due to friction with the ground, and
depends on the terrain type. The design values of the surface roughness length given
by the Eurocode (CEN, 1995) on wind actions on structures are presented in Table
1. The friction velocity

6

f

can be determined by the measurement of the wind

velocity at a reference height.

The turbulent characteristics of the wind at the upstream boundary are described

by the values of the k and

m variables. It has been shown that these values can be

calculated by the following equations (Richards and Hoxey, 1993):

k =

6

f

2

C

v

(2)

and

m(z) =

6

f

3

K (z + z

o

)

(3)

where C

m

is a fitting parameter of the k –

m model and its most widely used value is

0.09. Eq. (2) and Eq. (3) satisfy simultaneously Eq. (1) and the k and

m transport

equations. Therefore, Eqs. (1) – (3) can describe the wind characteristics above a
terrain with roughness length z

o

.

4. Numerical calculation of aerodynamic coefficients for a tunnel greenhouse with
openings

Wind loads on the greenhouse cover are the result of external and internal

pressures induced by the external wind on the cover. The aerodynamic or pressure
coefficients, c

p

, describe the corresponding pressure distribution on the external or

the internal surface of a building normalised by the dynamic wind pressure:

P

x

=

1
2

c

p,x

z6

ref

2

(4)

where P

x

is the pressure at a point x on the roof,

6

ref

is the wind velocity at a

reference height z

ref

, and

z is the air density. In this way, the dependence of the

Table 1
Terrain categories and related design values of surface friction length, z

o

, and roughness sub-layer

thickness, z

min

(Eurocode-1, CEN, 1995)

z

min

(m)

z

o

(m)

Terrain type

Rough open area without obstacles

2

0.01

Farmland

0.05

4

0.30

8

Suburban or industrial areas

1.00

16

Urban areas

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wind loads on the shape of the structure is separated from the wind speed value.
Aerodynamic coefficients are given for external, as well as internal pressures by the
various design codes. The reference height is defined so that the height of the
structure is taken into account. Considering external pressures, in the case of tunnel
structures, Eurocode-1 (1995) proposes as reference height the mid-height of the
tunnel structure (or the mid-height of the vaulted roof in cases of structures with
cylindrical roofs), while the European standard prEN13031-1 (1999) suggests a
reference height equal to 75% of the ridge height , and other authors used a value
equal to the ridge height (Hoxey and Richardson, 1983).

As far as internal pressures are concerned, Eurocode-1 (1995) proposes as

reference height the mean height of the openings or the height of the dominant
opening, for any type of structure. On the other hand, the European standard
prEN13031-1 (1999) suggests that the reference height for internal pressures shall be
taken equal to the reference height for external pressures.

For low-rise buildings, however, the thickness of the roughness sub-layer should

also be taken into account for selecting the reference height. The logarithmic model
of the wind profile is realistic above a lowest surface layer where the wind speed
and direction are disperse due to intense turbulence generated by the friction with
the ground. This is called the roughness sub-layer. For this reason, the correspond-
ing standards for structural design propose a roughness sub-layer thickness, z

min

,

below which the logarithmic profile (Eq. (1)) is not valid any more. In order to
avoid possible underestimation of wind loads and ensure safety, all standards
propose a reference height equal to z

min

for all structures lying entirely in the

roughness sub-layer. The design values of z

min

given by the Eurocode (1995) on

wind actions on structures are presented in Table 1. The standard prEN13031-1
also adopts the same design values of z

min

as the Eurocode-1. Therefore, if

numerically calculated values of aerodynamic coefficients are to be compared with
the relevant provisions of standards, the reference height for structures lower than
z

min

should be taken equal to z

min

.

In the present work, a semi-cylindrical tunnel greenhouse with a radius of 3 m

(Fig. 1) is studied when the wind is blowing transversely to the greenhouse. Such
greenhouse structures are widely used in Mediterranean countries (Elsner et al.,
2000). The length of the greenhouse is considered much longer than their width and
height. Therefore, the pressure coefficients along a typical cross section of the
greenhouse away from the ends can be calculated by a two-dimensional steady-state
CFD simulation.

The reference wind speed at 10 m height is selected equal to 3 m s

− 1

. The surface

roughness of the ground is selected equal to 0.05 m corresponding to a rural
landscape. For such a landscape, z

min

is 4 m. Therefore, the reference height for the

estimation of all aerodynamic coefficients has to be selected equal to 4 m when
comparing the calculated pressure coefficients against those of the Eurocode-1
(1995) or the European standard prEN13031-1 (1999). The same reference height is
used for both external and internal aerodynamic coefficients, since all openings lie
below the z

min

limit.

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Fig. 1. Finite element mesh and geometrical characteristics of the tunnel greenhouse used in the CFD
simulations.

The external pressure coefficients for the tunnel greenhouse described above

when all openings are closed, have already been numerically estimated by finite
element CFD simulations (Mistriotis and Briassoulis, 2000), where the numerical
results have also been compared with measured values obtained by a full-scale
experiment (Hoxey and Richardson, 1983).

In the simulations presented here, the studied structure is considered as a rigid

shell of 3 cm thickness placed in a wind tunnel of dimensions 80 × 300 m. It is
positioned at 80 m away from the inlet of the wind tunnel (Fig. 1). The logarithmic
wind profile (Eqs. (1) – (3)) is assumed to extend as low as the ground level. Of
course, these assumptions do not allow any dynamic phenomena or the structural
response of the flexible structure of a plastic covered greenhouse to be taken into
account. In that respect, the results obtained represent a pseudo-static approxima-
tion of the real problem.

The air flow around and through the structure is numerically calculated by the

Finite Element method. The mesh consists of triangular elements with three nodes,
which allow detailed refinement around the studied structure (

ANSYS

, 2000). The

degrees of freedom are the velocity components, the pressure, and the turbulence
parameters, k and

m. The element size near the building is two orders of magnitude

smaller than that at the upper wall of the wind tunnel (Fig. 1).

In finite element (FE) calculations, the solution strongly depends on the selected

mesh used for the partitioning of the solution domain. Any FE solution, which
satisfies the conditions imposed, is acceptable only if it converges with the repetitive
refinement of the mesh. In the current problem, the solution is most sensitive to the
mesh along the external surface of the greenhouse cover, where flow separation
takes place. For this reason, the fineness of the mesh is expressed as function of the
number of elements along the structure. Two characteristic pressure values are

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monitored with respect to convergence as the number of elements along the external
surface of the greenhouse increases: (a) minimum (negative) pressure along the
cover; and (b) pressure near the leeward foundation. Convergence is obtained for a
mesh with more than 900 elements along the greenhouse cover.

The purpose of the present work is to investigate the influence of openings to the

external and internal aerodynamic coefficients of the studied structure. For this
reason two different configurations of openings (Fig. 2) have been studied: (A) in
the first case, two symmetric continuous openings of equal size exist on both sides
of the greenhouse; (B) in the second, only one opening exists on the leeward side.
These two cases have been selected as the most common configurations of the
ventilation openings in tunnel greenhouses. The first one corresponds to situations
where very high air renewal rates are required. The second case provides moderate
ventilation rates, while the crop is protected from the direct wind coming through
a windward opening.

5. Results

Fig. 3 presents the external aerodynamic coefficients along the structure in case

(A) for three different opening sizes. The openings are located near the ground level
with their centre at height equal to 75 cm above the ground. Their size is expressed
as an angle along the cylindrical surface of the structure: (1) 1.2°; (2) 6°; and (3)
17.8°. These values correspond to (1) 1.3%; (2) 6.7%; and (3) 19.8% opening ratios
(opened/total structure area), respectively, and to an opening ratio

v=0.5, as

defined by Eurocode 1 (1995) (leeward and parallel to the wind opened area/total
opened area). The results show a weak influence of the opening size on the external
aerodynamic coefficients. The comparison between numerically obtained external

Fig. 2. The two opening configurations studied in this paper: (A) symmetrical openings at windward and
leeward sides; (B) one leeward opening.

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Fig. 3. External aerodynamic coefficients for a tunnel semi-cylindrical greenhouse of 6 m diameter with
two symmetrical openings for three different opening ratios: (1) 1.3%; (2) 6.7%; and (3) 19.8%.

aerodynamic coefficients and the relevant provisions of Eurocode 1 (1995) or the
Standard prEN13031-1 (1999) is discussed in a previous work (Mistriotis and
Briassoulis, 2000).

Fig. 4 presents the aerodynamic coefficients along the internal surface of the

greenhouse cover for the three different opening sizes described above, where the

Fig. 4. Internal aerodynamic coefficients for a tunnel semi-cylindrical greenhouse of 6 m diameter with
two symmetrical openings for three different opening ratios: (1) 1.3%; (2) 6.7%; and (3) 19.8%. The
numerical values are compared with the provisions of the Eurocode-1 (x marks) and the European
standard for commercial greenhouses prEN13031-1 (diamond marks).

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Fig. 5. Contour presentation of the air flow characteristics for the case A-2 (symmetrical openings with
opening ratio 6.7%): (a) pressure distribution (pressure is normalised by the dynamic wind pressure at
4 m height); (b) air velocity component,

6

x

(m s

− 1

), parallel to the wind direction. Negative values of

6

x

indicate circulating air flow.

reference height is taken equal to 4 m. In this case a strong dependence of the
aerodynamic coefficients on the opening size is observed. In the case (1) where the
opening size is small, the internal pressure coefficients vary between 0 and 0.05 with
the exception of points near the openings. As the opening size increases in case (2),
the internal overpressure increases as well. The corresponding values of c

pi

vary

between 0 and 0.3. However, if the opening size increases further in case (3), the c

pi

becomes negative and varies between 0.3 and − 0.6 with the exception of points
near the lips of the openings. The non-uniform internal pressure distribution
observed in this case indicates that the geometrical characteristics of the structure
influence the internal airflow.

The singular behaviour observed at the opening lips is a result of the high

pressure gradient along the openings as shown in Fig. 5a, which forces the airflow
through the narrow openings at high speed (Fig. 5b). This type of flow gives rise to

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high turbulence along the opening lips, which induces strong negative pressure
values. The scale of this phenomenon is small and probably comparable to the
element size used along the openings (7 mm). Therefore, the high negative values
shown in Fig. 3 and Fig. 4 may not be quantitatively correct and further refinement
of the mesh near the opening lips is required in order to treat this locally singular
behaviour of the solution. However, this was not possible in the current work due
to limitations of the available computer power. Thus, these particular results
concerning local values of wind pressure near the openings should be interpreted
with caution.

In Fig. 4, the numerical results are compared against the uniform c

pi

values given

by the European standard prEN13031-1 (1999) and the Eurocode 1 (1995) for the
same structure design, opening configuration, and wind direction. Attention has to
be made at the variability of the internal pressure coefficients when the openings are
large. This behaviour needs to be further investigated in terms of its effect on the
mechanical response of the structural arch-covering system.

In case (B) the influence of the opening size is weaker. Three different opening

sizes have been studied: (1) 1.2°; (2) 6°; and (3) 17.8°, corresponding to (1) 0.7%; (2)
3.3%; and (3) 9.9% opening ratios (opened/total structure area) respectively, and to
an opening ratio

v=1.0, as defined by Eurocode-1 (1995) (leeward and parallel to

the wind opened area/total opened area). As Fig. 6 shows, the external aerody-
namic coefficients are the same with those corresponding to the closed structure
(Mistriotis and Briassoulis, 2000). The internal pressure is equal to the pressure
along the opening and the corresponding internal pressure coefficient is approxi-
mately equal to − 0.4 (Fig. 7). Since the pressure at the leeward side of the
structure is uniform due to the existence of a large eddy (Fig. 8), the internal
pressure is also independent of the opening size.

Fig. 6. External aerodynamic coefficients for a tunnel semi-cylindrical greenhouse of 6 m diameter with
one openings at leeward side for three different opening ratios: (1) 0.7%; (2) 3.3%; and (3) 9.9%.

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Fig. 7. Internal aerodynamic coefficients for a tunnel semi-cylindrical greenhouse of 6 m diameter with
one openings at leeward side for three different opening ratios: (1) 0.7%; (2) 3.3%; and (3) 9.9%. The
numerical values are compared with the provisions of the Eurocode-1 (x marks) and the European
standard for commercial greenhouses prEN13031-1 (diamond marks).

The above numerical results demonstrate the strong dependence of the internal

aerodynamic coefficients on the spatial configuration and the size of the openings.
The oversimplified way in which internal pressures are treated in the Eurocode-1 or
the standard prEN13031-1 may not be sufficient for designing efficient and safe
greenhouse structures.

6. Discussion

Wind loading on open greenhouse structures is not analysed extensively enough

so far. Existing standards for structural design provide external aerodynamic
coefficients the estimation of which is based on wind-tunnel and full-scale experi-
ments measuring aerodynamic coefficients of closed buildings. The internal pressure
coefficients are estimated by full-scale measurements. The interaction between the
external and the internal air flows is not taken into account. Moreover, in most
cases, a single internal aerodynamic coefficient is given for characterising the wind
pressure on the total internal surface of the roof.

The main reason of such rough design values of internal pressure coefficients is

the lack of sufficient experimental data. A detailed investigation of the internal
pressure distribution requires a large number of experiments, which would consider
several configurations of the ventilation openings taking into account the size and
other geometric characteristics of the ventilators. The present numerical study
attempts to demonstrate the problem and proposes CFD numerical simulations as
an alternative to experiments.

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In the present work, a tunnel greenhouse structure with openings has been

studied as an illustrative example. The airflow around and through the open
structure is calculated by a CFD-FE method. The numerical results confirm that
under specific circumstances the external aerodynamic coefficients are approxi-
mately equal to those of the closed structure and the internal pressure coefficient is
uniform along the greenhouse cover. This is the case when only a leeward opening
exists. However, this is not a general rule. The ventilation flow can generate
non-uniform internal pressure distributions depending on the geometrical charac-
teristics and the position of the openings or windows, as well as on the geometrical
characteristics of the full structure.

Fig. 8. Contour presentation of the air flow characteristics for the case B-2 (one leeward opening with
opening ratio 3.3%): (a) pressure distribution (pressure is normalised by the dynamic wind pressure at
4 m height); (b) air velocity component,

6

x

(m s

− 1

), parallel to the wind direction. Negative values of

6

x

indicate circulating air flow.

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204

Comparison of the present numerical results with the relevant provisions of

widely used international standards, such as the Eurocode-1 and the European
standard for commercial greenhouse structures, prEN13031-1, reveal important
discrepancies. More specifically, the standard prEN13031-1 suggests a c

pi

for

greenhouses with vaulted roofs between 0.2 and − 0.2, while in the present work
values as low as − 0.6 are calculated. The prEN13031-1 provisions differ to the
numerically calculated c

pi

even for the commonly used leeward ventilation

configuration. In this case, the calculated c

pi

is uniform and its value varies

between − 0.35 and − 0.4. Eurocode’s provisions are closer to the present nu-
merical results. For example, it suggests a uniform c

pi

value equal to − 0.5 for a

structure without windward openings. This is close to the numerically calculated
value for the tunnel with only leeward openings. However, Eurocode suggests a
positive c

pi

value equal to 0.1 for symmetric openings, while the CFD calcula-

tions provide a wide range of values between 0.3 and − 0.6 depending on the
opening size. The internal overpressure proposed by the Eurocode-1 in the case
of the symmetric opening configuration agrees well with the numerical result
corresponding to the opening size (2), but the numerical results show that for
larger openings, the internal pressure becomes negative.

In order to derive conclusions about the design wind loads adopted by the

European standard prEN13031-1 (1999) and the Eurocode 1 (1995), one has to
consider the fact that the external and internal pressures are assumed to act
simultaneously so that the net pressure is analogous to the difference c

pe

− c

pi

. In

this respect, it is not the differences observed in the internal pressure coefficients
alone but rather, the differences between the calculated values c

pe

− c

pi

and the

corresponding values given by the codes that should be taken into consideration.
The estimation of the wind loads in open greenhouses together with the corre-
sponding structural analysis of the greenhouse structure should be the topic of
future studies.

7. Conclusions

The numerical results presented in the present work demonstrate the strong

dependence of the internal aerodynamic coefficients on the spatial configuration
and the size of the openings. The internal aerodynamic coefficients given in the
Eurocode-1 or even the standard prEN13031-1 are not described in sufficient
detail for optimally designing efficient and safe greenhouse structures. A wide
range of opening configurations should be studied before cases with similar
aerodynamic coefficients can be accurately categorised. CFD simulations could
help such a research effort if they are combined with carefully designed validat-
ing experiments.

This work provides new data supporting a more realistic determination of

wind loads for greenhouses, and so a more reliable design of greenhouses. More-
over, it demonstrates the need for further pre-normative research concerning
wind actions in support of the new European Standard for greenhouse design.

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205

Acknowledgements

Dr A. Mistriotis is fully supported by a Grant of the General Secretariat of

Research and Development of Greece (Contract No. 97EL-100).

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