combined porous plates - copy

J . Fluid Mech. (1971), vol. 46, p a ~ t 1, pp. 177-198

Printed in Great Britain

177

An investigation of the forces on flat plates normal to a turbulent flow

By P. W. BEARMANf National Physical Laboratory, Teddington, Middlesex

(Received 23 April 1970)

Measurements on square and circular plates in turbulent flow show the mean base pressure to be considerably lower than that measured in smooth flow. Power spectral density measurements of the fluctuating component of the drag on square plates in both smooth and turbulent flow are presented. The measurements in turbulent flow show the importance of the ratio of turbulence scale to plate size. There is shown to be a strong correlation between the fluctuating drag force and the velocity fluctuations in the approaching flow. The distortion of the turbulence structure approaching a plate is also discussed.

1. Introduction Many flow environments are turbulent and these are not always well simulated

by the smooth flow usually found in wind tunnels. The flow in the earth's boundary layer, for example, is highly turbulent and this will influence the response of flexible buildings and structures. In order to be able to determine this response it is important that the effects of turbulence on the flow around bluff bodies should be clearly understood. The object of this paper is to examine the relationship between the approaching turbulent flow and the mean and fluctuating forces on a series of flat plates set normal to this flow. The paper con- centrates on the effects of turbulence and does not discuss the effects of mean shear.

A body placed in a uniform turbulent stream can be affected in a number of ways, the most obvious of which is the production of fluctuating forces by the approaching fluctuating velocities. The mean flow and mean forces can also be affected because turbulence can promote transition in boundary layers and free shear layers at lower Reynolds numbers than those normally found in smooth flow. A turbulent stream will also influence the growth of boundary layers and wakes. Schubauer & Dryden (1935) were the first to notice that turbulence increased the mean drag of flat plates. Measurements of the mean base pressure on a series of square and circular plates are discussed in 3 3.2 of this paper. The effects of both intensity and turbulence scale have been examined and their influence on mean base pressure is considered in $3.3.

The measurements of the fluctuating component of the drag force on square plates in turbulent flow are presented in $ 3.5. This particular shape of body wa8

t Present address: Aeronautics Dept., Imperial College, London, S.W. 7.

I2 FLY 46

178 P. W. Bearman

chosen because it was hoped that there would be no regular vortex shedding and that the major part of the fluctuating drag force would be directly related to the approaching turbulent flow. Davenport (1961) has suggested the use of a frequency-dependent transfer function, relating fluctuating force to the longitudinal component of fluctuating velocity, called aerodynamic admittance. Measurements of the aerodynamic admittance of flat plates have been reported by Wardlaw & Davenport (1964) and Vickery (1965), but agreement between the two sets of measurements is poor. One of the aims of the present research was to carry out a more systematic investigation of aerodynamic admittance with particular attention being paid to the importance of the ratio of turbulence scale to plate size. A discussion of the aerodynamic admittance results is given in $3.6.

I n $3.7 the structure of the turbulent flow ahead of a plate is discussed. The extent of the correlation between the fluctuating drag force and the fluctuating velocity (indicated by a hot wire positioned at various distances ahead of the plate) was measured. The concept of aerodynamic admittance requires this correlation to be high. I n addition to the effect of the turbulence on the plates there will be some effect of the plates on the stream turbulence. Hunt (1970) has proposed a theory to analyze the distortion of the turbulence in the flow past a body. The measurements of turbulence structure are discussed in the light of Hunt’s findings.

2. Experimental arrangement The experiments were conducted in a wind tunnel with a 9 f t (2.74 m) x 7 f t

(2.13 m) by 12 f t (3.66 m) long working section. The tunnel is of the closed-return type and has a free-stream turbulence level of about 0-2 yo and a top speed of 200ft/sec (61 m/sec). A highly turbulent flow was generated by the installation of a square-mesh grid a t the beginning of the working section. The grid, which was of the bi-planar type, was constructed from 1.5 in. x 0.75 in. (3-81 cm x 1.9 em) wooden slats spanning the tunnel and the distance between the centres of slats, the mesh size, was 7-5 in. (19 em). With the grid in position, the efficiency of the fan dropped to about 50 yo and the maximum speed of the tunnel was reduced to 100ft/sec. The flow behind the grid is discussed in $3.1.

The flow was examined around square plates of side 2, 3, 4, 6 and 8 in. (5.08, 7.61, 10.16, 15.22 and 20.3cm) and circular plates of 4 and 7in. (10.16 and 17-77 em) diameter. Pressure measurements were made using an Infra-red De- velopment micromanometer and the electrical output from the manometer was integrated to obtain a time mean value of pressure. For the examination of the effect of turbulence on mean base pressure, the plates were attached to a string supported on a movable frame. The effect of intensity was examined by posi- tioning the plates a t various distances x, downstream of the grid, and the effect of turbulence scale was mainly examined by working with different sizes of plate.

Mean and fluctuating forces were sensed by a semi-conductor strain-gauged drag balance having two strain-gauged links, one on each side, and these were 0.1 in, (2-54mm) long, 0.075in. (1.91 mm) wide and 0-010in. (0.254mm) thick.

Forces on plates in a turbulent Jlow 179

These gauges formed two arms of a bridge and the two dummy gauges completing the bridge were attached to the body of the balance. The balance is discussed in more detail by Bearman (1969). The plates were supported on a light, hollow, tapered sting 18h . (0.457m) long. The sting was protected from the airflow by a fibre-glass shroud attached, at the balance end, to the earthing frame. The shroud tapered from: in. (2.22 cm) diameter down to 8 in. (169 em) at the model. Transverse oscillations of the sting and model were eliminated by placing a thin strip of foam rubber around the end of the sting, between it and the shroud. The lowest natural frequency of the balance, with the sting and a 4in. square plate attached, was about 1.5 KHz.

The whole assembly was supported on a massive Ibeam bolted to a concrete bed beneath the tunnel. The support system was so positioned as to place the plates a t 6.33 f t (1.93 m) downstream of the turbulence grid. The lowest natural frequency of the support system was about 200 Hz but oscillations of the support system were extremely small and only a very small apparent drag signal resulted from this vibration. The power spectra of the drag were smoothed across this very narrow frequency range.

The balance was calibrated with the sting vertical and, with applied dead- weight loads up to 2 lbf (8.9 N), no departure from linearity was observed. The balance was mainly sensitive to axial load and extremely insensitive to any bending moment applied to the string. With the 4in. square plate attached to the sting a load was applied a t the centre of the plate and then at each corner. The largest variation in the output only represented a difference of 0.7 yo of the load applied at the centre.

The bridge circuit was not temperature-compensated and the output of the balance showed a strong temperature dependence. The sensitivity of the balance, working in a constant-current mode, only changed by about 0.1 %/C. The zero, however, drifted by about 10 yo of full-scale reading per degree Centrigrade, thus making the accurate measurement of mean drag force difficult. The drift of the zero was found to be fairly well correlated with the temperature of the air in the neighbourhood of the active gauges. During a run this temperature was con- tinuously monitored by a thermocouple. Initially runs were made with the sting removed and with the balance completely sealed in order to estimate the dependence of zero drift on ambient temperature. For the determination of mean drag coefficient, correction was made to allow for this zero drift.

Turbulence measurements were made with DISA constant-temperature hot- wire anemometers. Fluctuating velocity and fluctuating drag signals were recorded on an AMPEX PR 1300 tape recorder and, except where indicated, these signals were later digitized and analysis was performed on a KDF-9 digital computer.

3. Experimental results and discussion 3- 1 Plow behind the turbulence producing grid

The variation of the intensity (G)t/U and the longitudinal integral scale Lx of the streamwise component of turbulence behind the grid, along the centre-line

12-2

180 P. W . Bearman

of the working section, is shown in figure 1. These measurements were made using an unlinearized hot-wire anemometer and the scale was estimated from spectra measured on a third-octave spectrum analyzer. At the plate position adopted

0.12

0.06

0.10

5 0.08

'p", .

1 % .* * rn 5 2 0.04 H

0.02

0

'x -

Scale o/o- - 4

- A \LX - 3

J 0- \

/o- *\ < \\ +

-

-

m 7 - x - x - x - iL)

Intensity % - 2 .;

4 - 1 E

-

6)

uz -

- Model position for fluctuating drag measurements

I I I Y I I I I I 0

x ft

FIGURE 1. Variation of intensity and scale of ' u' component of turbulence along working section centre-line ( U = 40ft/sec). x , intensity; 0, scale; unlinearized anemomet,er. + , intensity; A, scale; linearized anemometer.

0.10 Intensity

.-/.-,-o 0.08 - ,#

? 1 % -"", 0.06 - -Y

Velocity U ft/sec

FIGURE 2. Variation of turbulence intensity and scale with velocity at 10.1 mesh lengths from the grid (the test position). 0, intensity; x , scale.

h

$ 0.04 d

-Y

m

u H

.-

0.02

0

for the fluctuating drag measurements the turbulence was investigated more carefully, with a linearized hot-wire anemometer and the values of intensity and scale are also shown in figure 1. This position, 10.1 mesh lengths from the grid, will be referred to as the test position. The main reason for the discrepancy

m

- 2 5 .d

-

4 - - 1 %

u2

1 I I I I I I 0

Forces on plates in a turbulent flow 181

between the two sets of readings was the limited low frequency response of the instrument used to measure the r.m.6. voltage fluctuation indicated by the unlinearized anemometer. In order to keep the signal to noise ratio of the drag balance high the test position had to be in a region of high turbulence intensity

10-6 lo-* 10-1 1

nlU ft-I 10 102

FIGURE 3. Spectra of longitudinal component of turbulence a t test position. 0, U = 32 ft/sec; A , U = 72 ft/sec.

close to the grid. At the test position, over the area to be occupied by the plates, the mean velocity and the intensity of turbulence were found to be uniform to within 0.30 %. At a fixed distance x from the grid the turbulence intensity decreased very slightly with increase of tunnel speed. Figure 2 shows the variation of intensity and scale with velocity a t the test position. Spectra of the ‘u’ component of turbulence, measured at two wind speeds a t the test position, are shown in figure 3. X-probe measurements showed the turbulent energy to be approximately equally distributed among its three components.

3.2. Measurement of mean base pressure

The first part of the investigation consisted of the measurement of mean base pressure on the plates in smooth flow. In this paper smooth flow is to be in- terpreted as the flow in the tunnel in the absence of any turbulence producing

182 P. W . Bearman

grids (i.e. ( 2 ) 4 / U = 0.002). Figure 4 shows the base pressure distribution on the 8 in. square plate measured from a line of tappings running across half the rear face of the plate. The pressure is presented in the form of a pressure coefficient (C,),, where (C,), = ( p b - p ) / i p U 2 and pb is base pressure and p and u are respectively free stream static pressure and velocity. These results have been corrected for the effects of wind-tunnel blockage using the method of Maskell (1965). The pressure across the base is seen to be nearly uniform and all further base pressure coefficients presented were determined from the pressure at the position y/D fi 0.2.

(hi)h/U = 0.083, Lx = 3in. (7.62cm).

Plate size ,- r , (in.) Smooth Turbulent Smooth Turbulent 2 x 2 1.120 1-260 0.363 0.505 4 x 4 1.090 1.220 0.363 0.46 6 x 6 1.107 1.195 0-363 0.43 1 8 x 8 1.152 1.175 0.363 0.410

TABLE 1 . Comparison of mean drag coefficient of flat plates in smooth and turbulent flow

C D - (CJb A

The results from all the plates in smooth flow, over arange of Reynolds number, showed a good collapse. The values of ( c p ) b for the circular plates were found to be the same as those for square plates. These results showed that base pressure was independent of Reynolds number, over the range to be investigated in turbulent flow. All plates were tested with the same sting and therefore the collapse of results suggests that the size of the sting relative to the plate size had a negligible effect on the mean base pressure readings. The corrected values of (C,),, given in table 1, agree closely with previous measurements of Fail, Lawford & Eyre (1955) at a similar Reynolds number.

Figure 4 also shows the base pressure distribution across the 8 in. square plate in turbulent flow, at a position where (u")i/U = 0.083 and Lx/D = 0.375 ( D is plate width), and it can be seen that there was a marked decrease in base pressure suggesting an increase in drag. Base pressure coefficients measured in turbulent flow, for a,ll the plates, are shown in figure 5 plotted against the distance from the grid xlM. For each plate size, a t a given position, there was no variation of -(C,), with Reynolds number. The smaller plates had the higher values of - (C,), and these values varied little with distance from the grid. In turbulent flow, pressure coefficients were formed using the time mean values of free stream static pressure and velocity.

3.3. Discussion of mean base pressure results

A t these Reynolds numbers, in smooth flow, transition in the free shear layer springing from a plate occurs very soon after separation and the resulting turbulent shear layer rapidly entrains fluid from the base cavity formed by the

0.5.

0.4.

D

A

0.3 h

2 I

0.2

0.1

0.5 o'6 [

- -

" " ,. " .. ..

.+ Sting I

I 1 I I I

?D------l

- - - + -

-

0

8- v=

B =B

=51 P --+

e 0- -0 0 4

-.-.-. -.-.-.-.-.-.-.-.-.-.-.- .-.-. -.-.-.-.-.-.-.-.-.- I

'0 8 9 10 11 12 13 14 15 16 17

xjM distance from the grid

FIGURE 5. Base pressure measurements on flat plates in turbulent flow. Reynolds number range 0 . 4 8 ~ 106to 2 . 1 4 ~ los. a, 2in.x 2in.; 0, 3in. x 3in.; +, 4in. x 4in.; x , 6in. x 6in.; 0, gin. x gin.; A, 4in. dia.; v, Tin. dia.; -.-.-. , smooth flow results.

184 P. W . Bearman

flow. Explorations with a hot wire suggested that, in turbulent flow, the shear layer leaving the plate was laminar but that transition occurred at about the same distance downstream. Transition occurred very abruptly and was marked by a burst of turbulence of a much higher frequency content than that of the surrounding ambient turbulent flow. It is argued that the principal effect of the external turbulent flow is the extra entrainment of fluid out of the wake.

The rate mat which turbulence can entrain fluid from an adjoining undisturbed fluid is set by the scale and intensity of its energy-containing eddies. The scale of these energy-containing eddies is related to the integral scale Lr. Thus

and

Since the effect of turbulence Reynolds number is expected to be small, the turbulent entrainment rate is proportional to pLx2(2)6. It is now assumed that equation (1) also approximately describes the extra entrainment process in the near wake of the flat plates. In turbulent flow the base pressure p b - p can be described by

so that

Base pressure has been found to be independent of Reynolds number and, therefore, using the result of (1)

The base pressure coefficient is shown plotted against the turbulence parameter [(u2)4/U] Lx2/A, where A is plate area, in figure 6 . It is interesting to note that even quite small values of [(G)*/U] Lx2/A give substantial departures from the so-called smooth air value. In the smooth flow, for the 2 in. plate [(uzF/U] Lz2/A was approximately 5 x

It cannot be expected that, as Lx2/A becomes very large, -(CI,)b will also become very large. When the size of the energy containing eddies becomes much larger than the size of the body, their main effect will no longer be to mix with thc wake flow but to cause an effect similar to that of a slowly varying mean velocity. Under such conditions the drag in turbulent flow C,, is related to the turbulence intensity by

-

where C, is the drag coefficient measured in smooth flow. Therefore the relahion- ship in (3) will only apply where Lx is less than, or of the same order as, the size of the largest eddies in the wake. In the experiments reported here ( u " ) S / U was less than 0-1 and therefore the maximum increase in drag, due to this rectification effect, would not be greater than 1 yo. Figure 5 shows that, for each plate size, the

Forces on plates in a tuybulent flow 185

base pressure coefficient was sensibly independent of distance from the grid. Equation (3) suggests? therefore? that the turbulence parameter

[(u2)/uq (Lx/M)2

is also independent of distance from the grid and the measurements confirm this.

" 0.0 I 0.02. 0.04 0.06 0.1 0.4 0.6 1

- (u2$ L.r2

Turbulence parameter - - U A

FIGURE 6. Base pressure coefficients in turbulent. flow @, 2 in. x 2 in.; 0, 3 in. x 3 in.; + ,4in.x4in. ; x , Gin.xGin.;O, 8in.x8in.; A,4in.dia.; ~ , 7 i n . d i a .

3.4. Measurement of mean drag

When mounted on the drag balance the plates were positioned 10.1 mesh lengths from the grid, where (G)*/ U = 0.083, and it was only possible to investigate the effect of scale on mean drag. Drag coefficients were calculated from values of the drag force integrated over a suitable time period. Corrections were made to allow for the effects of any temperature drift during this period and for the effect of wind-tunnel blockage. The corrected values of mean drag ceofficient are shown in table 1 for both smooth and turbulent flows. The accuracy of the results is thought to be no better than about _+ 3 yo and the inaccuracy is reflected in the scatter of the C' values measured in smooth flow. Nevertheless, it can be clearly seen that, in turbulent flow, C, varied in the same manner as - (C,),. On a flat plate, in smooth flow, only just over 30 % of the drag results from the low pressure on the rear face. In turbulent flow it is to be expected that the front face pressure distribution will only be slightly modified and therefore, although in some cases (C,), changed by as much as 30 yo, the mean drag coefficient only varied by about 10%.

186 P. W. Bearman

3.5. Measurement of jiuctuating drag The fluctuating drag component of the square plates (of side 2, 4, 6 and Sin.) was measured over a range of Reynolds number. The power spectral density estimates of all the drag signals are plotted together in figure 7. This graph shows the power spectral density estimate of the fluctuating drag coefficient P(C,) (n)

lo-* lo - i

nD/U

10-3 10

FIUURE 7. Spectra of the unsteady component of drag of flat plates in turbulent flow (Lx = 3 in., ( d ) * / U = 0.083). x , 2 in. x 2 in., R = 0.69 x lo6; + , R = 0-98 x 106;LxlD = 1.5. 0, 4in. x 4in., R = 0-70 x lo6; @, R = 1.39 x loK; L x l D = 0.75. A, 6in. x 6in., R = 1-04 x 106; v, R = 2.08 x lo6; L x / D = 0.50. 0, Sin. x 8in., R = 0.88 x lo6; 0, R = 1-96 x lo5; LxID = 0.375.

at frequency n, plotted as the non-dimensional quantity U3'(CD) (n)/D against the non-dimensional frequency parameter nD/ U. All measurements were made at the test position where ( 2 ) 4 / U = 0.083 and Lx = 3 in. (7.6 cm). For each plate size the results show little dependence on the Reynolds number. The measurements illustrate the importance of the parameter Lx/D, the ratio of the integral scale of the turbulence to the size of the plate.

Since

0.04

Forces on plates in a turbulent $ow

- Smoothflow X-

-+-A

187

where C,,,. is the root-mean-square value of the coefficient of the fluctuating component of drag, it is clear that the smallest plate has the largest mean-square drag coefficient. This is primarily because, on the smaller plates, the correlation areas of the energy-containing eddies of the turbulence are comparatively larger.

" 0.01 0.02 0.04 0.06 0.08 0.1 0.2 0.4

1 /DZ ( i n . ) - Z

FIGURE 8. R.m.s. of drag coefficient fluctuations of flat plates in smooth and turbulent flow. x , 2in. x 2in.; 0, 4in. x 4in.; A , 6in. x 6in.; +, 8in. x 8in.

There are two possible length scales that could be used to non-dimensionalize the results shown in figure 7 , plate size or turbulence scale. The data are shown non- dimensionalieed by plate dimension D and in this case the variation of the parameter LxlD can equally well be thought of as being due to a plate of fixed size in a turbulent stream of fixed intensity and varying scale. Increasing the scale of turbulence, while the intensity remains constant, will have the effect of increasing the power spectral density a t long wavelengths and decreasing the power spectral density a t short wavelengths. This effect is manifest in the spread of results for the various values of Lx /D (shown in figure 7 ) a t low values of nD/ U. If the results had been non-dimensionalized by L x instead of D there would have been a much closer collapse of the data at long wavelengths and a spread at shorter wavelengths. Ther.m.s. values of fluctuating drag coefficient are shown in figure 8 plotted against 1/D2. It can be expected that the fluctuating drag will be a function of both (uz)*/U and Lx /D and, since ( s ) / U and L x were constant in this experiment, it seemed most appropriate to plot drag against the inverse of the plate area.

An interesting feature of the spectra in figure 7 is the collapse of the data on to a single curve a t high values of nD/U. Since the data are non-dimensionalized by plate dimension it suggests that, at these values of nD/U, the drag is not directly related to the approaching turbulence spectrum but is, perhaps related to wake-induced pressure fluctuations on the rear face. In order to obtain some

188 P. W . Bearman

ideas on the contribution from the rear face the fluctuating drag was measured on the plates in smooth flow. The power spectral density estimates of fluctuating drag coefficient in smooth flow are plotted in figure 9. The r.m.s. values were very

A n A

I A D A 0 A 0

I 0

D ~

10-3 1 0 - 2 10-1

nD/U 1 10

FIGURE 9. Spectra of the unsteady component of drag of flat plates in smooth flow. x , 2in. x 2in., R = lo6, U = 93*6ft/sec; 0, 4in. x 4in., R = 1.37 x lo6, U = 64.2ftlsec; A, Gin. x 6 in., R = 2.06 x lo6, U = 64*4ft/sec; 0, Sin. x Sin., R = 1.95 x lo6, u = 45.7 ft/sec.

small (about 0.02) and are plotted in figure 8. With this very low level of fluctuating drag signal the 1.111.5. noise to signal ratio of the balance and recording system rose to about 0.1.

The spectra show similar features to those measured in turbulent flow with a spread of the results for different plate sizes at low values of no/ U and an approximate collapse at high values. Fluctuations in drag can be caused by self-induced pressure fluctuations in the wake, tunnel turbulence and tunnel noise. The plates are not expected to experience significant drag fluctuations caused by the acoustic pressure fluctuations of the tunnel noise since the wavelengths of this noise, at these low frequencies, will be very long. The velocity fluctuations associated

Forces on plates in a turbulent flow 189

with these sound waves, which are measured as part of the tunnel turbulence level, although small, will be correlated over a large area and could induce a small force on the plates. The rest of the tunnel turbulence will probably be of smaller scale and mostly emanate from the fan and honeycomb (there were no screens in the tunnel). The turbulence level varies with wind speed and the results shown in figure 9 were measured a t a variety of wind speeds. This is thought to be the reason why, at low values of nDIU, UP((?,) ( n ) / D does not show as consistent a variation with plate size as that found in turbulent flow. The r.m.s. values of the drag coefficient in smooth flow, presented in figure 8, show a trend towards higher values a t smaller plate sizes. This suggests that a proportion of the fluctuating drag was produced by tunnel turbulence. At higher values of nDIU, however, there is a rough collapse of the data and a rapid fall off in power spectral density. At these higher values of nD/U the fluctuations in drag must be mostly self- induced in the sense that they origina,te from the unsteady motion within the near wake of the plates. The most important result of the smooth flow experiments was the discovery that the rate of fall off of the spectra at high values of nD/ U was exactly the same as that found in turbulent flow. The level of the spectra in smooth flow, however, was nearly three orders of magnitude down at the same value of nDIU.

3.6. Discussion of Jluctuating drag results Before discussing the effect of turbulence on fluctuating drag the simpler case of the drag of a body in a stream of varying longitudinal velocity will be considered. Equation ( 5 ) , which has been suggested by several authors including Bearman (1969), shows the relationship between the power spectral density of the fluctuating component of the drag coefficient and the power spectral density of the velocity of the approaching unsteady flow.

where C, is the coefficient of virtual mass. This equation shows the increasing importance of the virtual mass contributions as the frequency parameter nDIU is increased.

The use of equation ( 5 ) is limited by the fact that very little information exists on the value of C;, for bluff bodies with large separated wakes. Also CD and C, may be frequency dependent or may depend in some way on the complete spectrum of the approaching flow. In turbulent flow equation (5) will be modified in some wa,y by the extent of the spatial correlation of the fluctuating velocity. Davenport (1961) argues that, in turbulent flow, there will still be a linear relationship between drag fluctuations and the incident velocity fluctuations. He has termed the function X 2 ( n ) aerodynamic admittance where

I n the simple unsteady flow

and at small values of nD/ U , aerodynamic admittance will approach unity.

190 P. W. Bearman

Wardlaw & Davenport (1964) and Vickery (1965) have measured the aerodynamic admittance of flat plates in turbulent flow. Following these authors, figure 10 shows Xz(n ) plotted against nDfU for the four sizes of square plate examined in this investigation. The value of C, used in the calculation of X 2 ( n )

10-3 10-2 10-

nD/ U

A- \% \ \ \

\ \

\ L

FIGVRE 10.Aerodynamicadmittanceofflatplates. x , 2 h . x 2in.,Lx/D = 1-5;0,4in. x 4in. LxID = 0.75; A,6in. x 6in., LxlD = 0-50; 0, Bin. x 8in., LxlD = 0.375; -----, Vickery, LxlD = 1-05.

is that measured in turbulent flow and presented in table 1. As nDIU tends to zero, aerodynamic admittance rises to a value less than unity. The simple unsteady theory assumed an inh i t e lateral correlation length for the fluctuating velocity whereas in turbulent flow, at very long wavelengths, the correl a t' ion length will be of the same order as the integral scale. Therefore it can be argued that measured values of X2(n) will be less than unity. At high values of nD/U the aerodynamic admittance drops off a t a rate of about 14 dB/octave. Vickery (1965) suggests that at high values of nD/U the spatial correlation of the tur-

Forces on plates in a turbulent jlow 191

bulence decreases rapidly and that this will have a much stronger effect on XZ(.n) than the increase in the drag force resulting from the virtual mass contribution.

The measurements of X z ( n ) made by Vickery (1965) on a square plate in a turbulent flow of intensity 10% and with a scale approximately equal to the plate size, are also shown in figure 10 and are in agreement with the author’s results. Wardlaw & Davenport’s (1964) earlier measurements of X2(n) , however, show substantially less agreement. Perhaps the reasons for this may be found in the accuracy of the experiments. In the words of the authors, their experiments were of an exploratory character and there were certain features of the model design that could have introduced extraneous effects on the measurements.

Vickery (1965) has formulated a theory to calculate the aerodynamic admittance of a lattice plate which has individual members small compared to the correlation lengths of the velocity fluctuations of interest. The main assumptions are that the force on a member can be related directly to the local upstream velocity and that the correlation of forces is identical to the lateral correlation of upstream velocities. For a square lattice pIate Vickery finds

where F(ul, u2) ( r , n) is the normalized form of the lateral co-spectral density function of the longitudinal component of the oncoming turbulent flow. zl, y1 and x2, y2 are the co-ordinates of two points on the plate surface and

r = u.2 - + (Y2 - Y1)214

and

where Lr(n) is the lateral correlation length of the turbulence at frequency n. It has been shown by Bearman (1969) how (8) can be re-written in the simpler

Vickery further assumed that the lattice plate theory could be applied to solid plates and showed some comparisons of theory with experiment. He measured the function F(u,, u2) ( r , n) behind a grid (similar to the one used in this investigation), and fitted his results with the empirical relation

F(ul, u,) (r, n) = e-7.5(e/2n) cos 1.4.n(0/2n), (10)

e 2.nnLx 2.n 27TLx _ - where

Aerodynamic admittances have been computed, using (9) and (lo), and are presented as the full lines in figure 11, for the values of Lx/D investigated in the experiments together with the experimental results for the extreme values of LxlD. A t low values of nD/ U there is fairly close agreement with experiment when L x / D = 1.5 but for smaller values of LxjD the predicted large reduction in Xz(n)

192 P. W . Bearman

is not realized. An alternative form of the co-spectral density function, suggested by Wardlaw & Davenport (1964), is given by the equation

F(u,, u2) ( r , n) = e-8nr/U. (11)

Aerodynamic admittances, calculated using (11) are also plotted in figure 11 and show a better agreement with experiment at high values of nD/ U . Equation

1c

3 10-1

nD/U 1 10

FIGURE 11. Theoretical values of aerodynamic admittance. x , 2in. x 2in., Lx/D = 1.5; 0, Sin. x 8in., Lx/D = 0.375. -, theory using P(u,, ua) ( T , n) = e-75(@/2n) cos 1*4n(0/2n); _-- , theory using P(u,, u2) (T , n) = ecsnr'u.

(1 l), however, gives an incorrect description of isotropic turbulence, particularly at low wave-numbers. The agreement in X z ( n ) between theory and experiment at high values of nD/U, may be partly fortuitous because the measurements of power spectral density of drag at these values of nD/ U have suggested that the drag fluctuations are not directly related to the upstream velocity fluctuations.

Forces on plates in a turbulent $ow 193

3.7. Investigation into the structure of the $ow around the plates The theoretical ideas discussed in the previous section are based on the assumption that there is some correlation between the longitudinal component of the upstream fluctuating velocity and the fluctuating drag. To test this assumption a hot wire was introduced into the flow a t various distances, x, ahead of the 4 in.

Velocity leading force Force leading velocity 1 unit=6.5 x sec

FIGURE 12. Time-delayed cross-correlation between velocity and force. x , x /D = 0, x / D = 0.25; A, x /D = 0.5; 0, xID = 1.0; u = 32.6ft/sec and LxlD = 0.75.

0.125;

square plate, along the stagnation streamline. The fluctuating velocity and fluctuating drag signals were recorded simultaneously and later digitized. The cross-correlation coefficient between velocity and drag force, uCD/(u2)8 (C$)8 was computed at various time delays and the results are plotted in figure 12. At each position the maximum correlation occurred when the velocity led the drag force and, as expected, the time delay to maximum correlation increased with distance ahead of the plate. The maximum value of the correlation is shown plotted against position ahead of the plate in figure 13. As xID tends to zero the correlation will also approach zero because at the plate surface the longitudinal component of the fluctuating velocity must be zero. At x / D = 1 the correlation for the whole signal rose to the value 0.65 and, from the slope of the curve, appears to rise even higher further ahead of the plate. The high value of this correlation is surprising when it is remembered that for this plate LxlD = 0.75

_ _ _ -

13 F L M 49

194 P. W . Beurmun

and the velocity has only been measured at points on the stagnation streamline, whereas fluctuating velocities anywhere over an area of the same order as the size of the plate might affect its drag.

In addition to the unfiltered correlations, figure 13 shows maximum values of time-delayed, filtered cross-correlations for a high and a low value of the frequency parameter nD/U. At the high value there was small correlation and therefore these measurements also help to support the argument that at these values of nD/U most of the drag fluctuations are wake induced. Although at the low value of nD/U the measurements indicate a very strong correlation between drag and upstream velocity the simple linear theory of Vickery underestimates X 2 ( n ) , a t this value of Lx/D by about 50 yo.

0 0.2 0.4 0.6 1 .o

.ID FIGURE 13. Variation of the maximum time-delayed correlation between velocity and drag at various distances ahead of the plate along the mean stagnation line. 0, whole signal; A, nDjU = 5 x x , nD/U = 1.18.

In order to progress further with the understanding of the effect of turbulence on bodies the effect that the body has on the turbulence must be considered. Hunt (1970) has formulated a theory, based on turbulence rapid distortion theory, to analyze the turbulence in a flow sweeping past a body. Using the ideas of rapid distortion theory it is possible to analyze the effects of a body on the approaching turbulence and thus to obtain a clearer understanding of the mechanism that determines aerodynamic admittance. The principal assumption made in the theory is that, in the time it takes for the turbulence to be swept past the body, the changes in the mean flow around the body and the effects of its boundaries distort the turbulence far more than its own internal viscous and non-linear inertial forces. The turbulence will be distorted by stretching and twisting of the vortex line filaments as they are convected past the body. At this stage no attempt has been made to calculate the distortion of the turbulent flow

Forces on plates in a turbulent $ow 195

ahead of the plates because, when the scale of turbulence is of the same order as the size of the body, the amount of computation required is extremely large. The theoretical ideas will be used, however, to discuss qualitatively the effects of turbulence.

When the eddy sizes of the turbulence are large compared to the size of the body (Lx /D -+ a), the effect of the body on the turbulence will be similar to its effect on the mean flow. Therefore ahead of a plate, along the stagnation streamline, the uf fluctuation will decrease while the turbulence intensity based on local

1.0 I-

0.8

0.6

0.4

0.2

0

Distance ahead of plate, xiD

FIGURE 14. Stagnation line flow, LxiD = 0.75, (G)*/U = 0.083.

velocity will remain constant. As the plate is approached the uf energy will be transferred into the vf and wf components. On the other hand, as the eddy sizes become very small compared to the size of the body the dominant effect will be the stretching of the vortex lines. This gives the interesting result that, ahead of a plate, uf increases while v f and w f remains almost constant, i.e. the opposite effect to that for the large eddy sizes. When LxlD = 0 ( 1 ) there will be some combination of these effects.

In order to illustrate some of these features, further measurements along the stagnation line ahead of 4 in. plate are presented. Figure 14 shows measurements of mean velocity, and also the turbulence intensity, based on both local velocity

and free stream velocity U , plotted against x/D. The rise in (>)i/q near the plate suggests that the range of eddy sizes witrhin the turbulence was such as to produce some stretching of the vortex lines. Near the plate, around the stagnation region, very high levels of turbulence intensity were recorded and the accuracy of the hot wire must be considered to be rather low in this area.

The theory of Vickery, when applied to solid plates, assumes that the turbulence approaching each element of plate area behaves as if the body were in a stream where Lx/D = CQ. This suggests that along the stagnation streamline

13-2

196 P. W . Bearman

the power spectral density of the approaching flow F ( u ) ( T L ) ~ should decrease at all wave-numbers in such a way that

F(u) (n),/U12 = F ( u ) (n ) /U2

where F(u) (n) is the power spectral density of the fluctuating velocity far upstream. Power spectra of fluctuating velocity along the stagnation streamline

I

1 0 - 2 10-1 1

n p ft-1

FIGURE 15. Spectra of velocity fluctuations along the stagnation line. a, free stream in absence of plate.

10

at four stations ahead of the plate are shown in figure 15. F(u) ( n ) J U is shown plotted against n/U and the area under each spectrum is equal to the square of the turbulence intensity based on free stream velocity. Compared with the spectrum in the absence of the plate, the power F(u) (n )JU a t low wave-numbers shows a decrease, whereas a t higher wave-numbers there is little change. If Lx /D = co and there was no stretching of vortex lines by the mean flow the level of the spectrum a t all wave-numbers would be given by equation (12).

Forces on plates in a turbulent #ow 197

Taking as an example a value of n/U = 3 x at x/D = 0.25, where (from figure 14) q/U = 0.35, (12) gives P(u) (n), /P(u) (n) = 0.12. The measurements in figure 15, however, show F ( u ) (n)JP(u) (n) = 0.62. At high wave-numbers the effect of distortion by the mean flow is even more marked.

Returning to the theoretical values of aerodynamic admittance plotted in figure 11 it can be seen that as Lx/D decreases X 2 ( n ) becomes increasingly larger than Vickery predicts. This is perhaps in agreement with the finding that as Lx/D becomes smaller the distortion of the turbulence intensifies the longitudinal component of turbulence ahead of the body. More work is required to determine the importance of turbulence distortion and to determine whether, if LxlD is large enough, the much simpler ideas of Vickery are sufficient to predict X 2 ( n ) accurately at low values of nD/U. It is interesting to note that when LxlD = 1.5 the aerodynamic admittance values predicted by Vickery are only 20 yo too low. Another area requiring more attention is the understanding of the complex interaction between the turbulence and the wake.

4. Conclusions The time mean base pressure measured on square and circular plates in tur-

bulent flow was found to be considerably lower than that measured in smooth flow. It is suggested that the principal reason for this is that, compared to smooth flow, there is extra entrainment of fluid out of the wake resulting from the mixing of the near wake with the free stream turbulence. In support of this argument, the measurements of base pressure coefficient are shown to correlate well with the turbulence parameter [(u2)s/U] Lx2/A.

Power spectral density measurements of the fluctuating drag on square plates in turbulent flow show the importance of the scale parameter LxlD. As LxlD increases, the correlation areas of the energy containing eddies of the turbulence are comparatively larger and the root-mean-square value of the drag coefficient fluctuations increases. Correlations of the velocity signal from a hot wire, placed at various distances upstream of a plate (LxlD = 0-75), with the fluctuating drag signal confirmed that the majority of the drag fluctuations was linearly related to the velocity fluctuations in the approaching flow. This relationship between velocity and drag helps to justify, particularly at values of nD/U less than 0.1, the concept of aerodynamic admittance. In the range of values of LxlD from 1.5 to 0-375, however, the theory of Vickery, at small nDfU, was found to underestimate seriously the value of aerodynamic admittance. Measurements of the structure of the turbulence ahead of a plate suggest that this was primarily due to the significant distortion of the turbuIence by the body.

The measurements suggest a further contribution to drag fluctuations, un- correlated with upstream velocity, perhaps resulting from wake-induced pressure fluctuations on the rear face. Comparisons of drag spectra show that, a t high values of nD/U power spectral density decreases with increasing nD/U at the same rate in turbulent flow as in smooth flow. The level of the spectra in turbulent flow at the same value of nD/ U, however, are nearly three orders greater.

198 P. W. Bearman

Thanks are due to Mr G. S. Smith for the design of the drag balance. The work described in this paper, which was carried out as part of the general research programme of the National Physical Laboratory, was supported in part by the Construction Industry Research and Information Association.

R E F E R E N C E S

BEARMAN, P. W. 1969 Nut. Phys. Lab. Aero. Rep. no. 1296. DAVENPORT, A. G. 1961 Proc. Inst. Civ. Engrs 19, 449-472. FAIL, R., LAWFORD, A. & EYRE, R. C. W. 1955 Aero. Res. Coun. R . & M. no. 3078. HUNT, J. C. 12. 1970 A theory of turbulent flow over bodies. To be published. MASKELL, E. C. 1965 Aero. Res. Coun. R . & M . no. 3400. SCHUBAUEIL, G. B. & DRYDEN, H. L. 1935 NACA Rep. no. 546. VICRERY, B. J. 1965 Nat. Phys. Lab. Aero. Rep. no. 1143. WARDLAW, R. L. & DAVENPORT, A. G. 1964 Nut. Res. Coun.of Canada. Aero. Rep. LR-416.

Journal of Wind Engineering and Industrial Aerodynamics 51 (1994) 1-27 1 Elsevier

Wind loads on free-standing walls in turbulent boundary layers

C.W. Letchford a and J.D. Holmes b

a Department of Civil Engineering, The University of Queensland, Brisbane 4072, QId, Australia b Division of Building, Construction and Engineering, CSIRO, Highett 3190, Vic., Australia

(Received June 9, 1992; accepted in revised form February 8, 1993)

S u m m a r y

Pressure measurements on walls immersed in turbulent boundary layer flow from two different wind tunnel facilities are presented and compared. A variety of wall configurations, wind directions and shielding arrangements were studied. Some of this data has been incorporated into codes of practice for the design of free-standing walls. Differences in the most fundamental case, that of a wall completely spanning the wind tunnel, are attributed to differences between the two wind tunnel flow simulations over the height of the wall.

1. I n t r o d u c t i o n

Wind load is the majo r design load on impermeable f ree-s tanding walls, r ang ing from low (2 m high) garden walls and mo to rway sound bar r ie rs to pr ison walls 10 m in height . Unt i l recent ly , the force or ne t pressure coefficients given in design codes and s tandards were based on wind tunne l measurement s on normal flat plates in smooth un i form flow, in the absence of a g round plane. The presen t paper describes measuremen t s on walls car r ied out in s imula ted a tmospher ic bounda ry layer flow at Oxford Univers i ty (UK) and CSIRO (Aus- tral ia) , to provide be t t e r design informat ion . A l though these two studies were car r ied ou t independen t ly of each other , the re was some informal coord ina t ion dur ing the course of the work. Due to the s imilar i t ies be tween the two studies, it is appropr ia te to p repa re the presen t jo in t paper, summaris ing and comparing the results . Some of the resul ts of bo th s tudies have a l ready been incorpor- a ted in the Aus t r a l i an S tanda rd for Wind Loads [1], and in design da ta publ ished by E.S.D.U. I n t e rna t i ona l [2].

In Sec t ion 2 of the paper, some previous wind- tunnel studies on surface- m o u n t e d r e c t a n g u l a r p la tes and walls a re descr ibed. The expe r imen ta l

Correspondence to: C.W. Letchford, Department of Civil Engineering, The University of Queensland, Brisbane 4072, Qld., Australia.

0167-6105/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved. SSDI 0167-6105(93) E0027-V

2 C.W. Letchford, J.D. Holmes/Wind loads on free-standing walls

techniques used in the two studies for the present paper are described and compared with each other in Section 3. The results for both point pressures and area-averaged pressures are described in Section 4. Summarising the results and their application for design purposes is considered in Section 5.

2. Previous experimental work

Until the present studies, measurements of drag forces on surface-mounted plates and walls have been limited in quanti ty and scope. Good and Joubert [3] measured the mean pressures and drag on a two-dimensional wall in a smooth wall turbulent boundary layer for various ratios of plate height to boundary- layer thickness. Sakamoto and Arie [4] carried out measurements on walls of finite aspect ratio, varying between 0.5 and 10, immersed in a smooth wall turbulent boundary layer; a minimum mean drag coefficient was found for a width/height ratio of 5.

The Jensen Number, h/zo, is an alternative non-dimensional scaling parameter which represents the relationship between the wall height and the characteristics of the boundary layer flow [5,6]. Ranga Raju et al. [7] analysed measurements on two-dimensional walls of various heights in turbulent boundary layers of several different thicknesses. The ratio of wall height to boundary-layer thickness varied from less than 0.05 to greater than unity. A functional relationship between mean drag coefficient, C~, based on the friction velocity, and Jensen Number, h/zo, was presented. However, the drag coefficient based on the friction velocity, can be related to the drag coefficient, CDh, based on the mean velocity at the height of the wall, uh, for walls fully immersed in the inner region of the boundary layer in which the logarithmic law applies, by the following expression:

• k _ _ ~¢ C D -- CDh [1/k In(h/z0)/2, ( 1 )

where k is yon Karman's Constant. Holmes [8], found Eq. (1), with CDh set equal to 1.1, to be a good fit to the data

of Ranga Raju et al. and also Good and Joubert, in the range of Jensen Number from 40 to 1000. Thus, the drag coefficient when it is based on the velocity at the top of the wall, appears to be only weakly dependent on h/zo over a large range of the latter.

3. Experimental techniques

3.1. Atmospheric boundary-layer simulation The wind tunnel at Oxford University had a test section 4 m wide and 2 m

high, with a fetch length of 12 m. A coarse wooden grid at the start of the test section, followed by surface roughness, consisting of inverted plastic coffee cups, were used to simulate a turbulent atmospheric boundary layer. At a nominal geometrical scale ratio of 1/75, the flow was equivalent to full-scale

C.W. Letchford, J.D. Holmes/Wind loads on free-standing walls 3

1000

800

E E

600 ¢, J::

c c "" 400 "o ._.R

200

X

X

X

X

I Full scale /

logarithmic law Zo= 30mm - . ~

I z o = 100mm

o CSIRO

x Oxford /

T Range of " / -L wall h e l g h t J

I ~ ' ~ ° ' ~ ' x l x I I 0.2 0.4 0.6 0.8 1.0 1.2

u/uls3 or u/ulo

I I

0 1.4 1.6 1.8

70

60

50

40

30

20

10

c

:3" ~ °

.v. " 4 O1

3

Fig. 1. The mean velocity and turbulence intensity profiles from the wind tunnel at Oxford University.

flow with a roughness length of about 100 ram, representative of farmland with hedges and trees.

The boundary-layer test-section in the CSIRO wind tunnel (now dismantled) was 2 m wide and 1 m high with a usable length of 10 m. The atmospheric boundary layer was simulated in this tunnel using the barrier-roughness technique [9]. A barrier of 250 mm height was mounted at the start of the test section, and followed by surface roughness consisting of carpet. This gave a roughness length equivalent to about 30 mm in full scale, at a scaling ratio of 1/75.

The mean velocity and turbulence intensity profiles from both wind tunnels, at the positions of the respective models, are plotted in Figs. 1 and 2, respectively. The mean velocity profiles from the two wind tunnels (normalised to the mean velocity at 10 m full-scale height) are quite similar at full-scale heights between about 5 and 20 m. However, below 5 m height the Oxford mean velocities decrease less rapidly with decreasing height than those from CSIRO, and the target logarithmic law. This was probably due to the short fetch length of smooth turntable floor immediately upwind of the model positions in the Oxford tests.

The lines shown in Fig. 2 for full-scale longitudinal turbulence intensity are derived from an approximate formula previously used by Roy and Holmes [10]


1000

800

E E

600 ,Jl=

C r-,

-: 400 "0 ._c

200

x

Full scale o x (approximation to

Deaves-Harris x t equations)

CAIRO o x ~ . z o = l O O m m o 1

* O * , o r °

z o = 3 O m m ~ ~ x

T Range of ~ ~,c ~w, , h,loh. %

, I , I I 0.05 0.10 0.15 0.20 0.25 0.30

Longitudinal turbulence intensity

70

60 -n r-

50 ~

4 0 us

30 ~

2 0 3

10

Fig. 2. The mean velocity and turbulence intensity profiles from the CSIRO wind tunnel.

fitted to the detailed equations for "gale"-type winds proposed by Deaves and Harris [11]. The approximations are very close to those obtained by the Deaves-Harris equations near the ground (below 30 m), and for mean wind speeds (at 10 m height) of about 30 m/s. As shown in Fig. 2, the turbulence intensities agree quite well with the target full-scale values, over the height range of interest, for the respective roughness lengths. At an equivalent full-scale height of 10 m, the Oxford tests had a turbulence intensity of about 0.23, and in the CSIRO wind-tunnel the value was about 0.19. At 5 m full-scale the values were about 0.24 and 0.21, respectively.

The longitudinal length scales of turbulence were obtained from the longitudinal turbulence spectra. In the Oxford wind tunnel, the length scales were equivalent to about 45 and 50 m in full scale, at 5 and 10 m height, respectively. In the CSIRO tunnel, a value of about 32 m at a height of 7.5 m was achieved. These are at the lower end of the range of values quoted recently by Levitan and Mehta [12] for rural terrain with somewhat lower roughness lengths. However, it is commonly believed that this is a parameter that can be relaxed by a factor up to 2-3 for wind tunnel studies on low-rise structures.

Lateral length scales for the longitudinal turbulence component, which may be significant when considering fluctuating loads on finite widths of wall normal to the wind direction, were measured in both wind tunnels. In the Oxford tunnel, a lateral scale equivalent to about 17 m at a height of 10 m in


tO

~P (4

0

0

0

133mm wall panel

11.5 22

j •

o

o

22 11.5

0 •

0 •

0 0

• 0

0 0

67mm wall panel

Fig. 3. Model used at Oxford University.

full scale was obtained. At CSIRO, a va lue equ iva len t to 9 m at 7.5 m was obtained. These va lues are also somewhat lower t h a n those proposed for full scale (e.g., by E.S.D.U. [13]), bu t are la rge ly de te rmined by the avai lable tes t sec t ion width. The values are, however , l a rger t h a n the larges t wall panel on which f luc tua t ing loads were measured in the tests.

3.2. Wall models Model walls of two dif ferent heights , 67 mm and 133 ram, r ep resen t ing full-

scale he ights of 5 m and 10 m at a scal ing ra t io of 1/75, were used a t Oxford Univers i ty . Three i n t e r changeab le pressure- tapped panels were cons t ruc ted for each height . Each panel was fi t ted wi th fifteen pressure tappings on bo th the f ron t and r ea r faces, d is t r ibuted as shown in Fig. 3. The pressure tappings were e i the r connec ted indiv idual ly to a pressure t r ansduce r moun ted wi th in a " S c a n iva lve " pressure scann ing switch, or connec ted toge the r via an averaging manifold to enable wind pressures over finite areas, or "pane ls" , of a wall to be obtained.

A single wall panel , wi th a he igh t of 64 mm, was cons t ruc ted at CSIRO; the dimensions and pressure tap a r r a n g e m e n t are shown in Fig. 4. In this case, the model was cons t ruc ted in the form of a sandwich, wi th pressure channe ls mach ined wi th in the th ickness of the inner and ou te r layers. A to ta l of 48 pressure tappings were provided, wi th 24 located on each face. The pressure tappings were in te rna l ly manifolded in groups of six, so t h a t a rea-averaged pressures could be measu red on e ight d iscre te areas, four on each face. Po in t pressures could not be ob ta ined from this model.


lmm channels

. . . . " i: =; II I ®I

, , , ,_ . . , , , , ! ! If H II ',J i

Fig. 4. Dimensions and pressure tap arrangement of CSIRO.

For the Oxford tests described in this paper, the Jensen Numbers, h/zo, for the two wall heights were approximately 50 and 100. In the CSIRO tests, the value was 160, the larger value indicating less-rough terrain characteristics in relation to the wall, and lower turbulence intensities in the flow, as discussed previously.

3.3. Pressure measurement techniques At Oxford University, single-tube and single-stage and double-stage mani-

fold tubing networks were used to measure point and area-averaged pressures. A computer program based on the theoretical analysis of Gumley [14] was used to design the networks. Each system had a single small diameter restrictor in the final tubing stage. Details of the networks, and the computed amplitude and phase response characteristics are given elsewhere [15,16]. All the systems had near-fiat amplitude response and linear phase response up to 150 Hz. Front and rear-face pressure tappings were connected to separate Setra 237 pressure transducers mounted within Scanivalve Type D scanning switches. A low-pass filter, set at 100 Hz, was used to filter off unwanted high-frequency components in the signals caused by resonances in the tubing. Pressures from the front and back faces could be monitored separately, or the outputs from the individual transducers could be subtracted, to obtain a single output representing the pressure difference across the wall.

In the case of the CSIRO study, the eight area-averaged pressures were transmitted to eight separate Honeywell 163 pressure sensors through connecting tubing, each containing two small diameter restrictors. The frequency response of the pressure measurement system, consisting of the machined


channels within the model, the connecting plastic tubing, the restrictors and the pressure sensor, was determined experimentally, using the equipment described by Holmes and Lewis [17]. The amplitude frequency response was flat, and the phase response linear, to about 200 Hz. At the geometric scaling ratio of 1175, this is equivalent to about 10 Hz in full scale.

In both laboratories, the pressure data was sampled and processed by digital computers. In both cases, the sample period was equivalent to 10 min in full scale. At CSIRO the data was sampled at 1000 Hz, equivalent to about 50 Hz in full scale. At Oxford the sampling frequency was considerably lower at about 60 Hz, equivalent to 4 Hz in full scale. At Oxford, sixteen separate runs were obtained for each case; a t CSIRO, either four or eight runs were made and averages taken.

3.4. Definition of pressure coefficients Point pressure coefficients for local pressures on the front or rear faces of

a wall are defined conventionally, i.e., the instantaneous pressure coefficient is given by:

C _ p ( t ) - p o P-- &~7,2 ' (2)

2y~h

wherep0 is the reference static (atmospheric) pressure, and uh is the mean wind speed at the top of the wall, measured at the location of the wall without the wall in place and related to a suitable reference during testing.

The net, total or differenced pressure coefficient is a non-dimensional form of the pressure difference across the wall, defined by:

C pf(t)--pb(t) p~ = ~ , ( 3 )

2Pt~h

where pI(t) and pb(t) are the front and back face pressures, respectively. Area- averaged pressure coefficients are non-dimensional forms of the average pressure over finite areas associated with the group of tappings manifolded together, and defined for single faces and net pressures as in Eqs. (2) and (3) above.

Mean, root-mean-square fluctuating (rms), maximum and minimum values of the pressure coefficients are denoted by the symbols, -, ', ^, and v respectively. The mean wind direction was measured relative to the normal to the wall in e a c h c a s e .

Mean and root-mean-square fluctuating pressure coefficients from the two wind-tunnels were directly comparable, but the peak (maximum and minimum) pressure coefficients were obtained differently and are not directly comparable. In the CSIRO tests, the values obtained were the average maxima or minima recorded by the instrumentat ion (with a full-scale frequency response of about 10 Hz), with the average taken over four or eight separate wind-tunnel runs, each of duration equivalent to about ten minutes in full scale. At Oxford, the


pressure signals were first low-pass filtered by a digital moving-average filter (full scale averaging time of 1 s) before sampling and extracting peak values. Sixteen separate runs, each of durat ion equivalent to about ten minutes in full scale were made and a Type I extreme value distribution was fitted. The mean extreme was calculated from the mode and dispersion of the distribution in the manner proposed by Cook and Mayne [18].

At Oxford 10 repeated measurements of a typical point pressure and an area-averaged pressure were obtained to estimate the standard error in the statistical parameters. For the point pressure the standard error in the mean was 1.2%, the rms 11% and the 1 s mean extreme 5.9%. For the case of 45 tappings pneumatically averaged the standard errors were 1.0%, 7.8%, and 3.3%, respectively.

3.5. Blockage corrections Corrections derived by McKeon and Melbourne [19] were used to correct the

results in this paper for blockage. These corrections appear to be the only current ly available for bluff bodies immersed in turbulent boundary-layer flow. The method is similar to tha t of Maskell for the total net pressure, but apportions different percentage corrections for the windward and leeward face pressures. Different corrections were derived by McKeon and Melbourne for mean pressures and forces with width/height ratios varying between 0.25 and 4. For the present paper corrections applicable to a ratio of 4 were applied to all the cases studied. In the absence of any other corrections for fluctuating pressures, the same corrections were applied to rms and peak values as well as the mean values. The correction to the net pressure is:

ACpn=- 1.6 Cpn,m (S/A), (4)

where ACpn is the increment in net pressure due to blockage, C~n,m is the measured net pressure coefficient, S is the projected area of the wall normal to the flow, and A is the cross-sectional area of the wind tunnel.

The windward wall pressure correction is:

ACp= - 1.1 = Cp,, (S/A), (5)

and the leeward wall pressure correction is:

ACp= - 2 . 7 Cp,m (S/A), (6)

where Cp.m is the measured net pressure coefficient. The maximum correction to a wall pressure coefficient was about 10% (for the infinite wall).

4. Re su l t s

4.1. Point pressure measurements Point pressure measurements were obtained only at Oxford. Front, back and

differenced point pressures were obtained for a number of wall configurations


1.0

0 . 8

.c 0 . 6

N 0 . 4

0 . 2

1sac, lOmin mean extreme

, , ,

t" :i '/

, 1 . 0 2 . 0 3 . 0

Pressure dif ference coef f ic ients

h / z o : 5 0 , y l h = tm • h l z o = l O 0 y / h = ~ • y l h = 2 . 8 3

- - . o - . y / h =1.8

- - 0 - - . y l h = 0 .17

Fig. 5. Variation of point pressure differences adjacent to the free end of a wall extending from the tunnel centreline to the wind tunnel wall (semi-infinite wall) and point pressure differences for the case of the wall extending the full width of the wind tunnel (infinite wall).

and wind di rec t ions . One of the purposes for these m e a s u r e m e n t s was deter- m i n a t i o n of the cen t re of p re s su re on the wall , f rom which es t ima tes of o v e r t u r n i n g m o m e n t s could be made.

F igu re 5 shows the v a r i a t i o n of po in t p ressure d i f ferences ad j acen t to the free end of a wal l ex t end ing f rom the tunne l cen t re l ine to the wind tunne l wall. Also shown for c o m p a r i s o n are po in t p ressure d i f ferences for the case of the wal l ex tend ing the full wid th of the wind tunnel . The fo rmer case is r e fe r red to as the semi-infini te wal l and the l a t t e r the inf ini te wall. The wind flow is n o r m a l to the wal l and the mean , rms and 1 s m e a n ex t r emes h a v e been co r rec t ed for b loc kage acco rd ing to Sec t ion 3.5. Resu l t s a re shown for h/zo = 50 and 100 for the inf ini te wal l case.

A p a r t f rom ve ry close to the free end (y/h-= 0.17) the m e a n p ressure d i f ference d i s t r ibu t ions a re r e a s o n a b l y un i fo rm wi th height , i nd ica t ing a cen t re of pressure jus t be low wal l m idhe igh t (---0.49h). The m e a n p res su re d i f ferences r e a c h a m a x i m u m a r o u n d y / h = 1.5, whi le a t a d i s tance of 3h f rom the free end the m e a n p res su re profi le is in good a g r e e m e n t wi th the inf ini te wal l case. N e a r the free end the m e a n p ressure d i f ferences r educe subs t an t i a l l y n e a r the base of the wal l leading to a shif t in the cen t re of p ressure upwards to a p p r o x i m a t e l y 0.53h. These cha r ac t e r i s t i c s a re ref lected in the enve lope of rms and ex t r eme p ressure coefficients, a l t h o u g h the ex t r emes are no t as un i fo rm wi th height , i nd ica t ing a h ighe r cen t re of p ressure for ex t r eme pressures t h a n wal l midheight . The impl i ca t ion of th is to o v e r t u r n i n g m o m e n t s on walls is cons idered in Sec t ion 4.3. For all va lues o f y /h , the l a rges t ex t r eme ne t p re s su re coefficient occurs jus t above s t a g n a t i o n a t z / h = 0.7.

E x a m i n i n g the f ron t and r e a r p ressu res separa te ly , i t was obse rved t h a t in all cases the r e a r or l eeward p res su re was p rac t i ca l l y cons t an t ove r the wal l he ight , w i th all p re s su re profi le v a r i a t i o n assoc ia ted wi th those on the front .


1.0

0.8

~= 0.6

N 0.4

0.2

- . . . . , . . , % . . .

• Good & Jouber t (3) o h l z e = 5 0 IO h l z o = 1 0 0 .,

".~** Iff

I % ' , o o ' , ' o'. oi. 0.4 1.0

C ' P / C P r o a x

Fig. 6. Infinite wall mean front pressures, normalised by the maximum mean front pressure, compared with the smooth wall results of Good and Jouber t [3].

Figure 5 also reveals tha t there was not a very good collapse of mean pressure differences for the two h/zo cases examined. The rms and mean extreme pressures did collapse well, but differences in the turbulence levels and the doubling of tapping spacing for the taller wall should have led to reduced fluctuating coefficients for the taller wall.

Infinite wall mean front pressures, normalised by the maximum mean front pressure, are compared with the smooth wall results of Good and Jouber t [3] in Fig. 6. The present results lie within the bands found by Good and Jouber t for wall height to boundary layer depth ratios ranging from 0.082 to 1.75.

4.2. Area-averaged pressure differences Data on area-averaged pressures across walls of various lengths and corner

configurations could be obtained from both the Oxford and CSIRO measurements. In some selected cases, the same configuration was tested in both wind tunnels, enabling quanti tat ive comparison to be made. In addition some effects of shielding were examined. At Oxford measurements were made on an infinitely long wall with an adjacent parallel wall present. These results are discussed in Section 4.2.4. At CSIRO, the effects of a building of rectangular planform, upwind or downwind of an infinite wall were studied. This work is described in Section 4.2.5.

4.2.1. Infinite and semi-infinite walls Mean, rms fluctuating and peak pressure coefficients were obtained from

both wind tunnels for infinite walls (i.e., completely spanning the wind tunnel floor), and for semi-infinite walls (i.e., spanning half the wind tunnel width and terminating in a free end). In the case of the infinite wall, the mean pressure difference coefficient, averaged over the wall height, is independent of the position along the wall, as there is no free end or corner. The same is t rue of the rms and peak pressure difference coefficients, although, in these cases, the values obtained depend on the length of the wall over which the area averaging

C.W. Letchford, J.D. Holmes/Wind loads on free-standing walls

Table 1

Mean pressure difference coefficients for infinite walls

11

Source h/zo S/A Wind direction Corrected Cp~

Oxford 50 0.0335 0 ° 1.27 100 0.0665 0 ° 1.38

CSIRO 160 0.064 0 ° 1.15

Oxford a 50 0.0335 45 ° 0.66 CSIRO 160 0.064 45 ° 0.68

aValue obtained by averaging point pressures.

is carried out, due to correlat ion effects. In the case of the semi-infinite wall, all the coefficients depend on both the distance from the free-end, and on the length of the area-averaging "panel".

The mean pressure difference coefficient for the infinite wall for wind directions of 0 and 45 degrees to the normal to the plane of the wall are tabulated in Table 1. These values have all been corrected for blockage, using the method described in Section 3.5.

The values obtained in the Oxford Universi ty tests for the 0 ° wind direction were noticeably higher than those found at CSIRO, and higher also than the value of 1.1 which fitted the data analysed by Ranga Raju et al. [7], as discussed in Section 2 of the present paper. One reason for this may be the less-steep velocity profile over the height of the walls produced by the less-steep velocity profile over the height of the walls produced by the smooth wind-tunnel floor immediately upwind of the walls. Although this might be expected to mainly affect the windward face pressure coefficients, the increased net pressure coefficients in the Oxford tests were largely produced by lower leeward face coefficients compared with the CSIRO tests. It should be noted that the area blockage ratios, and hence the correct ion factors, were nearly the same for the Oxford tests (Je = 100), and the CSIRO tests, so that incorrect blockage correction should not be the reason for the differences in these two cases.

Baines [20] noted lower, more negative, leeward or wake pressure coefficients on infinite walls in near uniform approach flow when compared with boundary layer flow. It may be reasoned that this is because the actual flow velocity at separation, as a proport ion of the undisturbed velocity at wall top, was greater in uniform flow with the consequence of lower wake pressures. This is consistent with the present observations, al though the conclusions drawn by Holmes [8] show this effect is apparently small for a large range of Jensen Number, as discussed in Section 2. Increased turbulence producing more entra inment from the wake in the Oxford tests, may also contribute.

The rms fluctuating pressure coefficients were closely related to longitudinal turbulence intensities in the approach flow in each case, as expected. They

12 C.W. Letchford, ,I.D. Holmes/Wind loads on free-standing walls

were also dependent on the length of wall over which the area averaging was carried out. Comparison could be made between one of the Oxford test results (h/zo = 100) and the CSIRO tests for the ratio of rms fluctuating pressure coefficient (Cp) to turbulence intensity at wall height, for a panel of length/ height equal to 1.5, for the wind direction normal to the wall (0°). The ratios were 1.17 and 1.21, respectively. At a wind direction of 45 ° to the infinite wall, only CSIRO data was available for area-averaged pressure differences. The mean pressure coefficient was 0.68, slightly greater than the value of 1.15 sin 2 45 °, (=0.58), that would be obtained by assuming that only the normal velocity component was effective in producing a normal force, and using the value of mean pressure coefficient in Table 1 for the normal wind. The rms pressure coefficient for the 45 ° case was 80% of the value for the 0 ° wind direction.

For the semi-infinite walls, the area-averaged mean pressures depend on the location of the panel from the free end, and on the length of the panel. There was reasonable agreement between the Oxford and CSIRO values for panels of length 1.5h located immediately adjacent to the free end of the wall, for the normal wind direction. The values from the Oxford tests were: 1.31 (for Je = 50), and 1.34 (for J e = 100); at CSIRO ( J e = 160) a value of 1.23 was obtained. For a wind direction equal to 45 ° to the plane of the wall and blowing on to the free end, the corresponding values of mean pressure coefficient over the length of 1.5h adjacent to the corner were 2.85 (Oxford, J e = 50), 3.06 (Oxford, J e = 100), and 2.30 (CSIRO, J e = 160). The slightly distorted mean velocity profile at Oxford may be one reason for the differences. Another reason may be the slightly denser distribution of pressure tappings for the Oxford tests.

The corresponding values for the rms pressure coefficients were: 0.44, 0.37, and 0.32 for the 0 ° wind direction, and 0.85, 0.69 and 0.61 for the oblique (45 °) wind direction. These values are for Jensen Numbers of 50, 100 (Oxford) and 160 (CSIRO), respectively. Decreasing rms pressure coefficients with increasing Jensen Number is expected due to the lower turbulence intensities over the wall height, and correlation effects due to larger wall dimensions relative to the turbulence scales.

Figures 7 and 8 give further examples of area-averaged mean and rms fluctuating pressure coefficients for various panels, for the normal (0 °) and oblique (45 ° ) wind directions, respectively. In the case of the normal wind, both pressure coefficients are relatively uniform across the wall, al though there is a slight reduction near the free end. However, for the oblique wind direction, high values of both coefficients occur for small panels near the windward free end; the magnitudes reduce with increasing distance from the free end and with increasing panel area.

4.2.2. F in i t e -w i d t h walls: Effect o f aspect ratio Measurements were made on a number of walls of finite width at both Oxford

and CSIRO. For the lower wall height at Oxford (Je = 50) widths of lh, 2h, and 3h were tested; at the larger value of h (Je = 100), widths of 0.5h, lh, and 1.5h


. . . . . (o . , ) 1 (o.,,)1 1~'3~10'41 ~ '3Sl "~" ' t '1'0"3 8 )~

L 1.5h !_ 1.5h J J e = l O 0 J e = l O 0

- t ~ ~ " 'h P - - t '" ~ - -

i , ,o.), , ,o.) , ,(o..~ , o . ) , | I I I " [ 3h ) J e = 5 0 t J e = 5 0

~= 0 °

/ I / ~ 1 . 2 S l 1 . 2 7 I

(o.39) i {(0.381

Je = 5 0 J e = 5 0

Fig. 7. Area-averaged mean and RMS fluctuating pressure coefficients for various panels for normal (0 °) wind directions.

I(o.',)!,o.,,)!co.,,)l,o.,,~! I,o.,o):(o.-)',(o.,,fi,o.-fi

I- 3h J J e = 5 0 Je = 1 6 0

,, o,),, I,o.,0,, , I,o,,,: L ~" .) Jo=so / J,,=16o

O. 9 = 4 5 0 2h 2h 1.5h 1.5h

(o.Te) I J (0.38) I (o .e , ) I ! J I 1 .

J" Je = 5 0 Je = 160

Fig. 8. Area-averaged mean and RMS fluctuating pressure coefficients for various panels for oblique (45 ° ) wind directions.

were tested. In these tests, the pressure taps comple te ly covered the wall width. In the CSIRO tests, wall widths of 1.5h, 5h, and 10h were used. The pressure- tapped sec t ion was of length 1.5h (as shown in Fig. 4), and this was inser ted at var ious posi t ions a long the longer wall for di f ferent tests.

14

4-

3


extren~ I I I o o

. . . . . . . . i . . . . . . . . 1"o . . . . . . . loo I~h

I N CS IR IO o O x l 0 r d ~ • O x l o ~ l h t ~ = , l O 0 J

Fig. 9. Mean and maximum pressure difference for the total wall for all test cases with flow normal to the wall.

mean extreme ] o -o" -~'....~-r

- ~ - - - ] ..~,. o _ o ,Q- - i - .= - - o - - - ~ . _ . i r . . . . .

- - ' ' - - - - '4

. . . . . . . . i . . . . . . . . I '0 . . . . . . . : I00

I M ~ R O o OxfoaJtct~ •

Fig. 10. Net pressure coefficients for an oblique (45 °) wind direction.

F i g u r e 9 s h o w s t h e m e a n a n d m a x i m u m p r e s s u r e d i f f e r e n c e for t h e total w a l l for a l l t h e t e s t c a s e s w i t h f low n o r m a l to t h e wa l l . E x t r e m e d a t a is o n l y a v a i l a b l e for b/h e q u a l to 1.5 in t h e C S I R O t e s t s , a s i n s t a n t a n e o u s p r e s s u r e d i f f e r e n c e m e a s u r e m e n t s w e r e o n l y a v a i l a b l e for t h i s case . H o w e v e r , fo r t h e l o n g e r wa l l s , m e a n p r e s s u r e s c o u l d be o b t a i n e d b y a v e r a g i n g t h e m e a n v a l u e s


Je =100 Je =100

15

Je =160 Je =160 Je =100

(o.,5) j(o.47) I (o.47) I Je : 50 Je = 50

b /h=2

[ 122 I ~ b/h=3 I 1"20 I 1"28 I 1"20 I ,o. . , e= oo i,o.,,, j ,o.,,, I ,o. , , I

Je = 50 Je = 50

Fig. 11. Mean and RMS net pressure coefficients for sections of finite walls for the wind direction normal to the wall.

obtained separately for 1.5h long sections of the walls. The individual values obtained for these sections were previously given by Holmes [8].

The CSIRO values invariably fall slightly below the Oxford values, probably for the same reasons given previously for the infinite and semi-infinite walls (Section 4.2.1). The mean pressure coefficients clearly show a decrease as b/h increases to about 5. The apparent minimum value for a value of b/h of about 5 was discussed previously by Sakamoto and Arie [4] and Holmes [8]. The maximum values also show a reduction as b/h increases from 0.5 to 5. This can be explained by reduced correlat ion as well as aerodynamic effects.

Net pressure coefficients are shown for an oblique wind direction (45 ° ) in Fig. 10. Again only mean pressure coefficients are available for values of width/height of 5 or greater. For this wind direction, there appears to be a maximum at a value of b/h of around 3. From the Oxford test results the maximum pressure coefficients increase with increasing width, no doubt due to stronger wake pressure fluctuations at the windward end.

Mean and rms net pressure coefficients for sections of finite walls are shown in Figs. 11 and 12 for the wind direction normal to the wall, and in Figs. 13 and 14 for the oblique wind direction. For the normal wind direction, both the mean and rms values do not vary greatly with horizontal position along the wall, a l though for the longer walls, the values tend to be somewhat higher near the ends than in the middle (Fig. 12), as previously observed for semi-infinite walls.

16 C.W. Letchford, J.D. Holmes[ Wind loads on free-standing walls

b/h = 5

(o1.17 I , . , , ' ' 10e l I .42)L(0.42)1 I(o.=s)l S y m m e t r i c a l l I-o:~7 I T .~- I l -o~ i - i

J(o.34) I (o.se) I ](o.ss) I

Je - 1 6 0

b l h =10

t:,,,..,,.,o,,.,,,,.,,, ,,.., I .411 j.(0.401J (O.S?).J. 10.3611 (0.3all ~ (O.S41 ~ ~'.0~" j T.I~ 1" ~'.~ I T.O~ "~ ~'.1~" ! ~O~ 'J S y m m e t r i c a l o.s=); ( o . , ) i (o., , ) i (o.=o) l(o.2°) i I (o.28) I

Ja = 1 8 0

t 0 = 0 °

Fig. 12. Mean and RMS net pressure coefficients for sections of finite walls for the wind direction normal to the wall.

~ b /h = 1

Je = 1 O0 Je = 1 O0

Je = 1 6 0 Je = 1 6 0 Je= 100

1.21

(0.49)

Je = 5 0

1.32

(0.46)

Je = 50

1.55 I I 0.66

1o.651 (o.391

J e = 5 0

J e = 4 5 °

b /h = 2

b / h = 3 1.67 == 1.a6 I 0 .74

(0.67) (0.57) J (0.31)

Je = 50

Fig. 13. Mean and RMS net pressure coefficients for sections of finite walls for the oblique wind direction.

The oblique wind direct ion produces large mean and f luctuat ing net pressures on wall sect ions ad jacent to the windward free end. This effect is amplified as the wid th /he ight ra t io increases, wi th mean net pressure coefficients ap- p roach ing three for the longest walls. This phenomenon, which also occurs on

0 = 4 5 ° /


b l h - - 5

f~.2.28 : 1.80 I I 1 .22 I 0 .88 ; I 8 .86 I 8 .47 .72)~(8.,8) I 1(0.37)1(o.20) 1(o.20)1(o.21)i

.e2) (o.ee) I ;(0.24)i(8.22) ] [(0.22)i(0.17) I J e m 1 6 0

17

b l h = 10

~_(~02.86 ~ 2.31 i 1.60 i 1.17 0 .87 w 0.7'8 i 0 7 2 " i 0 .04 i O.OO I 0 .60 8.81 I 0 .88 | -88)1 (0 .83 ) ! ( 0 .44 ) I (0 .3~ , ) ! (0 .31) I ! (8 .20 )~ (0~28) ~ ; (0 .22 )~ (0 .24 ) 1 (0 .22 ) : ( 0 .22 ) 1(0.18) I

,8)1(o.1);(o,o);,o,,);(o2,); ;co-)its, ,); ;co-);(8.2,)[(o,o);~o,s):co1,) I J e - 1 6 0

Fig. 14. M e a n and RMS ne t p ressure coefficients for sec t ions of f inite walls for t he obl ique wind di rect ion.

I

v~nd dm~ion

i - N - C~RK) " 4 - O~lkxdhtzo-100 I

Fig. 15. V a r i a t i o n s in m e a n and m a x i m u m ne t wal l p ressure coefficients wi th wind d i rec t ion for a wal l w i th a w i d t h / h e i g h t r a t io of 1.5.

semi-infini te wal ls (Sect ion 4.2.1), has on ly r ecen t ly been a c c o u n t e d for in design codes and s t anda rds [1]. The m e a n and rms pressures decrease p rogress ive ly in m a g n i t u d e as the d i s t ance away f rom the w indward end increases .

The v a r i a t i o n s in m e a n and m a x i m u m net wal l p re s su re coefficients wi th wind d i rec t ion are shown for a wal l wi th a w id th /he igh t r a t io of 1.5 in Fig. 15. A wind d i rec t ion of 30 ° p roduces a s l ight ly h igher m a x i m u m net p ressure t h a n the 0 ° or 45 ° cases. I t should also be no ted t h a t the 90 ° wind direct ion, i.e., pa ra l l e l to the wall , p roduces a non-zero m a x i m u m load due to the f luc tua t ing componen t .


4.2.3. Effect of corners Free-s tand ing walls will genera l ly i nco rpo ra t e changes in d i rec t ion and,

consequent ly , tes ts to m e a s u r e wal l p ressures in the v ic in i ty of a 90 ° co rne r were u n d e r t a k e n a t Oxford and CSIRO. At Oxford, m e a n p n e u m a t i c a l l y averaged row pressures a t va r ious d is tances (y/h) f rom the co rne r for a r ange of wind d i rec t ions were m eas u red for the 67 m m high wal l (h/zo = 50). W h e r e a s the CSIRO tes ts invo lved p n e u m a t i c a l l y ave r aged panels , l/h = 1.5 ad jacen t to the corner , for the full r ange of wind direct ions.

F igure 16 shows the resu l t s for angles of a t t a c k of 0 ° and 180 °. Also shown in the f igure a re the resu l t s of the semi-infini te wal l for flow no rma l to the wall. The s i t ua t ion of l a rge y /h is r ep re sen ted by the infini te wall. The p resence of a wal l p ro jec t ing u p s t r e a m (180 °) c lea r ly inc reases the ne t load on the wal l in the v ic in i ty of the corner . Sepa ra t e f ron t and back pressure m e a s u r e m e n t s r evea l t h a t the inc rease der ives p r edomina t e ly f rom a lower r e a r or wake pressure , wi th the f ront p ressure h igher only immedia t e ly ad jacen t to the co rne r where the flow is cons t r a ined to flow over the top of the wall.

F igure 17 shows the resu l t s for angles of a t t a c k of 45 ° and 225 ° , t h a t is, wi th the co rne r po in t ing u p s t r e a m and d o w n s t r e a m respect ive ly . Also shown in the figure a re resu l t s for the semi-infini te wal l a t 45 ° and 225 ° , whi le la rge y /h is r ep resen ted by the infini te wal l a t 45 °. The p resence of the co rne r enhances the spa t i a l ex ten t of the vo r t ex formed behind the wal l for the 45 ° case when com pared to the semi-infinite wal l or free end case. So a l t hough the ne t p ressure is g r ea t e r immedia t e ly ad jacen t to the free end, a w a y f rom the co rne r the net p ressures are g r e a t e r t h a n those n e a r a free end. Once aga in this d i f ference ar ises p r e d o m i n a t e l y f rom a l a rge r suc t ion on the back

2

1.5 ~ _

I

0.5 ! T >Y

o

1 . . . . . . . . i . . . . . . . . 1"0 . . . . . . . t

Fig. 16. Results for angles of attack of 0 ° and 180 ° and of the semi-infinite wall for flow normal to the wall.


4,

y~

Fig. 17. Results for angles of attack of 45 ° and 225 ° and the results for the semi-infinite wall at 45 ° and 225 ° .

-1

-2

I : h = r - - - 1

D

4~5 90 1~15 11~0 225 2"70 3i5 360 w~ld ekl~lk~

i '-u'-CSIRO o C K k ) n : I ~ • Q d 0 r d ~ 1 0 0 I

Fig. 18. CSIRO results for mean net pressure on a panel, l/h = 1.5, adjacent to the corner for the complete range of wind directions.

of t he wal l . S u r p r i s i n g l y , for flow a p p r o a c h i n g a t 225 ° , i.e. c o r n e r p o i n t i n g d o w n s t r e a m , t he n e t p r e s s u r e s a d j a c e n t to t he c o r n e r a re v e r y s i m i l a r to t he i n f i n i t e wa l l v a l u e .

F i g u r e 18 shows t he CSIRO r e s u l t s for m e a n n e t p r e s s u r e s o n a pane l , l /h = 1.5, a d j a c e n t to t he c o r n e r for t he c o m p l e t e r a n g e of w i n d d i r e c t i o n s . I n t h i s i n s t a n c e t he n e t p r e s s u r e coeff ic ient is de f ined p o s i t i v e for p r e s s u r e s a c t i n g


I

O-

-1"

~w~ - - ' ~ h I

F N N ~ J L I

.io 1'0 ~0 30 a~

Fig. 19. Effects of shelter.

towards the corner as shown on the figure. Only two Oxford resul ts are comparable and are somewhat g rea te r t han the CSIRO results. The more extens ive tapping d is t r ibut ion and the dif ference in mean veloci ty profiles in the Oxford model may be the reason for this discrepancy.

4.2.4. Two parallel walls Walls and fences in u rban areas are of ten cons t ruc ted ad jacent to o the r

s t ruc tu res which will p roduce considerable in te r fe rence to the flow, modifying the mean and f luc tua t ing loads on the wall. Two simple cases of in t e r fe rence effects were studied. At Oxford, the shielding of a para l le l wall was investigated while at CSIRO, shielding by an ad jacent bui lding was examined.

Two paral le l walls spanning the wind tunne l were set up for flow normal to the walls. The net pressure coefficient for a pneumat ica l ly averaged ver t ica l row of five tappings was measured on one wall as the o the r wall was trans- gressed from 30h ups t ream to 20h downst ream. Figure 19 shows tha t the effects of shel ter are s ignif icant when the ups t ream wall is closer t h an 30h and tha t the d i rec t ion of wind loading is reversed at spacings less t h an 5h. The wall spacing which minimised the combined wind loading on the pair of walls was approx imate ly 2h, but a t this spacing the ups t ream wall ne t pressure coefficient was some 15% grea te r t han the isolated wall case.

Bai ley and Vincen t [21] s imula t ing only mean ve loc i ty profiles observed tha t the windward wall pressures on a typica l model house (h: b : d = 1 : 2: 4) were at a minimum when shielded by an ident ica l house at a spacing of approximate ly twice the eaves height .

4.2.5. Effect of an adjacent bui ld ing Enclosed buildings will cause s ignif icant in te r fe rence to the flow over walls

and fences. A few simple cases of the effect of an ad jacen t bui lding on the


b l h --~ ~

; J - 2 6 . 0 I I

21

FI4.2F3e.~ i \

L t

Instrumented / / section

•

I I . w e l l h e i g h t

.I 3.2 well heights

Fig. 20. Effect of an adjacent building on the pressures recorded on a section of an infinite wall.

pressures recorded on a section of an infinite wall were investigated at CSIRO, and some of the results are presented in Figs. 20 to 24.

These figures show the percentage change in mean net wall panel pressure resulting from the presence of the building. An upwind building, whether located centrally upwind of the instrumented wall section, or in a half overlap position, produces lower mean pressures, with the exception of the most exposed quarter panel for the oblique wind direction (Fig. 21).

The presence of a building downwind of the wall (Figs. 23 and 24), produces much smaller effects. However, on the upper part of the wall there is an increase in net mean pressure produced by the building. This is produced by an increase in suction on the leeward side of the wall and is a similar effect to that noted for parallel walls noted in Section 4.2.4. above.

The changes in fluctuating pressures produced by the adjacent building are generally similar to the changes in mean pressures.

4.3. Base moment measurements Free-standing walls will ult imately resist loading by moment action about

the base. To examine the assumption that the force or pressure difference coefficient acting at the wall midheight adequately described the base moment, experiments were conducted at Oxford to measure the base moment directly.

22 C.W. Letchford, J.D. Holmes] Wind loads on free-standing walls

b/h --~ oo

-,s., [, /

1-14.01-62.81

I 1. wall heights

Instrumented ~ . sect ion

,7 3.2 wall heights

Fig. 21. Effect of an adjacent upwind building on the pressures recorded on a section of an infinite wall.

Th ree addi t iona l pane ls were cons t ruc t ed wi th a non-un i fo rm t app ing distri- but ion. F ive t app ings in a ve r t i ca l row were loca ted so t h a t the t r i b u t a r y a r ea assoc ia ted wi th each t app ing mul t ip l ied by the lever a rm abou t the base was a cons tan t . P n e u m a t i c a l l y a v e r a g i n g these pa rabo l i ca l ly d i s t r ibu ted taps yielded a con t inuous record of the f luc tua t ing m o m e n t on the wall f rom which mean , rms and m e a n ex t reme coefficients were obta ined . F u r t h e r de ta i l s m a y be found in Refs. [16,22]. The m o m e n t coefficient was defined as;

M Cm = ½ p ~ lh 2 , (7)

where M / l h 2 was p ropo r t i ona l to the ou t pu t of the non-un i fo rm p n e u m a t i c a v e r a g e r and l is the l eng th of wal l p n e u m a t i c a l l y averaged .

F igure 25 shows the regress ion of m eas u red m e a n ex t reme m o m e n t coefficients aga ins t predic ted m e a n ex t reme force coefficients ac t ing a t wal l midheight . The resu l t s a re for t h ree di f ferent pane l l eng ths ( l / h = 1 , 2 , 3 ) a t loca t ions p rev ious ly found to exper ience the h ighes t ne t pressures . As can be seen the re is genera l ly exce l len t a g r e e m e n t thus jus t i fy ing the a s sumpt ion of wal l midhe igh t as the loca t ion of the cen t re of p ressure for even ex t reme moments . S imi la r ly good regress ion resu l t s were ob ta ined for mean and rms coefficients.


bib --*

-74.5; 1 1

23

, i ,

1 - 4 2 . 5 1 - 9 8 . 6 1 i i

t L

Instrumented f . section

I I .wall height

3.2 wall heights 7

Fig. 22. Effect of a building on the pressures recorded on a section of an infinite wall.

5. D i scuss ion and conc lus ions

Wind loads on free standing walls are important because of their poor performance under wind loading. For example, falling walls in wind storms have been responsible for approximately one death per year on average in the United Kingdom [23]. In addition, extensive use is being made of walls as sound barriers on urban motorways and railways to improve the quality of the built environment. Walls are going up, not coming down!

The results of two wind tunnel studies on free standing walls of various aspect ratios, end effects and shielding arrangements have been described. Comparison between measurements at CSIRO and Oxford shows reasonable agreement. The Oxford net mean and rms pressure coefficients were somewhat larger than those at CSIRO, whereas mean extremes were approximately the same. The difference in mean values is most likely associated with the differences in mean velocity profile over the wall height, which was fuller in the Oxford simulation. Similar arguments can be used for rms coefficient discrepancies as well as the increased turbulence levels and denser tapping distribution employed at Oxford. The inconsistency in extreme values is most likely due to the moving average filter applied to the Oxford extremes. These differences highlight the importance of modelling the boundary layer in the near wall region for low rise structures.


1. wall height z

b/h,-* oo

3.2 wall heights =i

J 3.2 wall heights

Instrumented / section

+ 0.8

! -z'] /

1" Fig. 23. Effect of a building downwind of the wall on the pressures recorded on a section of an infinite wall.

The largest mean and extreme pressure coefficients were obtained near the windward free end for oblique wind directions. Even when a corner was added wind loads were larger than those previously specified for design. Extreme base moments calculated from extreme area-averaged pressures assumed to act at wall midheight were seen to be in good agreement with those obtained directly.

The effects of shielding were noted when a parallel wall was within 30h and at a spacing of 5h the load on the downstream wall was reversed. A spacing of 2h minimised the combined loading on the pair of walls. Somewhat similar shielding effects were noted with the presence of a building.

These two extensive studies have indicated that even for this relatively simple s tructure the wind loads are complex functions of panel size, panel location relative to free end or corner, shielding and wind direction. Much of this data has been codified for designers [1,2].

The information provided by these studies, net pressure or force coefficients with centre of pressures, gives the designer freedom to choose the s tructural mechanism resisting the load, whether it be direct canti lever action or two way spanning panels between piers. While panel size and location have been shown to be important parameters, s t ructural design considerations mean that large panels will increasingly resist load as cantilevers and a practical panel size


1. wall height]

b l h --. oo

3.2 wall he igh ts

1

l h e i g h t s

I ns t r umen ted / , . s e c t i o n

i !'"' i /

, . 5 . 6 ; . 9 . 0 I

I " , " |

Fig. 24. Effect of a bui lding downwind of the wall on the pressures recorded on a section of an infinite wall.

4

3,

1'

°o ~ ~

i .. Iniin#ee-C) e Sen~rdlr~0-0 u SemHrdin~e,,4S " ~ m e r e - 1 8 0 N ~mer0.4S • FinifBe-0

Fig. 25. Regression of measured mean extreme moment coefficients against predicted mean extreme force coefficients act ing at wall midheight.


l i m i t w o u l d be l /h= 3. T h i s w a s t h e l a r g e s t p a n e l s ize i n v e s t i g a t e d he re . I n a d d i t i o n , fo r s o m e c o n s t r u c t i o n m a t e r i a l s , e.g. m a s o n r y , p a n e l l e n g t h s wi l l be d i c t a t e d by s e r v i c e a b i l i t y r e q u i r e m e n t s a s s o c i a t e d w i t h t h e r m a l e f fec t s o r g r o u n d m o v e m e n t s .

Acknowledgements

T h e a s s i s t a n c e o f Dr . C.J . W o o d a n d R.E. B e l c h e r d u r i n g t h e s t u d i e s a t Oxford , a n d o f R.V. C r o w l e a n d R.E. L e w i s fo r t h e C S I R O w o r k , is a c k n o w - l e d g e d b y t h e a u t h o r s .

References

[1] Standards Association of Australia, SAA Loading Code, Part 2: Wind Forces, ASl170 Part 2, 1989.

[2] ESDU International, Boundary walls, fences and hoardings: mean and peak wind loads and overturning moments, Data Item 89050, ESDU International, London, 1989.

[3] M.C. Good and P.N. Joubert, The form drag of two-dimensional bluff plates immersed in turbulent boundary layers, J. Fluid Mech., 31 (1989) 547-582.

[4] H. Sakamoto and M. Arie, Flow around a normal plate of finite width immersed in a turbulent boundary layer, J. Fluids Eng., ASME, 105 (1983) 98-104.

[5] M. Jensen, The model-law for phenomena in natural wind, Ingenioren, 2 (1958) 121-128. [6] N.J. Cook, Jensen Number: A proposal, letter to the editor, J. Wind Eng. Ind. Aerodyn.,

22 (1986) 95-96. [7] K.G. Ranga Raju, J. Loeser and E.J. Plate, Velocity profiles and fence drag, for

a turbulent boundary layer along smooth and rough flat plates, J. Fluids Mech. 76 (1976) 383-399.

[8] J.D. Holmes, Pressure and drag on surface-mounted rectangular plates and walls, Proc. 9th Australasian Fluid Mechanics Conf., Auckland, N.Z., 8-12 December 1986, pp. 383-386.

[9] J.D. Holmes and C. Osonphasop, Flow behind two-dimensional barriers on a roughened ground plane, and applications for atmospheric boundary-layer modelling, Proc. 8th Australasian Fluid Mechanics Conf., Newcastle, N.S.W., 28 November-2 December 1983, pp. l l B - 13-11B 16.

[10] R.J. Roy and J.D. Holmes, The effects of scale distortion on total wind loads on a low-rise building model, J. Wind Eng. Ind. Aerodyn., 29 (1988) 273-282.

[11] D.M. Deaves and R.I. Harris, A mathematical model of the structure of strong winds, Construction Industry Research and Information Association (UK), Report 76, 1978,

[12] M.L. Levitan and K.C. Mehta, Texas Tech field experiments for wind loads, Part II: Meteorological instrumentation and terrain parameters, presented at 8th Int. Conf. on Wind Engineering, London, Ontario, Canada, 8-12 July, 1991.

[13] ESDU International, Characteristics of atmospheric turbulence near the ground, Part III: Variations in space and time for strong winds (neutral atmosphere), Data Item 86010, ESDU International, London, 1986.

[14] S.J. Gumley, A detailed design method for pneumatic tubing systems, J. Wind Eng. Ind. Aerodyn., 13 (1983) 441-452.

[15] C.W. Letchford, Wind loads on free-standing walls, University of Oxford, Department of Engineering Science, Report OUEL 1599/85, 1985.

[16] C.W. Letchford, further studies of wind loads on walls, University of Oxford, Depart- ment of Engineering Science, Report OUEL 1620/86, 1986.


[17] J.D. Holmes and R.E. Lewis, Optimization of dynamic-pressure-measurement systems, I, Single point measurements, J. Wind Eng. Ind. Aerodyn., 25 (1987) 249-273.

[18] J.R. Mayne and N.J. Cook, On design procedures for wind loading, Building Research Establishment (UK), Current Paper, CP25/78, 1978.

[19] R.J. McKeon and W.H. Melbourne, Wind-tunnel blockage effects and drag on bluff bodies in a rough wall boundary layer, Proc. 3rd Int. Conf. on Wind Effects on Buildings and Structures, Tokyo, 1971.

[20] W.D. Baines, Effects of velocity distribution on wind loads and flow patterns on buildings, Proc. 1st Int. Conf. on Wind Engineering, Teddington, 1963.

[21] A. Bailey and N.D.G. Vincent, Wind-pressure on buildings including effects of adjacent buildings, J. Inst i tut ion of Civil Engineers, 20 (1943) 243-275.

[22] C.W. Letchford, Wind loads and overturning moments on free standing walls, Proc. 2nd Asia Pacific Symposium on Wind Engineering, Beijing, June 1989.

[23] N.J. Cook, The designers guide to the wind loading of building structures, Part 1, BRE]Butterworths, London, 1985.

Journal of Wind Engineeringand Industrial Aerodynamics 83 (1999) 455}465

Wind loads on porous structures

P.J. Richards!,*, M. Robinson",#

!Department of Mechanical Engineering, University of Auckland, Private Bag 92019, Auckland, New Zealand"Robinson Design Ltd, Private Bag, Waimauku, NW Auckland 1250, New Zealand

#Ultra Span Inc, 15135, 86th Ave, Surrey, BC, Canada V3S 4T8

Abstract

The wind loads on porous structures depend strongly on the resistance to through #ow,which may be characterised by the loss coe$cient. It is shown that for round wire mesh screensthe loss coe$cient is related to the porosity (b). For other structures the loss coe$cient isa function of the porosity and the construction. It is therefore suggested that it is useful to use ane!ective porosity (b

%), which is the porosity of a round wire mesh screen with the same loss

coe$cient. It is shown that loads on porous structures are less than those on solid structures bya factor (1!b

%). When porous structures are at an angle to the wind, the e!ective loss

coe$cient is reduced by a cos2(h) factor, where h is the angle between the wind and a normal tothe surface. As a consequence the corresponding e!ective porosity increases and the loadsdecrease. These concepts are shown to match results from a number of sources. ( 1999Elsevier Science Ltd. All rights reserved.

Keywords: Wind loads; Porous strutures; Round wire mesh

1. Introduction

Porous structures are widely used for a variety of applications including windbreakfences, bird canopies for horticultural crops, shade houses and hail shelters. Althoughthe wind loads on such structures are similar to those on solid structures the #owthrough the structure modi"es the pressure distribution and therefore requires consid-eration. In general the wind loads on planar porous surfaces are a!ected by theirresistance to through #ow and the overall geometry of the structure: the size, shapeand angle to the wind. A number of these aspects will be discussed in the subsequentsections.

*Corresponding author. Tel.: #64-9-3737599; fax: #64-9-3737479.E-mail address: [email protected] (P.J. Richards)

0167-6105/99/$ - see front matter ( 1999 Elsevier Science Ltd. All rights reserved.PII: S 0 1 6 7 - 6 1 0 5 ( 9 9 ) 0 0 0 9 3 - 8

2. Resistance to through 6ow

The resistance of any porous structure to #ow through the structure may becharacterised by a loss coe$cient k, which relates the pressure drop across thestructure to the volume #ow rate per unit area through the structure in the form

*p"k0.5o<2T

(1)

where o is the air density (+1.2 kg/m3) and <T

is the volume #ow rate of air per unitarea through the structure in m/s. The loss coe$cient itself is a function of the porosityb of the structure, the type of construction and the Reynolds number (Re) of thethrough #ow, such that

k"k(b,Re, construction) (2)

with

b"Area open to through flow

Total area(3)

and

Re"o<

Td

k, (4)

where d is a characteristic dimension of the elements making up the structure and k isthe kinematic viscosity (+1.8]10~5 Ns/m2) for air.

2.1. The ewect of porosity on the loss coezcient

Fig. 1 shows data derived from Annand [1] and Hoerner [2] for round wire meshscreens at high Reynolds numbers ('2000). Also shown is the correlation given byESDU item 72009 [3], which "ts most of the data shown but does not behave at lowand high porosities in the manner expected. Hoerner [2], (quoting Borda [4]) suggeststhat at low porosities it is expected that

kN(1!b)2/b2, (5)

whereas at high porosities he suggests that

kNC$(1!b)/b2, (6)

where C$

is the sectional free #ow drag coe$cient of the elements of the structure. Thedivision by b2 in Eq. (6) is included to allow for the increased velocity around anelement due to other elements. However, this formulation includes an allowance forthe blockage of the element onto itself, which would occur even if the element was inisolation, and hence Eq. (6) tends to overcompensate. For a rectangular mesh, such asthat illustrated in Fig. 2, analysis of the geometry suggests that a better allowance forthis increase gives

kNC$(1!b)/(1!0.75(1!b))2. (7)

456 P.J. Richards, M. Robinson / J. Wind Eng. Ind. Aerodyn. 83 (1999) 455}465

Fig. 1. Loss coe$cients for round wire mesh screens.

Fig. 2. Mesh geometry.

Although Eqs. (6) and (7) give similar values for k with porosities greater than 0.8, it isfound that Eq. (6) overestimates the size of k in the range 0.5(b(0.8 whereas Eq. (7)matches the measured values more closely.

For cylindrical elements at Reynolds numbers in the range of 103}104 the sectionalfree #ow drag coe$cient C

$+1.0. Eqs. (5) and (7) may be combined into a single

equation

k(b,Re'2000,round)"((1!b)8/b8#(1!b)4/(1!0.75(1!b))8)0.25 (8)

P.J. Richards, M. Robinson / J. Wind Eng. Ind. Aerodyn. 83 (1999) 455}465 457

Fig. 3. The variation of loss coe$cient with Reynolds number.

which, as illustrated in Fig. 1, also "ts the data reasonably well and has the logicallimits of kNR as bN0 and kN0 as bN1.

2.2. The ewect of reynolds number on the loss coezcient

With round wire mesh screens it is generally found that the loss coe$cient isreasonably constant at Reynolds numbers greater than 2000 but increases at lowerReynolds numbers. It may be expected that this low Reynolds number variationwould be similar to that of a circular cylinder. Mills [5] gives a correlation for the dragcoe$cient of a cylinder in cross #ow, which is valid for 1(Re(104. This takes theform

C$"1#10/Re2@3. (9)

Both Annand [1] and ESDU [3] give information on the variation of the losscoe$cient of round wire screens with Reynolds numbers less than 2000. In either case,as illustrated in Fig. 3, the trends are reasonably modelled by a function similar toEq. (9), such that

k(b,Re)/k(b,Re'2000)"1.0#14.5/Re0.75. (10)

In practice, many porous structures are constructed from woven or knitted fabricswith element sizes between 0.25 and 1 mm. As a result typical Reynolds numbers are


of the order of a few hundred. In many design situations it may be impractical to takeinto account Reynolds number e!ects, in which case it may be reasonable to usea single Reynolds number of say 300 and k(b)"1.2k(b,'2000). This should beconservative in most cases since the highest wind loads will occur at the highest windspeeds and hence the highest Reynolds numbers and lowest loss coe$cients.

2.3. The ewect of construction on the loss coezcient

The data presented in Sections 2.1 and 2.2 are strictly valid for round wire meshesbut is also useful in order to de"ne an e!ective porosity b

%for other types of

construction. In dealing with round wire screens it is reasonable to assume that theminimum #ow area occurs at the point of greatest restriction in the geometry.However, if a mesh is constructed from #at webs or sharp-edged elements then the#ow will form a vena contracta and so the minimum #ow area is smaller than thatestimated from the structure. With such structures, we have found it useful to quote ane!ective porosity. The e!ective porosity is de"ned as being equal to the porosity ofa round wire mesh screen with the same loss coe$cient. For porous structures madefrom #at webs the e!ective porosity, as suggested by Morgan [6], may be about 2/3 ofthe geometric porosity b. For example, the windbreak material Paraweb, as used byRichardson [7], has a geometric porosity of b"0.475 but since it is constructed from50 mm-wide #at webbing strips, may be expected to have an e!ective porosityb%"0.317 and hence from Eq. (8), k"4.8. Experimental measurements in the wind

tunnel at Auckland showed the value of k to be 5.3. With structures made from slats orother elements with a depth comparable to their width it is suggested that b

%+0.75b.

Although the e!ective porosity of a structure may be estimated, it is usually better tomeasure the loss coe$cient and hence deduce the e!ective porosity from Eq. (8) orFig. 1.

The Reynolds number e!ects on meshes made from #at webs or other structures islikely to be slightly di!erent from that given in Section 2.2. However, Hoerner [2]shows that both circular and square plates, normal to the #ow, have a drag coe$cientat Re"10 about three times that at Re"104, which is in line with Fig. 3, and so wemight expect a similar Reynolds number dependency with meshes constructed from#at webs or sharp-edged elements. Hence Eq. (10) may be a reasonable approximationwith most styles of construction.

3. Wind loads on rectangular planar porous surfaces

The wind loads experienced by rectangular planar porous surfaces depend not onlyon the porosity but also on factors such as aspect ratio, orientation to the wind andthe e!ects of the ground, both in terms of the interaction between the surface and theground and the e!ect of the ground roughness on the turbulence of the wind. In manysituations it is di$cult to isolate any particular e!ect, however a number of trends arediscernable.


3.1. The ewect of porosity on wind loads for surfaces normal to the wind

One of the few porous structures for which both full-scale and wind-tunnel experi-mental data is available is a windbreak fence. Fig. 4 shows the drag coe$cient datafor winds normal to fences with length to height ratios greater than 9, derived fromRefs. [7}14], plotted against the e!ective porosity which was estimated fromthe details of the structure. Also shown in the graph is a curve based on Taylor'smomentum theory (valid for k(3(b'0.4)), which as quoted by Cook [15]gives

CD"k/(1#k/4)2. (11)

Another theoretical approach is to assume that with high porosities most of the#ow approaching a normal surface will pass through it and so

CDNk (12)

which together with Eq. (7) gives

CDNC

$(1!b)/(1!0.75(1!b))2. (13)

This equation, with C$"1.0, is also shown in Fig. 4 and is very similar to Eq. (11)

at high-porosities but increases more rapidly for porosities less than 0.7. Althoughthere is little data at high-porosities to con"rm these trends it may be noted thatboth of these high-porosity theories suggest a near-linear variation of drag coe$cientwith e!ective porosity. Extending this linear behaviour to lower porosities givesa curve

CD"C

D(Solid)](1!b

%) (14)

Fig. 4. Drag coe$cients for windbreak fences (Wind normal to the fence).


Fig. 5. The reduction in drag coe$cient of porous fabrics perpendicular to the onset #ow with e!ectiveporosity. Wind tunnel data.

which passes through the porous fence measurements and intersects the axis atC

D(Solid)+1.5. Which is in the midst of the fairly scattered solid wall measurements.AS1170.2-1989 [16] suggests that the wind load on free standing walls, when the

wind is normal to the wall, is given by

CD"1.2](1!b2), (15)

where b is the geometric porosity. Eq. (15) is also a reasonable "t to the porous fencedata if b

%+b but is signi"cantly higher than Eqs. (11) or (13) at high porosities. The

solid fence limit of 1.2 in Eq. (15) is supported by full-scale and wind-tunnel measure-ments such as those in Refs. [12,14] but is substantially lower than those given inRef. [10].

Support for Eq. (14), which suggests that the wind loads reduce in proportion to(1!b

%), has been obtained from measurements in the University of Auckland wind

tunnels. A range of eight porous fabrics were tested in a 0.3 m]0.3 m closed sectionwind tunnel to determine their loss coe$cient and then the samples were mounted ona 0.3 m]1.5 m frame which was located in a 1.5 m]1.5 m slotted walls wind tunnel.The roof and #oor of the tunnel adjacent to the 0.3 m-long ends were solid and so thetests were e!ectively two-dimensional. Forces were measured parallel and perpendicu-lar to the frame for a range of angles to the onset #ow. In order to provide data fora solid object the frame was covered with plastic "lm. Fig. 5 shows the ratio of porousto solid drag coe$cients plotted against e!ective porosity for the situation where thefabrics were perpendicular to the #ow. The values for the e!ective porosity wereobtained by inverting Eq. (8). Although there is considerable scatter in this data thegeneral trend is in line with Eq. (14).


3.2. The ewect of angle to the wind on wind loads

When a planar porous structure is not perpendicular to the wind the forces actingon the structure may be split into a normal force due to the pressure di!erence anda frictional drag force parallel to the plane of the structure. The frictional drag forcemay be accounted for by using a friction drag force coe$cient in the range of 0.01}0.04depending on the surface roughness [16]. This coe$cient applies when the wind isparallel to the plane of the structure and may be reduced by a factor sin(h) at othertimes [14]. The angle h is the angle between the onset wind and a normal to thestructure.

The normal force coe$cient Cn, which equals the drag coe$cient when h"03,

reduces as the angle h increases. Fig. 6 shows the results obtained from theUniversity of Auckland tests which were described in the previous section. With theexception of the two most solid fabrics the behaviours are all very similar. Thisbehaviour may be reasonably matched by an extension to the theory used to deriveEq. (11) which gives

Cn(h)"

k cos 2(h)

(1#k cos 2(h)/4)2(16)

and hence

Cn(h)

Cn(Normal)

"cos 2(h)A4#k

4#k cos 2(h)B2

(17)

Fig. 6. The variation of Cn

with wind angle, high aspect ratio structures.


Fig. 7. The variation of Cn

with angle from normal, low aspect ratio structures.

Shown in Fig. 6 is Eq. (17) with k"2.0. It may be noted that if Eq. (16) is comparedto Eq. (11) then it appears that when the plate is at an angle h the e!ective losscoe$cient is k cos2(h).

Both Seginer [9] and Richardson [7] have made experimental observations of thevariation of the drag force on slatted porous windbreak fences (k+5) with azimuthangle. Each of them concluded that the data was matched by

CD"C

D(Normal)] cos(h) (18)

which also matches the general shape of the low to medium k data band in Fig. 6.It is clear from Fig. 6 that with high solidity a change in behaviour is observed at

high angles. As might be expected, at high angles the solid plate induces circulationand the normal force is proportional to the usual angle of attack. It does appear thateven relatively low levels of porosity do a!ect this circulation.

Similar e!ects are apparent in data obtained by Letchford et al. [17], who havewind-tunnel tested 1 : 50 scale models of various porous and solid canopy roofs witha nominal plan of 15 m]15 m. The two porous structures tested were made fromperforated plates with geometric porosities b"11% and 23%. Loss coe$cientmeasurements on these two plates gave k"340 and 33, respectively. Monoslope roofdata was obtained at roof pitches of 73, 153 and 273, with the wind approaching fromboth directions. Fig. 7 shows Letchford's results along with data given by Hoerner [2]for solid square plates. The solid monoslope roof data of Letchford is very similar toHoerner's square plate data but shows slight di!erences for the two wind directions.In each case a slightly larger normal force was obtained when the wind approachedfrom the low end of the roof. These di!erences are probably due to interactions with


the ground plain, which was 5 m (full-scale equivalent) below the roof. With theporous roof data there is a progressive reduction in the normal force with increasedporosity.

4. Conclusions

The wind loads on porous structures depends strongly on the resistance to through#ow, which may be characterised by the loss coe$cient. It has been shown that forround wire mesh screens the loss coe$cient is related to the porosity (b). For otherstructures the loss coe$cient is a function of the porosity and the construction. It istherefore suggested that it is useful to use an e!ective porosity (b

%), which is the

porosity of a round wire mesh screen with the same loss coe$cient. It is shownthat loads on porous structures are less than those on solid structures by a factor(1!b

%). When porous structures are at an angle to the wind the e!ective loss

coe$cient is reduced by a cos 2(h) factor, where h is the angle between the wind anda normal to the surface. As a consequence, the corresponding e!ective porosityincreases and the loads decrease. These concepts have been shown to match resultsfrom a number of sources.

Acknowledgements

The assistance of Ultra Span Inc. in sponsoring some of the work reported in thispaper is gratefully acknowledged.

References

[1] W.J.D. Annand, The resistance to air #ow of wire gauzes, J. Roy. Aeronaut. Soc. 57 (1953) 141}146.[2] S.F. Hoerner, Fluid Dynamic Drag, published by the author, 1965.[3] ESDU72009, Engineering Science Data Unit, London, 1972.[4] Borda, Experience sur la resistance des #uides, Mem. de l' Academie Royale des Science, Paris, 1763.[5] A.F. Mills, Heat transfer, Irwin, Homewood, IL, 1992.[6] P.G. Morgan, Flow through screens of low solidity, J. Roy. Aeronaut Soc. 66 (1962) 54}56.[7] G.M. Richardson, A permeable windbreak: its micro-environment and its e!ect on structural loads,

J. Agric. Eng. Res. 38 (1987) 65}76.[8] D. Painter, Measured porosity, drag and shelter: polymesh `Lenoa shelter cloth, F.A.O (Agric. Eng.)

Conference, Lincoln College, New Zealand, 1982.[9] I. Seginer, Flow around windbreaks in oblique wind, Boundary-Layer Meteorology 9 (1975)

133}141.[10] A.P. Robertson, R.P. Hoxey, P.J. Richards, Design code, full-scale and numerical data for wind loads

on free-standing walls, J. Wind Eng. Ind. Aerodyn. 57 (1995) 203}214.[11] L.J. Hagen, E.L. Skidmore, Windbreak drag as in#uenced by porosity, Trans. ASAE 14 (4) (1971)

464}465.[12] A.P. Robertson, R.P. Hoxey, P.J. Richards, W.A. Fergusson, Full-scale measurements and computa-

tional prediction of wind loads on free-standing walls, J. Wind Eng. Ind. Aerodyn. 67&68 (1997)639}646.


[13] E.F. Kay, Aerodynamic design of arti"cial windbreaks, ME Thesis, University of Auckland, NZ, 1984.[14] J.D. Holmes, Pressure and drag on surface-mounted rectangular plates and walls, ninth Australasian

Fluid Mechanics Conference, Auckland, NZ, 8}12 December 1988.[15] N.J. Cook, The designer's guide to wind loading of building structures, Part 2, 1985.[16] Standards Australia, SAA Loading Code, Part 2: Wind loads, Australian Standard AS1170.2-1989.[17] C.W. Letchford, A. Row, A. Vitale, J. Wolbers, Mean wind loads on porous canopy roofs, IV

Asia-Paci"c Symposium on Wind Engineering, Surfers Paradise, Australia, July 1997.


Journal of Wind Engineering

and Industrial Aerodynamics 89 (2001) 135–151

Wind loads on rectangular signboards andhoardings

C.W. Letchford*

Department of Civil Engineering, The University of Queensland, Brisbane, Qld 4072, Australia

Received 16 January 1998; accepted 7 July 1999

Abstract

Drag or normal force coefficients on a range of rectangular signboards or hoardings with

varying aspect ratios, clearance ratios and porosity’s are presented for a range of winddirections and compared with various design data. Whereas, there is reasonably goodagreement for data for walls on ground, significant discrepancies exist in normal force

coefficients for cases as the panel becomes elevated in the boundary layer. Discrepancies incodification have been highlighted and revised loading data recommended. # 2001 ElsevierScience Ltd. All rights reserved.

1. Introduction

Wind loads on panels mounted on the ground and above the ground representperhaps the simplest structure for investigation and indeed have been the subject ofmany studies [1–6] and even a 15th century drawing by Leonardo Da Vinci, asreproduced by Hoerner [7]. Flachsbart in the early 1930s conducted perhaps themost extensive study of these types of structures and the pertinent results are wellsummarised by Simiu and Scanlan [8]. In that study, basically two configurationswere studied, panels on the ground plane, and panels well clear of the ground plane.Results were presented as net force coefficients as a function of aspect ratio (width/height) ranging from the three dimensional flow around a square, aspect ratio=1, tothe ‘two-dimensional’ flow around an ‘infinite’ strip. The measurements wereobtained in smooth uniform flow with no real attempt to simulate a turbulent

*Tel.: +61-7-3365-3511; fax: +61-7-3354-4599.

E-mail address: [email protected] (C.W. Letchford).

0167-6105/01/$ - see front matter # 2001 Elsevier Science Ltd. All rights reserved.

PII: S 0 1 6 7 - 6 1 0 5 ( 0 0 ) 0 0 0 6 8 - 4

boundary layer. These results largely formed the basis of codified values for manyyears for both walls and signboards or hoardings [9]. ESDU summarised much ofthis earlier work in their data item 70015 [10]. Indeed, the current InternationalStandard [11] still draws on this work as does the Australian wind load standard [12]for hoardings well clear of the ground.

The work of Letchford and Holmes [5,6] revised the wind loads on walls attachedto the ground with wind-tunnel measurements conducted in properly simulatedturbulent boundary layer flows. For flows normal to the wall there was remarkablygood agreement between these results and those of Flachsbart. The major changewas the introduction of increased loading at the free ends of walls for obliquewind directions. This data has now been incorporated into several design documents[12–15].

Hoardings, however, represent a different story in that there appears to be verylimited information [5,14,16] on wind loads on these structures in turbulentboundary layer flows. Bearman [2] did conduct studies of wind loads on squareplates in smooth and turbulent flow, but these were in uniform flow and hence not inturbulent boundary layer flow.

This paper deals specifically with wind-tunnel measurements to determine theeffect of aspect ratio, clearance ratio, porosity and wind direction on loadingcoefficients on signboards and hoardings in turbulent boundary layer flows. Thefollowing section will describe the experimental arrangement. Section 3 will presentthe results of this study and compare with earlier work. Section 4 will makeconclusions and recommendations.

2. Experimental procedure

The parameters chosen for investigation in this study were aspect ratio ÿb/c,clearance ratio ÿc/h, porosity ÿp and wind direction, Y. The geometry is defined inFig. 1 and the terminology is the same as in the Australian wind load code [12].

The porosity ( p) or solidity (f) of the materials studied was calculated from

p ¼ 1ÿ f ¼ open area

total enclosed area: ð1Þ

With reference to Fig. 1, total enclosed area=bc. An alternative to porosity is thepressure loss coefficient which is defined as

K ¼ Pu ÿ Pd

rU2=2; ð2Þ

where Pu and Pd are the upstream and downstream static pressures either side of themesh and �U is the average approach velocity. The pressure loss coefficient is ameasure of the resistance to flow through a porous surface and includes the effects ofporosity as well as shape and distribution of ‘holes’. The pressure loss measurementswere performed in a small wind tunnel, approximately 300mm2, in which the entirecross section was covered by the porous materials being tested. Two perforated metal

C.W. Letchford / J. Wind Eng. Ind. Aerodyn. 89 (2001) 135–151136

plates of porosity 11% and 23% were chosen for the wind tunnel study. The K valueswere 330 and 33, respectively. The 11% porous plate had 2.4mm diameter holes at6.4mm spacings while the 23% porous plate had 0.8mm diameter holes at 1.5mmspacings. Each porous plate was 0.5mm thick. Solid metal plate of the samethickness was also employed in this study.

A simple one-component force balance was constructed [17] to measure the verysmall loads. A paddle in a container of a viscous fluid was used to dampen thefluctuating loads. Only mean values are presented here which represent the averageof several 90 s duration runs sampled at a frequency of 100Hz. The drag force onthe exposed supporting leg (5mm2) was measured separately and was subtractedfrom the overall loads to produce loads on the hoarding alone. When simulatingwalls, i.e., no gap under the hoarding (c=h ¼ 1), the models were sealed to the groundby a ‘clingfilm’ membrane. Zero load measurements before and after each windloaded run ensured that any hysteresis effects were eliminated from the data.

The mean dynamic pressure was obtained from a pitot–static tube mounted at topof hoarding height away from the influence of the model and connected toHoneywell pressure transducer which was similarly sampled at 100Hz for 90 s. It isexpected that this will lead to approximately 6% overestimate of the true dynamicpressure [22] for the turbulence intensities in this study. This was deemed acceptablebecause of the convenience of the pitot–static tube over a hot wire for the largenumber of model heights to be studied. Normal force coefficients were obtained bydividing the measured force by the mean dynamic pressure at top of hoarding heightand the actual area of the panel. The 08 wind direction was defined as normal to thehoarding. Models ranged in size from 50 � 50mm to 100 � 400mm with gapsbeneath the panels extending from 5 to 150mm. No blockage corrections have beenmade as the largest blockage was less than 1%. The typical wind speed at the top ofpanel was 10m/s, making a test Reynold’s Number of approximately 5� 104.

To examine fluctuating wind loads and those causing twisting, a second forcebalance was employed for a selected number of panel configurations. This balanceconsisted of a stiff 12mm square rod that was strain gauged to measure threemoments. This balance had natural frequencies of 65Hz in overturning moment and25Hz in torsion. These frequencies are above dominant frequencies in the flowsimulation. The panels employed for this balance were manufactured from 5mm

Fig. 1. Geometry of model configuration.

C.W. Letchford / J. Wind Eng. Ind. Aerodyn. 89 (2001) 135–151 137

thick masonite. In these tests, normal (or drag) force overturning moment andtorque were monitored at 100Hz for 36 s and repeated 10 times. The 36 s periodcorresponded to approximately 10min at full scale for a typical design situation.Mean, standard deviation and mean hourly extreme value coefficients were obtainedby dividing the measured moments by the mean dynamic pressure at top of hoardingheight, the panel area and a lever arm. The normal force was assumed to act at thecentre of height of the panel while the twisting moment or torsion coefficient aboutthe vertical central axis of the panel was defined by

Ct ¼Mt

1=2rU2b2cð3Þ

with Mt being the torsion about the central vertical axis and U the mean velocity attop of panel height. The mean extremes were obtained from the 10min mode anddispersion estimated from fitting a Fisher–Tippett type-1 extreme value distributionto the 10 extremes. The mean hourly extreme coefficient being defined by

Cf ¼ mod e10 min þ ð0:577þ ln ð6ÞÞ*dispersion10 min: ð4Þ

The tests were conducted in the Department of Civil Engineering’s BoundaryLayer Wind Tunnel which is 3m wide� 2m high and has some 12m of upstreamfetch for boundary layer simulation. The simulation consisted of a fetch of carpet, a300mm fence and a grid of 100mm wide beams at 300mm horizontal and 400mmvertical centres placed immediately upstream of the fence. The mean velocity andturbulence intensity profiles are compared with AS1170.2 [12] values in Figs. 2 and 3at a length scale of 1 : 50. It is seen that the simulation is between terrain categories 2and 3 (rural/suburban) at this scale. The spectrum of longitudinal turbulence at

Fig. 2. Mean velocity profile is compared with AS1170.2, TC2 and TC3 values.


200mm height is presented in Fig. 4. It is noted that there is significantly higherenergy content in the high frequencies/smaller turbulence scales that wouldbe expected at full scale, however this is a fairly typical shortcoming of large-scalewind-tunnel simulations.

Fig. 3. Turbulence intensity profile is compared with AS1170.2, TC2 and TC3 values.

Fig. 4. Spectrum of longitudinal turbulence at 60mm height.


3. Results and discussion

Mostly mean force measurements were recorded because the earlier work on walls[4,5] indicated that the overall loading on walls and hoardings behaved largely quasi-statically as long as the mean load was not near zero. However, Cook [14] indicatesthat pseudo-steady pressure coefficients (peak coefficient/gust factor squared) wereconsistently larger than mean coefficients for a series of four hoardings tested inthe range 0:255b=c52, with c=h � 0:5. Additional fluctuating measurements toexamine this effect are discussed in Section 3.4.

Several configurations were tested 10 times and the standard errors in the meanforce coefficients were estimated to be 3%. Table 1 summarises the results of themean force investigation for the solid panel with wind normal to the panel.

The results for the wall on ground case, c=h ¼ 1, compare favourably with earlierstudies [1,4,6,20] and more recent comparisons of model and full scale measurementsof wind loads on free standing walls [18]. These are summarised in Table 2.

3.1. Effect of aspect ratio

Fig. 5 plots the results of Table 1 as mean drag force coefficient as a function ofaspect ratio (b/c) for various clearance ratios (c/h). A clearance ratio of c=h ¼ 1represents a wall on the ground and it has been previously noted [1,4,18,21] that themean drag force coefficient reaches a minimum at b=c � 5 and increases slightly forlarger b/c. It is seen that as the aspect ratio increases from that of a square, b=c ¼ 1,the drag coefficient will decrease for hoardings with small gaps beneath (c=h > 0:67)but increase for those with large gaps (c=h50:3). As the aspect ratio decreases fromthat of a square, the drag coefficient now increases irrespective of clearance ratio.

These phenomena can be explained by the increased drag arising from the greateropportunity for interaction of the shear layers separating from around the hoarding.For very low aspect ratios (b=c � 0:1), the hoarding is tall and narrow and

Table 1

Mean drag force coefficients for 08 wind direction for various b/c and c/h ratios

Cf

c/h b/c

0.1 0.2 0.25 0.5 1 2 4 5 10

1.0 1.42 1.41 1.17 1.15 1.14 1.08 1.04

0.95 1.43 1.43 1.33 1.27 1.24 1.14

0.9 1.55 1.44 1.45 1.41 1.34 1.33 1.20 1.15

0.8 1.46 1.49 1.44 1.43 1.39 1.32

0.67 1.46 1.42 1.38 1.35 1.32

0.5 1.47 1.38 1.42 1.45 1.44

0.3 1.42 1.45 1.53 1.57 1.55

0.16 1.48 1.51 1.63


irrespective of the clearance ratio the wake flow is dominated by separating shearlayers from each vertical side of the hoarding. This is very similar to the flowaround very wide and narrow hoardings (b=c � 10), that are well clear of theground, c=h50:3, where again interaction of the separating shear layers leads toincreased drag. However, as the gap beneath the hoarding is reduced, separatingshear layer interaction is stifled and eventually prevented for the case of c=h ¼ 1 andthe ground plane serves the same purpose as a splitter plate in reducing the drag [8].It is interesting to note that significant interaction occurs for even c=h ¼ 0:95,representing a 5% of height gap.

Table 2

Comparison of total drag force coefficient on solid walls on ground, for 08 wind direction from various

sources

Cf

b/c [6,21] [18] [4,1] Present

Oxford CSIRO Oxford Silsoe

1 1.33 1.24 1.06 1.09 1.15

1.5 1.17 1.06

2 1.24 1.04 1.14

3 1.22 1.17 0.96

4 0.99 1.08

5 1.07 1.13 � 0.97 0.98 1.04

9 1.16 � 0.98

10 1.13 1.04

Very large 1.32 1.21 1.15

Fig. 5. Mean drag or normal force coefficient (Cf ) on solid panels versus aspect ratio (b=c) for 08 winddirection and various clearance ratios (c=h).


3.2. Effect of clearance ratio

Fig. 6 presents the same information as Fig. 5 only this time the mean drag ornormal force coefficients are plotted as a function of clearance ratio (c/h) for variousaspect ratios (b/c). There is a decrease in drag force as the gap beneath the hoardingis reduced. The trend is very similar for aspect ratios between 0.5 and 2, butmarkedly greater for aspect ratios greater than 4 and less for aspect ratios less than0.5. At a clearance ratio c=h ¼ 0:5, the drag coefficient appears to be independent ofaspect ratio, taking a value of approximately 1.45.

As might be expected, for small gaps the results tend to those of a wall, while forlarge gaps they tend to the isolated panel results, leaving a middle region in whichboth the aspect ratio (b/c) and clearance ratio (c/h) are important parameters. Incodifying results for designers, the literature [12–15] has typically drawn theboundaries to these regions as c=h50:2 for the isolated panels and c=h > 0:7 or 0.8for walls on the ground.

Fig. 7 highlights the results of Fig. 6 for an aspect ratio of 2 and compares thepresent results with other experimental data [5,14,16,20] and the Australian windload code [12]. Whereas, there is good agreement for the wall on ground case,c=h ¼ 1, where Cf ¼ 1:2, significant differences arise as the gap beneath the hoardingincreases, particularly for Cook [14] and Langtree’s [16] original results. Cook’s dif-ferences have been previously discussed and are in fact pseudo-steady pres-sure difference coefficients. Interestingly, Langtree’s results are also mean pressuredifference coefficients, but Ref. [20] has revealed that an incorrect reference pressurewas used and the corrected results are plotted in Fig. 7. Langtree’s model was

Fig. 6. Mean drag or normal force coefficient (Cf ) on solid panels versus clearance ratio (c=h) for 08 winddirection and various aspect ratios (b=c).


160 � 80mm and 12mm thick resting on two 12mm diameter legs. His simulationwas also between a TC 2 and 3 as was the case with this study. Despite the excessivemodel thickness, twice that of Letchford [5] and Cook [14] and 20 times that of thepresent study the agreement with the present results is now excellent. In passing, theAustralian wind load code [12] values highlight the artificial step at a clearance ratioof 0.7.

Fig. 8 shows the results for hoardings or panels well away from the ground,c=h50:2, i.e., uniform flow. It is clear the earlier results of Flachsbart (as reported inRef. [8]) have influenced the Australian [12] and US [19] wind load codes. Alsoshown in Fig. 8 are the present results for c/h=0.16 which are clearly greater thanthe others. This is no doubt due to the increased turbulence present in the boundarylayer compared to the smooth uniform flow employed by Flachsbart as reported inRef. [8]. The effect of turbulence scale is also likely to have contributed to thedifferences as Bearman [2] has reported. Here, the somewhat excessive high-frequency/small-scale turbulence present in the flow will lead to greater shear layercurvature and hence reduced base pressures and thence larger drag forces as outlinedby Gartshore [23].

Fig. 9 shows the present results for the medium clearance ratios (0:25c=h50:8)together with various other data sets. The lower values of Newberry [9], ASCE-7 [19]and the International Standard [11] reflect the heritage of smooth low turbulent flowas previously commented on. The significantly higher results of Cook [14] arepseudo-steady coefficients and are perhaps a result of significant non-quasi steadyloading. Although, as noted in Section 2, this was not observed to be the case inother studies on walls and hoardings [4,5] for situations where the mean force

Fig. 7. Comparison of mean drag or normal force coefficient (Cf ) on solid panels versus clearance ratio

(c=h) for 08 wind direction and aspect ratio b=c ¼ 2 from various data sources.


coefficient was well away from zero. This feature is examined with the aid ofadditional measurements in Section 3.4.

Fig. 10 shows the present results for hoardings with small gaps compared withliterature values for walls and hoardings with c=h > 0:8. As noted in Table 2, thepresent results for walls on the ground are in good agreement with earlier studies.However, for tall thin walls or hoardings close to the ground the measured normalforce coefficients are higher than present recommendations.

3.3. Effect of porosity

Many of the solid wall configurations were repeated with the 11% and 23%porous panels and a porosity reduction factor Kp formed. Kp was defined as the drag

Fig. 9. Mean normal force coefficients for solid panels at intermediate distances above the ground

(0:25c=h50:8).

Fig. 8. Mean normal force coefficients for solid panels well away from the ground, c=h50:2.


or normal force coefficient for the porous panel divided by the corresponding solidpanel coefficient and the results are presented in Fig. 11. As expected, there is a smalldecrease in drag coefficient with porosities up to the 23% investigated here. Theaverage value for all the configurations tested is also plotted along with therecommendation of the Australian Standard [12]. That code suggests

Kp ¼ 1ÿ p2: ð5Þ

Fig. 10. Mean normal force coefficients for solid panels close to the ground (c=h > 0:8).

Fig. 11. Values of Kp, Cf (porous)/Cf (solid), as a function of porosity for various aspect ratios.


Whereas these results would tend to suggest a faster decay, of the order of (1ÿ p1:5)for porosities up to 23%. ASCE-7 [19] recommends no reduction in loading forporosities up to 30%.

It is worth noting in passing, that porous signboards are treated incorrectly in theEUROCODE [15] in that the reference area used is the enclosed area, whereas theslenderness (and porosity) reduction factor is based on a summation of projectedareas. This error leads to an increase in load for increasing porosity.

3.4. Effect of wind direction

Employing the second stiffer force balance meant mean and fluctuatingoverturning and torsion moment coefficients were obtained. The overturningmoment was converted to a drag or normal force coefficient by assuming the loadacted at the panel mid-height.

Fig. 12 shows the mean drag or normal force coefficient as a function of winddirection for a panel with aspect ratio b=c ¼ 2. Also shown in the figure are meanpressure difference coefficients from Letchford’s earlier study [5] for the same aspectratio panel (b=c ¼ 2) for 08 and 458. Good agreement is evident. As Cook [14] notedfor hoardings, the normal force coefficient remains approximately constant for winddirections up to 458 and thereafter decreases linearly.

For codification purposes however, the mean coefficient is only useful while thequasi-steady assumption is valid, which is approximately the case when the meancoefficient is well away from 0. An alterative approach is that of employing pseudo-steady coefficients, defined by:

~Cf ¼Cf

G2; ð6Þ

Fig. 12. Mean normal force coefficients for a panel, b=c ¼ 2, as a function of wind direction for various

c=h.


where, ~Cf is the pseudo-steady coefficient, Cf is the mean extreme coefficient, definedby Eq. (4) and G the gust factor taking the value G ¼ 1þ 3:7 Iu, where Iu is theturbulence intensity at the top of hoarding.

Fig. 13 plots these pseudo-steady coefficients for the same panel, b=c ¼ 2, as afunction of wind direction. Also plotted on the figure are the pseudo-steadycoefficients of Letchford [5] and Cook [14] obtained from pressure measurementsand the AS1170.2 values [12]. Here, the normal force coefficients are approximatelyconstant up to 608 and only then decreasing. Cook’s results are somewhat higherthan those found in the present study while the earlier results of Letchford [5] are ingood agreement. The AS1170.2 [12] values represent a reasonable upper bound forthese configurations. Cook’s results have generally been higher for all configurationsand this may be due to the low probability of exceedence peaks to allow for the jointprobability of exceedance of wind speed and pressure coefficient. He defines a designextreme coefficient as: mode+1.4� dispersion, instead of the mean extreme asdefined by Eq. (4).

Fig. 14 shows the results of holding the clearance ratio constant at c=h ¼ 0:5 andvarying the aspect ratio b/c. Once again pseudo-steady coefficients are used to allowfor a greater comparison with other sources. The trend of approximately constantnormal force coefficient with wind direction up to 458 is again observed with littledifference between these two aspect ratios. As previously noted, the results of Cookare substantially above the present data set.

Instead of presenting torsion coefficients, an eccentricity, e, about the centralvertical axis has been evaluated. Here this is defined as the mean extreme torsioncoefficient (Eq. (4)) divided by the mean extreme drag or normal force coefficient andis non-dimensionalised by the panel width b. Fig. 15 presents the non-dimensional

Fig. 13. Pseudo-steady normal force coefficient for a panel of aspect ratio, b=c ¼ 2, as a function of wind

direction for various c=h.


eccentricity as a function of wind direction for the panels studied here. In general theeccentricity increases as the wind direction increases and as the panel comes closer tothe ground. This can be explained by the enhancement of the vortex that formsbehind the leading edge of the panel as the angle of attack increases and as thedisrupting flow under the panel is prevented. This has recently been discussed by

Fig. 14. Pseudo-steady normal force coefficient for a panel with clearance ratio, c=h ¼ 0:5, as a function of

wind direction for various aspect ratios ÿb=c.

Fig. 15. Horizontal eccentricity of the normal force coefficient as a function of wind direction for panel

b=c ¼ 2 and various c=h.


Letchford and Robertson [18] in regard to walls on the ground. The actual maximumtorsion moment coefficient occurs consistently for the 608 wind direction.

The recommendation of Cook [14], e=b ¼ 0:25, and ASCE [19], e=b ¼ 0:2, havealso been plotted as well as one deduced from AS1170.2 [12]. It is seen that Cook’srecommendations represent a pragmatic solution whereas that of AS1170.2 issignificantly unconservative. In fact the latter value is more representative of theeccentricity obtained when the mean torsion coefficient is divided by the meannormal force coefficient.

4. Conclusions

A detailed parametric study of wind loads on signboards and hoardings has beenundertaken to investigate the effects of aspect ratio, clearance ratio and porosity fora range of wind directions in a correctly simulated turbulent boundary layer.

For a clearance ratio c=h ¼ 0:5, the drag or normal force coefficient is practicallyindependent of aspect ratio in the range 0:55b=c55, taking a value of 1.45. Foraspect ratios greater than one, i.e., panels becoming wider, the drag force increasesfor lower clearance ratios – bigger gaps, while decreases for greater clearance ratios –smaller gaps. For aspect ratios less than 1, i.e., panels becoming tall and thin, thedrag force increases for all clearance ratios. This can be explained by the increasinginteraction of separating shear layers from each side of tall, thin panels, or from thetop and bottom sides of well-elevated wide panels which results in increased drag. Asthe gap between the panel and the ground decreases the shear layer interaction isreduced and so to the drag force, eventually the ground acts somewhat akin to asplitter plate in stabilising the wake and reducing the drag.

Codification of this data in the past has typically drawn artificial boundariesbetween the behaviour of panels on the ground, c=h ¼ 1, or c=h > 0:7, and panelswell clear of the ground c=h50:2. It has been shown that no distinct step exists andthat a formulae representation would better represent the data. A simple expressionthat fits the present data set with an error in normal force coefficient Cf of lessthan� 0.1 Cf for 0:25b=c55 and 0:25c=h51:0 is

Cf¼ 1:45þ 0:5ð0:7þ log10 ðb=cÞÞð0:5ÿ c=hÞ: ð7Þ

Outside the limits of applicability of Eq. (7), it is suggested for high aspect ratios,b=c > 5, the actual variation of net pressure from the free end needs to be consideredas discussed in Refs. [5,6]. For objects well removed from the ground, c=h50:2, it ispossible to use the values from Eq. (7) at c=h ¼ 0:2 as the earlier work [8,12,19]summarised in Fig. 8 may be unconservative due to the smooth flow of those studies.

Torsion coefficients about a central vertical axis were measured and werepresented in terms of an eccentricity (e) of the normal force coefficient. Cook’s [14]recommendation of e ¼ b=4 was seen to be a reasonable match to the present dataset. The eccentricity that was deduced from the Australian wind load code [12] wasseen to be unconservative.


The drag or normal force coefficient was seen to remain approximately constantup to a wind direction of 458 to the normal and then decrease almost linearly beyondthis angle. This was in qualitative agreement with earlier results [5,14]. No evidenceof strong non-quasi-steady behaviour was observed with pseudo-steady pressurecoefficients being in good agreement with mean coefficients over the 0–458 winddirection range. This contrasted with the earlier pressure measurement results ofCook [14].

The results for porous panels with up to 23% porosity indicate a reduction innormal force coefficient proportional to (1ÿ p1:5), a somewhat faster decay thanrecommended in the Australian wind load code [12].

Acknowledgements

The author wishes to thank Andrew Vitale and Peter McMillan for softwaredevelopment in data acquisition and Graham Illidge for model making and datacollection.

References

[1] M.C. Good, P.N. Joubert, The form drag of two dimensional bluff plates immersed in a turbulent

boundary layers, J. Fluid Mech. 31 (1968) 547–582.

[2] P.W. Bearman, An investigation of the forces on flat plates normal to a turbulent flow, J. Fluid Mech.

46 (1971) 177–198.

[3] K.G. Ranga Raju, J. Loeser, E.J. Plate, Velocity profiles and fence drag for a turbulent boundary

layer along smooth and rough flat plates, J. Fluid Mech. 76 (1976) 383–399.

[4] H. Sakamoto, M. Arie, Flow around a normal plate of finite width immersed in a turbulent boundary

layer, J. Fluids Eng. ASME 105 (1983) 98–104.

[5] C.W. Letchford, Wind loading on free standing walls, OUEL Report 1599/85, Oxford University,

1985.

[6] C.W. Letchford, J.D. Holmes, Wind loads on free-standing walls in turbulent boundary layers,

J. Wind Eng. Ind. Aerodyn. 51 (1994) 1–27.

[7] S.F. Hoerner, Fluid dynamic drag, published by the author, 1965.

[8] E. Simiu, R.H. Scanlan, Wind Effects on Structures, 3rd Edition, Wiley, New York, 1996.

[9] C.W. Newberry, K.J. Eaton, Wind Loading Handbook, Building Research Establishment Report,

HMSO, London, 1974.

[10] ESDU International, Fluid forces and moments on flat plates, Data Item 70015, ESDU International,

London, 1970.

[11] International Standards Organization, ISO 4354, Wind actions on structures, Geneva, 1997.

[12] Standards Australia, AS1170.2, SAA loading code, Part 2: Wind loads, 1989.

[13] ESDU International, Boundary walls, fences and hoardings: Mean and peak wind loads and

overturning moments, Data Item 89050, ESDU International, London, 1989.

[14] N.J. Cook, The Designer’s Guide to Wind Loading of Building Structures, Part 2: Static structures,

BRE/Butterworths, London, 1990.

[15] European Committee for Standardisation, EUROCODE ENV 1991-2-4, Part 2.4: Wind actions,

1994.


[16] B. Langtree, Wind loads on free-standing walls and hoardings, B.E. Thesis, Department of Civil and

Environmental Engineering, James Cook University, 1997.

[17] A. Row, J. Wolbers, Wind loads on shade cloth structures, B.E. Thesis, Department of Civil

Engineering, The University of Queensland, 1996.

[18] C.W. Letchford, A.P. Robertson, Mean wind loading at the leading ends of free standing walls,

J. Wind Eng. Ind. Aerodyn. 79 (1998) 123–134.

[19] ASCE, Minimum design loads for buildings and other structures, ANSI/ASCE 7-95, ASCE,

New York, 1995.

[20] J.D. Ginger, private communication 1998.

[21] J.D. Holmes, Pressure and drag on surface-mounted rectangular plates and walls, Proceedings of the

Ninth Australasian Fluid Mechanics Conference, Auckland, 8–12 December 1986.

[22] C.J. Wood, On the use of static tubes in architectural aerodynamics, J. Wind Eng. Ind. Aerodyn. 3

(1978) 374–378.

[23] I.S. Gatshore, The effects of free stream turbulence on the drag of rectangular two dimensional prism,

BLWT Report-4-73, University of Western Ontario, Canada, 1973.




Wind pressures on permeably andimpermeably-clad structures

A.P. Robertsona,*, Ph. Rouxb, J. Gratraudb, G. Scarasciac,S. Castellanoc, M. Dufresne de Vireld, P. Palierd

aSilsoe Research Institute, Wrest Park, Silsoe, Bedford MK45 4HS, UKbCEMAGREF, BP 5095, 34033 Montpellier, Cedex 1, France

cUniversity of Bari, Amendola 165/A, 70126 Bari, ItalydCSTB, F-44071 Nantes, Cedex 3, France

Abstract

The first European Standard for the design of commercial-production greenhouses passed

through the formal voting stage in 2000 and its publication is imminent. For structural design

considerations, it is based on the Eurocodes, and so for wind loading it is based on ENV 1991-

2-4: 1995, although it provides additional information where specific data are available.

During the drafting exercise, one deficiency identified in available wind loading information

was that of pressure coefficient data for permeably clad structures. Greenhouses, particularly

flat shading structures and curved roof houses, are often clad in permeable shade or insect-

proof netting in southern Europe to reduce solar radiation gain and to increase ventilation. To

facilitate reliable design of such structures, pressure data were obtained from large-scale tests

conducted in the Jules Verne climatic wind tunnel at CSTB, Nantes, in November 1999. This

paper reports the experiments conducted on an arch structure and on a flat-roof structure,

where each was clad in turn in an impermeable plastic film, an ‘insect net’ of 33% open area,

and a ‘shade net’ of 39% open area. The pressure coefficient data obtained with each cladding

are compared for each of the two structural forms. r 2002 Elsevier Science Ltd. All rights

reserved.

Keywords: Wind loads; Porous cladding; Netting; Pressure coefficients; Greenhouses

1. Introduction

There are some 90,000 ha of commercial greenhouses in the EU. These are theproduction sites for the European protected horticultural industry. Such greenhouses

*Corresponding author. Tel.: +44-1525-860000; fax: +44-1525-861735.

E-mail address: [email protected] (A.P. Robertson).

0167-6105/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved.

PII: S 0 1 6 7 - 6 1 0 5 ( 0 1 ) 0 0 2 1 0 - 0

are designed to lower levels of structural safety than are conventional structures.This is for a variety of reasons, including tradition, low levels of human occupancy,the need to minimise capital costs in an extremely competitive market, and becausecrop yield is directly proportional to light transmission level, so demanding aminimum of opaque structural members. Greenhouses are consequently verylightweight structures that are particularly sensitive to wind and snow loading.Because of the low safety margins employed in design, it is particularly importantthat the loading data are accurate and relate directly to the special forms andfeatures of greenhouses.Such considerations have featured throughout the deliberations of CEN/TC 284

between 1992 and 2000 in developing prEN 13031-1: Greenhouses: design andconstruction. Part 1: commercial production greenhouses [1]. This draft EuropeanStandard (EN) is based on the Structural Eurocodes, but wherever supplementaryinformation was needed and was available, or wherever dedicated information(derived specifically from reputable tests on greenhouse structures) was available, ithas been incorporated into the draft EN. For example, no appropriate rules werecontained in Eurocode 3 [2] for the design of slender monotubular steel arches thatare commonly used for ‘polytunnel’ greenhouses, so structural tests were conductedon representative frames to formulate rules [3] that have been included in the draftEN for greenhouse design. It was also recognised that there was a general shortage ofwind loading data in Eurocode 1 [4] for permeably clad structures which are fairlycommonplace in horticulture when woven, porous, shade (or insect-proof) nettingsare used for the cladding material. Snow load distributions on arched-roof structureswas a further area where a shortfall in data was seen to exist and research has beenundertaken to try to address this [5]. A successful application was made to theEuropean research programme ‘‘Training and mobility of researchers: Access tolarge scale facilities’’ to utilise the Jules Verne climatic wind tunnel facility at CSTB,Nantes, to undertake tests on large models of greenhouse structures in order toprovide new wind and snow loading data. The snow loading tests were undertaken inOctober 1999, and the wind loading part of the programme was undertaken during alimited 5 day period from 15th to 19th November 1999.

2. Methodology

2.1. Wind tunnel facility

The inner ‘Thermal circuit’ wind tunnel at the CSTB Jules Verne facility was used(Fig. 1). The working section measures 10m wide by 7m high by 25m long, throughwhich a maximum wind speed of 38 m/s can be achieved. The tests were conducted atwind speeds of 8–16m/s as measured at the 4.06m high reference position near thetop of the 4.5m high by 6m wide jet inlet section.An attempt was made to reproduce the near-ground atmospheric boundary layer

characteristics for a rural site as reported by Hoxey and Richards [6] by introducinghorizontal wooden slats across the tunnel and roughness elements on the floor

A.P. Robertson et al. / J. Wind Eng. Ind. Aerodyn. 90 (2002) 461–474462

(Fig. 1). The velocity profile was measured just upwind of the model position (butwith no model present) using an array of pitot-static probes, and the static pressurewas measured at the model ridge position (again with no model present) to provide astatic pressure correction. The velocity ratio between the model ridge height and thereference was 0.88. The resulting velocity profile approximated to a logarithmicprofile with a roughness length of 9mm. The turbulence intensity at the mouth of thejet decreased from approximately 15% near the ground to approximately 5%between 2 and 3m height. The static pressure correction was of the order of 0.07Cp

when no model was present.

2.2. Experimental models and claddings

Two test models were constructed at 1:2 scale, as indicated in Figs. 2 and 3. Thepolytunnel arch was of 4m span and 1.83m height (its profile differed from semi-circular in that it had a flatter top). The shade house was a flat roofed structure of6m span and 1.68m height; it had rounded eaves (radius of curvature 0.33m).The models were clad in 3 different materials, all of which are used in practice:

conventional impermeable 120 mm thick polythene film sheet, plastic insect netting,

Fig. 1. Schematic of test arrangement in the ‘Thermal circuit’ of the Jules Verne wind tunnel facility at

CSTB, Nantes (dimensions in m).

0

50

100

150

200

-300 -200 -100 0 100 200 300

Fig. 2. Outline cross-section of the arched ‘polytunnel’ model with 15 pressure monitoring locations

(dimensions in cm).

A.P. Robertson et al. / J. Wind Eng. Ind. Aerodyn. 90 (2002) 461–474 463

and plastic shade netting. The porosities of the nets were determined atCEMAGREF, Montpellier, using a binocular microscope equipped with a digitalcamera, and Optimas software to analyse the images. The porosity (or open arearatio), b, of the insect netting was 33% (b33 ¼ 0:33), and of the shade netting was39% (b39 ¼ 0:39), where the ratio is defined simply as the open area per unit totalarea. The shade netting comprised both flat and cylindrical (knitted) elements andrectangular holes, whilst the insect netting comprised principally cylindrical elementsand rectangular holes. Loss coefficients, k; and discharge coefficients, CD; wereevaluated for the netting materials using a fan test rig at Silsoe Research Institute [7].The loss coefficients were k33 ¼ 4:3; and k39 ¼ 3:6: The discharge coefficients wereCD33 ¼ 0:49; and CD39 ¼ 0:53; although these coefficient values varied by up to 0.1depending on air flow rate and pretension in the net. The relationship between the band k values is in reasonable agreement with that given by Richards and Robinson[8] for ‘low porosity’ materials:

k ¼ ð1� bÞ2=b2;

The above experimentally measured values of k and CD are in reasonably goodagreement with their theoretical relationship:

k ¼ 1=C2D

when both parameters are evaluated with respect to the total area of the sample.The polytunnel model clad in the insect netting is shown in Fig. 4, and the shading

house model clad in the shade netting is shown in Fig. 5. Both figures show smokebeing used to visualise air flow in the Jules Verne thermal circuit wind tunnel.

2.3. Instrumentation

External and internal pressures were sensed on either side of the permeablecladding using special static probes developed for full-scale measurements of windpressures on buildings under natural, turbulent wind conditions [9]. The probes weremounted in pairs approximately 5 cm to either side of the cladding (as close aspossible whilst avoiding any fouling arising from displacement or flapping of the

0

50

100

150

200

-400 -300 -200 -100 0 100 200 300 400

Fig. 3. Outline cross-section of the rectangular ‘shading structure’ model with 15 pressure monitoring

locations (dimensions in cm).


cladding). Fifteen pairs of sensors were mounted around a line at the mid-length ofeach building (Figs. 2 and 3). The static pressure probes can be seen positionedaround each model at the central position across the width of the wind tunnel inFigs. 4 and 5. All the sensed pressures were transmitted pneumatically along lengths

Fig. 4. Polytunnel model clad in 33% open area insect netting.

Fig. 5. Shade house model clad in 39% open area shade netting.


of flexible plastic tubing to the CSTB wind tunnel pressure acquisition system, whichsampled the records at 16Hz for 60 s [10].The central (4m wide) section of each model was constructed on a rigid base

framework which was mounted on four load-cells. These load-cells enabled theoverall uplift and drag forces on the central section to be monitored. The cladding tothese central sections was tensioned through 3 additional, load-cells, which enabledthe pre-tension and wind-induced tension to be monitored. In all cases, the claddingwas fixed in the conventional manner along the bottom edge on either side of thestructure only (no intermediate fixings around the wall/roof faces). A dummy sectionwas added to either end of each model to extend the models to within approximately1m of the side walls of the 10m wide tunnel (i.e. such that the models wereapproximately two-dimensional). The data from the load-cells remain to beprocessed, and so will be reported in a subsequent publication. In each test,the gable-ends were clad in the same material as was used to clad the length of thestructure.When the polytunnel model was clad in impermeable polythene film sheet,

external surface pressures were monitored using flush-mounted tappings located atthe centre of thin aluminium discs clamped to the polythene film, as shown in Figs. 6and 7. These flush-mounted tappings were the same as those used in earlier full-scale

Fig. 6. Polythene film sheet cladding on polytunnel with pressure tappings mounted in the film.


wind pressure measurements on polytunnel structures [11]. For selected tappings, astatic probe was positioned transversely to the flow and close to the tapping(approximately 5 cm away) to enable comparisons to be made between tapping-holeand pressure-probe measurements (Fig. 6), and very good agreement was found.Displacements of the film plastic were also measured using a laser. A white coatingwas applied to the film plastic to provide a reflective surface for the lasermeasurements (Fig. 7). These results also remain to be processed and so will also bereported at a later date.

3. Results

Observations of displacements of the film-plastic cladding on the polytunnelstructure during testing indicated that representative pressure distributions werebeing achieved in the wind tunnel. Fig. 8 shows the extent of lifting of the claddingaway from the timber arch just to the windward side of the ridge. This concurredwith full-scale observations and measurements where high external suctions reachtheir greatest magnitude just to the windward side of the ridge and producemaximum lifting of the cladding away from the structure [12].Mean pressure coefficients were determined from the experimental data in the

conventional manner. The reference static pressure, and reference free-stream winddynamic pressure were corrected to obtain representative values at the modelposition. In all the presented results, the wind direction is from left to right andnegative coefficients denote pressures acting away from the cladding (i.e. suctions).Unless otherwise stated, all the data were obtained for a 12m/s reference wind speed.

Fig. 7. General view of polytunnel model clad in impermeable polythene film sheet.


Fig. 9 shows the mean external pressure coefficients for the polytunnel arch whenclad in all 3 materials. Also shown are results from full-scale measurements on a film-plastic clad polytunnel structure of similar geometry [11]. It can be seen that themodel test on the film-plastic polytunnel reproduced the positive windward pressureswell, but failed to reproduce the severity of the external suctions over the top of thearch, both in terms of magnitude and extent around the arch. This is indicative of

Fig. 8. Depiction of wind-induced lifting of film plastic cladding to windward side (left) of ridge of

polytunnel arch.

-1.5

-1.0

-0.5

0.0

0.5

1.0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

% Circumference

Cpe

FilmInsect netShade netFull-scale filmEurocode

Fig. 9. External pressure coefficients for polytunnel arch, and comparisons with full-scale data and

Eurocode 1.


early separation from the curved surface, which is consistent with flow observationssuch as that shown in Fig. 4, although this is for the polytunnel clad in the insect net(b33=0.33). The early flow separation is probably a result of the jet inletarrangement and the consequential divergence of the flow on leaving the mouth ofthe jet. The static pressure correction indicated an adverse pressure gradient, which isconsistent with flow divergence. The absence of negative external pressures on theleeward side of the arch suggests that adequate correction of the static pressuregradient may not be achievable from the single-point correction measurement at themodel ridge location, or that a deficient wake flow was being reproduced.Fig. 10 shows the effect of wind speed on the external suctions generated over the

arch in the wind tunnel. The maximum suctions steadily increase with wind speed,but not to an extent that approaches the full-scale distribution (Fig. 9). There are atleast three possible explanations for this modest increase in suctions with wind speed:Reynolds number, blockage, and aero-elasticity. An aero-elastic effect arises withpolytunnels because the flexible plastic-film cladding is usually simply wrappedaround the arch from one side to the other and is anchored only at the ground level,with no intermediate fixings around the circumference of the arch. The film plastic isthus able to lift away from the arches in regions of high uplift, as illustrated in Fig. 8.The extent of uplift depends strongly on the pre-tension achieved at the time ofcladding, the elasticity of the film, temperature, etc. Uplifting of the cladding changesthe geometry and tends to increase the suctions over the region where upliftingoccurs, particularly with flatter-topped arches [12]. The process thus tends to beprogressive, and so although there may be a blockage and/or Reynolds numbereffect, this is a likely explanation for the variations shown in Fig. 10.The effect of changing the impermeable film cladding to a permeable cladding is to

destroy the external suctions (Fig. 9) and so remove the tendency for lifting of the

-1.0

-0.5

0.0

0.5

1.0

0 0.2 0.4 0.6 0.8 1

% Circumference

Cpe

8 m/s12 m/s14 m/s16 m/s

Fig. 10. Effect of wind speed on external pressure coefficients around film-clad polytunnel arch.


cladding (which was supported by observations). The highest positive pressures arejust slightly reduced (by an amount related to the porosity), but the extent of thepositive pressure area increases significantly from just over 20% to nearly 40% of theway around the circumference. The CEN Eurocode 1 [4] provides a distinct worst-case envelope, over-estimating even the most severe, full-scale, impermeably cladexternal pressure distribution (Fig. 9). The Eurocode data on vaulted roofs wereobtained from the results of studies dating back to the early 1960s. It is for reasonssuch as these that new data for curved roof greenhouse structures have been includedin the impending European Greenhouse Standard. The data contained therein arebased on the results of a large programme of full-scale studies conducted in the 1980sand 1990s on curved roof polytunnel houses [11,12], and so are considered to providea more reliable basis for design.In the present work, the overall effect of replacing impermeable cladding with

permeable cladding was found to be a reduction in the external uplifts to an extentwhere they are effectively eliminated, but possibly to increase slightly the net drag.The corresponding mean internal pressure coefficients for the polytunnel are shownin Fig. 11. The coefficients are consistently of small magnitude (�0:05oCpio0:2),particularly with the two permeable claddings. The distributions show a rathersurprising periodic oscillation around the circumference of the arch, which isattributed to the presence of fairly substantial longitudinal timber purlins which werein close proximity to some of the internal probes (see Fig. 8) which formed part ofthe structural framework. The positions of these purlins are indicated in Fig. 11.The mean external pressure coefficients for the flat roof shade house when clad in

the 3 materials are shown in Fig. 12. Large suctions developed around the windwardcurved eaves when the house was clad with impermeable film, and suctions were

-1.5

-1.0

-0.5

0.0

0.5

1.0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

% Circumference

Cpi

FilmInsect netShade net

Purlin positions

Fig. 11. Internal pressure coefficients for polytunnel arch.


sustained across the full extent of the flat roof. As with the arch structure, however,these suctions were destroyed when the house was clad in the permeable materials,and pressures over the roof were close to zero, although very similar positivepressures were generated over the windward wall. Although not shown in Fig. 12(for reasons of clarity), Eurocode 1 gives a reasonable representation of the externalpressures around the impermeably clad, flat-roof, house with curved eaves. TheEurocode slightly under-estimates the peak suction just over the windward eaves,though the experimental values could have been enhanced slightly as a result of anaero-elastic effect, as described earlier for the case of an arch clad in plastic film.The internal pressure coefficients shown in Fig. 13 were again, as with the arch,

consistently small in magnitude (�0:05oCpio0:2), particularly with the twopermeable claddings. Local fluctuations in internal pressure are again probablyattributable to the presence of structural members acting as obstructions to internalflows in the vicinity of some of the internal probes.The small and generally fairly constant internal pressure distributions found

with both test structures may be the result of internal flows tending tobleed out transversely through the gable-ends of the models. The ends wereapproximately 1m from either side wall of the tunnel, and this together with therelatively close proximity of the model to the mouth of the inlet jet may have led tosuction zones around the gables that would tend to extract internal air from themodels.The general findings here of uplift forces being significantly reduced with porous

claddings are consistent with the findings of Letchford et al. [13] who conductedwind tunnel tests on 1:50 scale mono and duo-pitch canopies with claddings of 0%,11%, and 23% porosities. Drag loads were found to be much less affected byporosity of cladding, and for several roof geometries were essentially unaffected,which is also consistent with the present findings. Richards et al. [14] also found from

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

% Distance around cladding

Cpe

Film

Insect net

Shade net

Curved eave region

Fig. 12. Internal pressure coefficients for flat roof shade house.


a computational fluid dynamics simulation and a wind-tunnel study on a 1:50 scaleshade house (similar to the present shade house) that external suctions weresignificantly reduced in the case of a 50% porous cladding compared with animpermeable cladding. They further found that negative internal pressures weregenerated that approximately balanced the external roof suctions to producevirtually no net load on the roof. However, both Letchford et al. [13] and Richardset al. [14] found evidence of increased net loadings on permeably clad windwardfaces where positive external pressures were generated (in terms of the overall drag,this tended to be countered by a lower net drag on the corresponding leeward face).There is little evidence available from the present study to corroborate this particularpoint, although there are indications in Fig. 9 that the overall drag on the archedstructure increased slightly when it was clad with a permeable net.Further work remains to be done to complete the present study which should help

to clarify some of the above interpretations. In particular, the data from the loadcells that supported the central 4m wide section of each model remain to beprocessed. This will provide an independent measure of the overall loadings on thestructure. The data from the additional load-cells that monitored the membranetension in the film-plastic cladding on the arch also remain to be processed as part ofa further study needed to model the mechanism of load transfer from flexiblecladding to the structure. The implications for structural design of the differentloading distributions generated by permeable claddings needs to be assessed in orderto prepare design proposals to facilitate reliable design of permeably cladhorticultural structures.Unfortunately it was not possible in this programme of work to test for winds

other than in the spanwise direction. Limited time prohibited tests for a longitudinalwind direction, or for any cornering winds. As a result, it has not been possible toobtain pressure data to assist with the design of gable ends in this study.

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

% Distance around cladding

Cpi

Film

Insect net

Shade net

Curved eave region

Fig. 13. Internal pressure coefficients for flat roof shade house.


4. Conclusions

The study has compared the external and internal mean pressure coefficientdistributions over a large scale model of an arched ‘polytunnel’ structure and a flatroof ‘shade house’ structure, where each structure was clad in turn in animpermeable sheet, a 33% porous ‘insect net’ and a 39% porous ‘shade net’. Theprincipal findings were that the high external suctions developed over parts of eachstructure when impermeably clad were destroyed when permeably clad, resulting invirtually no net uplift. Positive pressures on windward faces, however, were littleaffected in terms of their magnitudes by the introduction of a porous cladding, buttheir zones of operation may be extended, leading possibly to slightly increased netdrag loadings. These findings are in line with those from other recent studies,although there are indications elsewhere that net loads on windward facesexperiencing positive external pressures can increase when clad with a porousmaterial, and that overall drag loads may increase slightly for this reason.Once the remaining load-cell data have been analysed and the structural design

implications of the results of this work have been established, the present pressurecoefficient data and those in the literature will be used to formulate a proposal forinclusion in the forthcoming European Standard for the design of commercialproduction greenhouses.

References

[1] European Committee for Standardization (CEN), prEN 13031-1 Greenhouses: Design and

Construction. Part 1: Commercial Production Greenhouses, CEN, Brussels, May 1999.

[2] European Committee for Standardization (CEN), DD ENV 1993-1-1: Eurocode 3: Design of Steel

Structures: Part 1.1: General Rules and Rules for Buildings, CEN, Brussels, 1992.

[3] Ph. Roux, A.P. Robertson, R. Motro, The design of slender, monotubular steel arches, Struct. Eng.

75 (9) (1997) 143–151.

[4] European Committee for Standardization (CEN), ENV 1991-2-4: Eurocode 1: Basis of Design and

Actions on Structures: Part 2.4: Wind Actions, CEN, Brussels, 1995.

[5] G. Scarascia, P. Palier, J. Gratraud, P. Roux, A.P. Robertson, Snow distributions on greenhouses,

Proceedings of the Fourth International Conference on Snow Engineering, Trondheim, Norway,

19–22 June, 2000.

[6] R.P. Hoxey, P.J. Richards, Structure of the atmospheric boundary layer below 25m and implications

on wind loading on low-rise structures, J. Wind Eng. Ind. Aerodyn. 43 (1992) 1641–1652.

[7] L.J. Moulsley, J.M. Randall, R.L. Hartshorn, C.J. Houghton, D.G. Randle, Facilities for measuring

fan performance, Divisional Note DN 1408, Silsoe Research Institute, Silsoe, Bedford, April, 1987.

[8] P.J. Richards, M. Robinson, Wind loads on porous structures, J. Wind Eng. Ind. Aerodyn. 83 (1999)

455–465.

[9] P. Moran, R.P. Hoxey, A probe for sensing static pressure in two-dimensional flow, J. Phys. E 12

(1979) 752–753.

[10] C. Solliec, J. Mary, Simultaneous measurements of fluctuating pressures using piezoresistive

multichannel transducers as applied to atmospheric wind tunnel tests, J. Wind Eng. Ind. Aerodyn. 56

(1995) 71–86.

[11] R.P. Hoxey, G.M. Richardson, Measurements of wind loads on full-scale film plastic clad

greenhouses, J. Wind Eng. Ind. Aerodyn. 16 (1984) 57–83.


[12] G.M. Richardson, Full-scale wind load measurements on a single-span film plastic-clad livestock

building, J. Agric. Eng. Res. 55 (1993) 251–264.

[13] C.W. Letchford, A. Row, A. Vitale, J. Wolbers, Mean wind loads on porous canopy roofs, J. Wind

Eng. Ind. Aerodyn. 84 (2000) 197–213.

[14] P.J. Richards, P.J. Shepard, P. Maharaj, Pressure distributions on shade houses, Proceedings of the

Second Asia-Pacific Symposium on Wind Engineering, Beijing, China, 1989, pp. 517–524.


TSINGHUA SCIENCE AND TECHNOLOGYISSN 1007-0214 12/21 pp354-358Volume 10, Number 3, June 2005

Software Practicalization for Analysis of Wind-Induced Vibrations of Large Span Roof Structures*

ZHANG Enuo ( ), YANG Weiguo ( ),

ZHEN Wei ( ) NA Xiangqian ( )**

Department of Civil Engineering, Tsinghua University, Beijing 100084, China; Beijing Institute of Architectural Design, Beijing 100045, China

Abstract: Wind loads are key considerations in the structural design of large-span structures since wind

loads can be more important than earthquake loads, especially for large flexible structures. The analysis of

wind loads on large span roof structures (LSRS) requires large amounts of calculations. Due to the com-

bined effects of horizontal and vertical winds, the wind-induced vibrations of LSRS are analyzed in this pa-

per with the frequency domain method as the first application of method for the analysis of the wind re-

sponse of LSRS. A program is developed to analyze the wind-induced vibrations due to a combination of

wind vibration modes. The program, which predicts the wind vibration coefficient and the wind pressure act-

ing on the LSRS, interfaces with other finite element software to facilitate analysis of wind loads in the de-

sign of LSRS. The effectiveness and accuracy of the frequency domain method have been verified by nu-

merical analyses of practical projects.

Key words: wind vibration coefficient; vertical wind; frequency domain analysis; vibration modes; large

span roof structures (LSRS)

Introduction

Large span roof structures (LSRS) are characterized by

low rigidity, low-mass, numerous vibration modes and

great sensitivity to wind loads. Wind loads are usually

the critical loads with the frequency domain method

normally used to analyze LSRS. In the analysis of the

maximum response of structures subjected to wind

loads, the fluctuating wind load is converted to an

equivalent static wind load with a wind vibration coef-

ficient used to account for the combined effect of the

average wind load and the fluctuating wind load.

At present, no special codes have been developed in

China to properly analyze the wind loads on LSRS.

Many designers still use ordinary methods similar to

high-rise structures in which the wind vibration coeffi-

cient is determined only by the first structural fre-

quency, which is not accurate for the flexible LSRS. A

practical and accurate method for wind vibration

analysis is needed to properly design LSRS.

The wind vibration coefficient is a function of the

fluctuating wind velocity and direction, the structure’s

natural vibration characteristics, and the structure’s

spatial form[1]

. The wind vibration coefficient is the

arithmetic product of the wind dynamic coefficient, the

influence coefficient, and the location coefficient. At

each point, the wind dynamic coefficient depends on

the damping ratio and the vibration period correspond-

ing to every vibration mode. The influence coefficient

depends on the fluctuation coefficient, the height coef-

ficient, the vibration mode, and the spatial coefficient.

Received: 2004-01-02; revised: 2004-07-16

Supported by the National Natural Science Foundation of China

(No. 50178035)

To whom correspondence should be addressed.

E-mail: [email protected]; Tel: 86-10-62786706

ZHANG Enuo ( ) et al Software Practicalization for Analysis of Wind-Induced 355

The location coefficient depends on the vibration mode

and the absolute height. Generally, roof structures have

various heights with definite slopes and many degrees

of freedom, which results in severely complex calcula-

tion of the wind vibration coefficient and the wind

pressure.

In addition, since the wind direction acting on the

structure is not always horizontal, the vertical compo-

nent of the wind also affects the structure. For ordinary

buildings, only the axial wind direction and velocity

are important, but for roofs, especially those with large

areas and no internal structural supports, the vertical

wind component is often more important; therefore,

the analysis of wind-induced vibrations in roof struc-

tures must consider the superposition of the horizontal

and vertical wind components[2,3]

.

The analysis of wind-induced vibrations requires

rapid and accurate calculation of the wind vibration

coefficient and the wind load[4,5]

. A program has been

developed based on Zhang’s work[6]

to analyze the

wind induced vibrations of LSRS that satisfies the ex-

isting design standards[1]

, which can calculate the wind

vibration coefficient and the wind pressure acting on

LSRS. The program uses the roof structural vibration

mode and the nodal mesh coordinates created by a

structure analysis package, such as STAAD, to calcu-

late the height variation coefficient and the spatial rele-

vance coefficient of each node. The program can also

calculate the horizontal and vertical wind vibration

coefficients of each subregion point and superpose

them to calculate an equivalent wind load for each

subregion point, which is the solution of the LSRS

wind load problem.

1 Theory

1.1 Horizontal wind vibration coefficient

The horizontal wind vibration coefficient[7]

is defined

as the ratio of the probabilistic value of the total wind

load ( ) to the probabilistic value of the

static wind load ( ). A dynamic analysis gives:

s d( ) ( )p z p z

s ( )p z

d

s

( , )1

( , )zi

p x z

p x z

0

s 0

( , ) ( , )1

( , ) ( )

i i ii i i

z

u x z m x z wu r

x z z w1 (1)

where zi is the horizontal wind vibration coefficient,

i is the vertical wind vibration coefficient, is the

influence coefficient, and is the location coefficient

corresponding to the i-th vibration mode.

iu

ir

Equation (1) can be modified for LSRS and general-

ized to structures with multiple degrees of freedom.

The coefficients are given by:

43

2

0

2

0

150 /1

(1 900 / )

i ii

i

w T

w T (2)

f s

1

2

1

( ) ( , ) ( )n

j j zj ij jj

i xn

j ijj

z x z z S

uM

yzi (3)

s s

( , )

( ) ( )

ij ij jij

j zj j zj j

x z m Mr

z z S (4)

where xyzi xi y zi is the spatial relevance

coefficient of the i-th vibration mode calculated from

the vibration mode function and the spatial relevance

function. The vibration calculations are simplified

assuming that the roof structure is a supported beam.

i is the damping ratio and is the vibration period

corresponding to the i-th vibration mode.

iT

fj is the

wind pressure fluctuating coefficient, sj is the shape

coefficient, zj is the height coefficient. Mj is the roof

mesh mass, and jS is the roof mesh area

corresponding to the j-th node. ij is the vibration

mode of the j-th node on the roof corresponding to the

i-th vibration mode.

1.2 Vertical wind vibration coefficient

The vertical wind component is classified into an aver-

age component and a fluctuating component, in a man-

ner similar to the horizontal wind component. The

power spectrum of the horizontal fluctuating compo-

nent is a Davenport spectrum, while the power spec-

trum of the vertical fluctuations is a Panofsky spectrum.

Therefore, the vertical wind vibration dynamic coeffi-

cients vi and the horizontal wind vibration dynamic

coefficients i are in different forms.

The vertical wind vibration coefficient can be ob-

tained using a method similar to that for the horizontal

fluctuations.

v v1 v vz i i iu ri (5)

Tsinghua Science and Technology, June 2005, 10(3): 354 358356

where 2

v 1 / (1 4 )i i i ix x (6)

in which 2

10 0/ / 41i i ix n z v z w T (7)

v10 is the velocity at the height of 10 m. vi , which is

similar to the horizontal fluctuation amplification coef-

ficient i , is related to the damping ratio i ,

and the height z. and are similar to their

counterparts for the horizontal fluctuation.

2

0 ,iw T

viu vijr

The expression for the vertical wind vibration coef-

ficients shows that the vertical fluctuation amplifica-

tion coefficient, vi , is much larger than the horizontal

fluctuation amplification coefficient i , even though

the vertical wind load is only about 20% as large as the

horizontal wind load on average. Therefore, the total

influences of the vertical and horizontal components

are of the same order of magnitude and cannot be

neglected.

1.3 Total wind loads

In both horizontal and vertical directions, the wind ef-

fect is equal to the product of the average wind load

and the wind vibration coefficient[8]

. The total response

is the superposition of the effects in the two directions:

(8) s v sv( ( ) 0.18 ( )) ( )j zj j z j j zj jp z z z 0S w

2 Software Characteristics and Function

The program requires the user to input parameters

(such as damping ratio, reference wind pressure, ter-

rain roughness, and shape coefficient) to determine the

structural characteristics and the influence of its loca-

tion. The program reads the structural vibration mode

data from the vibration mode output from the finite

element program such as STAAD, calculates the wind

vibration coefficient of the roof, and combines the ef-

fects of the vibration modes. The result includes the

horizontal and vertical wind vibration coefficients of

each node on the roof corresponding to each vibration

mode and to the combined vibration modes. The user

can also input the roof mass distribution and the area

for each mesh node to calculate the wind pressure on

each node, which can then be used directly for the

structural analysis of wind load.

Since the roof shape and the mesh sizes vary greatly,

the program can analyze the structure in various

subregions. Each subregion can be given its own shape

coefficient and mesh area. Since the analysis also

considers the height coefficient, the fluctuating

coefficient, and the spatial relevance coefficient,

relatively accurate results can be obtained when the

program is applied to relatively steep roofs.

The analyses of practical examples show that the de-

sign efficiency and accuracy are greatly improved by

the program. If the shape coefficient can be obtained

from wind tunnel test, can be reliably predicted, the

program can be completely applied as an auxiliary cal-

culation method in the final drawing design period.

The program is developed using Visual Fortran,

with a visual display interface to facilitate users to in-

put, as shown in Fig. 1. WVC represents the wind vi-

bration coefficient.

Fig. 1 Software input interface

The output data format is shown in Table 1 for node

i. The table is repeated for each node.

Table 1 Output data format for node i

Horizontal

WVC

Vertical

WVC

Combined wind

pressure

First vibration mode 1z v1z 1w

Second vibration

mode 2z v2z 2w

i-th vibration mode zj vz j jw

n-th vibration mode zn vz n nw

Sum of 1st to n-th vibration modes

z vz totalw

ZHANG Enuo ( ) et al Software Practicalization for Analysis of Wind-Induced 357

3 Application

A typical cantilevered gymnasium roof is shown in Fig.

2. The average height of the roof is 22 m with the low-

est point at 19 m and the highest point at 30 m. The

long axial span is 175 m and the maximum short axial

span is 33 m. The structure is supported by an anterior

peripheral truss at point J and a posterior steep cable

brace. The structure is supported at points A-E. The

gymnasium is located in a flat area, so the influence of

wind load is quite important. The basic terrain rough-

ness is Type B, the reference wind pressure 0 is

0.5 kN/m2, and the structural damping ratio is 0.02.

The analysis mesh has 120 nodes on the roof. The

mesh divides the roof into three subregions. The

subregions are identified by the Roman numerals I and

II in Fig. 2.

The area around each node in subregion I is aver-

aged 50 m2. The areas around each node in subregion

II is averaged 20 m2. The average roof density was

100 kg/m2. The wind vibration coefficients for each

node are calculated by the program. Ten typical nodes

shown in Fig. 2 are chosen along the x and y axes. The

wind vibration coefficients and wind pressures due to

the front 20 vibration modes of these ten nodes are

listed in Tables 2 and 3.

Fig. 2 Sketch of gymnasium roof structure

Table 2 Loads along the x axis

Node Horizontal WVC Vertical WVC Wind pressure

(kN/m2)

A 1.262 1.144 0.42

B 2.639 1.884 0.84

C 3.016 2.088 0.96

D 2.626 1.873 0.83

E 1.249 1.137 0.41

Table 3 Loads along the y axis

Node Horizontal WVC Vertical WVC Wind pressure

(kN/m2)

F 3.336 2.261 1.05

G 2.700 1.919 0.87

H 1.936 1.510 0.64

I 3.266 2.321 1.06

J 1.175 1.103 0.41

The horizontal and vertical wind vibration

coefficients and the wind pressure vary in the same

manner, which is related to the distribution of the

structural vibration modes. This confirms the reliability

of the calculated results.

Although the vertical wind load is only one-fifth of

the horizontal wind load, the vertical wind vibration

coefficient is equal to the horizontal wind vibration

coefficient; therefore, the effect of the vertical wind

load cannot be neglected in the analysis[9]

.

The vertical wind vibration coefficient and wind

pressure do not decrease uniformly from F to J, but

experience a large maximum at point I. The results

indicate that the fourth vibration mode contributes very

strongly to the wind vibration at node I. Because node

I is in the middle of the roof, it experiences larger

vibration amplitudes due to the wind load. These

results also indicate that the contribution of the high-

order vibration modes cannot be neglected in the

analysis of roof structural wind-induced vibrations[10]

.

4 Conclusions

The calculation of wind-induced vibrations and wind

pressures on LSRS is a complex problem, mainly be-

cause multiple vibration modes must be considered in

the frequency domain analysis. Based on the LoadCode for the Design of Building Structures, PRC, an

analysis program is developed considering the effects

of multiple wind vibrations and wind pressures on

LSRS. The results obtained from the program verify

the importance of multiple vibration modes in the

Tsinghua Science and Technology, June 2005, 10(3): 354 358358

analysis. The accuracy and reliability of the program

have been verified through several practical examples.

References

[1] Standard of People’s Republic of China. Load code for the

design of building structures (GB50009-2001). 2001: 24-48.

(in Chinese)

[2] He Yanli, Dong Shilin, Gong Jinhai. Wind responses

analysis method of spatial lattice structures in frequency

domain with mode compensation. Spatial Structures, 2001,

7(2): 4-10. (in Chinese)

[3] Hu Jijun. Study of dome’s wind vibration [Ph.D. Disserta-

tion]. Shanghai: Shanghai Jiao Tong University, 2000.

[4] Wang Zhihong. Simulation of wind load. Journal of Build-

ing Structures, 1994, 15(1): 44-52. (in Chinese)

[5] Li Yuanqi, Dong Shilin. Random wind load simulation and

computer program for large-span spatial structures. Spatial

Structures, 2001, 7(3): 3-11. (in Chinese)

[6] Zhang Xiangting. Calculation of Structural Wind Pressure

and Wind Vibration. Shanghai: Tongji University Press,

1985. (in Chinese)

[7] Yang Qinshan, Sun Xuedong. Horizontal and vertical wind

excitations. Journal of Harbin University of Architecture

and Engineering, 1997, 30(6): 43-50. (in Chinese)

[8] Lu Feng, Lou Wenjuan, Sun Binnan. Wind induced

dynamic response and wind load factor for long-span flat

roof structures. Engineering Mechanics, 2002, 19(2): 52-57.

(in Chinese)

[9] Lu Fei, Li Aiqun, Cheng Wenxiang, Chen Zhongfan. Study

of the main process and method of simulating fluctuant

wind load. Special Structures, 2002, 19(3): 18-20.

(in Chinese)

[10] Kolouse V, Pirner M, Fischer O. Wind Effects on Civil

Engineering Structures. Prague: Academia, 1984.

_____________________________________________________________________________

Chinese Society of Micro-Nanotechnology (CSMNT) Founded at Tsinghua

The Chinese Society of Micro-Nanotechnology (CSMNT) was founded at Tsinghua University on April 5, 2005.

Gu Binglin, the president of Tsinghua University, Bai Chunli, the vice president of the Chinese Academy of Sci-

ences, and other delegations from governmental research departments attended the opening ceremony.

Tsinghua Vice President Kang Kejun presided over the event. Tsinghua professor Zhou Zhaoying gave a speech

explaining the draft constitution of CSMNT. Academician Bai gave a speech congratulating the launch of the Soci-

ety, saying it would “boost the research in related fields”.

During the meeting, President Gu outlined the development of micro-nanotechnology in the world and in

Tsinghua University. He discussed the possibility of enhancing mutual cooperation between Tsinghua and

CSMNT in the areas of MNT.

(From http://news.tsinghua.edu.cn)

ARTICLE IN PRESS



0167-6105/$ -

doi:10.1016/j

�CorrespoE-mail ad

www.elsevier.com/locate/jweia

Wind tunnel evaluation of mean wind pressureon a frame-type signboard

Carlo Paulotto, Marcello Ciampoli, Giuliano Augusti�

Dipartimento di Ingegneria Strutturale e Geotecnica, Universita ‘‘La Sapienza’’, Via Eudossiana 18;

00184 Roma, Italy

Available online 28 February 2006

Abstract

In the context of the growing concern for the wind effects and the wind design of ‘‘street

architecture’’ (bill-boards, traffic signs, traffic lights, etc.), wind tunnel tests have been carried out on

a model of a frame-type signboard, placed within a regular array of buildings. The first experimental

results, reported here, help to clarify the relationship between the wind loading on the signboard and

the characteristics of the wind acting on the surrounding buildings.

r 2006 Elsevier Ltd. All rights reserved.

Keywords: Boundary layer wind tunnel; Experiments; Street architecture; Built-up environment; Wind fields

1. Introduction: previous work

In the last years, the interest on wind effects in urban environment has grown. This factcan be related on the one side to the magnitude of the social-economic losses due towindstorms that strike urban areas, on the other to the increasing sensitivity to airpollution problems and public health consequently.

As reported in Augusti et al. [1], losses related to wind storms in urban environmentshave increased dramatically in the last decades. This trend can be attributed not only tothe increasing concentration of activities and artifacts in urban settlements in areas at riskand to the presence of non-engineered buildings, but also to the challenges of modernengineering facilities, like bridges, telecommunication and high-tech facilities, largeroofs and lifelines; the reduction of the weight of the constructed facilities in general

see front matter r 2006 Elsevier Ltd. All rights reserved.

.jweia.2006.01.006

nding author.

dress: [email protected] (G. Augusti).


ARTICLE IN PRESSC. Paulotto et al. / J. Wind Eng. Ind. Aerodyn. 94 (2006) 397–413398

and of their load-carrying components in particular has determined a strong increase ofthe structural vulnerability to wind action. Moreover, the damages to secondary elements,i.e. the non-structural elements in modern buildings and infrastructures, have beenidentified as a major source of economic and social losses when a storm passes over a wideregion.The same can be said for the items of the so-called ‘‘street architecture’’ (bill-boards,

traffic signs and traffic lights, etc.) to which, until recent years, little attention has beenpaid in wind engineering circles. It is now recognized that possible damages to these itemsby wind may be not only the cause of significant economic losses, but also of injuries tohumans. Therefore, a significant research effort on the effects of wind and the design ofstreet architecture has begun.In particular, several research works have been devoted to the study of the wind effects

on signboards, e.g. Pulipaka et al. [2], Letchford [3], Quinn et al. [4]. One of the reasons forthis interest is probably that the provisions of wind design codes are perceived to beinappropriate. As reported by Quinn et al. [4], for example, the relevant British Standardsspecifies design wind speeds that are felt unrealistic and are, therefore, widely ignored. Thecurrently used rules for design of the foundation of fixed road furniture are consideredoverly conservative and thus expensive. In practice this results, on the one hand, in over-design of the sign mounting, and on the other, to dangerously inadequate sign mountings.Commercial competitive pressure clearly encourages the latter course of action. In Italy,the part of the structural design code [5,6] relative to wind actions does not cover theproblem of wind effects on signboards. But, for traffic signs, a specific mandatoryprovision [7] prescribes that these have to be checked to withstand a wind velocity of41.7m/s, hence a dynamic pressure of 1.40 kN/m2.Moreover, the codes normally give force and pressure coefficients based on wind tunnel

measurements on isolated buildings (open country terrain exposure); it is evident that, withreference to the case of an urban environment, this situation could be considered realisticfor isolated tall buildings, but it is unrealistic for low-rise buildings and for streetarchitecture items completely immersed in the urban canopy. How to systematically takeinto account the effects of the surroundings on the wind loads that effectively act on low-rise buildings is still an open problem. The reason is the large number of existing buildingconfigurations with varying dimensions and distances. As reported by Stathopoulos [8],Davenport suggested an empirical way to solve this problem; noting that the greatmajority of low buildings are in suburban terrain exposure and since the design gustpressure coefficients are provided regardless of wind direction, he argued that it would berather unlikely to expect the most critical wind speed to originate from the most criticalwind direction for a particular building orientation. On this basis, he suggested to multiplyby a factor 0.8 the most critical measured pressure coefficient.To obtain experimental indications about the influence of the surroundings on wind

loads, very simple configurations were examined at first: for example, in the investigationsby Husain and Lee [9,10] the urban complex was modeled by an array of cubes of the samesize arranged in normal and staggered grid patterns and pressures were measured on thesurface of one of these cubes. They observed that wind loads decrease, with respect toloads on isolated buildings, with increasing density of the cubes, except for the case of lowdensity and short up-wind fetch. Analogous tests were carried out by Jia and Sill [11] whofound that the pressure coefficients decreased for increasing density of the cubes andapproached asymptotically a constant value.

ARTICLE IN PRESSC. Paulotto et al. / J. Wind Eng. Ind. Aerodyn. 94 (2006) 397–413 399

More realistic models of urban complexes were investigated by Ho et al. [12] and Kieferand Plate [13]. Such tests must take into account that the approach wind is stronglymodified before striking the buildings under test by other nearby buildings, that therefore,should be included as a part of the model. In urban settings, this would typically requirethe scaled reproduction of all major buildings and structures within about 300–800m, thususually covering the entire turntable of the wind tunnel. However, the accuracy of themodel details, used in these near-field models, can be reduced with the distance from thesite, and block outline representations of buildings are usually acceptable. The model ofthe near field around the tested elements is often denoted proximity model [14].

Ho et al. [12] investigated 1:250 models of low-rise flat roofed buildings(38m� 24m� 5m, in real scale), either embedded in the model of a typical North-American industrial area or isolated. The proximity model was a circular area with a radiusof 340m. Two different approach flow profiles, corresponding to ‘‘suburban’’ and ‘‘opencountry’’ terrain categories, were used, but were found not to have a significant influence.It was concluded that the highest wind load would, as a rule, occur for isolated buildings.For built-up areas high pressures or suctions mostly decrease, while the smaller loadincreases. Furthermore, the wind loads relative to the ‘‘embedded’’ condition is shown tovary with the flow direction less than those relative to the isolated condition.

Kiefer and Plate [13] investigated the influence of the surroundings on the wind pressuresacting on different types of low-rise buildings. Two different proximity models were tested:(i) a uniform array of cubical building of the same size and (ii) a typical industrial area. Theinfluence of the size of the proximity model was also investigated. It was found that for theproximity model (i), the mean and fluctuating pressures remain constant when the radiusof the model is larger than approximately 10 building heights. For the ‘‘inhomogeneous’’model (ii), the fluctuating component varies with the turbulence of the approach flow,unless the proximity model is of the order of 40 building heights. For the examined cases, itwas found that the integral force acting on the roof of the considered building correlateswith a parameter formed by the frontal density (defined as the ratio between the sum of thefrontal areas of the roughness elements and the total plan area of the roughness field), themean height of the roughness elements and the test building height.

In Plate and Kiefer [15], a first attempt to define a conceptual framework for taking intoaccount the effects of urban canopy in code prescriptions can be found. With this aim theysuggested to introduce, besides the Davenport’s classical exposure coefficient, a secondexposure factor, defined as the ratio between the wind loads relative to the ‘‘embedded’’condition and relative to the isolated one.

The research reported in the present paper [16] intends to give a further contribution inthis direction: it describes the results of a series of wind tunnel tests focused on the study ofthe wind action on a frame-type signboard embedded in a regular array of identicalbuildings.

2. Experimental set up

The experimental tests have been performed in the boundary layer wind tunnel ofCRIACIV1, in Prato, Italy. This is an open circuit wind tunnel with a working cross

1CRIACIV: Inter-university Research Center for Building Aerodynamics and Wind Engineering (Universities

of Firenze, Roma ‘‘La Sapienza’’, Perugia, Trieste, Venezia IUAV, Chieti-Pescara).

ARTICLE IN PRESS

Fig. 1. Turbulence intensity profiles corresponding to the two wind tunnel configurations of the experimental

tests. Config 1: vortex generators at the entrance of the wind tunnel and wood cubes as surface roughness. Config

2: as Config 1, without wood cubes.

C. Paulotto et al. / J. Wind Eng. Ind. Aerodyn. 94 (2006) 397–413400

section 2.4m wide and 1.6m high and total length 11m. The velocity of the flow can bevaried between 0 and 30m/s. An 8m upstream fetch uses a combination of vortexgenerators and artificial surface roughness to obtain appropriate approach flowssimulating the lower part of the atmospheric boundary layer: two different arrangementshave been used in the experimental tests reported here. A first type of approach flow hasbeen obtained using both vortex generators at the entrance of the wind tunnel and woodcubes as surface roughness: this arrangement, indicated as Config 1, is characterized bythe profiles of turbulence intensity (Iu) and of integral length scale (Lux), shown in Figs. 1and 2, respectively. The second approach flow has been obtained using only the vortexgenerators and is denoted as Config 2.The model of the signboard has been realized in 1:100 scale by rapid prototyping (see

Fig. 3). It is a rigid model: the validity of this choice is confirmed by Letchford [3] andQuinn et al. [4] who did not observe any evidence of strong non-steady behavior in theirstudy on signboards. Nine pressure taps have been positioned on each face of the modelsignboard, as sketched in Fig. 4. Each tap has been pneumatically connected with aminiaturized pressure transducer, in turn connected with the data acquisition system(Pressure System 8400 SP) that incorporates a 16-bit A/D converter. The 1:100 scale wasconsidered suitable to allow the allocations, inside the model, of the pipes that realize theconnections between the taps and the transducer. Clearly, the model of the boundary layerwas also adjusted to this scale.The pressure signals have been recorded for a time interval of 40 s, with a sample

frequency of 541Hz. Only the mean values (evaluated on an appropriate time interval) ofthe pressure acting on the signboard can be considered significant. In fact, the pipes that

ARTICLE IN PRESS

Fig. 2. Integral length scale profiles corresponding to the two wind tunnel configurations of the experimental

tests.

Fig. 3. Photo of the signboard model tested in the present study.

C. Paulotto et al. / J. Wind Eng. Ind. Aerodyn. 94 (2006) 397–413 401

connect the pressure taps on the model with the pressure transducers were bent in order tobe inserted into the model; hence, the sectional area of the pipes was much reduced at the‘‘kinks’’, perhaps to less than 50% of the original value, and this reduction could stronglyaffect the fluctuating part of the pressure signal (a similar effect was noted by Yoshidaet al. [17]).

ARTICLE IN PRESS

Fig. 4. Arrangement of the pressure taps on the surface of the signboard model (dimensions in mm). The height of

the upper side of the signboard above the ground is 71mm.


Therefore, throughout the paper, only mean values of the pressure have been taken intoconsideration.The velocity of the flow has been measured by a hot-wire probe (DANTEC P11)

connected to an anemometric bridge (DANTEC CTA BRIDGE 56C17), in turn connectedto a 16-bit A/D converter (IOTECH ADC488/8SA). The velocity signals have beenrecorded for 32 s, with a sample frequency of 2 kHz.The particle image velocimetry (PIV) system consisted of a double pulsed laser with

maximum power of 220mJ, a KODAK MEGAPLUS CCD camera, a SynchronizerDANTEC 2100 and a personal computer. The size of the interrogation window forvelocity calculation was set at 32� 32 pixels; an overlap of 25% was permitted. Afterremoving spurious vectors, the statistical calculations were carried out by using the post-processing program DANTEC Flow Map, based on the two-frame cross-correlationmethod. Oil drops were used as seeding particles.The model was placed in the centre of a turntable, on which the proximity model (i.e.

according with the already quoted definition [14], the near field model) was mounted. It isin plan a circular surface with a radius of 75 cm (corresponding to 75m in a real scale): thecondition for which there are no obstacles on this surface is denoted as ‘‘free-standing’’condition, while ‘‘embedded’’ condition indicates that this surface is covered by a regulararray of identical buildings (Figs. 5 and 6).The recorded pressure values have always been divided by the same ‘‘mean reference

pressure’’, i.e. the dynamic pressure of wind in the same points in absence of the model,calculated from tests above an empty turntable (‘‘free standing’’ condition).

3. Description of the experimental work and discussion

3.1. Tests on free-standing signboard

A first series of tests has been carried out in order to evaluate the validity of theexperimental set up and the possibility of estimating correctly the values of the windpressure: in these tests, the model in a ‘‘free-standing’’ condition has been considered.The model has been invested by the boundary layer Config 1, characterized by the

profiles of turbulence intensity (Iu) and of integral length scale (Lux) shown in Figs. 1 and 2:from these profiles, at the height of the signboard, the values of Iu and Lux are 19% and20m (in real scale), respectively. If these values are compared with those suggested by theprovisional European Wind Code ENV 1991-2-4 [18] and the final EN 1991-1-4 [19],

ARTICLE IN PRESS

Fig. 5. Plan view of the model of proximity for the ‘‘embedded’’ condition (dimensions in mm).

Fig. 6. Photo of the model of proximity for the ‘‘embedded’’ condition.


reported in Table 1, it can be noted that: (i) the experimental value of Iu is close to that ofterrain category II (‘‘area with low vegetation such as grass and isolated obstacles withseparation of at least 20 obstacles height’’) and (ii) the experimental value of Lux is muchlower than any values indicated in either the provisional or the final version of the EurpeanCode. However, it should be considered that the integral length scale furnishes only arough indication (practically the order of magnitude) on the dimension of the majorvortexes present in turbulent flow. In the light of this consideration, the presentexperimental value of Lux can be reasonably acceptable for a terrain category not smaller

ARTICLE IN PRESS

Table 1

Values of turbulence intensity (Iu) and integral length scale (Lux) at the height of the signboard (about 7m above

ground), and values of displacement height (d) according to two successive versions of the Structural Eurocode on

Wind Actions

Code Terrain category Iu [%] Lux [m] d [m]

ENV 1991-2-4 I 15 184 2

II 20 113 4

III 30 78 8

IV 36 78 16

EN 1991-1-4 0 13 72 1

I 15 60 1

II 20 43 2

III 32 31 5

IV 43 31 10

Fig. 7. Mean velocity profiles corresponding to the two wind tunnel configurations of the experimental tests.


than category II, as defined in EN 1991-1-4 [19]. Moreover, if the height of the panel of themodel signboard (20mm) is compared to the height of the boundary layer (approximately800mm, see Fig. 7—Config 1), it appears evident that the shape of the mean velocityprofile is not crucial for the evaluation of the pressures acting on the signboard. Then it isfair to state that the characteristics of the flow at the test section of the wind tunnel can beconsidered representative of a terrain category II according to EN 1991-1-4 [19].Changes in wind direction have been simulated by rotating the turntable on which the

model was mounted. Tests have been carried out at 451 azimuth increments for the full


range of 3601 (the azimuth is defined as the angle y between the normal to the model andthe wind direction).

The mean values of the pressure coefficients Cp have been evaluated for all the pressuretaps existing on the model. These values have been interpolated in order to reconstruct thepressure field on the surface of the model; as examples, the results for y ¼ 01 and 451 areshown in Figs. 8 and 9. Then, the signboard surface has been ideally subdivided in squareregions (10 by 10mm), and the normal force coefficient Cf evaluated as the average of theCp values corresponding to the centroids of these regions: the results of this analysis arereported in Fig. 10 (‘‘free-standing’’ condition).

The value Cf ¼ 1:65 for a ¼ 01 has been obtained as the average of the experimental Cf’sfor y ¼ 01, 1801 and 3601: this value has been compared with the values given by ENV1991-2-4 [18], EN 1991-1-4 [19] and Letchford [3]. ENV 1991-2-4 (Section 10.4.4),assuming a slenderness reduction factor equal to 0.67, as suggested in Section 10.14 for thegeometrical characteristics of the signboard considered in this paper, yields a valueCf ¼ 1:68. The indication of EN 1991-1-4 (Section 7.4.3) is significantly different: in fact,the value of Cf results equal to 1.80 and there is no reference to a slenderness reductionfactor (i.e. no effect of the geometrical characteristics of the signboard is considered).

In Letchford [3] different types of frame-type signboards were tested, characterized bydifferent dimensions of the signboard and different values of the clearance above ground;all signboards are invested by a boundary layer with intermediate characteristics betweenthose corresponding to a TC2 (open) terrain category and those corresponding to a TC3(suburban) terrain category, as defined by the Australian Code (AS1170.2, Part 2). Cf

values were evaluated from measures obtained by an aerodynamic balance; the results for

Fig. 8. Mean values of the pressure coefficients at the pressure taps and corresponding interpolated contour plots

for y ¼ 01 (for wind tunnel configuration Config 1 and ‘‘free-standing’’ condition). See Fig. 3 for the definition of

the angle y.

ARTICLE IN PRESS

Fig. 9. Mean values of the pressure coefficients at the pressure taps and corresponding interpolated contour plots

for y ¼ 451 (for wind tunnel configuration Config 1 and ‘‘free-standing’’ condition). See Fig. 3 for the definition of

the angle y.

Fig. 10. Mean values of the normal force coefficient Cf for the model in ‘‘embedded’’ and ‘‘free-standing’’

condition (for Config 1). The values for a ¼ 01 have been obtained as the average of the corresponding Cf’s for

y ¼ 01, 1801 and 3601. In the same way the values for a ¼ 451 have been obtained from the Cf’s for y ¼ 451, 1351,

2251 and 3151 (see Fig. 3 for the definition of the angle y).


a ¼ 01 are reported in Table 2. The signboard studied in the present paper is characterizedby the following geometrical ratios: c=h ¼ 0:28, b=c ¼ 5: for these values, Table 2 furnishesa value of Cf approximately equal to 1.60.

ARTICLE IN PRESS

Table 2

Experimental values of the force coefficient Cf on a signboard for a ¼ 01, according to Letchford [3]

c/h b/c

0.1 0.2 0.25 0.5 1 2 4 5 10

1.00 – 1.42 1.41 1.17 1.15 1.14 1.08 1.04 –

0.95 – 1.43 1.43 1.33 1.27 1.24 1.14 – –

0.90 1.55 1.44 1.45 1.41 1.34 1.33 1.20 1.15 –

0.80 – 1.46 1.49 1.44 1.43 1.39 1.32 – –

0.67 – – – 1.46 1.42 1.38 1.35 1.32 –

0.50 – – – 1.47 1.38 1.42 1.45 1.44 –

0.30 – – – – 1.42 1.45 1.53 1:57 1.55

0.16 – – – – – 1.48 1.51 – 1.63

b and c are the width and the height of the signboard, respectively; h is the distance from the ground of its upper

side.

Fig. 11. Scheme of the signboard models used by Letchford [3] (a) and in the present study (b).


In conclusion, for a ¼ 01, the value of Cf obtained in the present research is in goodagreement with the values furnished by ENV 1991-2-4 [18] and Letchford [3]. On thecontrary, the value yielded by EN 1991-1-4 [19] is significantly larger.

When aa0, the considered codes do not give any information for the evaluation of themean value of Cf. So in order to validate the model for aa0, only the experimental resultsreported in Letchford [3] could be considered. In this case a significant difference has beenfound: Letchford found values of Cf approximately constant between 01 and 451, while inthe present work a value of Cf ¼ 1:15 has been found for a ¼ 451 (this value has beenobtained as the average of experimental Cf’s for y ¼ 451, 1351, 2251 and 3151). Thisdiscrepancy might be in part due to the different thicknesses of the signboard (0.5mm inLetchford vs 9mm in this study); however, it was felt that the different configuration of thesignboard and the consequent different aerodynamic interference between the board andthe posts was more significant, and this has been confirmed by an investigation with thePIV technique.

In Letchford’s models, the posts are connected directly to the lower edge of the board(Fig. 11a): in this case, the aerodynamic interference between signboard and posts is notvery strong and the wind loads on the signboard are like the loads on a plate. This canexplain the substantial equality between the Cf values relative to a ¼ 01 and 451 obtainedby Letchford [3]: in fact, as observed in [20] for an infinitely wide plate, up to a yaw angleof 451 the suction, which contributes more to the total force, is constant over the backsurface and its value is slightly less than that corresponding to a zero yaw angle. On thecontrary, the results reported in this paper have been obtained on a model in which the

ARTICLE IN PRESS

Fig. 12. Velocity field around the signboard model obtained by the PIV technique (plan view with shadows

created by a laser light from the left side. The small arrows represent the mean velocity field of the flow).


posts are connected to the lateral sides of the board (Fig. 11b); in this case, for a ¼ 451,there is a strong aerodynamic interference between signboard and posts: in fact, as shownin Fig. 12, the velocity field obtained by PIV technique shows clearly that the wake of thewindward post reattaches onto the signboard; as a consequence, the value of Cf issignificantly reduced. In Fig. 12 the signboard model is reproduced in plant with itsshadows created by a laser light from the left side of the picture. The small arrowsrepresent the mean velocity field of the flow. It can be noted that on the left side of thepicture the arrows have the same direction of the mean flow (the big arrow on the top ofthe picture). This indicates that the flow is not disturbed by the model. On the contrary,near the model, after the upwind post, the arrows points towards the right side of thepicture and against the model. This path describes the wake of the model and indicates thatthe wake is reattaching to it.As a conclusion, the relative position of posts and signboard is a feature that strongly

influences the wind loads, besides the geometry of the board itself: this should be taken intoaccount by the codes.

3.2. Signboard embedded in urban canopy

A further series of experimental tests aimed at simulating a situation near the border of abuilt-up area: namely, the signboard model has been ‘‘embedded’’, as already defined, inan array of blocs, which create a ‘‘urban canopy’’ downwind from an open countryroughness (Figs. 5 and 6). Another main aim of this part of the experimental research is the


evaluation of the sensitivity of the pressure field acting on the signboard with respect to thecharacteristics of the flow investing the buildings on the turntable.

The mean value of Cp relative to each pressure tap has been evaluated for the twoapproach flows corresponding to the already defined configurations of the wind tunnelConfig 1 and Config 2, and for eight different wind directions, in all cases using the samemean reference pressure as in the free-standing condition.

In the analysis of the pressure signals (two records of 40 s for each configuration and foreach wind direction), the first step has been the evaluation of the minimum time intervalfor which the mean value could be considered stable. In most cases, this time interval is13 s: this information has been used to obtain six shorter signals of 13 s from the twooriginal records. Therefore, six mean values of Cp have been evaluated for each tap. Incases in which the stable condition has not been attained in 13 s, longer intervals (even 40 s)have been considered.

In Figs. 13 and 14, as an example, the mean values of Cp corresponding to two taps, forall different values of y and for the two configurations of the wind tunnel are reported. Itcan be noted that if the configuration is changed, the pressures on the signboard alsochange: considering that in the present case the ratio between the radius of the proximitymodel and the building height is equal to 5, this agrees with the result by Kiefer and Plate[13], i.e. that in a homogenous roughness field the mean pressures remain constant only ifthe radius of the model of proximity is larger than approximately 10 building heights.More pronounced effects are observed with reference to the values of the negativepressures than for the positive ones and for the lateral taps than for the central ones. It canalso be noted that, in accord with the results on plates obtained by Bearman [21], the(absolute) mean values of the Cp are larger for Config 1, i.e. when the flow is characterizedby larger values of the turbulence intensity. It is worth noting that this holds both for the‘‘free-standing’’ condition and the ‘‘embedded’’ one.

The mean values of the normal force coefficients Cf have been obtained from the meanvalues of the pressures acting on the signboard, as described in Section 3.1. They arereported in Fig. 15, where it can be observed that, like the Cp’s, the values of Cf

Fig. 13. ‘‘Embedded’’ condition—mean values of Cp corresponding to the center taps AC2 and DC2, evaluated

for the two considered configurations of the wind tunnel (O Config 1; D Config 2) and for different wind directions

(each value is the average of six values of the mean Cp).

ARTICLE IN PRESS

Fig. 15. Comparison between the mean values of the normal force coefficient Cf for the ‘‘embedded’’ condition

for the two configurations of the wind tunnel. The values for a ¼ 01 have been obtained as the average of the

corresponding Cf’s for y ¼ 01, 1801 and 3601. In the same way the values for a ¼ 451 have been obtained from the

Cf’s for y ¼ 451, 1351, 2251 and 3151. See Fig. 3 for the definition of the angle y.

Fig. 14. ‘‘Embedded’’ condition—mean values of Cp corresponding to the taps A1 and D1, located at the edge of

the signboard, evaluated for the two considered configurations of the wind tunnel (O Config 1; D Config 2) and for

different wind directions (each value is the average of six values of the mean Cp).


corresponding to Config 1 are larger then those corresponding to Config 2 (the percentdifferences are equal to 22% for a ¼ 01 and 17% for a ¼ 451).The values of Cf are larger for the ‘‘free-standing’’ than for the ‘‘embedded’’ condition for

both wind tunnel configurations considered (see Figs. 10 and 16). It can be concluded that fewrows of building are sufficient to reduce the mean force of the wind acting on a ‘‘rigid’’ objectimmersed in the urban canopy with respect to the ‘‘free-standing’’ condition. Moreover, asreported by Ho et al. [12], it can be noted that the wind effects are less dependent on the winddirection in the ‘‘embedded’’ condition than in the ‘‘free-standing’’ condition.

ARTICLE IN PRESS

Fig. 16. Mean values of the normal force coefficient Cf for the model in ‘‘embedded’’ and ‘‘free-standing’’

condition for the wind tunnel configuration Config 2. The values for a ¼ 01 have been obtained as the average of

the corresponding Cf’s for y ¼ 01, 1801 and 3601. In the same way the values for a ¼ 451 have been obtained from

the Cf’s for y ¼ 451, 1351, 2251 and 3151. See Fig. 3 for the definition of the angle y.


For the given dimension of the model of proximity, the reduction factor of the wind loadis a function of the characteristic of the flow investing the buildings. It can be noted thatthe reduction factor is larger for Config 1 than for Config 2. In Config 1, it is equal to 0.64for a ¼ 01 and to 0.77 for a ¼ 451; in Config 2, it is equal to 0.56 for a ¼ 01 and to 0.64 fora ¼ 451.

Finally, it is interesting to note that in general the reduction factor increases with thefrontal density lf, i.e. the ratio between the area of the projection of the obstacles (in theconsidered case, the wood cubes) on a plane normal to the wind direction and the areaoccupied in plan by the same obstacles. In the test case, lf ¼ 0:42 for a ¼ 01 and lf ¼ 0:69for a ¼ 451, while the reduction factor is larger for a ¼ 451 than for a ¼ 01. Hence, the effectof the variation of wind direction is larger than the effect of the change in frontal density lf.

4. Concluding remarks

In this paper, the wind action on a frame-type signboard either free standing orembedded in an urban canopy layer has been studied experimentally. Only the mean valuesof the pressure field acting on the signboard have been considered.

Consequently, only he mean values of the aerodynamic coefficients Cp and Cf have beeninvestigated and compared with Code and other experimental values. This research has notdealt with the ‘‘peak’’ coefficients that are necessary to establish the design values.

Although further research is necessary, the results of the illustrated tests already allowthe following preliminary indications:

�
for the ‘‘embedded’’ condition, the pressure field acting on the signboard depends on thecharacteristics of the approach flow: since the proximity model used in this study is acircle with a radius equal to five times the height of the buildings, this result is in

ARTICLE IN PRESSC. Paulotto et al. / J. Wind Eng. Ind. Aerodyn. 94 (2006) 397–413412

agreement with the observation by Kiefer and Plate [13] that in an uniform roughnessfield the mean pressures remain constant only if the radius of the model of proximity islarger than approximately 10 building heights,
� the mean values of the normal force coefficient for the ‘‘embedded’’ signboard are
smaller than those corresponding to the ‘‘free-standing’’ condition, even if in the testsonly few buildings surrounded the signboard; at least for the ratio between the heightsof the buildings and the signboard used in the tests, no ‘‘street-canyon’’ effect wereobserved,
� the wind effects in the ‘‘embedded’’ condition are less dependent on the wind direction
than in the ‘‘free-standing’’ condition: in fact, the ratio between the Cf’s values fora ¼ 01 and 451 is equal to 0.70 for the ‘‘free-standing’’ condition and 0.83 for the‘‘embedded’’ condition. It has also been observed that the reduction of wind load islower for a ¼ 451 than for a ¼ 01: to a certain extent. This is an unexpected result,because the frontal density is larger for a ¼ 451 than for a ¼ 01, but it may be justifiedby the fact that also for a ¼ 451 the flow is in part directed along the central widercanyon, thus compensating for the reduction effect due to the increasing frontal density.

Acknowledgements

The experiments reported in this paper were carried out, in the framework of the‘‘Research Program of National Interest’’ (PRIN) WINDERFUL (2001-2003), in the windtunnel of CRIACIV in Prato, Italy. Sincere thanks are due to Ing. Lorenzo Procino for hisinvaluable help in performing the tests. Preliminary versions of this paper have beenpresented at the Final Conference of COST Action C14 ‘‘Impact of Wind and Storm onCity Life and Built Environment’’ (Rhode-Saint-Genese, Belgium; May 2004) and at theEighth Italian National Conference on Wind Engineering IN-VENTO-2004 (ReggioCalabria, June 2004).

References

[1] G. Augusti, C. Borri, H.J. Niemann, Is Aeolian risk as significant as other environmental risks?, Reliab. Eng.

Syst. Safety 74 (2001) 227–237.

[2] N. Pulipaka, J. McDonald, K. Metha, Wind effects on cantilevered traffic signal structures, in: Proceedings

of the Ninth International Conference on Wind Engineering, New Delhi, India, 1995.

[3] C.W. Letchford, Wind loads on rectangular signboards and hoardings, J. Wind Eng. Ind. Aerodyn. 89 (2001)

135–151.

[4] A.D. Quinn, C.J. Baker, N.G. Wright, Wind and vehicle induced forces on at plates. Part 1: wind induced

force, J. Wind Eng. Ind. Aerodyn. 89 (2001) 817–829.

[5] D. Min. LL.PP. 16 gennaio 1996, Norme tecniche relative ai 5Criteri generali per la verifica di sicurezza

delle costruzioni e dei carichi e dei sovraccarichib.

[6] Circ. Min. LL.PP. 4 luglio 1996, no. 156AA.GG./STC, Istruzioni per l’applicazione delle 5Norme tecniche

relative ai criteri generali per la verifica di sicurezza delle costruzioni e dei carichi e dei sovraccarichib di cui

al decreto ministeriale 16 gennaio 1996.

[7] Circ. Min. LL.PP 18591/1978 relativa al D.M. del 3 ottobre 1978.

[8] T. Stathopoulos, Wind loads on low buildings: in the wake of Alan Davenport’s contributions, J. Wind Eng.

Ind. Aerodyn. 91 (2003) 1565–1585.

[9] M. Husain, B.E. Lee, An investigation of wind forces on three dimensional roughness elements in a simulated

atmospheric boundary layer flow, Part I-III, BS 55, BS 56, BS 57, Department of Building Science, Faculty of

Architectural Studies, University of Sheffield, 1980.


[10] B.E. Lee, Wind loading on low-rise building, in: Proceedings of the Eighth Colloquium on Industrial

Aerodynamics, Part 2, 1–11 Aachen, 1980.

[11] Y. Jia, B.L. Sill, Pressures on a cube embedded in a uniform roughness field of variable spacing density,

J. Wind. Eng. Ind. Aerodyn. 77&78 (1998) 491–501.

[12] T.C.E. Ho, D. Surry, A.G. Davenport, Variability of low building wind loads due to surroundings, J. Wind

Eng. Ind. Aerodyn. 38 (1991) 297–310.

[13] H. Kiefer, E.J. Plate, Modeling of mean and fluctuating wind loads in built-up areas, J. Wind Eng. Ind.

Aerodyn. 74–76 (1998) 619–629.

[14] Aerospace Division of the American Society of Civil Engineers, Wind tunnel studies of buildings and

structures, ASCE manuals and reports on engineering practice no. 67, Reston, Virginia, 1999.

[15] E.J. Plate, H. Kiefer, Wind loads in urban areas, J. Wind Eng. Ind. Aerodyn. 89 (2001) 1233–1256.

[16] C. Paulotto, Analisi dell’azione del vento in ambiente urbano: aspetti teorici e sperimentazione in galleria del

vento, Dip. Ingegneria Strutturale e Geotecnica, University of Rome ‘‘La Sapienza’’, Ph.D. Thesis in

Structural Engineering, 2003.

[17] A. Yoshida, Y. Tamura, T. Kurita, Effects of bends in a tubing system for pressure measurement, J. Wind

Eng. Ind. Aerodyn. 89 (2001) 1701–1716.

[18] European Committee for Standardisation, EUROCODE ENV 1991-2-4: Wind Actions, 1994.

[19] European Committee for Standardisation, STRUCTURAL EUROCODE EN 1991-1-4: Wind Actions,

1994.

[20] P. Sachs, Wind Forces in Engineering, Pergamon Press Ltd., Oxford, 1978.

[21] P.W. Bearman, An investigation on the forces on flat plates normal to a turbulent flow, J. Fluid Mech. 46

(Part 1) (1971) 177–198.

1. INTRODUCTIONThe use of large billboards is becoming very popularfor outdoor advertisement in Thailand. Within the pastdecade, a surprisingly large number of large billboardshave been built along the main roads and highways inBangkok and several major cities in Thailand. They aremostly rectangular-shape billboards of 20 to 50 metershigh with the bottom edge elevated to a high positionabove the ground. The structures of these billboards arecommonly made from steel trusses or steel pipes.These billboard structures, however, have been foundto be quite vulnerable to wind loads. Many of themwere severely damaged and some collapsed duringstrong windstorms. In Bangkok alone the number ofcollapsed billboards in each year is, on the average,

Advances in Structural Engineering Vol. 12 No. 1 2009 103

Wind Tunnel Model Tests of Large Billboards

Pennung Warnitchai1,*, Suksit Sinthuwong2 and Kobchai Poemsantitham3

1Asian Institute of Technology, Pathumthani, Thailand2Asian Engineering Consultants Corp., Ltd., Bangkok, Thailand

3T.C.C. Capital Land Co. Ltd., Bangkok, Thailand

Abstract: Two series of wind tunnel tests on 1: 200 scale models of large billboardstructures were carried out in turbulent boundary layer flow. The tested configurationsin the first series are single-panel rectangular billboards with width to depth ratiovarying from 1 to 3 and depth to height ratio varying from 1/3 to 2/3, and in second seriesare two-panel billboards with the angle between two panels (φ) varying from 0° to 30°.The high-frequency force balance technique was employed. The test results show thatthe mean drag force coefficient CD of single-panel billboards attains its maximum valueof about 1.3 to 1.5 when the wind attack angle θ lies between −45° and +45°. Themaximum value of mean forces on two-panel billboards is slightly higher than that ofthe corresponding single-panel billboard. Wind-induced torsion about the vertical axisof single-panel billboards increases as θ increases, and attains its maximum value at θof about ±45°. The maximum torsion can be estimated by multiplying the maximumdrag force with the peak horizontal eccentricity of about 15% of the billboard width.For two-panel billboards, the eccentricity increases as φ increases, and reaches 24% atφ = 30°. The aerodynamic admittance function for all billboard configurations agreesreasonably well with the well-known Vickery’s admittance formula.

Key words: billboard, wind tunnel test, high-frequency force balance, drag force, torsion, aerodynamic admittancefunction.

*Corresponding author. Email address: [email protected]; Tel: +66-2-524-5530.

more than 5. A spectacular case of collapsed billboardsis shown in Figure 1.

A few years ago the first author has initiated apreliminary investigation on the safety of large billboards,with the aim to identify the primary causes of this problem.The investigation shows that outdated and over-simplifieddesign wind loads stipulated in the National Building Codeof Thailand (Ministerial Regulations No. 6 1984) is one ofthe key factors contributing to the problem. According tothe code, wind loads are represented by an equivalent staticpressure p which is a function of height above the ground z:p = 490 N/m2 for z < 10 m, 785 N/m2 for 10 m < z < 20 m,1180 N/m2 for 20 m < z < 40 m, and 1570 N/m2 for z > 40m. This equivalent static pressure is used for structures ofany configuration located at anywhere in Thailand. When

applied to a rectangular billboard, it will create a static dragforce acting normal to the billboard panel on its geometriccenter, and the structure and its members will be designedto have sufficient strength to resist the static drag force.

In reality, the wind-induced pressure is not static; it isfluctuating with time. The characteristics of thefluctuating pressure depend not only on height z but alsoon structural configuration, wind attack angle, windturbulence, and several other factors. The pressuredistribution over the entire billboard panel at any giventime is normally not uniform, so the resulting drag forcewill generally be offset from the panel’s geometric center.The horizontal offset (horizontal eccentricity) results intorsion, which might produce significant effects on thebillboard structure.

A practical and economical approach to identify windloading on billboard structures is to test scale-downmodels of billboards in a wind tunnel that can simulateboundary layer turbulent flow. Some studies in the pastsuch as the well known study on drag force coefficient ofrectangular plates and walls by Flashbart in 1932 (Simiu1996) was, however, conducted in a smooth uniform windflow condition, while another well-known study forsquare plates by Bearman (1971) was carried out in ahomogeneous turbulent flow condition. More recentworks on rectangular plates by Cook (1990), Letchfordand Holmes (1994), Holmes (2001), and Letchford (2001)were conducted in a boundary layer turbulent flow.Among these works the study by Letchford (2001)appears to provide the most useful information about thecomplex nature of wind forces on rectangular billboards.However, there are some inconsistencies among theresults obtained from these works, and there arepractically no information about wind forces on two-panelbillboards (see Figure 5) which are very common inThailand.


104 Advances in Structural Engineering Vol. 12 No. 1 2009

In this study, a series of wind tunnel model tests on avariety of billboard configurations were carried out byusing the high-frequency force balance technique. The testdetails and some key results that are critical to the designof billboard structures are presented in the followingsections.

2. WIND TUNNEL MODEL TESTS2.1. Boundary Layer Wind Simulation

The tests were conducted in a pushing-type open-circuitboundary layer wind tunnel which was developed by theAsian Institute of Technology (AIT) and ThammasatUniversity (TU). The working tunnel is 2.5 m wide, 2.5 mhigh, and 23-m long. A 2-m-diameter turntable for settingthe model is located at 18.5 m away from the trailing edgeof the contraction cone. A combination of three 1.8-m-talltriangular spires and a 12-m-long carpet of roughnesselements arranged in the upstream of the model wasemployed to generate boundary layer wind.

The initial design of spires and roughness elementswas based on Irwin’s empirical formulas (Irwin 1981).But the final arrangement of them was obtained byseveral trial-and-error adjustments until the mean windvelocity and turbulence intensity profiles were somewhatbetween those of open and suburban terrains in the scaleof 1:200 as shown in Figure 2(a). The fluctuating windvelocity was measured at the turntable center and at 0.5 mto the left and right (±0.5 m) of the center by a constant-temperature hot-film anemometer. The best-fitted power-law exponent, α, of the mean velocity profile is 0.214,and the boundary layer depth is 1.675 m whichcorresponds to 335 m in the full scale. The turbulenceintensity profile is closer to but slightly higher than that ofopen terrain. The spectrum of longitudinal turbulence at25 cm height is in good agreement with the von Kármánspectrum as shown in Figure 2(b).

2.2. High-Frequency Force Balance

The high-frequency force balance (HFFB) technique wasemployed in this study. In this technique, a very stiff andlight model of the structure is fixed on the top of a verystiff and sensitive multi-component force sensor(balance). This forms a very stiff high-frequency balance-model system, which is utilized to directly measure theoverall wind-induced drag force, side force, overturningmoment, and twisting moment at the model base. Thefrequency of the balance-model system must besufficiently high, nominally at least 100 Hz, to avoiddistortions of the dynamic wind forces in the frequencyrange that affects the resonant response of the full-scalestructure. This test technique, however, does not accountfor aeroelastic effects which might be important for somelow-frequency flexible structures. As the fundamental

Figure 1. Collapse of a large billboard in Bangkok during a severe

thunderstorm on June 26, 2002

frequency of typical billboard structures is rather high—about 1 Hz or higher, the aeroelastic effects are notanticipated to be significant in this case.

A multi-axis force-torque sensor manufactured byJR3 Inc. was used. It is highly sensitive and stiff, whichsatisfies the requirements of the HFFB technique. Thesensor can completely define the loading at the modelbase by measuring the forces on three orthogonal axesand the moment or torque about each of the axes (seeFigure 4). Load ranges which could be measured by thisforce sensor are ±80 N for Fx and Fy, ±160 N for Fz and±10 N.m for Mx, My and Mz components.

Before applying the sensor for model tests, a simplecalibration of the sensor was carried out by applying staticweight to each of the sensor’s orthogonal axes one-by-one.The output signals of the sensor showed some low-level‘cross-talk’ effects between six output channels. Theeffects were then eliminated by multiplying a conversionmatrix, which was derived from the static calibrationresults, to the vector of output signals to obtain thecorrected vector of force signals. After the calibration, theforce sensor was attached to the turntable in such a waythat the upper surface of the sensor was at the same levelas the turntable. Plasticine clay was applied to seal gaps inorder to prevent air leakage without touching the sensorsurface.

2.3. Billboard Models

Two series of tests were carried out. In the first series, ninescaled models of single-panel rectangular billboards withaspect ratio b/d of 1, 2, and 3 and clearance ratio d/h of

Pennung Warnitchai, Suksit Sinthuwong and Kobchai Poemsantitham


4( fLxu U )

Measured spectrum

von Kármán spectrum

10−310−3

10−2

10−1

100

10−2 10−1 100 101 102

(Note: Lu = 0.67 m, U = 12.5 m/s)x

xfL u /u

=

f ·su ( f )uσ 2

fsu( f )σu

2( )fL Uu

x+( )2 65

1 70 8.

α = 0.21

U(z) / Ug

lu (z)

350

00.4

Normalized mean wind speedU(z) /Ug

Ful

l-sca

le h

eigh

t, z

(m)

Turbulence intensity

Iu(z) (%)(a) (b)

50

100

150

200

250

300

0.6 0.8 1.0

8 2012 16

Figure 2. Mean wind speed and turbulence intensity profiles (a) and spectrum of longitudinal turbulence (b)

0.33, 0.50, and 0.67 (see Figure 3) were tested. This testseries was intended to cover various possibleconfigurations of single-panel billboards in Thailand. Thegeometric scaling ratio was set to 1:200. All models in thefirst series were 25 cm high, which corresponds to 50 m in

b

d

h

Wind

θ

Figure 3. Model geometry of single-panel billboard

the full scale. To make it rigid and light, each model wasmade from a 5-mm-thick balsa wood panel fixed on twoaluminum columns with a bracing between them as shownin Figure 4. The columns were bolted to a thick aluminumbase plate.

In the second series, one single-panel model andthree two-panel models were tested. For the latter, the



test series, the lowest natural frequency was in mostcases that of the x-direction fundamental sway modeand was close to or greater than 100 Hz except for thecase of d/h = 0.67 and b/d = 3. A low torsional frequencyof about 50 Hz was obtained for this case, thereforesome data associated with fluctuating torsion on thismodel were discarded to avoid distorted results. In thesecond test series, several modifications were made inthe design and fabrication of the models to make themmore rigid and light. As a result, the lowest naturalfrequency (considering both sway and torsional modes)is greater than 125 Hz in all cases.

Separate models of supporting columns below thelower edge of panel were also made, so that the force onthe supporting columns could be separately measured.By subtracting the mean force acting to the columnsfrom the mean force acting on the billboard model, themean force on the panel alone could be identified.

2.4. Test Program

By using the turntable, each model was tested for windattack angle θ of 0°, 15°, ±30°, 45°, ±60°, and 75° in

Fz (Vertical force)

Wind

Mz (Torsion)Mx

Fy (Side force)

Fx (Drag force)

(Transverse moment)

My (Overturning moment)

Figure 4. A billboard model fixed on a multi-component

force sensor

Supportingcolumn

billboardpanel

w

b2

b

2b

(b) Plan view

(a) 3-D view

h

d

b

φ

Figure 5. Model geometry of two-panel billboard

angle between two panels (φ) as defined in Figure 5 wasset to 0°, 15° and 30°. The minimum spacing (w)between two panels in all cases was set to 0.2 d. Theaspect ratio (b/d) and clearance ratio (d/h) of all modelsin this series were set to 2.0 and 0.5, respectively. Thecenter of supporting column was set at the intersectionof two reference lines, where each line is normal to and

passing through the geometric center of each panel(Figure 5b). All models in this series were 20 cm high.The objective of this test series was to compare windloads on two-panel billboards typically found inThailand with those of the corresponding single-panelbillboards.

The natural frequencies of the balance-model systemwere checked in all test cases. This was made by simplyknocking the model by a rubber hammer and recordingthe force signals in the free vibration phase. In the first

the first series. The test runs for negative θ were madeto confirm the symmetrical nature of wind loadcharacteristics with respect to θ = 0° for single-panelbillboards. In the second test series, each model wastested for wind attack angle θ of 0°, ±15°, ±30°, ±45°,±60°, ±75° and ±90° because the symmetrical loadcharacteristics cannot be assumed for two-panel billboardswith φ = 15° and 30°.

For each attack angle, three test runs were made. Ineach test run, all six components of dynamic wind forces

were measured for a duration of 66 seconds (whichcorresponds to one hour in the full scale). The outputforce signals were passed through low-pass filters with acut-off frequency of 100 Hz, transformed into digitalsignals by an A/D converter at a sampling frequency of500 Hz, and finally stored in a personal computer. In alltest runs, the mean wind velocity at 25 cm above the floorat the turntable center was set to 12.5 m/s. This referencemean velocity was measured before setting the model intothe wind tunnel. The Reynolds number of the flow in thetest runs was approximately 1 � 105. The largestblockage ratio was less than 1.5%, and hence no blockagecorrection was made.

3. WIND LOADS ON SINGLE-PANELBILLBOARDS

In this section, the results from the first test series onsingle-panel models are presented. As mentioned earlierin section 2.2, all six components of wind loads on themodels were measured, but only two components aretruly relevant to the structural design of billboards: dragforce Fx(t) and torsion Mz(t). The other components suchas side force Fy(t), vertical force Fz(t), and transversemoment Mx(t) are relatively very low in most cases, andthus can be discarded. The overturning moment My(t)also can be reasonably estimated by multiplying thedrag force with an approximate moment arm h − d/2.The following sub-sections are therefore focusing ondrag force and torsion.

3.1. Mean Drag Force Coefficient

The first and probably most important aerodynamicforce coefficient is the mean drag force coefficient CD

which is given by

(1)

where F–

x is the mean value of the force component normalto the panel, ρ is the mass density of air (ρ = 1.25 kg/m3),and U

–is the mean wind velocity at the top of billboard (at

z = 25 cm)—which is equal to 12.5 m/s.The obtained CD are summarized in Table 1. The

mean drag force coefficients are also plotted against thewind attack angle in Figure 6. It can be seen that CD

remains approximately constant for wind attack anglefrom 0° up to 45° and afterward decreases linearly andtends to approach zero at 90°. This characteristic wasfirst noted by Cook (1990) and also reported byLetchford (2001). The critical range of wind attackangles that produce the maximum level of mean dragforce is therefore −45° to +45°. Within this criticalrange, CD for all tested configurations falls betweenapproximately 1.3 and 1.5. These CD values are veryclose to those obtained by Letchford (2001) and thevalues recommended by the AS/NZS code (2002).

3.2. Dynamic Drag Force and Torsion

Considering that the response of billboard structures toslowly fluctuating wind forces is likely to be quasi-staticdue to their relatively high fundamental frequency, wewill then need to pay attention to the extreme values ofdrag force Fx(t) and torsion Mz(t). By this reason, thedynamic drag force and torsion were normalized intotheir non-dimensional form:

and (2, 3)

The normalized drag force Cd(t) and torsion Ct(t) forthe case of b/d = 3 and d/h = 0.5 for wind attack anglesof 0° and 45° over a duration of 66 sec are plotted inFigures 7(a) and (b). The plot appears like an egg-shapedcloud of black dots, where each dot represents the valuesof Cd(t) and Ct(t) at a time instant. A white marker, �, atthe center of the cloud is the point of mean drag forcecoefficient and mean torsion coefficient (CD, CT).

C tM t

U b dtz( )( )

=1

22 2ρ

C tF t

U bddx( )( )

=1

22ρ

CF

U bdDx=

12

2ρ



Table 1. Mean drag force coefficients (CD) of single-panel billboards

Wind attack angle; θ

d/h b/d 0° 15° 30° 45° 60° 75°

0.33 1 1.347 1.411 1.413 1.326 0.955 0.3882 1.400 1.401 1.396 1.346 1.017 0.4753 1.427 1.485 1.467 1.405 0.973 0.400

0.50 1 1.361 1.342 1.300 1.228 1.081 0.5482 1.361 1.429 1.381 1.431 1.047 0.4583 1.382 1.440 1.450 1.483 1.033 0.418

0.67 1 1.294 1.296 1.307 1.237 1.140 0.5792 1.300 1.327 1.334 1.387 1.122 0.4673 1.346 1.389 1.412 1.432 1.106 0.434

As torsion can be considered as a horizontaleccentricity e of the drag force from the geometriccenter of panel, several linear lines—each for a givenvalue of e/b—are plotted in Figure 7 for reference. The dashed lines are for e/b = ± 0.1, while the dashed-dotted lines are for e/b = ± 0.2. The solid lines are for e/b = ep/b = Cd/Ct, where Cd and Ct are the maximumvalues of Cd(t) and Ct(t), respectively. Note that the peak horizontal eccentricity ep is considered to be animportant wind load parameter in this study because one can estimate the maximum torsion Ct by simplymultiplying the maximum drag force Cd with ep/b.

In the case of θ = 0°, Ct(t) is distributed around zero ina symmetrical manner, and hence the mean torsioncoefficient CT is zero. The distribution of Ct(t) isapproximately bounded by the lines e/b = ±0.1,indicating that the maximum horizontal eccentricity ofthe dynamic drag force is about 0.1b. The plot alsoshows that the maximum drag force and the maximumtorsion do not occur at the same time. High torsion isessentially caused by an intermediate-level drag forceacting at a high eccentricity, while a high-level dragforce appears to act near the geometric center of thepanel. The maximum torsion, however, can be estimated



2.0

1.8

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.0

CD

0 15 30 45 60 75 90

d/h = 0.33 b/d = 1d/h = 0.50 b/d = 1d/h = 0.67 b/d = 1

d/h = 0.33 b/d = 2d/h = 0.50 b/d = 2d/h = 0.67 b/d = 2 d/h = 0.67 b/d = 3

d/h = 0.50 b/d = 3d/h = 0.33 b/d = 3

Wind attack angle (°)θ

Figure 6. Mean drag force coefficient of single-panel rectangular billboards

0.8

0.6

0.4

0.2

0

−0.2

−0.4

−0.6

−0.8

0.8

0.6

0.4

0.2

0

−0.2

−0.4

−0.6

−0.80 0.5 1 1.5 2 2.5 3 3.5 0 0.5 1 1.5 2 2.5 3 3.5

Cd(t) Cd(t)

(a) = 0°θ (b) = 45°θ

Ct(t) Ct(t)

Figure 7. Distribution of normalized dynamic drag force and torsion

from the maximum drag force by multiplying the latterwith ep = 0.077 b.

In the case of θ = 45°—which is the maximum windangle within the critical range, the distribution of Ct(t) isno longer symmetrical around zero. The distribution istotally shifted into the positive range (i.e. the fluctuatingtorsion is always clockwise), and is approximatelybounded by the line e/b = +0.2. The peak horizontaleccentricity ep is, however, only 0.124 b.

It is clear from the overall results that the horizontaleccentricity increases as the wind attack angle θincreases. To illustrate this point, the ratio ep/b for alltested cases (except the one with d/h = 0.67 and b/d = 3)are plotted against θ in Figure 8. For the same θ, the ratioep/b does not vary much among different billboardconfigurations. The ratio increases with the increase in θ,and reaches its maximum at θ = 75° (the maximum testedangle). However, beyond θ = 45° the maximum (andmean) drag force reduces rapidly, so the higher value ofep/b outside the critical range of θ does not necessarilycorrespond to higher torsion. The test results instead showthat the maximum torsion is attained at either θ = 45° or60° or somewhere between 45° and 60°. Therefore onecan conservatively estimate the maximum torsion bymultiplying the maximum drag force with ep at θ = 60°.

Based on the results shown in Figure 8, the ratio ep/b= 0.15 should be sufficiently conservative to be used forestimating the maximum torsion from the maximumdrag force. This value, however, is significantly lowerthan 0.20, which is recommended by the AS/NZS(2002), and 0.25 as recommended by Cook (1990). Noexplanation was provided by Cook (1990) on why sucha high eccentricity ratio (0.25) was recommended. Onthe other hand, the eccentricity ratio of 0.20 in theAS/NZS code was based on the wind tunnel study byLetchford (2001). A comparison of the Letchford’s work

with the present study suggested that the difference in theeccentricity ratio might be due to the use of relativelylow frequency force balance system (65 Hz in the swaymode and 25 Hz in the torsional mode) in a ratherdistorted boundary layer wind with significantly higherenergy content of longitudinal turbulence in the highfrequency range (when compared to the reference vonKármán spectrum) in the Letchford’s work.

3.3. Aerodynamic Admittance Function

In practice, the dynamic drag force acting on a structure isessentially computed from the approaching wind velocityby the quasi-steady assumption. The validity of theassumption is therefore needed to be checked. For thispurpose, the quasi-steady force spectrum Sq(f) wascomputed by multiplying the spectrum of longitudinalturbulence Su(f) with 4F–2

x /U–2, and then compared with themeasured force spectrum Sf (f). An example for the case ofd/h = 0.50 and b/d = 2 with θ = 0° is shown in Figure 9(a).

The comparison confirms that the force spectrumSf (f) can be well computed from Su(f) by the quasi-steadyassumption but with some correction. The correctionfunction Sf (f)/Sq(f), which is known as the aerodynamicadmittance function χ2(f), was then computed and plottedin Figure 9(b). The obtained function is compared wellwith the empirical expression of χ2(f) proposed byVickery (1968). Similar results were also obtained forother billboard configurations with θ = 0°.

4. WIND LOADS ON TWO-PANELBILLBOARDS

In this section, the results from the second test series arepresented. In order to define the force components actingon two-panel billboards with non-zero φ, a reference planeis introduced between the two inclined panels such thatthe angle between the reference plane and each panel is



d/h = 0.50 b/d = 3d/h = 0.33 b/d = 3

d/h = 0.67 b/d = 2d/h = 0.50 b/d = 2d/h = 0.33 b/d = 2

d/h = 0.67 b/d = 1d/h = 0.50 b/d = 1d/h = 0.33 b/d = 1

0.40

0.35

0.30

0.25

0.20

0.15

0.10

0.05

0.000 15 30 60 75 9045

ep/b

Wind attack angle (°)θ

Figure 8. Peak horizontal eccentricity of single-panel billboards

equal to φ/2. The horizontal force component normal tothe reference plane is called drag force Fx(t), thehorizontal force component parallel to this plane iscalled side force Fy(t), and the torsion around the centeraxis of supporting column which is located on thereference plane is called Mz(t) (see Figure 10).

4.1. Mean Total Force Coefficient

Unlike single-panel billboards, the side force Fy(t) oftwo-panel billboards can be quite significant in somecases. Therefore, instead of presenting mean drag forcecoefficient, it is more meaningful to describe mean wind



100

100

10−1

10−2

10−3

10−4

10−5

10−1 101 102

f(Hz)

(a) Drag force spectrum (b) Aerodynamic admittance function

Sd(f)

Quasi-steady spectrum

Measured spectrum

100

10−1

10−3 10−2 10−1 10−0

Measured

Vickery's

χ f21( ) =

fbU

f bd U43

1 2+ )

χ (f)2

(

Figure 9. Comparison of quasi-steady force spectrum and measured force spectrum (a) and the corresponding aerodynamic admittance

function (b)

−105 −90 −75 −60 −45 −30 −15 0 15

1.80

CFt

Fy

Ft

Wind

θ

θFx

Ft

1.60

1.40

1.20

1.00

0.80

0.60

0.40

0.2045 60 75 90 10530

Wind attack angle ( ° )

Single−panel

Two panels with = 15°


Two panels with = 30° φφ

φ

θ

Figure 10. Mean total force coefficient of two-panel billboards

force in terms of the mean ‘total’ force coefficient CFt

and its corresponding direction θFt which can be definedas follows:

(4)

and (5)θFy

xt

F

F=

−tan 1

CF

U bdF

tt=

12

2ρ

Where (6)

The obtained CFt and θFt are plotted against the windattack angle in Figures 10 and 11, respectively.

For the single-panel and two-panel with φ = 0° cases,CFt is approximately symmetrical with respect to θ = 0°and is nearly uniform within the critical range of windattack angles (−45° < θ < +45°). Outside the criticalrange, CFt reduces rapidly and approaches zero at θ = 90°and −90°. The force direction θFt is close to zero withinthe critical range, indicating that the mean side force isnegligibly low and the total mean force is approximatelyequal to the mean drag force. Hence CFt for these casescan be well represented by CD which is computed fromF–x by Eqn 1.

For two-panel cases with φ = 15° and 30°, CFt is, asexpected, not symmetrical with respect to θ = 0° due tothe non-symmetrical geometry of the billboards. Highvalues of CFt are still found within the critical range ofwind attack angles (−45° < θ < +45°). When θ is between0° and −45°, θFt is nearly uniform and approximatelyclose to −φ/2, suggesting that the mean total force isdominated by the drag force that is acting on and normalto the windward panel. On the other hand, when θ isbetween 0° and +45°, θFt increases approximately linearlywith θ, indicating the increasing contribution of the dragforce on the leeward panel to the total force. Themaximum CFt is attained at θ somewhere between 15°and 30° and is found to be 1.53. As the direction of themean total force θFt is close to zero, CFt can also be wellrepresented by CD for these cases.

Figure 10 shows that the maximum CFt obtained fromall tested two-panel billboard configurations is onlyslightly higher than that of the single-panel billboard.The results suggest that CFt of two-panel billboardscould be approximately represented by CD of single-panel billboards with the same aspect and clearanceratios. More additional tests on two-panel billboards arerequired to verify this point.

4.2. Dynamic Drag Force and Torsion

To estimate the extreme wind loads on billboards, oneneeds to pay attention to the extreme values of totaldynamic force Ft(t) and torsion Mz(t). But since thedirection of measured extreme total force was found to bewithin ±15° in most cases, Ft(t) can be well represented bydynamic drag force Fx(t).

As mentioned earlier in section 3.2, the dynamic dragforce acting on a structure is, in practice, computed fromthe approaching wind velocity by the quasi-steadyassumption. The validity of the assumption was thencarefully examined. The aerodynamic admittancefunctions χ2(f) were computed for various cases(Poemsantitham 2005). The obtained functions werefound to compare reasonably well with the empiricalexpression of χ2(f) proposed by Vickery (1968). Theresults therefore confirmed the applicability of the quasi-steady assumption.

The correlation between the normalized drag forceCd (t) and torsion Ct(t) for two-panel billboards wasfound to be similar to that of single-panel billboardsdescribed earlier in section 3.2. In order to present thenon-symmetrical wind loading characteristics in some

F F Ft x y= ( ) + ( )2 2



60

90 −75 −60 −45 −30 −15 15 30 45 60 75 90

45

30

15

0

−15

−30

−45

−60


Wind

Single panel




θFt

θ FtFy

Ft

Fx θ

θ

φ

φφ

Figure 11. Relationship between the direction of mean total force and wind attack angle



Wind attack angle (°)

(a) Single-panel (b) Two panels with = 0°

(d) Two panels with = 30°(c) Two panels with = 15°


−60 −45 −30 −15 150−75 30 45 60 75 90 105

0.8

0.6

0.4

0.2

−0.2

−0.4

−0.6

0−105−90

Ct

−60 −45 −30 −15 150−75 30 45 60 75 90 105

0.8

0.6

0.4

0.2

−0.2

−0.4

−0.6

0−105−90

Ct

−60 −45 −30 −15 150−75 30 45 60 75 90 105

0.8

0.6

0.4

0.2

−0.2

−0.4

−0.6

0−105−90

Ct

−60 −45 −30 −15 150−75 30 45 60 75 90 105

0.8

0.6

0.4

0.2

−0.2

−0.4

−0.6

0−105−90

Ct

Mz

Wind

meanCt max Ct minCt

θ

φ

φ

φ

θ φ

θ

θ

Figure 12. Upper bound, mean, and lower bound values of normalized torsion

−0.30

−0.20

−0.10

0.00

0.10

0.20

0.30

−75 −60 −45 −30 −15 0 15 30 45 60 75 90

Single-panel Two panels with = 0°

Two panels with = 15° Two panels with = 30°

Wind attack angle (°)

ep /b

−90

θ

φφ φ

Figure 13. Normalized peak eccentricity ratio of two-panel billboards

cases, the upper bound, mean, and lower bound valuesof Ct(t) denoted by max Ct, mean Ct, and min Ct,respectively, are plotted against the wind attack angle θin Figure 12. The results show that as the angle betweentwo panels (φ) increases, the extreme clock-wisetorsion also increases significantly in the positive θrange, while the extreme counter clock-wise torsion inthe negative θ range remains practically unchanged.The wind attack angle θ at which the extreme clock-wise torsion occurs is also shifted from 60° (for the caseφ = 0°) to 30° (for the case φ = 30°). These results canbe presented in terms of normalized peak horizontaleccentricity ep/b as shown in Figure 13. The highestep/b of 0.24 is attained in the case of two-panelbillboard with φ = 30°. This value is much higher thatof single-panel billboards (ep/b = 0.15).

5. CONCLUSIONSTwo series of wind tunnel tests on 1:200 scale models ofrectangular-shape billboards were carried out in asimulated turbulent boundary layer flow. The high-frequency force balance technique was employed, wheresix-components of dynamic wind loads on a rigid modelwere simultaneously measured. From the analysis of testresults, the following conclusions can be made:

1. The mean drag force coefficient CD of single-panel billboards attains its maximum value whenthe wind attack angle θ lies between −45° to +45°.Within this critical range of θ, CD for all testedconfigurations falls between approximately 1.3and 1.5. The results are similar to those obtainedby Letchford (2001) and are in line with therecommendation of the AS/NZS (2002).

2. The mean total force coefficient CFt of two-panel billboards also attains its high value withinthe same critical range of θ. The maximum CFt

obtained from all tested two-panel billboardconfigurations is only slightly higher than that ofthe corresponding single-panel billboard,suggesting that CFt of two-panel billboardscould be approximately represented by CD ofsingle-panel billboards with the same aspect andclearance ratios.

3. Wind-induced torsion on single-panel billboardsincreases as θ increases, and attains its maximumvalue at θ between 45° and 60°. The maximumtorsion for all tested single-panel configurationscan be conservatively estimated by multiplyingthe maximum drag force with the peak horizontaleccentricity ep = 0.15 b. This eccentricity value issignificantly lower than 0.20b, which isrecommended by the AS/NZS (2002), and 0.25 bas recommended by Cook (1990).



4. For two-panel billboards, the maximum torsionincreases significantly as the angle between twopanels (φ) increases. The peak horizontaleccentricity ep is found to be as high as 0.24 bfor the case of φ = 30°.

5. In all tested billboard configurations, thespectrum of fluctuating drag force can be wellestimated from the spectrum of longitudinalwind turbulence by the quasi-steady assumptionwith some correction. The correction functionagrees reasonably well with the empiricalaerodynamic admittance function proposed byVickery (1968).

The above findings, when combined with a properstudy of extreme wind speeds, could form a basis for thedevelopment of more rational wind load standard forlarge billboard structures in the future.

ACKNOWLEDGEMENTSThis work is among the first series of research studiesconducted at the recently developed TU-AIT boundarylayer wind tunnel laboratory. The development of thewind tunnel laboratory took nearly ten years from itsconception to its opening due to several problemsencountered. But finally the development was madepossible and successful by strong support from severalcolleagues of the first author at AIT and his goodpartners at Thammasat University. Professor EmeritusPisidhi Karasudhi was among the key supporters of thisdevelopment, particularly during when he was servingas the Founding Dean of the School of CivilEngineering at AIT. For this reason, this paper wasspecifically made to honour his contributions to thedevelopment of the wind tunnel laboratory.

REFERENCESAS/NZS 1170.2. (2002). Structural Design Actions, Part 2: Wind

Actions, Standards Australia and Standard New Zealand,

Australia and New Zealand.

Bearman, P.W. (1971). “An investigation of the forces on flat plates

normal to a turbulent flow”, Journal of Fluid Mechanics, Vol. 46,

No. 1, pp. 177–198.

Cook, N.J. (1990). The Designer’s Guide to Wind Loading of Building

Structures-Part 2: Static Structures, BRE/Butterworths, London, UK.

Holmes, J.D. (2001). “Wind loading of parallel free-standing walls

on bridges, cliffs, embankments and ridges”, Journal of Wind

Engineering and Industrial Aerodynamics, Vol. 89, No. 14,

pp. 1397–1407.

Irwin, H.P.A.H. (1981). “The design of spires for wind simulation”,

Journal of Wind Engineering and Industrial Aerodynamics, Vol.

7, No. 3, pp. 361–366.

Letchford, C.W. and Holmes, J.D. (1994). “Wind loads on free-

standing walls in turbulent boundary layers”, Journal of Wind

Engineering and Industrial Aerodynamics, Vol. 51, No. 1,

pp. 1–27.

Letchford, C.W. (2001). “Wind loads on rectangular signboards and

hoardings”, Journal of Wind Engineering and Industrial

Aerodynamics, Vol. 89, No. 2, pp. 135–151.

Ministry of Interior. (1984). Ministerial Regulations No. 6, Issued

under the National Building Control Act of Legislation (1979),

Ministry of Interior, Thailand.



Poemsantitham, K. (2005). Interference Effects from Adjacent

Structures on Wind-induced Forces in Large Billboards, MEng.

Thesis No. ST-05-5, Asian Institute of Technology, Bangkok.

Simiu, E. and Scanlan, R.H. (1996). Wind Effects on Structures, 3rd

Edition, John Wiley and Sons, New york.

Sinthuwong, S. (2004). Wind Tunnel Model Test of Large

Rectangular Billboards, MEng. Thesis No. ST-04-1, Asian

Institute of Technology, Bangkok.

Vickery, B.J. (1968). “Load fluctuations in turbulent flow”, Journal

of Engineering Mechanics, ASCE, Vol. 94, No. 2, pp. 31–46.

J. Wind Eng. Ind. Aerodyn. 98 (2010) 808–817

Contents lists available at ScienceDirect

Journal of Wind Engineeringand Industrial Aerodynamics

0167-61

doi:10.1

n Corr

E-m

journal homepage: www.elsevier.com/locate/jweia

Experimental and numerical investigation of the airflow around a raisedpermeable panel

A. Giannoulis n, A. Mistriotis, D. Briassoulis

Department of Agricultural Engineering, Agricultural University of Athens, Iera Odos 75, 11855 Athens, Greece

a r t i c l e i n f o

Article history:

Received 20 October 2009

Received in revised form

30 July 2010

Accepted 30 July 2010Available online 15 September 2010

Keywords:

Agricultural nets

Airflow

Elevated panel

Field measurements

Numerical simulation

05/$ - see front matter & 2010 Elsevier Ltd. A

016/j.jweia.2010.07.005

esponding author.

ail address: [email protected] (A. Gianno

a b s t r a c t

Analysis of the airflow around an elevated permeable panel is presented in this paper. The airflow was

studied by both a 3D computational simulation and a full scale experiment using two kinds of cladding

material, namely an impermeable plastic film and permeable nets. The air velocity at different locations

around the panel was measured by rotary cup anemometers in order to investigate the airflow. A three-

dimensional numerical simulation (CFD) was employed to analyze the edge effects. In the numerical

model, the net was simulated as a porous medium obeying Forchheimer’s law. Both numerical results

and full-scale experiments indicate important differences between the airflow around the panel

covered by impermeable material (film) and the airflow around and through the permeable panels

(nets). Airflow around the elevated experimental panel was found to become smoother when the plastic

film is replaced by permeable nets. The numerical results derived by the 3D computational model show

good qualitative and quantitative agreement with the full scale experimental data in the case of

permeable (net-covered) panels.

& 2010 Elsevier Ltd. All rights reserved.

1. Introduction

The use of plastic nets in agriculture is steadily grown in thelast years. They are used against hail, dust, snow and insects aswell as for shading purposes. They are also used for theconstruction of windbreaks and other agricultural structures suchas greenhouses. However, until very recently, design of thestructures that use agricultural nets was done mostly empiricallydue to lack of data regarding the interaction of wind with suchstructures (Castellano et al., 2008; AGRONETS, 2004)

Impermeable panels, usually used as windbreaks, have beenstudied extensively (Letchford and Holmes, 1994; Robertson et al.,1995, 1996, 1997a, 1997b, 1998; Letchford and Robertson, 1999;Briassoulis and Mistriotis, 2010). Airflow and loads at sensitivezones near the free ends, where turbulent quantities are intense,have been thoroughly studied. Several research works have alsobeen devoted on studying the airflow around permeable obstacleslike permeable panels. The reduction of wind velocity in theirleeward side as well as suppression of intense turbulentcharacteristics are of main interest and therefore a significantamount of previous research works can be found in literature(Perera, 1981; Bradley and Mulhearn, 1983; Crosby et al., 1990;Yaragal et al., 1997).

ll rights reserved.

ulis).

The efficiency of a windbreak, namely its shelter effect, has beenextensively investigated so far. It was clear from various studies(Raine and Stevenson, 1977; Gandemer, 1979) that the shelter effectprovided by a windbreak is related not only to leeward velocityvalues but also to leeward turbulence intensity as well. The twoaforementioned studies analyze the wake flow of different types ofwindbreaks. By examining velocity drop and turbulence intensitiesvariations with parameters like porosity, geometry and shape of thewindbreak, they presented a number of results on protection areathat each windbreak was able to provide. Gandemer (1979) inparticular, also provided results for elevated porous windbreaks butno details on elevation height were present. Results from bothstudies seem to be in good agreement.

Even though there are several publications on elevated panels,not many of them concern porous panels. Furthermore, most ofthese studies focused on the estimation of wind loads on suchstructures for design purposes (Letchford, 2001; Paulotto et al.,2006; Briassoulis et al., submitted).

Studies concerning the vector field of flow at the wake of aporous elevated panel are limited. Park and Lee (2001) conducteda wind tunnel experiment in order to study the interaction of aporous elevated fence with a gap (distance of the elevated panelfrom the ground zg) and a triangular prism leeward of the fence.They also introduced non-uniform porosity of the panel bydividing the fence into two halves with each half having differentporosity. They measured mean pressures on the prism fordifferent gap sizes zg in order to estimate the shelter effectprovided by the porous fence.


dx.doi.org/10.1016/j.jweia.2010.07.005

mailto:[email protected]

dx.doi.org/10.1016/j.jweia.2010.07.005

A. Giannoulis et al. / J. Wind Eng. Ind. Aerodyn. 98 (2010) 808–817 809

Kim and Lee (2002) studied an elevated fence with a specificgeometric porosity close to 40%. They used different gap sizes zg

starting with no gap at all to a value of zg¼0.3h (h being theheight of the panel), in order to estimate how the shelter effectand turbulent quantities (namely turbulence intensity, Reynoldsstresses and turbulent kinetic energy at the leeward side of thefence) are affected. Their main conclusion was that the mosteffective, as a shelter, appeared to be the fence with zg/h ratio (gapratio as defined by Kim and Lee (2002)) of 0.1 and not thegrounded one. They also concluded that turbulent quantitiesbecome more intensive when the gap ratio increases. For thepanels that are tall and narrow, they showed that dominatingvortices appear at the vertical sides and not after the top andbottom gap separations. In this case panel’s turbulent quantitiesare almost unaffected by gap size. Results from this study showeda qualitative agreement with those of Letchford (2001) thatturbulent intensity depends on a combination of geometricalcharacteristics and gap size.

The present work analyzes the airflow around a free-standingelevated panel covered by permeable or impermeable materials.Two different permeable agricultural nets and an impermeablefilm were used as cladding materials of the elevated panel. Theairflow was studied by full scale experiment and a 3D computa-tional simulation. The computational analysis results werevalidated against the full scale experimental measurements. Thevortices that are created at the free ends of the panel and thereduction of wind velocity leeward of the panel were studied forboth, the two different nets and the film covering.

2. Methods and materials

2.1. Airflow through permeable materials

Permeable materials (nets) can be modeled as porous mediathat obey the Forchheimer equation (Lage, 1998). The pressuredrop, Dp (N/m2), across a porous material of thickness Dx (m) isexpressed by the following equation (1):

Dp

Dx¼mD

VþCrV2 ð1Þ

where V (m/s) is the velocity of fluid, m (kg m�1 s�1) the viscosityand r (kg/m3) the density of the fluid. D (m2) is the specificpermeability of the material and C (m�1) the aerodynamicresistance coefficient.

Eq. (1) can be simplified in the case of a thin permeablematerial to

Dp¼ bVþaV2 ð2Þ

where

b¼mDDx, a¼ CrDx ð3Þ

The factors a (Ns2/m4) and b (Ns/m3) describe the airpermeability characteristics of the porous material, and can bedetermined by wind tunnel measurements (Hemming et al.,2005).

Table 1Characteristics of nets used as covering material.

Net (name) Porosity (%) a (kg m�3) b (kg m-2 s-1)

WBTAPE 38 3.0229 0.1179

SCMD 62 0.3637 0.4953

Two commercial nets, specified by the code names WBTAPEand SCMD, were used as cladding materials during the full-scaleexperiment and the CFD simulation. Their optical porosity wasfound to be equal to 38% and 62%, respectively, using acommercially available image analysis tool (Adobe Photoshop).Table 1 provides the aerodynamic characteristics of the two usednets. Values of a and b for the two nets have been measured bywind-tunnel experiments and reported in Hemming et al., 2005.Through the combined full-scale experiments and the numericalanalysis the effect of porosity of the specific cladding materials onairflow around the elevated panel was studied.

2.2. Full scale experiment

A full scale experiment was conducted using a specialexperimental setup located in the experimental field of theAgricultural University of Athens at Spata, Attiki, Greece. Since themeasurements took place inside the surface layer we expect thewind to obey the logarithmic profile. The roughness length z0 atthis location was found to be equal to 0.11 (Briassoulis et al.,submitted). Moreover, details of the undisturbed flow field areprovided in the same work. The panel was 7 m long and 2 m highand was elevated 3 m above the ground (zg¼3 m, h¼2 m, l¼7 m).

Rotary cup anemometers were placed at nine differentlocations around the studied panel in order to record data andcarry out a qualitative and quantitative analysis of the airflow(Fig. 1). Three anemometers were placed in the windward face ofthe raised panel and three in the leeward side (the leeward onesare depicted with circles in Fig. 1). These six anemometers wereplaced symmetrically at the mid-height level of the panel, 0.8 maway from it (Fig. 1). Two more anemometers were placed 0.8 maway from each side edge, also at the mid-height level of thepanel. The last anemometer was placed 0.3 m above the top edgeof the panel and at the center line. An additional anemometer,besides the nine already mentioned, was constantly placed on amast 50 m away from the panel at 10 m height (Fig. 2). On themast there was also a wind vane monitoring the direction of thewind at 10 m height. Fig. 3 provides a top view of the position ofthe nine anemometers around the elevated panel. Not allmeasurements could be simultaneously obtained, since only sixrotary cup anemometers were available. For this reason, themeasured velocity values were correlated to air velocitiesmeasured at both the 10 m high anemometer on the mast 50 m

Fig. 1. Full-scale experimental setup; rotary cup anemometers on the raised panel

measure wind velocities; circles show the three leeward anemometers.

Fig. 2. Position of rotary cup anemometers at 10 and 5 m height and wind vane 50 m away from the elevated panel.

Fig. 3. Top view of nine locations of the rotary cup anemometers.

Fig. 4. Representation of the elevated panel model inside the tunnel created in

computational simulation.

A. Giannoulis et al. / J. Wind Eng. Ind. Aerodyn. 98 (2010) 808–817810

away from the panels as shown in Fig. 2 (reference anemometer)and the anemometer at position 1.

The design of the experimental elevated panel used in thepresent full scale experiments (Fig. 1) was aimed not only atstudying the airflow around the panel but also at measuring windloading on such a structure. For this reason, the elevated panelwas divided into three segments (Fig. 1), of which the central onewas supported on spring units, monitoring wind forces (Briassou-lis and Mistriotis, 2006). In this way, the influence of extremeedge effects on the side segments was excluded. The gapsbetween the three segments of the panel represent only 6% ofthe total panel area. Their influence on the overall airflow aroundthe panel was analyzed numerically and is presented later inSection 3.2.

The used rotary cup anemometers (Vector Instruments, modelA100LK) were able to measure up to 75 m/s wind speeds. Theiraccuracy was 0.1 m/s and their lower operational threshold was0.2 m/s. Only the data recorded for wind perpendicular (7101) tothe panel were selected for analysis purposes. Measurementswere taken for long periods (1 week) and then the analysis of theairflow was restricted only to cases of wind normal to the panel.Data were recorded every 15 s and averaged over 2 min periods.Low velocities (anemometer No. 1, velocity o2 m/s) wereneglected in order to ensure that the measurements of allanemometers were well above their lower operational threshold.

2.3. Numerical simulation

The computational simulation of the elevated panels wascarried out by means of the computational software ANSYS-FLOTRAN. The underlying computational method of this softwareis the finite element method. A 3D model was created in order tosimulate the airflow around the elevated panel. The panel wassimulated as an elevated orthogonal obstacle perpendicular to the

wind flow inside a 3D rectangular wind tunnel, dimensionedaccordingly. The model wind tunnel size was 42, 20 and 27 malong the x, y and z directions, respectively, or 21h, 13.5h and 10h,where h is the panel height, which is h¼2 m (Fig. 4). The panelwas placed at a distance of 12 m from the wind tunnel inlet or 6h.

Three cases were simulated corresponding to the threedifferent covering materials. The two permeable cladding materi-als (nets) of different porosities, which have been used in the fullscale experiments, were modeled as porous materials andcompared to the case of an impermeable panel simulating theplastic film covering.

The finite element mesh consisted of different element types ineach analyzed case, depending on the modeled covering material.Thus, in the case of the permeable nets the panel model itself hadto be discretised along the thickness direction too. On the otherhand, the impermeable panel covered by the film was modeled asan impermeable obstacle, namely no elements were defined inthe panel volume. Both 3D hexahedral rectangular elements and3D tetrahedral elements were used to develop the mesh. Thiscombination was preferred because although tetrahedral ele-ments could be treated easier and the mesh could also be easierformulated, the use of 3D hexahedral elements was essential inorder to improve refinement, to efficiently simulate the perme-able panel model, and thus improve convergence.


As a result, 3D tetrahedral elements were used for modellingthe flow around the film covered panel, while 3D rectangularhexahedral elements were used in the case of the panel coveredby permeable nets. In order to analyze the grid sensitivity ofthe numerical solution, two different simulations have beenconducted for the solid and two more for a net covered panel(SCMD net). For the solid case the grid of the initial run consisted

Fig. 5. Section of the mesh close to the panel using (a) 3D rectangular hexahedral

elements (impermeable panel) and (b) 3D tetrahedral elements (permeable panel).

Fig. 6. Structure of the mesh on the panel model, when a permeable net is used as

panel model.

of 162,088 elements. After doubling the number of elementsalong the surface of the panel, the total number of elementssignificantly increased to 242,214. The same procedure wasfollowed for the permeable case as well. The initial grid had168,192 elements while the refined one consisted of 296,856. Itwas expected to have higher number of elements in the perme-able panel simulation because in this case the interior of the panelis discretised as well. Comparing velocity values for the initial andthe refined grid at the locations of interest, it was found that thedifferences do not exceed 1% for both cladding cases.

Fig. 5a and b shows a section of the finite element model abovethe upper edge of the panel for both cases. The mesh had a similarshape along a section close to the lower edge of the panel. It is wellknown that turbulent quantities increase at the region of flowseparation (Awbi, 1991). For this reason high mesh refinement wasneeded in the regions close to the panel in both meshes.

The mesh structure in the permeable panel model is shown inFig. 6. The enlargement (Fig. 6b) shows detailed geometricalcharacteristics of the orthogonal hexahedral elements along the x-axis (thickness of panel). In the case of an impermeable film thepanel volume is not discretised.

The actual thickness of agricultural nets is very small, in therange of 0.2 mm. When simulating a net as a porous materialusing FEM (ANSYS, 2006), the parameters K and C (Eq. (1)) are anecessary input. Since a and b were known (i.e. measured in thelaboratory), the thickness, Dx, could be selected arbitrarily, and K

and C could be calculated using Eq. (3).Although the choice of the thickness value does not influence

air permeability of the modeled net, since a and b areindependent of Dx, it may influence the aerodynamic behaviourof the panel. Therefore, the thickness of the porous panelsimulating the net had to be small in comparison with its height,so that the panel preserves its two-dimensional character. For thisreason, the thickness of the panel was taken equal to 30 mm,which corresponds to an aspect ratio (height/thickness) equal to200/3. The effect of thickness of the panel on the computationalresult was investigated by analyzing the numerically calculatedstatic pressure on a 2D panel of the same height (2 m). It wasfound that a thickness of 30 mm is small enough to generate theexpected sharp pressure drop between windward and leewardfaces at the upper and lower edges of the panel, which is typicalfor a flat thin panel. This is not true in numerical 2D simulationswhen thicker panels of 50–100 mm thickness are considered.

The y–z faces of the panel (Fig. 6a) were uniformly meshed insquare elements. The height of the panel was divided into 12elements and the width into 42 elements. Proper simulation of apermeable material demands a more refined mesh along thedirection of panel’s thickness.

the covering material: (a) whole panel and (b) enlargement of the mesh on the


The numerical solution is sensitive to mesh refinement,particularly inside the porous material. In order to investigatethe numerical error due to discretisation of the space covered bythe porous medium, the flow through a two-dimensional windtunnel fully blocked by a porous material was numericallysimulated. A fixed uniform air velocity was set as a boundarycondition at the inlet, while the pressure at the outlet was setequal to zero (open outlet). It was found that accuracy of thenumerical simulation improves quickly with number of elementsspanning the thickness of the porous material. More specifically,for a given panel thickness, the difference (expressed as error %)between the theoretical calculation of pressure drop (Dp) usingEq. (1) and results from numerical simulation was 4% when onlyone element was used but decreased to 0.04% for three elementsand it was negligible (3�10�5) for 10 elements. Therefore, thechoice of six elements, which was used in the present simulations,was a compromise between accuracy and computational time.

2.3.1. Modelling turbulence

Both standard k–e and RNG k–e turbulence models were used.It is well known that standard k–e model overestimates in manycases the kinetic energy of turbulence, k. This usually happens inflows that impinge on bluff bodies and the problem is especiallyintense in regions characterised by high variations of velocitygradient such as flow separation points (Awbi, 1991). The RNG k–emodel treats the dissipation of kinetic energy of turbulence moreeffectively. It does not assume a uniform dissipation rate for alleddies irrespective of their size, like the standard k–e does, butsome eddies are filtered out. Results obtained by both modelswere validated against the full scale experimental data.

Fig. 7. Correlation between wind velocity measurements of the reference

anemometer and anemometer No. 1.

2.3.2. Boundary conditions

Wind velocity profile was set to be logarithmic at the inlet ofthe wind tunnel (Richards and Hoxey, 1993), where the velocityVz (m/s) of the wind at a height z (m) is given by

Vz ¼u�K

lnzþz0

z0

� �ð4Þ

where z (m) is the height, Vz (m/s) the velocity at height z, u* (m/s)the so called friction velocity (e.g. Shames, 1992), z0 (m) thesurface roughness and K the von Karman constant (E0.41)

Inlet boundary conditions should also provide profiles for theturbulent characteristics of the wind, k (m2/s2) and e (m2/s3).Richards and Hoxey (1993) proved that these profiles are given bythe following equations:

k¼u2�ffiffiffiffiffiffiCm

p ð5Þ

and

e¼ u2�

K zþz0ð Þð6Þ

where Cm (¼0.09) is one of the k–e model constants.At the lower wall it was assumed that wall boundary

conditions exist. This means that all components of wind velocityat the wall were set to zero. If the plastic film was used ascovering material then the same conditions were assumed alongthe panel surface. If the net was used, no boundary conditionswere assumed on the panel. At the outlet of the wind tunnelpressure was set to zero to simulate open wind tunnel end.Finally, the upper wall of the wind tunnel was assumed as africtionless barrier, so only the vertical wind velocity componentwas set equal to zero.

3. Results

The aim of this study was the analysis of the airflow around anelevated panel when covered by permeable or impermeablematerials. Experimental and numerical techniques were used toinvestigate qualitatively and quantitatively the two correspond-ing airflows.

3.1. Air velocity results—full scale experiment

Air velocity was measured at nine points around the panel(Fig. 3) by full scale experiments as described in Section 2.2. Inorder to simplify comparison with the numerical results themeasurements were scaled with respect to the undisturbed windvelocity simultaneously measured at 10 m height, 50 m awayfrom the experimental setup (reference anemometer). Fig. 7presents the correlation between the reference anemometer andanemometer 1, when the panel was covered by an impermeableplastic film. The correlation coefficient R2 was found equal to 0.9.Similar correlation coefficients were found when the panel wascovered by permeable materials (nets). This small loss ofcorrelation is a result of the distance (50 m) between the twoanemometers, introducing a small time delay in the simultaneousmeasurements, and the turbulent character of the airflow in thesurface layer. Therefore, the use of the reference anemometer fornormalising air velocities around the panel introduces additionaluncertainty, and makes comparison to numerical results moredifficult.

For this reason, the wind velocities measured at distance 0.4h

around the panel are presented in two different formats. InTable 2, they are presented normalised with respect to thereference anemometer, so they can be used for comparisons toother existing or future experimental data. In Table 3, air velocitymeasurements are normalised with respect to anemometer No. 1in order to be used for validating the current numerical results.

3.2. Air velocity results—numerical simulation

Numerical results were obtained by both the standard k–e andthe RNG k–e models as explained in Section 2.3. Qualitative andquantitative characteristics of the airflow were numericallyanalyzed. An important advantage of the CFD method is that itallows for a detailed visualisation of the airflow around astructure. The main airflow characteristics, such as eddy forma-tion, flow separation, etc. can be determined and quantified.

Table 2Air velocities normalised to the reference anemometer velocity for all covering materials.

Anemometer groups Panel cladding/anemometer location

Film SCMD WBTAPE

FS k–e RNG 3Sa FS k–e RNG 3Sa FS k–e RNG 3Sa

Windward 2 0.42 0.43 0.40 0.43 0.68 0.74 0.72 0.73 0.58 0.62 0.59 0.61

1 0.41 0.34 0.32 0.35 0.67 0.72 0.71 0.72 0.57 0.58 0.56 0.58

3 0.42 0.43 0.40 0.45 0.67 0.74 0.72 0.73 0.59 0.62 0.59 0.61

Panel level 5 0.74 0.92 0.89 0.88 0.74 0.82 0.79 0.79 0.75 0.84 0.82 0.82

9 0.62 0.79 0.77 0.74 0.82 0.85 0.83 0.83 0.74 0.79 0.81 0.83

4 0.77 0.92 0.89 0.87 0.74 0.82 0.79 0.79 0.76 0.84 0.82 0.82

Leeward 6 0.34 0.21 0.18 0.27 0.54 0.61 0.62 0.63 0.30 0.37 0.30 0.31

7 0.28 0.19 0.20 0.19 0.58 0.61 0.61 0.63 0.34 0.37 0.32 0.32

8 0.35 0.21 0.18 0.27 0.54 0.61 0.62 0.63 0.31 0.37 0.30 0.31

a Numerical simulation using the RNG k–e turbulence model where the panel was divided into three segments.

Table 3Air velocities normalised to anemometer No. 1 velocity for all covering materials.

Anemometer groups Panel cladding/anemometer location

Film SCMD WBTAPE

FS k–e RNG 3Sa FS k–e RNG 3Sa FS k–e RNG 3Sa

Windward 2 1.03 1.28 1.27 1.24 1.00 1.02 1.01 1.01 1.02 1.06 1.06 1.05

1 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

3 1.04 1.28 1.27 1.28 1.00 1.02 1.01 1.01 1.03 1.06 1.06 1.05

Panel level 5 1.88 2.71 2.81 2.53 1.11 1.14 1.12 1.10 1.33 1.44 1.47 1.41

9 1.52 2.34 2.43 2.13 1.23 1.17 1.17 1.16 1.29 1.43 1.44 1.44

4 1.81 2.71 2.81 2.51 1.11 1.14 1.12 1.10 1.34 1.44 1.47 1.41

Leeward 6 0.84 0.62 0.58 0.77 0.81 0.85 0.87 0.88 0.53 0.64 0.54 0.54

7 0.69 0.57 0.62 0.54 0.86 0.84 0.87 0.87 0.6 0.63 0.56 0.56

8 0.85 0.62 0.58 0.77 0.81 0.85 0.87 0.88 0.54 0.64 0.54 0.54

a Numerical simulation using the RNG k–e turbulence model where the panel was divided into three segments.


The detailed airflow pattern around the panel is shown inFig. 8. Fig. 8 is a z-plane section of the airflow at half height of thepanel, namely 4 m above the ground, which is presented withthe help of velocity vectors calculated by CFD at each node of themesh. The first picture corresponds to film covering and thesecond and third one to the permeable nets WBTAPE and SCMD,respectively. These pictures provide a visualisation of the airflowaround the raised panel depending on each covering case. Theairflow in the case of the film covering material, shown in Fig. 8a,reveals the creation of vortices at the free ends of the panel, wheresignificantly increased turbulent activity is observed. The airflowin the case of the net covering material, shown in Fig. 8b and c,suggests that no vortices are created and turbulent quantitiestend to become mild. The use of the porous net coverings allowsthe air to pass through it, thus suppressing vortices at the freeends of the panel.

Qualitative characteristics of the airflow, shown in Fig. 8, arealso validated by the experimental data. Tables 2 and 3quantitatively present the air velocities around the panel for thethree studied cases of cladding materials normalised with respectto the reference anemometer and anemometer No. 1, respectively.Numerical results obtained using the k–e and RNG k–e turbulencemodels are reported separately for comparison.

For more accurate validation of the numerical method, theairflow around a divided panel made of three segments with theexact dimensions of the experimental setup (Fig. 1) was alsosimulated for both the film covered and the net covered panels. Inthis way the effect of the gaps between the central and the sidesegments of the panel was taken into account. The normalised airvelocities calculated by this numerical simulation are alsoreported in Tables 2 and 3.

As shown in Table 2 the normalised air velocity at locations1–3 along the windward face of the panel is almost constant forboth cases of net cladding. At the leeward locations 6–8 normal-ised air velocities are lower than the windward ones, indicatingwindbreak effect of the panel. Normalised air velocities at the leftand right side edges of the panel (points 4, 5) and at the top (point9) have higher values as air accelerates near the free ends. Whennet cladding is used, air velocity at the edge points 4, 5 and 9decreases as porosity increases due to the bleed flow. The sametendency is observed in full scale measurements (Table 2).

Despite the qualitative agreement between numerical andexperimental data shown in Table 2, important quantitativediscrepancies were observed for both the permeable andimpermeable panels. A weak agreement between experimentaland numerical (k–e) results was expected in the case of the filmcovered panel due to flow separation, However, discrepancies aslarge as 17% were also found in the case of the net covered panels.These discrepancies were partially due to the loss of correlationbetween the reference anemometer and anemometer 1. For thisreason, numerical and experimental data were also comparedusing Table 3, where the normalised air velocities are notinfluenced by the loss of correlation between the referenceanemometer and the wind around the panel. In Table 3discrepancies between numerical and experimental data decreasebelow 12%, which appeared at point 9 (top edge of the panel) inthe case of the denser net (WBTAPE). Discrepancies at the leewardpoints 6–8 were lower (1–8%) compared to 1–17% as shown inTable 2. The RNG k–e turbulence model provided results with aslightly better agreement with the experimental data comparedwith the simple k–e model. The existence of gaps between thethree segments of the panel did not influence air velocity at the

Fig. 8. z-plane section of velocity contours at half height of the raised panel: (a)

film covering, (b) net covering—WBTAPE and (c) net covering—SCMD.


selected nine measuring points in the case of net covered panels.These results confirm the validity of the CFD simulations formodelling the airflow around permeable panels. Therefore theCFD approach can be used for analyzing with accuracy the

aerodynamic performance of net covered panels or windbreaksunder normal wind.

Higher discrepancies were observed in the case of the filmcovered panel (Tables 2 and 3) as expected due to flow separationand intense turbulent activity at the leeward side of such a panel.For the film cladding case, the numerical simulations at thewindward locations 2 and 3 gave higher air velocity values than atlocation 1, in poor agreement with the full-scale experiment.Since impermeable cladding does not allow bleed flow, highacceleration of the wind was found close to the panel free endsbefore flow separates (locations 4, 5 and 9), resulting in highdiscrepancies between the experimental and numerical data, asshown in both Tables 2 and 3. The qualitative characteristics ofthe airflow around a film covered panel are shown in Fig. 8a,demonstrating the formation of large eddies at the leeward face ofthe panel. These results confirm the poor performance of the k–eand RNG k–e turbulence models in separated flows (Awbi, 1991).

As shown in Table 3, discrepancies (30%) between experi-mental and numerical results were also found at the leeward side(locations 6–8). These discrepancies were alleviated (Table 3)when the exact three-segment structure of the experimentalsetup was taken into account, suggesting that in the case of thefilm covered panel the gaps between the central and the sidesegments influence the air velocity only at locations 6 and 8.Similarly to the net covered panel, the RNG k–e model gave resultsresembling slightly better the experimental data. The inability ofk–e models to properly represent separating or recirculating flowsdoes not allow a reliable comparison between results in Tables 2and 3 in this case.

Since the computational results for wind velocities at thelocations of the anemometers were validated for the case of a netcovered panel through the full scale experimental results, thecomputational model was used to further analyze the completeairflow pattern around such a panel. Despite quantitativediscrepancies, analysis of the airflow was carried out also forthe film cladding case since the corresponding airflow patternaround the elevated panel was shown to be qualitativelypredicted by the simulation (Fig. 8a).

Initially, velocities leeward of the panel on a vertical x–z planesection were studied. Profiles of wind velocity on this planethat cross the middle of the panel were numerically derivedat a distance 0.4h from its leeward side. Fig. 9 shows velocityx-component profiles at a middle vertical cross section for thethree studied cladding materials as predicted by the numericalsimulation. Velocities were normalised with respect to thereference upstream velocity at 10 m height. Height z was normal-ised by the height of the panel, h¼2 m. The incoming wind farupstream of the panel obeys a logarithmic law profile (representedby the red lines on the diagrams).Velocities leeward of the paneldepend on air permeability characteristics of the material.

A full scale air velocity value, corresponding to the measuringpoint No. 7 (lying on the same x–z plane), is also incorporated inFig. 9 (yellow mark). For both net cladding cases numericalanalysis results and full scale measurements show a very goodagreement. For the film cladding case though, discrepanciesappear between numerical results and full-scale measurements,as expected. Fig. 9 supports the previously reported findingsthat the airflow is qualitatively described correctly, even in thecase of the impermeable cover. More specifically, negativevelocities are calculated at the leeward side of the panel coveredby the impermeable cladding, indicative of the creation ofvortices. However, these negative velocities that occur due toincreased turbulence cannot be correctly estimated by CFD asshown in Fig. 9.

Fig. 10 shows the (x–y plane) velocity profile at the horizontalmid-height cross section of the panel and at its leeward side

Fig. 9. Profile of velocity component at x-axis (wind’s direction) in an x–z plane (red line or line A) and at position x¼0.4h leeward of the panel (blue line or line B) for

impermeable and permeable covering materials (impermeable plastic film–WBTAPE–SCMD). Numerical results (A and B lines) and full scale measurements (yellow

mark—leeward measurement). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 10. Velocity profile (x-component) on an x–y plane at mid-height of the panel (red line or line A) and at specific position x¼0.4h leeward of the panel (blue line or

line B) for the impermeable cladding case and the two cases of covering material as a permeable net (impermeable plastic film–WBTAPE–SCMD). Numerical results ( A and

B lines) and full scale measurements (yellow mark—leeward measurement). (For interpretation of the references to colour in this figure legend, the reader is referred to the

web version of this article.)


positioned at x¼0.4h. Velocities and lengths are normalised as inFig. 9. Full scale results are indicated in Fig. 10 with yellow marks,as in Fig. 9. Three full scale measuring points (Nos. 6–8) are alsoincorporated in the corresponding graphs of the x–y plane. Fig. 10indicates discrepancies between numerical and experimentalresults only in the case of the impermeable film covered panel.Air velocities at the three measurement points (Nos. 6–8) werecorrectly predicted for the two net covered cases. At the x–y plane,negative velocities were determined both experimentally andnumerically only in the case of the impermeable covering,indicating the existence of vortices at the free ends. Therefore,the presence of leeward vortices was correctly predicted by thenumerical simulation, although intensity of various turbulentquantities and the corresponding air velocity field were notestimated accurately.

The above results are in agreement with those in literature(Perera, 1981) reporting that vortices do not exist for permeablepanels with porosity higher than 30%. This finding was confirmedin Fig. 8b and c for both studied nets, which have high porosity(62% for SCMD and 38% for WBTAPE). Despite this apparentagreement with the existing literature, one should keep in mindthat permeable materials are characterised by their a and bparameters (Eq. (3)), while porosity does not completely describetheir aerodynamic behaviour. The study of the creation of vorticesis a major issue in the design and construction of light agricultural

structures because they impose high and dangerous localizedloads at the zones near free ends where they develop (CEN, 2005).

Turbulent quantities have also been studied numerically.Results derived from the computational simulation (Fig. 11)showed that in the impermeable case the highest value for theturbulent kinetic energy reaches 0.71 m2/s2 and it is located at thefree ends of the panel, where flow separation initiates and thehighest velocity gradient variations occur. At the vortices, valuesof turbulent kinetic energy fluctuate between 0.46 and 0.54 m2/s2.In the permeable covering cases, analysis showed that the highestvalues of turbulent kinetic energy occur in the area leeward of thepanel. Turbulent kinetic energy was significantly lower than inthe film covering case and reached a maximum value of 0.33 m2/s2 for WBTAPE and 0.14 m2/s2 for SCMD. This behaviour was anadditional evidence of the existence of a smooth flow associatedwith weak turbulence in the case of the net covering.

4. Conclusions

The present work provides new experimental data andnumerical analysis results concerning the wind flow around anelevated panel covered by permeable or impermeable claddingmaterials. Net covered structures cannot be easily studied bywind tunnel experiments, because in this case the porous

Fig. 11. Contours of kinetic energy of turbulence in three covering cases (at mid-

length of panel): (a) film, (b) WBTAPE net and (c) SCMD net.


characteristics of the covering material and geometric character-istics of the structure have to be scaled by the same factor. Inother words, the aerodynamic characteristics of the nets shouldbe scaled to fit the similitude ratio selected for the structure.Therefore, a scale model of the covering material with the samefabric type details has to be developed for the wind tunnelexperiments. This scaling procedure requires tedious technicalwork. For this reason, computational fluid dynamics is anappealing low cost alternative. However, CFD results can betrusted only if validated by experimental measurements. Hencenumerical results presented in this work are validated in detail byfull-scale experiments against wind velocity data indicating theairflow qualitative and quantitative characteristics. The possibi-lities and the limitations of CFD analysis are identified.

More specifically, full scale experiments were conducted inorder to measure wind velocities and analyze the flow patternaround the panel for both permeable and impermeable coveringmaterials. Increased turbulence that was present in the case of thefilm covered panel showed differences in velocity comparisonsat the free ends, where flow separates and vortices are generated.It was already known from literature that such locationsare very difficult to be properly simulated by numericalmethods (Awbi, 1991). Despite this quantitative discrepancy, theairflow pattern is well reproduced and CFD simulations could be

used for a qualitative analysis of the wind flow around animpermeable panel.

In the case of permeable net-covered structures, numericalsimulations can provide even quantitatively realistic results,because flow separation and eddy formation are suppressed dueto the porosity of the cladding material. Full scale data andnumerical results showed very good agreement for the netcladding case. The numerical CFD simulation appeared to bereliable for the study of wind flow problems with permeablepanels. In this case, air velocity values are more accuratelypredicted by numerical methods in comparison to the filmcovered case.

Contours of turbulent kinetic energy demonstrate the magni-tude of turbulence close to the panel for both cases. As expected,flow was smoother when nets were used. High value of turbulentkinetic energy was associated with the use of impermeableplastic film.

For the numerical simulation two different numerical turbu-lence models have been used: standard k–e model and RNG k–emodel. Both models provided similar air velocity results.Discrepancies for these results appear when compared with thefull scale measurements only for the impermeable cladding case.This renders CFD simulations as an efficient tool for a fast, low-cost, reliable estimation of the behaviour of the wind aroundstructures consisting of permeable panels such as net-coveredwindbreaks and canopy roofs, and anti-insect nethouses. How-ever, further experimental research is needed to validate theefficiency of CFD in modelling such more complicated structures.

Acknowledgements

This work is part of the 03ED375 research project, implemen-ted within the framework of the ‘‘Reinforcement Programme ofHuman Research Manpower’’ (PENED) and co-financed byNational and Community Funds (25% from the Greek Ministry ofDevelopment-General Secretariat of Research and Technology and75% from EU-European Social Fund).

References

AGRONETS project, 2004. Development of protective structures covered withpermeable materials for agricultural use. SME-2003-1-507865 (DG 12), Craft,2004, /http://www.agronets.aua.grS, Agricultural University of Athens,Greece.

Awbi, H.B., 1991. Ventilation in Buildings. E & FN Spon, London, G. Britain(Chapter 7).

Bradley, E.F., Mulhearn, P.J., 1983. Development of velocity and shear stressdistributions in the wake of a porous shelter fence. Journal of WindEngineering and Industrial Aerodynamics 15, 145–156.

Briassoulis, D., Mistriotis, A., 2006. Full-scale measurement of the aerodynamiccoefficients for agricultural nets. In: Proceedings of the InternationalConference of Agricultural Engineers, AgEng, AgEng2006/XVI CIGR WorldCongress, Bonn, Germany, September 3–7, Archive no 440119580829, Conf.page 4401/1958.

Briassoulis, D., Mistriotis, A., 2010. Integrated structural design methodology foragricultural protecting structures covered with nets. Journal of BiosystemsEngineering 105, 205–220.

Briassoulis, D., Mistriotis, A., Giannoulis, A., 2010. Wind forces on porous elevatedpanels. Journal of Wind Engineering and Industrial Aerodynamics, submittedfor publication.

Castellano, S., Scarascia Mugnozza, G., Russo, G., Briassoulis, D., Mistriotis, A.,Hemming, S., Waaijenberg, D., 2008. Plastic nets in agriculture: a generalreview of types and applications. Applied Engineering in Agriculture 24 (6),799–808.

CEN, 2005. Eurocode 1: Actions on structures—part 1-1-4: General actions—windactions 1-1-4. EN 1991-1-4:2005, Comite Europeen de Normalisation, Brussels.

Crosby, C.P., Mathews, E.H., Du Plessis, J.P., 1990. The numerical prediction ofairflow through and around permeable windbreaks and buildings. Journal ofWind Engineering and Industrial Aerodynamics 35, 213–224.

Gandemer, J., 1979. Wind shelters. Journal of Industrial Aerodynamics 4, 371–389.

http://www.agronets.aua.gr


Hemming, S., Campen, J., Waaijenberg, D., 2005. Testing of air permeabilityperformance of agricultural nets. Internal Report, Agrotechnology and FoodInnovations B.V., Wageningen UR, Wageningen, The Netherlands.

Kim, H.B., Lee, S.J., 2002. The structure shear flow around a two-dimensionalporous fence having a bottom gap. Journal of Fluids and Structures 16 (3),317–329.

Lage, J.L., 1998. The Fundamental Theory of Flow through Permeable Media fromDarcy to Turbulence. In: Ingham, D.B., Pop, I. (Eds.), Transport Phenomena inPorous Media. Pergamon Press, Oxford, pp. 1–31 1998.

Letchford, C.W., Holmes, J.D., 1994. Wind loads on free-standing walls in turbulentboundary layer. Journal of Wind Engineering and Industrial Aerodynamics 51,1–27.

Letchford, C.W., Robertson, A.P., 1999. Mean wind loading at the leading ends offree-standing walls. Journal of Wind Engineering and Industrial Aerodynamics79, 123–134.

Letchford, C.W., 2001. Wind loads on rectangular signboards andhoardings. Journal of Wind Engineering and Industrial Aerodynamics 89,135–151.

Park, C.W., Lee, S.J., 2001. The effects of a bottom gap and non-uniform porosity ina wind fence on the surface pressure of a triangular prism located behindthe fence. Journal of Wind Engineering and Industrial Aerodynamics 89,1137–1154.

Paulotto, C., Ciampoli, M., Augusti, G., 2006. Wind tunnel evaluation of mean windpressure on a frame-type signboard. Journal of Wind Engineering andIndustrial Aerodynamics 94, 397–413.

Perera, M.D.A.E.S., 1981. Shelter behind two-dimensional solid and porous fences.Journal of Wind Engineering and Industrial Aerodynamics 8, 93–104.

Raine, J.K., Stevenson, D.C., 1977. Wind protection by model fences in a simulatedatmospheric boundary layer. Journal of Industrial Aerodynamics 2, 159–180.

Richards, P.J., Hoxey, R.P., 1993. Appropriate boundary conditions for computa-tional wind engineering models using the k–e turbulence model. Journal ofWind Engineering and Industrial Aerodynamics 46 & 47, 145–153.

Robertson, A.P., Hoxey, R.P., Richards, P.J., 1995. Design code, full-scale andnumerical data for wind loads on free-standing walls. Journal of WindEngineering and Industrial Aerodynamics 57, 203–214.

Robertson, A.P., Hoxey, R.P., Short, J.L., Ferguson, W.A., Osmond, S., 1996. Full-scaletesting to determine the wind loads on free-standing walls. Journal of WindEngineering and Industrial Aerodynamics 60, 123–137.

Robertson, A.P., Hoxey, R.P., Richards, P.J., Ferguson, W.A., 1997a. Full-scalemeasurements and computational predictions of wind loads on free-standing-walls. Journal of Wind Engineering and Industrial Aerodynamics 67&68,639–646.

Robertson, A.P., Hoxey, R.P., Richards, P.J., Ferguson, W.A., Blackmore, P.A., 1997b.Wind loads on boundary walls: full-scale studies. Journal of Wind Engineeringand Industrial Aerodynamics 69-71, 451–459.

Robertson, A.P., Hoxey, R.P., Short, J.L., Ferguson, W.A., Blackmore, P.A., 1998.Prediction of structural loads from fluctuating wind pressures: Validation fromfull-scale force and pressure measurements. Journal of Wind Engineering andIndustrial Aerodynamics 74-76, 631–640.

Shames, I.H., 1992. Mechanics of Fluids 3rd ed. McGraw-Hill, Singapore(Chapter 9).

Yaragal, S.C., Govinda Ram, H.S., Keshava Murthy, K., 1997. An experimentalinvestigation of flow fields downstream of solid and porous fences. Journal ofWind Engineering and Industrial Aerodynamics 66, 127–140.

J. Wind Eng. Ind. Aerodyn. 98 (2010) 919–928

Contents lists available at ScienceDirect

Journal of Wind Engineeringand Industrial Aerodynamics

0167-61

doi:10.1

n Corr

E-m

journal homepage: www.elsevier.com/locate/jweia

Wind forces on porous elevated panels

Demetres Briassoulis n, Antonis Mistriotis, Anastasios Giannoulis

Agricultural University of Athens, Department of Agricultural Engineering, Iera Odos 75, 11855 Athens, Greece

a r t i c l e i n f o

Article history:

Received 11 June 2010

Received in revised form

17 September 2010

Accepted 17 September 2010Available online 12 October 2010

Keywords:

Wind forces

Elevated panel

Permeable materials

Impermeable materials

05/$ - see front matter & 2010 Elsevier Ltd. A

016/j.jweia.2010.09.006

esponding author. Tel.: +30 210 529 4011.

ail address: [email protected] (D. Briassoulis).

a b s t r a c t

Agricultural nets are used in fruit and ornamentals production as covering material in various light

structures such as anti-hail and/or anti-frost shields, windbreaks, and coverings of shading or anti-insect

structures. There is limited information in the existing standards for the calculation of wind loads on

structures with permeable cladding like nets. Moreover, there are few experimental data concerning the

wind pressure distribution around air permeable structures. For this reason, the wind-pressure

distributions over permeable claddings need to be systematically investigated by field experiments

and numerical simulations. In the present work, special full-scale field tests were designed and carried

out to measure the wind pressures on experimental scale panels covered by various types of nets and by

film. The film covering was functioning as impermeable reference material, for comparative purposes. The

forces were measured at a central independent segment of the panel suspended on specially designed

spring units by using displacement transducers. The measurements were compared to data obtained from

a similar structure covered with impermeable plastic film and against the provisions of relevant

standards. The full scale measurements were also compared to computational results obtained by CFD

simulations.

& 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Light agricultural structures covered with plastic nets wererecently introduced in fruit tree and vegetable farming for protectingcrops against natural hazards such as hail and wind, or biologicalprotection against birds and insects (Castellano et al., 2008).Net-covered structures are light, low-cost, easy to install construc-tions, which generate moderate greenhouse and windbreak effects.However, their design with respect to wind loading is poorly studiedso far. An integrated design methodology for this type of structuresis presented in Briassoulis and Mistriotis (2010).

There are only few experimental data published concerningthe aerodynamic characteristics and the wind pressure distribu-tion on air permeable rigid structures (Richardson, 1987; Richardsand Robinson, 1999; Letchford et al., 2000; Letchford, 2001; Kimand Lee, 2002; Robertson et al., 2002). Although there are severalstudies concerning air flow through plastic nets and screens,which are used in greenhouses either for insect protection atventilation openings or for energy savings (Miguel et al., 1997;Bailey et al., 2003; Valera 2005; Harmanto et al., 2006), theseworks focus on airflows of low velocities, which are typicalindoors during ventilation. Therefore, these results are notrelevant to the analysis of wind forces, at high wind velocities,which is critical for the design of structures covered by nets.

ll rights reserved.

Moreover, several publications exist analysing wind loads onfences and walls (Robertson et al., 1995, 1997; Richards andRobinson, 1999; Packwood, 2000). These studies on permeableand impermeable walls of various aerodynamic characteristicsinvestigated the corresponding wind loads by wind tunnelexperiments, and computer simulations. The presented resultsindicated that the numerical technique could be a promisingapproach for the analysis of the airflow around walls and fences.

Wind loads on a panel depend on the wind velocity and theaerodynamic characteristics of the structure. The aerodynamicforce coefficient, cf, describes the dependence of the wind loads onthe shape and the material of the structure, separated from thewind intensity:

F ¼1

2cf Arefrv2

ref ð1Þ

where F is the force acting on the structure, Aref is the referencearea on which the wind loads are applied, vref is the wind velocityat a reference height zref, and r is the air density. Eurocodes 1 and3 (CEN, 2005a, 2005b) and other relevant European standards likethe standard for greenhouse design (CEN, 2001) do not provide amethodology for the calculation of wind loads on structures withpermeable cladding of low solidity ratios, like nets. For thisreason, net supporting structures are currently calculated follow-ing the provisions of non-permeable structures but with anarbitrarily reduced safety factor, or by reducing the aerodynamiccoefficients as a function of the solidity ratio, f, of the net.


dx.doi.org/10.1016/j.jweia.2010.09.006

mailto:[email protected]

dx.doi.org/10.1016/j.jweia.2010

Fig. 1. Symbol key for elevated panels.

Nomenclature

List of symbols

A sum of the projected area of the solid members of aporous panel (e.g. net area of face of the windbreak),m2

Ao gross area of a porous panel (e.g. the area enclosed bythe boundaries of the face Ao¼ lh of a windbreak), m2

(A¼Ao in the case on impermeable panel)Aref reference area for cf (Aref is equal to Ao or A depending

on the Standard)b linear term coefficient of the simplified Forchheimer

equation, N s m�3

cf force coefficient based on the reference area Aref of apanel

cf0 force coefficient applied on the net solid area A of a

panelcscd structural factorc coefficientC aerodynamic resistance coefficient of a porous mate-

rial, m�1

Fspring unit wind force on a spring unit, N

F wind force on the panel, N

h vertical dimension of a panel, m

Iv(z) wind turbulence intensity at height z

k elastic constant of a spring, N m�1

kr terrain factor

K specific permeability of a porous material, m2

Kp net porosity factor (AS/NZS 1170.2)l horizontal dimension of a panel, m

p probabilitypd(z) dynamic pressure at height z, kg m�1 s�2

qm(z) mean wind pressure at height z, kg m�1 s�2

qp(z) peak wind pressure at height z, kg m�1 s�2

v(z) air velocity at height z, m s�1

vb(z) basic wind velocity at height 10 m, m s�1

vm(z) mean wind velocity at height z, m s�1

z height from the ground, mzo roughness length, mzg clearance height between the panel and the

ground, mzref reference height, m

Greek letters

a quadratic term coefficient of the simplifiedForchheimer equation, N s2 m�4

gQ1 partial factor for wing actionDp pressure difference, kg m�1 s�2

Dx thickness, displacement, mm dynamic viscosity, kg m�1 s�1

r air density, kg m�3

f solidity ratio (A/Ac)

D. Briassoulis et al. / J. Wind Eng. Ind. Aerodyn. 98 (2010) 919–928920

The solidity ratio is defined as

f¼A

Aoð2Þ

where A is the sum of the projected area of the solid members(i.e. fibres of nets) of the panel (net area of face of the panel) andAo is the gross area of the face that is the area enclosed by theboundaries of the face of the panel. This arbitrary approach maylead to substantial overestimation of the supporting structures,which become unnecessarily expensive, less functional, and mayrequire higher installation cost. For this reason, the wind-pressuredistributions over permeable claddings need to be systematicallyinvestigated.

The American Standard ANSI (2006) is more detailed thanother relevant standards, in terms of design provisions for thecase of free standing walls and signs (elevated panels). For thesetypes of structures, ANSI provides wind pressure coefficients,which depend on the solidity ratio of the permeable structure.However, ANSI does not recommend a design methodology forother types of permeable structures. Similar recommendations forfree standing walls and hoardings are provided by the AustralianStandard AS/NZS 1170.2 on ‘‘structural design actions—Windactions’’ (AS/NZS 1170.2, 2002).

The current work aims at analysing wind loads on a flatelevated vertical panel covered by nets (Fig. 1). This is one of thesimplest structures to be studied for wind loads. The effect ofthe air permeability characteristics of the cover on the windloads can be investigated in this way. An elevated panel is alsocharacterised by two geometrical parameters: the aspect ratiol/h and the clearance ratio zg/h (Fig. 1).

Permeable and impermeable elevated panels have beenstudied by Letchford (2001) by means of wind tunnel experi-ments, where the dependence of the force coefficient on thegeometric characteristics of the panel (height, width, bottom gap)has been analysed. Although Letchford’s (2001) work focuses

mainly on an impermeable signboard (elevated panel), it has alsoaddressed the case of a permeable panel with high solidity ratio(fZ0.77). In this solidity range, Letchford (2001) estimated acorrection factor for wind loading equal to 1�(1�f)1.5.

Moreover, Paulotto et al. (2006) studied an impermeablesignboard with aspect ratio l/h¼5 and clearance ratio zg/h¼2.55.The force coefficient was measured by wind tunnel experiments.In the free standing case, the force coefficient cf was found equalto 1.65. This value confirms the corresponding results of Letchford(2001), where the cf of a signboard with similar aspect andclearance ratio was found equal to 1.57. The reference height, zref,for the calculation of cf was considered equal to the height h+zg ofthe structure in both these studies. In a work less relevant to thecurrent study, Quinn et al. (2001) investigated wind pressurecoefficients for a variety of sign shapes such as circles, triangles,rectangles of various dimensions.

The velocity field around an elevated permeable panel has alsobeen investigated. Kim and Lee (2002) analysed the air flowaround a permeable fence having a bottom gap by using a hybrid

D. Briassoulis et al. / J. Wind Eng. Ind. Aerodyn. 98 (2010) 919–928 921

particle tracking velocimetry (PTV) method in wind tunnelexperiments.

The ANSI Standard (ANSI, 2006) addresses elevated panels(signs), under the general category of ‘‘free standing walls andsigns’’. According to the ANSI Standard provisions, in the case ofsolid elevated panels the force coefficient, cf, depends on theaspect ratio (l/h) and the clearance ratio (zg/h). These recommen-dations are based on the results presented in Letchford (2001). Forwalls with high solidity ratios (f40.7), cf is reduced by the factor(1�(1�f)1.5), according to Letchford’s (2001) results. Whenthe solidity is lower (fo0.7), the structure is considered in thecategory ‘‘open signs and lattice frameworks’’. In this casecf values are given as the product fcf

0, where the force coefficientcf0 in the ANSI standard (ANSI, 2006) is applied on the net solid

area of face of the panel, A. In order to get comparable measures,the provisions of this standard are expressed in the present workin terms of the force coefficient as defined by Eurocode 1-1-4(CEN, 2005a) as follows: cf

0¼cf/f: cf

0 ¼2.00 for fo0.10 (cf¼0.2);cf0 ¼1.80 for 0.1ofo0.29 (0.2ocfo0.5); cf

0 ¼1.60 for0.3ofo0.70 (0.5ocfo1.1). According to the ANSI standard(ANSI, 2006) the equivalent cf values for porous walls and signs(as described above) are based on wind-tunnel tests conductedunder conditions of uniform flow and low turbulence, and theirvalidity in turbulent layer flows has yet to be established.

The Australian Standard AS/NZS 1170.2 (2002) provisions forhoardings and free standing walls are also based on Letchford’s(2001) results. The force coefficient for impermeable panelsdepends on the aspect ratio (l/h) and the clearance ratio (zg/h)similarly to ANSI Standard. However, force coefficients, cf, forporous panels are estimated in a different way. They arecalculated from the corresponding cf of a solid panel with thesame dimensions multiplied by the factor, Kp¼(1�(1�f)2),where f is the solidity of the panel. This reduction factor isused for panels of any solidity and results into larger forcecoefficients than the ANSI Standard (ANSI, 2006) for the samepanel dimensions and solidity ratios.

Eurocode 1 (CEN, 2005a) recommends only a single designforce coefficient cf¼1.8 for solid signboards (elevated panels)when the clearance height zg is larger than h/4, where h is thevertical dimension of the signboard. No reference is made toporous elevated panels.

In the present work, wind forces were measured by full scalefield experiments and numerical simulations. Special full-scalefield tests were designed and carried out to measure the windpressures on experimental scale panels covered by various typesof nets and by film, for comparative purposes. The panels wereelevated resembling signboards. This allowed direct comparisonsof the results obtained for the panel covered by film, used as areference control case, against other experimental data availablein the literature (Letchford, 2001; CEN, 2005a; ANSI, 2006). Thefull scale measurements were also compared to numerical resultsobtained by CFD simulations using the computational modeldeveloped by Giannoulis et al. (2010).

2. Methods and materials

2.1. Design of the experimental setup according to Eurocode 1

The steel frame used in the present experimental setupwas designed following the wind loading recommendations ofEurocode 1-1-4 (CEN, 2005a). Since the structure was designed forapplying both permeable and impermeable cladding materials,wind loads were estimated for the case of a solid panel. The windforces were calculated following the recommendations forparapets and panels. Then, the global forces acting on a panel or

a flexible structure are calculated as follows:

Fw ¼ cscdcf qpðzref ÞAref ð3Þ

where (Eurocode 1-1-4 (CEN, 2005a)) cf is the force coefficient,cscd is the structural factor (taken as 1.0; for buildings with aheight less than 15 m; for facade and roof elements having anatural frequency greater than 5 Hz), Aref is the reference area forcf (projected area of the structure normal to wind) and it is equalto Ao in this case, and qp(zref) is the peak velocity pressure at thereference height zref (in m/s). The peak velocity pressure includesmean and short-term velocity fluctuations and may be deter-mined by the following recommended expression as a function ofseveral coefficients (Eurocode 1-1-4 (CEN, 2005a)):

qpðzÞ ¼ 1þ7IvðzÞ½ �1

2rvmðzÞ

2¼ 1þ7IvðzÞ½ �qmðzÞ ð4Þ

The mean wind velocity vm(z) at height z is calculated byassuming a logarithmic wind profile:

vmðzÞ ¼ crðzÞcoðzÞvbðzÞ ¼ kr lnz

z0

� �vb ð5Þ

where cr(z) is the roughness factor; co(z) is the orography factor(taken as 1.0); kr is the terrain factor; zo is the roughness lengthdepending the landscape type; r is the air density (1.25 kg/m3);vb is the basic wind velocity at 10 m above ground as defined inEurocode 1-1-4 (CEN 2005a); Iv(z) is the wind turbulenceintensity at height z, defined as the standard deviation ofthe turbulence divided by the mean wind velocity vm(z); qm(z)is the mean wind pressure at height z.

Eurocode 1-1-4 (CEN, 2005a) recommends a force coefficient cf

equal to 1.8 for impermeable signboards separated from theground by at least zg¼h/4 height. Otherwise the panel is assumedas a free-standing wall with a force coefficient cf equal to 1.2. Theresultant force normal to the signboard should be taken to act atthe height of the centre of the board, with a horizontaleccentricity of e¼70.25b. The reference height is defined inEurocode 1-1-4 as zref¼zg+h/2 and the reference area is Aref¼ lh.

The full-scale experimental setup was designed and constructedin the form of two steel frame-lattice structures supporting threeelevated panels each, especially designed for the purpose ofdetermining the aerodynamic coefficients of agricultural nets(Fig. 2). The two structures were constructed in the experimentalfield of the Agricultural University of Athens (Spata, Attiki). Thestructural elements used for the design of the experimental steelframeworks were steel pipes S235. The design of the experimentalsetup was based on the wind forces calculated according toEurocode 1-1-4 (Robertson et al., 1995) for this particular type ofstructure (a type of signboard). The wind loads were calculated forthe eastern area of Attiki, for a basic value of the reference meanwind velocity of 30 m/s, having an annual probability of excee-dance, p, of 0.02. Considering a partial factor for wind action ofgQ1¼1.5 (CEN, 2005a), the design wind pressure on the panels wascalculated to be 2.7 kPa. The steel frames were designed accordingto Eurocode 3 (CEN, 2005b).

Each of the three panels of the first structure was covered byfilm, while those of the second one were covered by selectedplastic nets, commercially characterised as windbreak nets(Fig. 3). The central panel in both frames was supported at thefour corners by spring units, specially designed for measuring thewind forces applied on these panels for both wind directionsperpendicular to the panel (Fig. 3). Wind forces were measuredonly on the central panel in order to minimise possible edgeeffects on the measured wind pressures. The films and the netswere all supported on the panels by using a ‘‘clipping and locking’’mechanism along special grooves of the frames of the panels, so

Fig. 3. Design details of central panel with spring supports.

Fig. 2. The experimental steel frameworks supporting the elevated panels.


that they could be easily replaced to allow the measurement ofthe aerodynamic coefficients of various nets. The expectedmechanical behaviour of the nets and films placed on the centralpanels was calculated based on the methodology of Briassoulisand Schettini (2003). Thus, for the LDPE film and for the 3 mlength of the central panel, assuming one-way load carryingmechanism of the wind pressures to the vertical sides(a conservative assumption in this case), the 200 mm thick filmis able to withstand wind pressures up to 2.0 kPa for assumedtensile strength of the film of 20 MPa (usually the tensile strengthof LDPE film is higher, in the range of 25 MPa), corresponding to awind velocity of 32 m/s. Yielding of the film assumed at 10 MPa,would be initiated at wind load of 1.3 kPa, corresponding to awind velocity of 26 m/s (note that in calculating the filmresistance to wind load, the safety coefficient of gQ1¼1.5 wasnot taken into account). The two-way load carrying mechanismactivated in reality by the film panel supported along all four sidesshould allow it to withstand significantly higher wind pressures.

High strength steel pipes were used for the construction of thespring units supporting the central panels (Fig. 4). The springconstant k of the springs was derived from Eq. (3) under thefollowing assumptions: The force coefficient cf was set equal to1.8 as suggested by Eurocode 1-1-4 (CEN, 2005a). The referencearea of the central section of the panel was 6 m2.

Since the purpose of the experiment was to measure the meanforce coefficient of the panel, the mean displacement Dxm andthe mean wind velocity vm(z) were simultaneously measured.Therefore, for the selection of the constant k of the springs onlythe mean wind pressure qm(z) was considered, and the windturbulence intensity Iv(z) at height z was set equal to zero inEq. (4). The mean wind pressure, qm(z), was calculated at heightz¼zref¼4m (i.e. in the middle height of panel; according toEurocode 1-1-4 (CEN, 2005a), the resultant force normal to thesignboard should be considered to act at the height of the centreof the signboard).

Moreover, the selected elastic constant of the springs shouldallow for significant displacements of the supported panel in theexpected range of wind velocities in order to facilitate themeasurements. From the statistical analysis of available longterm measurements of the wind characteristics in the area, it wasfound that the probability for a mean wind velocity higher than9 m/s at 10 m height to occur in a period of 1 month wasapproximately 0.5%. Therefore, springs were selected reachingtheir maximum displacement at a force of 100 N. This maximumallowed force per spring unit corresponds to a basic wind velocityof vb¼9 m/s (measured at 10 m height) acting on the solidelevated panel. Extension of the spring units beyond theirmaximum displacement limit was mechanically blocked. Follow-ing these considerations the spring units were built by using twocompression springs each (Fig. 4) having a spring constant of2.11 kN/m and a maximum allowed displacement of 5 cm. Theselected maximum displacement is such that the airflow aroundthe structure is not influenced by the movement of its centralpanel, but it is large enough to allow for an accurate measurementof the displacement.

The displacements of the central panels under the action of thewind pressure were monitored through two displacementtransducers (model AML/IE550) placed in the middle of thevertical sides of the central panels (Fig. 5). The measuring range ofthese displacement transducers was 75 cm, which is equal to themaximum allowed displacement of the springs, and theiraccuracy was 7�10�3 cm.

2.2. Analysis of wind characteristics

The experimental setup constructed in the experimental fieldof the Agricultural University of Athens at Spata, Attiki, is shownin Fig. 6. The elevated panels were installed in an open field wherethe basic wind velocity vb was also measured at 10 m height.A long tree windbreak of approximately 6 m height was standingat a distance of 65 m NE of the 10 m mast of the anemometermeasuring the basic wind velocity and at a distance 110 m fromthe experimental setup. A low-rise building (4 m high) waslocated South of the experimental panels at a distance of45–65 m. These obstructing objects were expected to have limitedinfluence on the measurements of the basic wind velocity becauseof their relatively small height and in comparison to their distanceto the measuring anemometer. The anemometer measuring thebasic wind velocity and wind vane were located at a distance of50 m away from the panels, as shown in Fig. 6. Wind velocity anddirection at 10 m height were measured every 15 s and averagevalues were recorded every 2 min at the experimental field. Thesemeasurements were validated against wind data available from

Fig. 4. Detailed design of the spring units supporting the central section of the panels in order to measure wind forces.

Fig. 5. Panels covered by net and the displacement transducer unit measuring the

displacements at the middle of one of the vertical sides of the central panel.

Fig. 6. Overview of the experimental field where the elevated panels were

installed (Google Earth).


the nearby meteorological station of the Athens Internationalairport (AIA, 2004) where upwind terrain characteristics aresimilar. The airport is located 5.7 km south of the location of thefull scale experiment. Average wind velocities values are recordedby the airport meteorological station every 30 min.

Fig. 7 presents the angular distribution of the wind direction atthe location of the full scale experiment (data of year 2003). Themost frequent wind direction was found to be North East. For lowwind velocities, vo5 m/s, also northern winds seem to besignificant. For basic velocities higher than 10 m/s, North Eastwinds are dominant. The probability of North East direction isabout 50% for wind velocities higher than 5 m/s.

The roughness length zo of Eq. (5) was measured with thehelp of an additional anemometer, which was installed onthe elevated panel frame at 4 m height, while all coveringmaterials had been removed from the panels. Measurementswere recorded and compared to simultaneous measurements at10 m height. The roughness length zo (Eq. (5)) can be estimatedfrom the average ratio of the wind velocities at 4 and 10 mheights.

Fig. 6 indicates that the impinging wind was influenced byboth the continuous tree windbreak (6 m high) 110 m away in theNE direction, and the obstructing low-rise building (4 m high)45–65 m away in the S direction from the panels. In order toanalyse in detail the wind characteristics of the two dominantwind directions considered in the experiment, the roughnesslength, zo, was measured separately for the NE and the SWdirections. The average wind velocity ratio v(4)/v(10) was foundequal to 0.804 for the NE direction (Fig. 8a), and 0.767 for the SWdirection (Fig. 8b). These correspond to zo values obtained fromEq. (6), approximately equal to 0.09 m for the NE direction and0.19 m for the SW direction:

vð4Þ

vð10Þ¼

lnð4=z0Þ

lnð10=z0Þð6Þ

These measured values of zo characterise the terrain of theexperimental field between categories II and III following the

Fig. 7. Wind direction angular histogram at the location of the full scale

experiment.

Fig. 8. Correlation graph between simultaneous wind velocity measurements at 4

and 10 m height during (a) NE and (b) SW winds.


classification of Eurocode 1-1-4 (CEN, 2005a) which recommendszo¼0.05 m for category II and zo¼0.3 m for category III. Thedifferent measured friction length values indicate a weakdependence of the wind characteristics on the wind direction.This wind direction dependence of zo was taken into account inthe analysis of the measurements in order to obtain moreaccurate values for the force coefficient.

3. Results

3.1. Measurements of the wind force on panels made of nets

Three nets (SCMD, SC75, and WNDBRTP) have been tested onthe experimental setup (Fig. 2; frame on the left). Their solidityratio, f, was estimated optically by an image analysis software(Table 1). The film used for comparative studies was a conven-tional UV-stabilised LDPE film used as greenhouse coveringmaterial (Fig. 2; frame on the right). The displacements weremeasured every 15 s and recorded as values averaged over aperiod of 2 min. For the same period the average values of windvelocity and the wind direction at 10 m were measured andrecorded with the same frequency.

The airflow through a permeable or porous material isdescribed by a quadratic equation, known as Forchheimerequation (Lage, 1998):

Dp

Dx¼

mK

� �vf þCrv2

f ð7Þ

where K is called the specific permeability of the porous materialand m is the fluid dynamic viscosity, The variable vf is the fluidvelocity, Dp is the pressure difference across the porous material,and Dx is the thickness of the porous material. C is theaerodynamic resistance coefficient related to the microscopicgeometrical characteristics of the permeable medium and r is thedensity of the fluid.

Eq. (7) can also be presented in a simpler form, where the netis considered as a two-dimensional material with negligiblethickness:

Dp¼ av2f þbvf ð8Þ

Dp is the pressure difference across the porous material thickness,while a and b express the air permeability characteristics of thematerial. The values of a and b (Table 1) of the three plastic netsused in the present full-scale experiments, have been measuredby wind-tunnel experiments (Hemming et al., 2005).

The orientation perpendicular to the panel is NE–SW. Morespecifically, the direction normal to the panel surface is 301,assuming that North direction is at 01. Measurements concerningwind directions normal or almost normal to the panel (winddirection between 101 and 501 (North direction), or between 1901and 2301 (South direction) were selected. Moreover, all measure-ments concerning weak wind strengths (wind velocity at 10 mheight less than 3 m/s) were neglected since the objective of thiswork was to obtain aerodynamic force coefficients for estimatingdesign wind loads. The experiments lasted 5 months divided intotwo periods (September–November 2005, and October 2006).Basic wind velocities (i.e. at height 10 m), vb, as high as 15 m/swere measured. Wind loads on both the net-covered and the film-covered structures were measured simultaneously. During theseperiods, the air temperature was mild and varied in the range of10�23 1C corresponding to an air density variation in the range of1.19–1.25 kg/m3. Since this variation was small, an average valueof 1.22 kg/m3 was used for the calculation of the force coefficient,cf, introducing an error of about 2% into the measurements.

It is known that the force due to wind exerted on the windpanel is proportional to the square of the wind velocity. Assumingan elastic behaviour of the spring units, the spring displacements,Dx, were correlated to the wind velocities vb measured simulta-neously at 10 m height and fitted by a second order polynomial ofthe type:

Dx¼ cv2bþoffset ð9Þ

where vb is the basic wind velocity at 10 m height. The springdisplacement Dx was obtained as an output of the displacement

Fig. 9. Displacement of panels supported by springs as a function of the square

basic wind velocity at 10 m height.

Table 1Values of the force coefficient cf obtained through full scale experiments and numerical simulations for the three tested nets and the film.

Material Solidity (%) Aerodynamiccoefficients

Force coefficients measuredexperimentally cf�exp

Force coefficients calculated numericallycf-num

a (N s2/m4) b (N s/m3) North South 1-Segmentn 3-Segmentnn

1 SCMD 38 0.36 0.50 0.6070.1 0.6070.1 0.47 0.47

2 SC75 62 0.76 0.98 0.9570.2 0.8570.3 0.76 0.75

3 WNDBRTP 62 3.02 0.12 1.1070.3 0.9570.1 1.02 1.00

4 Film—1st period of measurements 100 1.3570.6 1.4570.2 1.62 1.54

5 Film—2nd period of measurements 100 1.6570.6 1.5070.3 1.62 1.54

n These force coefficients were calculated by numerical simulations for the elevated panel considered as 1 segment.nn These force coefficients were calculated by numerical simulations for the elevated panel considered as 3 segments reproducing the exact geometry of the full scale

experiment.

Fig. 10. Comparison between experimentally obtained probability function and

the Weibull distribution for the 2 min average cf of an impermeable panel

measured during the first measuring period for North winds.


transducers in mV and translated into length. In this way theoffset of the sensor and the second order coefficient (c) weredetermined. The spring force Fspring unit was obtained from thedisplacement value:

Fspringunit ¼ kðDx�offsetÞ ð10Þ

where k is the elastic constant of the spring unit. For the springunits used in this experiment k¼2.11 kN/m, measured at thelaboratory. The total wind-induced force F on the panels wascalculated by merging Eqs. (9) and (10):

F ¼ 4kcv2b ð11Þ

The factor 4 takes into account the fact that the wind load onthe panel is transferred to the four supporting springs at thecorners of the panel.

Fig. 9 presents a typical fit of experimental data by usingEq. (9). The displacements of both moving panels (film and net)were measured by two sensors each. The displacement ofthe film-covered panel increases faster with the wind speedcompared to the net-covered panel, indicating a stronger force asexpected. The correlation factor, R2, for the data shown in Fig. 9was found in the range between 0.75 and 0.80 indicating goodcorrelation between the basic wind velocity at 10 m height andthe force measured on the panel.

The force coefficient cf for the panel was estimated by dividingthe force F (Eq. (11)) by the area of the panel, Ao, and the meanwind pressure qm:

qmðzref Þ ¼1

2rvmðzref Þ

2ð12Þ

where the reference height, zref, is the panel midheight (4 m). Thereference mean wind velocity vm(zref) was estimated from Eq. (5)

assuming that zo is 0.09 and 0.19 for the NE and SW winddirections, respectively, as derived from local measurements inSection 2.2. The value of the air density, r, depends on thetemperature. In order to comply with the average temperatureduring the measuring periods, r was selected equal to 1.22 kg/m3:

cf ¼8kc

rlnð10=zoÞ

lnðzref =zoÞ

� �2

ð13Þ

3.2. Calculation of the mean force coefficient cf

The dispersed data shown in Fig. 9 indicate that the measure-ment of the mean force coefficient, cf, through this full scale fieldexperiment can be statistically obtained as an average. Forcecoefficient values obtained in time intervals of 2 min from Eq. (13)using the simultaneous measurements of wind velocity and paneldisplacement were analysed statistically. Similarly to the windvelocity, the values of cf obtained in 2 min intervals, were found toobey the Weibull distribution (Fig. 10) in agreement with existinginformation given in the literature (Dyrbye and Hansen, 1996).Therefore, mean force coefficients were calculated as the mean valueof the 2 min measured data, while the experimental errors wereestimated as the corresponding variance.

The results show a good repeatability in the case of theimpermeable panel, where experimental data were obtainedduring both measuring periods. Fig. 11 presents the fourexperimentally obtained probability functions corresponding tothe four measurement sets obtained for the impermeable panelduring the two measuring periods for North and South winds,respectively.

Fig. 11. Experimentally obtained probability functions for the cf of an imperme-

able panel measured during the two measuring periods for two different wind

directions.


Following the same methodology the force coefficients, cf, forthe three tested nets were measured. Table 1 presents themeasured force coefficient cf on the three tested windbreak netsand the impermeable plastic film. The measurements obtainedduring north or south wind are reported separately.

Mean force coefficients obtained during North or South windsdo not differ considerably and the differences found are smallerthan the corresponding variance. The experimental error(variance) is larger for North winds (Fig. 11). This reflects thedifferent wind characteristics between North and South winds, asNorth winds are more turbulent due to the presence of the treewindbreak shown in Fig. 6. A difference between the twomeasuring periods for the film covered panel is apparent in theN wind direction (1.35–1.65), while S wind values almost coincide(1.45–1.50). The variance of both N-wind measurements is largerthan that of the other measurements indicating a possiblecalibration error (Table 1). Moreover, based on the general trendof the values measured during North and South winds (Table 1),the value of 1.35 measured during the first period in the N winddirection is considered rather low.

For design purposes, Standards use mean force coefficientsusually obtained from wind tunnel experiments (Dyrbye andHansen, 1996). Published comparisons between wind tunnel andfull scale experiments show a good agreement with respect tomean pressure coefficients (e.g. Okada and Ha, 1992). Therefore,the mean force coefficient values obtained through the full scaleexperiments, given in Table 1, can be used for design purposes.Moreover, the variance values reported in the same table can beused for the estimation of extreme force coefficients following astatistical approach as suggested by Cook (1990).

3.3. Numerical calculation of the mean force coefficient cf

The airflow around the same elevated panel (h¼2, zg¼3, l¼7)has been studied by full scale experiments and computationalfluid dynamics (CFD) simulations (Giannoulis et al., 2010). Besidesthe details of the airflow characteristics obtained by the CFDsimulations, presented by Giannoulis et al. (2010), mean forcecoefficients, cf, were also numerically calculated for both theimpermeable, film-covered, panel, and the permeable net-coveredones.

The computational results obtained using the RNG k–eturbulence model are presented in Table 1, and they are compared

to the corresponding full scale measured values. The meshstructure and the boundary conditions used in these numericalsimulations are described in detail in Giannoulis et al. (2010). Thewind velocities at the inlet boundary obeyed the logarithmicprofile law. For the numerical results presented in Table 1, thebasic air velocity at 10 m height was selected equal to 4 m/s.

The difference between numerical and experimental values isless than the corresponding variance measured by the full scaleexperiments for all the studied cases. In particular in the case ofthe WNDBRTP net, the numerical prediction may be consideredaccurate. A good agreement is observed even in the case of theimpermeable panel, although it is known that numerical simula-tions have problems in modelling the separating flow behindimpermeable panels (Giannoulis et al., 2010). However, thenumerical cf values are smaller than the measured ones in thecase of the two more permeable nets (SC75 and SCMD).

A possible source contributing to the small discrepanciesshown in Table 1 between experimental and numerical valuescould be attributed to the design of the experimental setup shownin Fig. 2. The panel studied in the full scale experiments wasdivided into three segments for facilitating the measuring of theaverage wind force away of the boundaries. The division of thepanel into three segments intended to eliminate edge effects fromthe measurement of the wind force on the central panel. Theeffect of the gaps between the three segments of the experimentalpanel on the measurement of the force coefficient was investi-gated by numerical CFD simulations. The numerical results(Table 1) indicated that the effect of the gaps between the threepanels on the calculated wind force in the central panel isapproximately 5% for the case of the impermeable panel, while itbecomes negligible for the net-covered panels.

The numerically calculated force coefficients (Table 1) for panelsof low aerodynamic resistance coefficient (SC75 and SCMD) arelower than the mean measured values. This discrepancy, whichis smaller than the corresponding variance of the full scalemeasurements, cannot be attributed to the performance of thecomputational method, since it has been found that the airflowaround the same panels covered by the same nets of small solidityis accurately predicted by CFD simulations (Giannoulis et al., 2010).This small discrepancy may be related to the aerodynamicbehaviour of the specific covering materials (i.e. the effects of thefabric structure and the fibre properties of the nets on theiraerodynamic characteristics), which needs further investigation.

4. Discussion

The present work investigates the wind forces on an elevatedpanel covered by permeable and impermeable flexible claddingmaterials as a typical example of a structure covered by flexibleplastic nets or film. The mean force coefficients, cf, of an elevatedpanel were measured by full scale experiments for the cases of animpermeable film cladding and three plastic nets of differentporosities and fabric. Numerical cf values for the same panel andthe corresponding covering materials were also obtained by CFDsimulations.

For the impermeable elevated panel the measured mean forcecoefficient, cf, was found to vary in the range of 1.35–1.65(Table 1). These values can be compared with the cf valueinterpolated from the measurements of Letchford (2001) for apanel with the same aspect ratio, l/h¼3.5, and clearance ratio,zg/h¼1.5. The value 1.5, given by Letchford (2001) should beadjusted for the different reference height (zref¼zg+h¼5 m) usedin that work, instead of zref¼zg+h/2¼4 m, which is used in thepresent paper following Eurocode 1-1-4 definition (CEN, 2005a).The adjusted cf value was calculated by applying the following


formula:

cf�4 ¼ cf�5lnð5=zoÞ

lnð4=zoÞ

� �2

ð14Þ

Taking into account that Letchford’s (2001) experiment wasperformed in a boundary layer wind tunnel with a wind velocityprofile of zo¼0.02 m, the corresponding force coefficient isadjusted to 1.63. This value lies within the range of the currentmeasurements and almost coincides with the numerical valuecalculated by CFD in this work (Table 1: single segment model).This confirms the observation mentioned earlier that the value of1.35 obtained during the first period appears to be rather law.Perhaps this measurement has been affected by a technicalcalibration-related problem, as the corresponding probabilityfunction (Fig. 11) is the only one that indicates a significantprobability for wind force coefficient values below 0.5 (Fig. 11).

The ANSI standard (ANSI, 2006) recommends a design value,cf¼1.75, for a panel with the same geometric characteristics(Table 2). ANSI standard has based its recommendations onLetchford’s (2001) results. However, the recommended designcf values are derived by dividing the measured mean cf valuesby the term 0.85 in order to make them compatible with theformat of the relevant gust factor, as defined in this standard(ANSI, 2006). Therefore, the corresponding ANSI provision shouldbe multiplied by 0.85 to be compared to the present measure-ments. This reproduces the value cf¼1.5 measured by Letchford(2001). This value is further adjusted for the different referenceheight (zref¼zg+h/2) used in the present paper following Eurocode1-1-4 by applying Eq. (14). Two cf values, 1.67 and 1.71, wereobtained corresponding to the two different zo’s measured in Section2.2 for the NE and SW directions, respectively (Table 2).

Eurocode 1-1-4 (CEN, 2005a) recommends a single design value,cf¼1.8, for all elevated panels. The reference height is defined aszref¼zg+h/2 instead of zref¼zg+h, which is the ANSI definition. Thehigher design value recommended by Eurocode 1-1-4 compensatesfor the provision of a single force coefficient covering a wide range ofpanels of various geometric characteristics.

The Australian Standard AS/NZS 1170.2 (2002) recommenda-tions are also based on Letchford’s (2001) results. The cf valuesuggested for the panel studied in the present work is 1.47. Whenthis value was adjusted for the different reference height usingthe two different friction length values of Section 2.2, twocf values were obtained equal to 1.65 and 1.69 for the NE andSW directions, respectively.

Since no other results are available for permeable panels withsolidity lower than 70%, the present results can only be comparedto the recommendations of ANSI (2006) and AS/NZS 1170.2Standards after they are adjusted to the same reference heightusing Eq. (14). ANSI recommendations are also multiplied by thedesign related coefficient 0.85 similarly to the impermeablepanels (ANSI, 2006; Table 2).

Table 2Comparison between measured force coefficients and ANSI design recommendations.

Material Solidity (%) Aerodynamic coefficients Average measurcoefficient cf-exp

a (Ns2/m4) b (N s/m3)

SCMD 38 0.36 0.50 0.6

SC75 62 0.76 0.98 0.9

WNDBRTP 62 3.02 0.12 1.0

SOLID 100 1.5

n The recommended ANSI design cf is multiplied by 0.85 and corrected for the refenn The recommended AS/NZS 1170.2 design cf is corrected for the reference height

In the case of the SCMD net (f¼0.38), the average measuredcf is equal to 0.6. This value agrees with the suggested adjustedvalue 0.58 of ANSI standard (ANSI, 2006). For the same panel,AS/NZS 1170.2 (2002) recommends an adjusted value for thedifferent reference height value cf¼1.0, which is much highercompared to both the current measurements and the ANSIprovisions. When the nets (SC75 and WNDBRTP) of higher solidity(f¼0.62) are considered, the ANSI standard (ANSI/SEI 7-05, 2006)recommends a design cf¼0.95 and AS/NZS 1170.2 cf¼1.4. Inboth cases the AS/NZS 1170.2 strongly overestimates forcecoefficients for permeable panels. Therefore, the net porosityfactor, Kp¼(1�(1�f)2), used as a reduction factor of the forcecoefficients was obtained for panels of high solidity (f40.7)(Letchford, 2001), and cannot be extrapolated to cases of smallsolidity, as the ones studied in this work.

Another interesting conclusion derived by the above resultsconcerns the two panels of the same solidity (f¼0.62), but ofdifferent aerodynamic resistance, a, namely WNDBRTP and SC75.The measured mean cf values are different for the two studied nets(Tables 1 and 2). The average value corresponding to SC75 is cf¼0.9,while for the WNDBRTP net, the measured value is higher (cf¼1.0).This difference is a consequence of the different air permeabilitycharacteristics of the two nets (Table 1). More specifically, thesecond order coefficient, a, in Eq. (8) is equal to 3.02 N s2/m4, for theWNDBRTP net, and 0.76 N s2/m4 for the SC75. The differentaerodynamic resistance of the two nets reflects into the differentforce coefficients despite the fact that the solidity ratio of the twonets is the same. These results indicate that the second ordercoefficient, a, of Eq. (8) is a better measure of the aerodynamicbehaviour of a net than its solidity ratio, f.

5. Conclusions

The aerodynamic force coefficients of an elevated panelcovered by an impermeable film and three different plastic netsof solidity between 38% and 62% were measured by full scaleexperiments. These measurements provided new data withrespect to the wind loading on net covered structures, for whichthe existing design Standards offer limited information.

Numerical CFD simulations were also used for modelling theairflow around the panel and calculating the corresponding forcecoefficients, cf. Numerical values are comparable to the corre-sponding mean values measured by full scale experiments. Thecorresponding differences between experimental and numerical cf

values are in the range of 0.1–0.15 (absolute values). The obtainedresults offer new information concerning the range of validity ofthe numerical (CFD) analysis of the airflow around net-coveredstructures in support of a recent work on the airflow andturbulence characteristics around the same elevated panelcovered by impermeable film and three different plastic nets(Giannoulis et al., 2010).

ed force ANSI design forcecoefficient cf-ANSI

AS/NZS 1170.2 design forcecoefficient cf-ASNZS

Recommended Adjustedn Recommended Adjustednn

0.61 0.58 0.90 1.0

1.00 0.95 1.26 1.4

1.00 0.95 1.26 1.4

1.75 1.7 1.47 1.67

rence height zref¼zg+h/2 used in this work.

zref¼zg+h/2 used in this work.


Both the full scale measurements and the numerical resultsindicated that the solidity ratio of the net is not sufficient, as asingle parameter, for accurately determining the wind load on anet covered panel. For high wind speeds the aerodynamicresistance coefficient, C or a, is a better measure of theaerodynamic behaviour of a permeable panel, since in this casethe linear term of Eq. (7) is negligible in comparison to thequadratic term. It is recommended that the next revisions ofStandards take into consideration this result, in order to improvethe relevant design provisions offered.

The present results were derived specifically for a verticalelevated impermeable or permeable panel placed perpendicularto the wind. The aerodynamic behaviour of non-vertical perme-able panels cannot be directly derived based on the experimentspresented in this work. Further research work is required forinvestigating wind loads in this case. Numerical (CFD) simula-tions, which were proven to be an efficient, low-cost, and easy touse alternative to wind tunnel experiments or full scale experi-ments, may be utilised in the investigation of the aerodynamicbehaviour of a wide range of permeable structures.

Acknowledgements

The present work has been supported by the European CRAFTproject ‘‘Development of protective structures covered withpermeable materials for agricultural use’’ (Contract no. SME-2003-1-507865). The authors also thank AGREK SA for supportingthis research by constructing the experimental setup frame.

References

ANSI, 2006. ANSI Standard: ANSI/SEI 7-05, 2006, Minimum Design Loads forBuildings and Other Structures, The American National Standards Institute(ANSI), New York, N.Y.

AS/NZS 1170.2, 2002. Structural design actions—wind actions, Standards Australia.AIA, 2004. Athens International Airport ‘‘El. Venizelos’’ meteorological station.

Private Communication.Bailey, B.J., Montero, J.I., Parral, J.P., Robertson, A.P., Kamaruddin, R., 2003. Air flow

resistance of greenhouse ventilators with and without insect screens.Biosystems Engineering 86 (2), 217–229.

Briassoulis, D., Mistriotis, A., 2010. Integrated structural design methodology foragricultural protecting structures covered with nets. Biosystems Engineering105, 205–220.

Briassoulis, D., Schettini, E., 2003. Analysis and design of low—density poly-ethylene greenhouse films. Biosystems Engineering 84 (3), 303–314.

Castellano, S., Scarascia Mugnozza, G., Russo, G., Briassoulis, D., Mistriotis, A.,Hemming, S., Waaijenberg, D., 2008. Plastic nets in agriculture: a general reviewof types and applications. Applied Engineering in Agriculture 24, 799–808.

CEN, 2005a. EN 1991-1-4:2005 – Eurocode 1: Basis of design and actions onstructures, Part 1-1-4: General actions–Wind actions 1-1-4, Comite Europeende Normalisation, Brussels.

CEN, 2005b. EN 1993-1-1:2005 – Eurocode 3 – Design of Steel Structures, Part 1-1:2005/AC:2006: General rules and rules for buildings, Comite Europeen deNormalisation, Brussels.

CEN, 2001. prEN-13031-1 Final Draft: Greenhouses: Design and Construction, Part1: Commercial Production Greenhouses, Comite Europeen de Normalisation,Brussels.

Cook, N.J., 1990. The Designer’s Guide to Wind Loading of Building Structures.Butterworths, London.

Dyrbye, C., Hansen, S.O., 1996. The atmospheric boundary layer—natural wind,Wind Loads on Structures. John Wiley & Sons, New York pp.19–48.

Giannoulis, A., Briassoulis, D., Mistriotis, A., 2010. Experimental and numericalinvestigation of the airflow around a raised permeable panel. Journal of WindEngineering and Industrial Aerodynamics 07, 005. doi:10.1016/j.jweia.2010.

Harmanto, H., Tantau, J., Salokhe, V.M., 2006. Microclimate and air exchange ratesin greenhouses covered with different nets in the humid tropics. BiosystemsEngineering 94 (2), 239–253.

Hemming, S., Campen, J., Waaijenberg, D., 2005. Testing of air permeabilityperformance of agricultural nets. Internal Report,Agrotechnology and FoodInnovations B.V, Wageningen UR,Wageningen, The Netherlands.

Kim, H.-B., Lee, S.-J., 2002. The structure of turbulent shear flow around a two-dimensional porous fence having a bottom gap. Journal of Fluids andStructures 16, 317–329.

Lage, J.L., 1998. The fundamental theory of flow through permeable media fromDarcy to turbulence. In: Ingham, D.B., Pop, I. (Eds.), Transport Phenomena inPorous Media. Pergamon Press, Oxford, pp. 1–31.

Letchford, C.W., 2001. Wind loads on rectangular signboards andHoardings. Journal of Wind Engineering and Industrial Aerodynamics 89,135–151.

Letchford, C.W., Row, A., Vitale, A., Wolbers, J., 2000. Mean wind loads on porouscanopy roofs. Journal of Wind Engineering and Industrial Aerodynamics 84,197–213.

Miguel, A.F., Van de Braak, N.J., Bot, G.P.A., 1997. Analysis of airflow characteristicsof greenhouses screening materials. Journal of Agricultural and EngineeringResearch 67 (1), 105–112.

Okada, H., Ha, Y.-C., 1992. Comparison of wind tunnel and full-scale pressuremeasurement tests on the Texas Tech building. Journal of Wind Engineeringand Industrial Aerodynamics 41–44, 1601–1612.

Packwood, A.R., 2000. Flow through porous fences in thick boundary layers:comparisons between laboratory and numerical experiments. Journal of WindEngineering and Industrial Aerodynamics 88, 75–90.

Paulotto, C., Ciampoli, M., Augusti, G., 2006. Wind tunnel evaluation of mean windpressure on a frame-type signboard. Journal of Wind Engineering andIndustrial Aerodynamics 94, 397–413.

Quinn, A.D., Baker, C.J., Wright, N.G., 2001. Wind and vehicle induced forces on flatplates—Part 1: wind induced force. Journal of Wind Engineering and IndustrialAerodynamics 89, 817–829.

Richards, P.J., Robinson, M., 1999. Wind loads on porous structures. Journal ofWind Engineering and Industrial Aerodynamics 83, 455–465.

Richardson, G.M., 1987. A permeable windbreak: its micro-environment and itseffect on structural loads. Journal of Agricultural Engineering Research 38,65–76.

Robertson, A.P., Hoxey, R.P., Richards, P.J., 1995. Journal of Wind Engineering andIndustrial Aerodynamics 57, 203–214.

Robertson, A.P., Hoxey, R.P., Richards, P.J., Ferguson, W.A., 1997. Journal of WindEngineering and Industrial Aerodynamics 67–68, 639–646.

Robertson, A.P., Roux, P., Gratraud, J., Scarascia Mugnozza, G., Castellano, S.,Dufresne de Virel, M., Palier, P., 2002. Wind pressures on permeably andimpermeably-clad structures. Journal of Wind Engineering and IndustrialAerodynamics 90, 461–474.

Valera, D.L., 2005. Contribution to characterization of insect-proof screens:experimental measurements in wind tunnel and CFD simulation. ActaHorticulturae 69 (1), 441–448.

dx.doi.org/10.1016/j.jweia.2010

combined porous plates - copy

Documents