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Journal of Wind Engineering

and Industrial Aerodynamics 95 (2007) 1384–1399

Wind-tunnel modelling of the Silsoe Cube

P.J. Richardsa,, R.P Hoxeyb, B.D. Connella, D.P. Landera

aDepartment of Mechanical Engineering, University of Auckland, Auckland, New Zealand bSilsoe Research Institute, Silsoe, UK

Available online 13 March 2007

Abstract

1:40 scale wind-tunnel modelling of the Silsoe 6 m Cube at the University of Auckland is reported.

In such situations, it is very difficult to model the full turbulence spectra, and so only the high-

frequency end of each spectrum was matched. It is this small-scale turbulence that can directly

interact with the local flow field and modify flow behaviour. This is illustrated by studying data from

tests conducted in a range of European wind tunnels. It is recommended that spectral comparisons

should be carried out by using turbulence-independent normalising parameter, such as plotting fS ( f )/U 2 against reduced frequency f ¼ nz/U . Using parameters such as the variance and integral

length scale can easily mask major differences. It is noted that it is the size of the tunnel that limits the

low-frequency end of the spectra, and so the longitudinal and transverse turbulence intensities were

lower than in full scale. In spite of this similar pressure distributions are obtained. Some differences

are observed and these are partially attributed to the reduced standard deviation of wind directions,

which affects both the observed mean and peak pressures by reducing the band of wind directions

occurring during a run centred on a particular mean direction. The reduced turbulence intensities

also affect the peak-to-mean dynamic pressure ratio. However, since the missing turbulence is at low

frequencies, the peak pressures appear to reduce in proportion. By expressing the peak pressure

coefficient as the ratio of the extreme surface pressures to the peak dynamic pressure observed during

the run, reasonable agreement is obtained. It is argued that this peak–peak ratio is also less sensitiveto measurement system characteristics or analysis method, provided the measurement and analysis of

the reference dynamic pressure is comparable with that used for the surface pressures.

r 2007 Published by Elsevier Ltd.

Keywords: Wind tunnel; Turbulence; Cube

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www.elsevier.com/locate/jweia

0167-6105/$ - see front matterr 2007 Published by Elsevier Ltd.

doi:10.1016/j.jweia.2007.02.005

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

http://www.elsevier.com/locate/jweiahttp://localhost/var/www/apps/conversion/tmp/scratch_4/dx.doi.org/10.1016/j.jweia.2007.02.005mailto:[email protected]:[email protected]://localhost/var/www/apps/conversion/tmp/scratch_4/dx.doi.org/10.1016/j.jweia.2007.02.005http://www.elsevier.com/locate/jweia

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variance and integral length scale determined from the turbulence it appears that all six

studies are similar. However, plotting the same data using turbulence-independent

normalising parameters in Fig. 2(c) reveals a different picture. It can now be seen that the

high-frequency small-scale turbulence levels vary significantly. Wind-tunnels 4 and 5 had

the lowest levels of small-scale turbulence, but still larger than Silsoe, and these gave the

pressures closest to the Silsoe results. On the other hand, tunnel 10 has one of the highest

small-scale turbulence levels and has produced the least negative roof pressures. The

exception to this pattern is tunnel 11, which has high small-scale turbulence but gave

pressures that are in the middle of the bunch.In the past it has often been stated that pressures are more sensitive to changes in the

total turbulence intensity than to changes in integral length scale. For example, Melbourne

et al. (1997) state: ‘‘The length scale, while of importance, does not have a major influence

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Fig. 1. (a) The Silsoe 6 m Cube and (b) the 1:40 scale model.

P.J. Richards et al. / J. Wind Eng. Ind. Aerodyn. 95 (2007) 1384–13991386

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on wind load estimates and an error by a factor of 2 will introduce errors in the load of the

order of 10%. Of greater significance is the intensity of turbulence, which defines the

magnitude of the wind spectrum.’’

As is the case with all the spectra shown in Fig. 2(c), it is quite common for wind-tunnelspectra to be deficient in low-frequency turbulence in comparison with full scale. This is

caused by the physical limits created by the tunnel walls that restrict the maximum eddy

size that can exist within the tunnel. Hence, in order to match the full-scale turbulence

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0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.0001 0.001 0.01 0.1 1 10f=nz/U(z)

f S u u

( f ) / U ( z ) ^ 2

345101114Silsoe

c

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.001 0.010 0.100 1.000 10.000100.000

nLux /U(z)

n S u u

( n ) / v a r ( u )

345101114

b

-1.5

-1

-0.5

0

0.5

1

0 1

Distance Over Cube (Cube Heights) M e a n P r e s s u r e C o e f f i c i e n t

3 4

5 10

11 14

Silsoe F-S

a

2 3

Fig. 2. (a) Mean pressure coefficients on the vertical centreline of a cubic building, (b) longitudinal spectra at

z/h ¼ 0.6 plotted in von Ka ´ rma ´ n form and (c) normalised by turbulence-independent parameters (the Silsoe

spectra is at z/h ¼ 0.5).

Table 1

Characteristics of the flow for six of the wind-tunnel studies of flow around a cubic building reported by Ho ¨ lscher

and Niemann (1998) and Niemann (2000)

WT Scale U (0.6h) I u (0.6h) Lux (0.6h) Lux (30m)

3 500 5.775 0.2067 0.22 110

4 312.5 9.17 0.162 0.3 93.75

5 250 ? 0.166 0.38 95

10 250 6.425 0.227 0.338 84.5

11 750 4.356 0.224 0.077 57.75

14 500 6.28 0.217 0.295 147.5

P.J. Richards et al. / J. Wind Eng. Ind. Aerodyn. 95 (2007) 1384–1399 1387

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intensity, it is necessary to increase the high-frequency content. It should be noted that if

both the model-scale and full-scale spectra are of the von Ka ´ rma ´ n form and have the same

turbulence intensity, but the integral length scale in the tunnel is only one half of that

which the geometric scaling would suggest, then the low-frequency spectral density will be

half of the target value (obtained with the correctly scaled integral length scale) and thehigh-frequency spectral densities will be 22/3 (1.59) times bigger than the target. While wind

tunnel engineers would normally question the turbulence intensity being nearly 26%

higher than the target (variance 59% larger), accepting a situation where the turbulence

intensity is matched and the integral length scale is only half the target implies accepting a

high-frequency spectral density 59% higher than target. It is therefore suggested that when

comparing full-scale and model-scale spectra, it is better to use full-scale turbulence

intensity and integral length scale data, together with the von Ka ´ rma ´ n or similar spectral

equations, to create a target spectrum and to transform this into a form, such as that

shown in Fig. 2(c), which makes use of turbulence-independent normalising parameters to

carry out the comparison in that form. This will highlight where the measured wind tunnel

spectrum matches the target and where there are significant differences.

Both the work of Castro and Robins (1977) and Ogawa et al. (1983) show that increased

turbulence tends to promote earlier reattachment of the flow on the roof of a cube. It is

probably such changes that lead to the pressure changes observed in Fig. 2(a). Earlier

reattachment has been promoted on the roof of the Silsoe Cube by pitching it into the

wind. Fig. 3 illustrates the changes in roof pressure brought about by pitching the cube

forwards by 2.51 and 51. It may be observed that when flat (01 pitch) the roof suctions are

almost constant for the windward third of the roof and are generally more negative over

the centre of the roof. On the other hand, with the roof pitched 51

, the pressures reach ahigher peak one-quarter of the way across and then become less negative more rapidly. It is

believed that this is associated with earlier flow reattachment on the roof.

It appears from Fig. 2 that in order to adequately model the flow over the Silsoe Cube, it

will be necessary to match the small-scale turbulence levels. However, as illustrated in

Fig. 2(c), all six European wind tunnels had low-frequency turbulence levels much less than

observed at Silsoe, and hence it is likely that this will also occur in the Auckland tunnel.

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0 2Distance Over Cube (Cube Heights)

M e a n P r e s s u r e C o e f f i c i e n t

zero pitch

2.5 deg pitch

5 deg pitch

1 3

a b

Fig. 3. (a) Mean pressure coefficients on the vertical centreline of the Silsoe Cube when pitched forwards and

(b) the cube at 51 pitch.


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As a result, matching the high-frequency spectrum will inevitably mean that the wind-

tunnel turbulence intensities will be lower.

3. The full-scale facility

The Silsoe 6 m Cube has a plain smooth surface finish and has been instrumented with

surface tapping points on a vertical and on a horizontal centreline section with additional

tappings on one-quarter of the roof. Simultaneous measurements have been made of 32

pressures and of the simultaneous wind dynamic pressure and direction derived from a

sonic anemometer positioned upstream of the building at roof height. Tapping points are

constructed of simple 7 mm diameter holes (a size sufficient to prevent water blocking of

the tapping points) and the pressure signals transmitted pneumatically, using 6 mm

internal diameter plastic tube to transducers mounted centrally. Tube lengths of up to 10 m

are used in this system giving a frequency response of 3 dB down at 8 Hz.This paper will consider the ring of taps on the vertical centreline and at mid-height,

together with the 30 tappings on one-quarter of the roof, as shown in Fig. 4. The corner

roof tappings are in a grid of five columns and six rows with a spacing of 0.52 m (0.087h) in

both directions. The tappings nearest the roof edges are 0.4 m (0.066h) from the edge.

For the basic data recording, simultaneous measurements of the pressures were made at

a rate of 4.17 samples per second, together with the three components of the wind speed.

A 36-min record length was used (9000 samples) which was sub-divided into three 12 min

segments. The records were processed to give mean, peak and fluctuating properties. For

some of the runs the cube was rotated 451 clockwise, relative to that shown in Fig. 4, so

that the instrumented corner was towards the prevailing winds. In order to fully investigatethe roof pressure distribution, it would have been necessary to carry out measurements

with the corner roof taps in a variety of orientations. However, due to a shortage of

suitable wind during the testing period, the only tests completed had the taps on the

windward corner.

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a

Roof Tap 6

Wall Tap 17

Reference Mast

(1.0h high,

1.04h to the side

of cube centre)

3.48h

Wind

Directionθ

0.066h 0.087h

0.066h

0.087h

b

Fig. 4. (a) Plan view of wall and roof tappings on the Silsoe Cube and (b) taps on the Auckland model.


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quite similar, there are significant differences to the turbulence intensities, which is further

illustrated by the spectra and cospectra in Fig. 6.

A number of points may be noted from Fig. 6:

The Auckland wind-tunnel spectra match the full-scale spectra in the high-frequencyrange.

At both full-scale and model scale, the vertical (w) spectral density becomes muchsmaller than that of longitudinal (u) or transverse (v) components at reduced frequencies

below 0.3. The wind-tunnel longitudinal (u) and transverse (v) spectra are much smaller than thefull-scale spectra at reduced frequencies below 0.03.

Both cospectra, which indicate the frequencies contributing to the uw Reynolds shearstress, have their peaks at about f ¼ 0.1 and are quite small below f ¼ 0.01.

In spite of the significant differences in the u spectra, the two cospectra are very similar.

It appears that although the wind-tunnel model has not matched the low-frequency end

of the full-scale spectra, it has matched the medium to high-frequency bands and has hence

been able to reproduce the 3D turbulence effects which result in the uw Reynolds shear

stress. The missing turbulence is primarily horizontal and has large effective length scales.In the wind-tunnel, a reduced frequency of 0.03, at a height of 0.075 m, means that such

frequencies are associated with longitudinal length scales of the order of 2.5 m, which is

slightly larger than the 1.8 m width of the tunnel. It is therefore not surprising that

fluctuations at reduced frequencies below 0.03 are relatively suppressed. In full scale, at a

height of 3 m, the longitudinal length scale associated with f ¼ 0.03 is 100 m, which can

easily exist but will be constrained to be primarily horizontal by the ground.

The nature of the low-frequency 2D turbulence has been studied at Silsoe by

simultaneous measurements at heights of 1, 3, 6 and 10 m with sonic anemometers

(Richards et al., 2003). Cross-spectral analysis of the time series showed that both

horizontal components were well correlated for frequencies below 0.01 Hz and that at thesefrequencies the spectral density was proportional to the mean velocity squared. This

indicated that these low-frequency fluctuations were affected by processes similar to those

creating the mean velocity profile and hence are effectively low-frequency fluctuations in

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0

0.002

0.004

0.006

0.008

0.01

0.012

0.0001 0.001 0.01 0.1 1 10

Reduced Frequency f=nz/U(z)-0.1

0

0.1

0.2

0.3

0.4

0.0001 0.001 0.01 0.1 1 10

Reduced Frequency f =nz/U(z)

- f C u w

( f ) / u

2

ba

f S a a

( f ) / U ( z )

2

Fig. 6. Comparison of (a) spectra and (b) cospectra for the Silsoe site and the Auckland wind-tunnel at half cube

height.


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the mean wind speed and direction. Cross-correlation analysis between pressures on the

Silsoe Cube and the dynamic pressure at the reference anemometer shows high correlations

for frequencies below 0.01 Hz. Further quasi-steady predictions of the pressure

fluctuations, which account for both changes in wind speed and direction, at these low

frequencies closely match the measured pressures.In summary, it should be noted that an approach has been taken where the wind-tunnel

model reasonably matches the velocity profile but not the turbulence intensities. The

measured turbulence spectra do match full scale in the high-frequency end of each

spectrum but do not include all of the low-frequency fluctuations observed in full scale.

A similar approach has previously been taken by Irwin (2004), who reports using a partial

simulation approach in studies of bridge decks. In that study, the vertical turbulence was

normalised using the mean velocity, only the high-frequency part of the spectrum was

matched and the turbulence intensity was less than half the full-scale value. In the

following sections, the impact of this approach on the measured pressures will be

considered.

5. Mean pressure distributions

In Section 2, the European variation in vertical centreline mean pressure distributions

was attributed to the differences in high-frequency turbulence. Since the University of

Auckland wind-tunnel tests have high-frequency turbulence levels similar to those at

Silsoe, one may expect the pressure distribution to match.

Fig. 7 shows that in general there is considerable similarity between the wind-tunnel

and full-scale vertical centreline mean pressure distributions at both 901 and 451. In thisand subsequent figures, the various ‘Test’ cases represent experiments carried out with the

corner pressure taps oriented in various ways. It does appear that these roof tappings have

some affect on the flow over the roof. In Fig. 7(a) the two wind-tunnel tests, one with the

corner taps to windward and the other to leeward, produce distributions that are similar to

the 01 and 51 tilted cube results shown in Fig. 3(a). This suggests that the positioning of the

corner roof taps may be slightly modifying the flow reattachment behaviour and hence

the mean pressure distribution.

In Fig. 8, the wind-tunnel results from the various tests have been combined to give

contour maps for the complete roof. These contour diagrams do not include the edge strip

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0.0 0.5 1.0 1.5 2.0 2.5 3.0

Distance OverCube (Cube Heights)


Full-scaleTest ATest B

a

-1.5

-1.0

-0.5

0.0

0.5

1.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Distance OverCube (Cube Heights)


Full-scale

Test A

Test B

Test C

b

Fig. 7. Vertical centreline mean pressure distributions at (a) 901 and (b) 451.


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which is 0.066h wide. Both the wind-tunnel and full-scale results show a similar evolution

of the contours with direction and similar ranges of pressures occurring in each case.

In Fig. 8(a), with a 901 wind direction, the most negative mean pressures lie in the 1 to

1.2 range, whereas in Fig. 8(d), for a 451 wind direction, mean pressure coefficients in the

2 to 2.2 range were recorded both in full-scale and the wind-tunnel.

More obvious differences between full-scale and wind-tunnel were observed with the

mid-height ring of tappings. Fig. 9 shows that there are noticeable differences on thesidewalls with a wind direction of 901 and on the leading edges of both windward walls

with a 451 wind direction. Unfortunately, the wind-tunnel results do show that the model

was not exactly perpendicular to the wind for the 901 case. The effects of this can be seen in

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c60°

-0.4 to-0.2-0.6 to-0.4-0.8 to-0.6-1.0 to-0.8-1.2 to-1.0

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Key formeanCp

tour plots

b

75°

-0.4 to -0.2-0.6 to -0.4

-0.8 to -0.6-1.0 to -0.8-1.2 to -1.0-1.4 to -1.2-1.6 to -1.4-1.8 to -1.6-2.0 to -1.8-2.2 to -2.0-2.4 to -2.2-2.6 to -2.4

Key for meanCp

contour plots

-0.4 to -0.2-0.6 to -0.4

-0.8 to -0.6-1.0 to -0.8-1.2 to -1.0-1.4 to -1.2-1.6 to -1.4-1.8 to -1.6-2.0 to -1.8-2.2 to -2.0-2.4 to -2.2-2.6 to -2.4

Key for meanCp

contour plots

90°

d45°

-0.4 to -0.2-0.6 to -0.4-0.8 to -0.6-1.0 to -0.8-1.2 to -1.0

-1.4 to -1.2-1.6 to -1.4-1.8 to -1.6-2.0 to -1.8-2.2 to -2.0-2.4 to -2.2-2.6 to -2.4

Key for meanCp

contour plots

a

Fig. 8. Roof mean pressure contours for wind directions: (a) 901, (b) 751, (c) 601 and (d) 451. In each case, the

diagram to the left is the combined wind-tunnel result and to the right is the full-scale results for windward quarter

of the roof.

-1.5

-1

-0.5

0

0.5

1

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Distance Around Cube (Cube Heights)


Full-scale

Test A

Test B

a

-1.5

-1

-0.5

0

0.5

1

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Distance Around Cube (Cube Heights)


Test ATest BTest CFull-scale

b

Fig. 9. Mid-height mean pressure distributions at (a) 901 and (b) 451.


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the asymmetry of the windward wall pressure distribution and in the difference between

the two sidewall distributions. Both of these results suggest that the actual wind angle was

slightly less than 901. This results in a slightly more positive pressure between position 0

and 0.5 than between 0.5 and 1. The change in sidewall pressures is again similar to that on

the roof of the cube when it was tilted forwards. The wind approaches the sidewall 1–2 at aslightly bigger angle and hence the flow will be slightly more separated, resulting in a flatter

distribution with less suction at the windward end and slightly more at the leeward end. At

the same time, the lower angle of attack for sidewall 3–4 means that the flow is slightly

more attached and has a higher maximum suction about one-quarter of the way across the

face and then rapid recovery. The misalignment is thought to have affected all the data,

since the 451 results in Fig. 9(b) also show some asymmetry. Fig. 10 shows the effects of

altering the angle in 151 steps. Comparing the asymmetry of Fig. 9 with the data in Fig. 10

suggests that the misalignment was of the order of a few degrees.

Although the difference in sidewall pressure distributions in Fig. 9(a) may be simply

caused by incorrect modelling of the flow reattachment on these walls, this cannot explain

the differences in Fig. 9(b). With a wind direction of 451 it might be expected that the flow

is primarily attached to both windward walls. However, Fig. 10(b) shows that the pressures

on these walls are highly sensitive to wind direction, for example, for locations nearer

position 4, a change of wind direction of only 301 can alter the pressure coefficient from

about 0.7 at 451 to 0.9 at 751.

One of the consequences of the lower turbulence intensity in the wind-tunnel is a lower

standard deviation of wind directions. Fig. 11(a) shows typical examples of the distribution

of wind directions in the wind tunnel and in full scale. At the Silsoe site during a typical

12-min run the standard deviation of the wind direction was around 101

, whereas in thewind tunnel it was only 5.61. If the flow field responds to these direction changes in a quasi-

steady manner, then the observed mean pressures will be weighted averages of the values

associated with particular wind directions. In the wind-tunnel, the range of wind directions

is approximately7151 around the nominal value, so when the nominal wind direction is

451, it may be expected that the pressure on most of the windward faces of the cube would

remain positive at all times. In contrast, in full scale the range of wind directions is about

7301, and so at times the leading edge pressures may become quite negative as a

consequence of the instantaneous wind direction swinging around to 751 or 151. This can

be seen to be the case for Tap 17 in Fig. 12(a), where at 451 the wind-tunnel peak minimum

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0

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Distance Over Cube (Cube Heights) M

e a n P r e s s u r e C o e f f i c i e n t

a

-1.5

-1

-0.5

0

0.5

1

0 0.5 1 1.5 2 2.5 3 3.5 4

Distance Around Cube (Cube Heights) M

e a n P r e s s u r e C o e f f i c i e n t

b

1 2

Fig. 10. The effect of wind direction on wind-tunnel mean pressure distributions for (a) the vertical centreline

section and (b) mid-height.


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pressure coefficient is only just negative whereas the full-scale peak minimum pressures are

consistently lower. It should be noted that in Fig. 12 the full-scale peak minimum and

maximum pressure coefficients are the ratios of the single most extreme pressures recorded

during a run to the peak roof-height dynamic pressure recorded during the same run. As a

result, there is a longer tail of negative pressures in the full-scale situation and so the

observed mean pressure is lower. This effect will be most significant for positions such as

Tap 17 (see location in Fig. 4(a)), which at 451 is close to the leading edge of the windward

wall and as shown in Fig. 10(b) has the greatest sensitivity to wind direction.

6. Peak pressures

Changes to the standard deviation of wind direction also affect the distribution of peak

pressures. Richards and Hoxey (2004) show that with a quasi-steady model extreme

pressures are expected when a high dynamic pressure combines with an instantaneous wind

direction which is associated with either a high or low pressure coefficient. For Tap 17, the

highest mean positive pressure coefficient occurs at about 651 whereas the lowest occurs at

about 51. With mean directions around say 301, the expected maximum and minimum

pressure coefficients will depend on the likelihood of occurrence of instantaneousdirections of 651 or 51, respectively. This is illustrated in Fig. 12(b) where the measured

wind-tunnel mean pressure coefficient distribution has been combined with both a narrow

band of wind directions (standard deviation 51) and a wide band (standard deviation 101)

to give two sets of quasi-steady maximum and minimum pressure coefficients. For both

maximum and minimum pressures, the higher standard deviation of wind directions leads

to a broadening of the range of mean directions where high extremes are expected.

Fig. 12(b) also shows the wind-tunnel maximum and minimum coefficients derived from

Lieblein analysis (Cook, 1985). In general, the wind-tunnel extremes are closer to the

narrow quasi-steady model, which is appropriate since the wind-tunnel standard deviation

of wind directions was 5.61.This broadening of the mean wind direction bands is also apparent in Fig. 12(a) where

the full-scale bands are broader than those from the wind tunnel. Both the full-scale and

wind-tunnel results show that in the ranges 101 to 301 and 170–1901 the measured

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0

0.02

0.04

0.06

0.08

0.1

-40 -30 -20 -10 0 10 20 30 40

Wind Direction (degrees)

P D F

a

y = 2.7788x

100

200

300

400

500

600

0 50 100 150 200

Mean Dynamic Pressure q

M a x D y n a m i c

P r e s s u r e q m a x

b

0

Fig. 11. Comparison of full-scale and wind-tunnel flow properties, at cube height, related to the turbulence levels.

(a) The distribution of instantaneous wind direction during typical runs. (b) The relationship between maximum

dynamic pressure and mean dynamic pressure.


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extremes are slightly larger than would be predicted by a quasi-steady model. This is

probably due to building-induced turbulence being created in the flows that are separating

and reattaching to the sidewalls at these angles.

The form of Fig. 12, with the peak pressures ratioed to the peak dynamic pressure,

partially masks the fact that at cube height the ratio of maximum dynamic pressure to

mean dynamic pressure is higher in full scale than in the wind-tunnel. Fig. 11(b) shows that

in full scale this ratio has a broad range of values when the wind is light, but is consistentlynear 2.78 in stronger winds. In comparison the wind-tunnel ratio is only 1.91. These are

both close to that expected if the wind speed is normally distributed. The sought peak

value has a probability of the order of 1 in 3000. For a normal distribution, this occurs

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-3

0

3

0 45 90 135 180 225 270 315 360

Mean Wind Direction (degrees)

P r e s s u r e C o e f f i c i e n t

Cp max WT Cp mean WT Cp min WT

Cp max FS Cp mean FS Cp min FS

a

-3

0

3

0 45 90 135 180 225 270 315 360

Mean Wind Direction (degrees)

P r e s s u r

e C o e f f i c i e n t

Cp max WT Cp mean WT Cp min WT

Cp max QS Narrow Cp max QS Wide

Cp min QS Narrow Cp min QS Wide

b

Fig. 12. (a) Peak maximum ( ^ p=q̂), peak minimum ( p=q̂) and mean ( ¯ p=¯ q) pressure coefficients from full-scale andwind-tunnel data for Tap 17. (b) The wind-tunnel data together with quasi-steady expectations for the peak

maximum and minimum pressure coefficients with either a 51 (narrow) or 101 (wide) standard deviation of winddirections.


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3.4 standard deviations above the mean. Hence, the expected peak-to-mean dynamic

pressure ratio is given by

q̂

¯ q ¼

ð1 þ 3:4I uÞ2

ð1 þ I 2uÞ , (1)

which with the typical full-scale turbulence intensity I u(h) ¼ 0.21 gives a ratio of 2.8,

whereas in the wind-tunnel with typically I u(h) ¼ 0.11 the expected ratio is 1.86.

With a higher peak-to-mean dynamic pressure ratio in full scale, it may be expected that

the ratio of peak pressure to mean dynamic pressure would also be greater. This is

illustrated in Fig. 13(a) for roof tapping 6 (the location of this tapping is marked in

Fig. 4(a)). In Fig. 13(a) both the mean and negative peak pressures are normalised by the

mean dynamic pressure. It may be observed that there is reasonable agreement between the

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Mean Wind Direction (Degree)

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Mean p/Mean q Full-scale

Min p/Mean q Full-scale

Mean p/Mean q Wind-tunnel

Min p/Mean q Wind-tunnel

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b

Fig. 13. Roof Tap 6 mean and peak minimum pressures. The peak minimum pressures are shown normalised by

either (a) the mean dynamic pressure at cube height for each run or (b) the maximum dynamic pressure at cube

height that occurred during the run.


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full-scale and wind-tunnel mean pressure variations but the full-scale peak pressures are

markedly larger than those from the wind-tunnel. However, as illustrated in Fig. 13(b),

much better agreement is obtained if the peak pressures are normalised by using a peak

dynamic pressure.

It is recognised that there are differences in the methods used to process the wind-tunneland full-scale extreme values as well as slight differences in the sampling periods and

sampling frequencies. The differences in data analysis are partially driven by the

circumstances. Hoxey et al. (1996) discussed how in the full-scale situation each record is

statistically slightly different, and so it is impossible to use analysis methods such as the

Lieblein BLUE method (Cook, 1985). In these circumstances, a large number of records

are required in order to provide data on both the typical values and the range. On the other

hand, in the wind-tunnel stationarity can be achieved and so multiple runs and the

associated extreme value analysis are appropriate, whereas to carry out a large number of

runs would be both expensive and unnecessary. Since different methods are necessary, it

makes sense to ratio the peak pressures measured on the building to the peak dynamic

pressure measured in the approach flow, both of which can be analysed in the same way for

a particular testing situation, thus removing the sensitivity of the ratio to the analysis

method. Using peak pressure/peak dynamic pressure ratio also minimises sensitivity to

slight differences in sampling period or frequency provided both the surface pressures and

reference dynamic pressure measuring systems have similar frequency responses.

As illustrated in Fig. 13(b) another advantage of using the peak-to-peak ratio is that it

minimises the sensitivity to low-frequency turbulence. As noted earlier, the primary

deficiency in the wind tunnel is the lack of low-frequency turbulence. Full-scale coherence

analysis between roof tapping pressures and the dynamic pressure at the upstreamreference mast show near unity coherence for all frequencies below 0.01 Hz (corresponding

to reduced frequencies o0.01). This high coherence suggests that the flow field is

responding to these fluctuations in a quasi-steady manner. Such low-frequency fluctuations

elevate the ratio of the peak to the mean but do not significantly alter the character of the

flow. Hence, by using the peak dynamic pressure as the reference, the results become far

less sensitive to the level of very low frequency fluctuations.

7. Conclusions

In order to compare wind-tunnel turbulence spectra with full scale, normalisingparameters that are independent of the turbulence should be used. One suitable form is to

plot nS (n)/U (z)2 against reduced frequency f ¼ nz/U (z), where the normalising parameters

are the mean wind speed (U (z)) and height (z) of the measuring point. Using turbulence-

dependant parameters, such as the variance and integral length scale, can easily mask

differences.

In situations where it is not possible to model the full turbulence spectra, such as

the large-scale modelling of low-rise buildings, care should be taken to correctly model the

high-frequency end of each spectrum. It is this turbulence that can directly interact with the

local flow field and modify flow behaviour. This has been illustrated by studying data from

tests conducted in a range of European wind tunnels.The approach taken at the University of Auckland in wind-tunnel modelling the Silsoe

6 m Cube at a scale of 1:40 was to match the velocity profile and the high-frequency

turbulence as closely as possible. Similar mean pressure distributions were obtained as a

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result. Although the high-frequency end of each spectrum was matched, the size of the

tunnel limited the low-frequency end and so the longitudinal and transverse turbulence

intensities were lower than in full scale. This has the effect of reducing the standard

deviation of wind directions and hence affects both the observed mean and peak pressures

by reducing the band of wind directions occurring during a run centred on a particularmean direction.

The reduced turbulence intensities also affect the peak-to-mean dynamic pressure ratio,

which in the Auckland wind tunnel was 1.91 in comparison with 2.78 in full scale.

However, since the missing turbulence is at low frequencies, the peak pressures appear to

reduce in proportion. By expressing the peak pressure coefficient as the ratio of the extreme

surface pressures to the maximum dynamic pressure observed during the run, reasonable

agreement is obtained. It is believed that the peak–peak ratio is a more reliable measure of

peak pressures, since it is less sensitive to spectral differences, measurement system

response characteristics and analysis methods, provided the reference dynamic pressure

and the surface pressures are measured and analysed in similar ways. It is also the

peak–peak ratio that is used in most wind loading codes.

References

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Cook, N.J., 1985. The Designer’s Guide to Wind Loading of Building Structures, Part 1. Butterworth, London.

Ho ¨ lscher, N., Niemann, H.-J., 1998. Towards quality assurance for wind tunnel tests: a comparative testing

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Hoxey, R.P., Richards, P.J., Richardson, G.M., Robertson, A.P., Short, J.L., 1996. The folly of using extreme-value methods in full-scale experiments. J. Wind Eng. Ind. Aerodyn. 60, 109–122.

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