richards 2007
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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.
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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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0.002
0.004
0.006
0.008
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0.014
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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
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0.10
0.15
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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
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-0.5
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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
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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
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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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M e a n P r e s s u r e C o e f f i c i e n t
Full-scaleTest ATest B
a
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0.0 0.5 1.0 1.5 2.0 2.5 3.0
Distance OverCube (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
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)
M e a n P r e s s u r e C o e f f i c i e n t
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)
M e a n P r e s s u r e C o e f f i c i e n t
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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-1
-0.5
0
0.5
1
0 0.5 1.5 2.5 3
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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0.02
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
ARTICLE IN PRESS
-8
-7
-6
-5
-4
-3
-2
-1
00 60 120 180 240 300 360
Mean Wind Direction (Degree)
P r e s s
u r e C o e f f i c i e n t
Mean p/Mean q Full-scale
Min p/Mean q Full-scale
Mean p/Mean q Wind-tunnel
Min p/Mean q Wind-tunnel
a
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
00 60 120 180 240 300 360
Mean Wind Direction (Degree)
P r e s s u r e C o e f f i c
i e n t
Mean p/Mean q Full-scale
Min p/Max q Full-scale
Mean p/Mean q Wind-tunnel
Min p/Max q Wind-tunnel
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.
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