The Seventh Asia-Pacific Conference on
Wind Engineering, November 8-12, 2009,
Taipei, Taiwan
GALLOPING EFFECTS ON INCLINED SQUARE CYLINDER IN
SMOOTH AND TURBULENT FLOWS
K.M. Shum1, K.C.S. Kwok2 and P.A. Hitchcock3
Visiting Scholar, CLP Power Wind/Wave Tunnel Facility, The Hong Kong University of
Science and Technology, Clear Water Bay, Kowloon, Hong Kong, [email protected]
2
Professor, School of Engineering, The University of Western Sydney,
Sydney, New South Wale, Australia, [email protected]
3
Associate Director, CLP Power Wind/Wave Tunnel Facility, The Hong Kong University of
Science and Technology, Clear Water Bay, Kowloon, Hong Kong, [email protected]
1
ABSTRACT
Slender prismatic structures with inherently low damping can be prone to serious vibration excited by galloping.
Extensive wind tunnel studies on galloping of vertical cantilevered structures exist in the literature, but none of
those studies have covered a structure with an inclination to the wind. Structures are now designed with more
complex and innovative architectural features and forms. For instance, some bridge pylons are designed with an
inclination mainly for aesthetic purposes. It is obvious that wind flow around an inclined structure can be
significantly different from that around a vertical structure. This paper presents the results from a program of
wind tunnel study on the galloping effect of an inclined square cylinder. A single-degree-freedom model
simulating the vibration of a slender structure in the transverse direction was designed and fabricated. A series of
wind tunnel tests were conducted to study the galloping effect of the structure in terms of angle of wind
incidence, inclination angle and structural damping ratio. The flow conditions being considered in this study
were uniform smooth flow and turbulent flow at a reduced wind velocity of 16. It was found that the negative
aerodynamic damping can be more significant for an inclined structure.
KEYWORDS: GALLOPING, INCLINATION, WIND INCIDENCE, STRUCTURAL DAMPING
Introduction
Slender prismatic structures with inherently low damping can be prone to serious
vibration excited by galloping. Galloping is a form of single-degree-freedom aerodynamic
instability which affects structural cross-sections such as square, rectangular, crucifix and
other sections with fixed separation points. Extensive wind tunnel studies on galloping of
cantilevered structures, such as Parkinson and Smith (1964), Novak and Davenport (1970),
Kwok and Melbourne (1980) and Kawai (1995), have been carried out to understand the
excitation mechanism of galloping. Kwok and Melbourne (1980) found that a slender square
cylinder with an aspect ratio of 18:1 vibrated excessively under the combined effect of
galloping and wake excitation when the reduced velocity was between 15 and 20. The effect
of wake excitation diminished when the reduced velocity was above 20. Kawai (1995)
showed that galloping of a building model with an aspect ratio of 10:1 could not be observed
when the angle of wind incidence was larger than 10o. Ziller and Ruscheweyh (1997)
presented two different methods of determining the onset velocity for galloping using the
aerodynamic coefficients measured from wind tunnel tests. A review of the existing literature
The Seventh Asia-Pacific Conference on Wind Engineering, November 8-12, 2009, Taipei, Taiwan
indicated that no relevant research has been published to date to investigate the wind effects
on inclined cantilever structures. Studies of wind effects on inclined structures have mostly
focused on stay-cables. However, structures are now designed with more complex and
innovative architectural features and forms for aesthetic purposes, such as inclined bridge
pylons. It is obvious that wind flow around an inclined structure can be significantly different
from that around a vertical structure.
This paper presents the results from a program of wind tunnel studies on the galloping
of an inclined square cylinder. A single-degree-freedom model simulating the vibration of a
slender structure in its transverse direction was designed and fabricated. A series of wind
tunnel tests were conducted to study the galloping of the structure in terms of angle of wind
incidence, inclination angle and structural damping ratio. The flow conditions being
considered in this study were uniform smooth flow and turbulent flow condition at a reduced
wind velocity of 16.
Experimental Setup
A series of wind tunnel tests were carried out at the high speed section of the CLP
Power Wind/Wave Tunnel Facility (WWTF) at the Hong Kong University of Science and
Technology (HKUST). For the uniform smooth flow condition, the tests were carried out in
the upstream test section of the high speed section. Mean wind speeds and turbulence
intensities were measured at the cross-section where the model was positioned. The
fluctuating wind velocity was measured at various heights at the centre of the working
sections using a hot-wire anemometer. Measured mean wind speeds at the centre of the model
were normalized with respect to the value at building height and are presented in Figure 1(a)
together with the measured turbulence intensities. The maximum turbulence intensity was
found to be less than 0.5% and the standard deviation of the mean wind speeds was found to
be less than 1% of the average value of the mean wind speeds. Hence, the uniformity of the
wind was satisfactory for the test. For the turbulent flow condition, the tests were carried out
in the downstream test section of the high speed section, where a boundary layer wind model
corresponding to an open terrain (Category 2) in AS/NZS 1170.2:2002 (Australian/New
Zealand Standard 2002) was simulated at a scale of 1:400 using a combination of solid
wooden fences and roughness elements over a 21 m fetch length. Measured and target gust
wind speed profiles were normalized with respect to the value at building height and are
presented in Figure 1(b) together with the measured turbulence intensity profiles. The
measurement results are reasonably consistent with the profiles suggested by AS/NZS
1170.2:2002, with the difference generally not exceeding 5%. It can also be seen from Figure
1(c) that the corresponding spectrum of longitudinal wind speed at building height is
comparable to a Harris-von Karman spectrum with a longitudinal turbulence length scale of
approximately 200m at prototype scale.
A slender square tower model was designed and fabricated with dimensions of 30 mm
× 30 mm × 540 mm (W×B×H), resulting in a height to breadth ratio of 18:1. The natural
frequency and the pivot point of the 1-D aeroelastic model were adjusted by the length of a 2
mm thick steel plate that was installed at the base of the tower model. The density and the
natural frequency of the model were found to be about 223 kg/m3 and 9.0 Hz. The inherent
damping ratio of the model was essentially the same at different angle of inclinations and was
found to be about 0.30% of critical damping. The model was effectively pivoted at its base
and had a straight line deflection mode. The transverse displacement (y) of the model was
measured by four strain gauges. Two strain gauges were installed on each side of the 2 mm
thick steel plate forming a Wheatstone bridge circuit. The output signals from these strain
gauges were amplified and low-pass filtered at a frequency of 100 Hz by a solid-state signal
The Seventh Asia-Pacific Conference on Wind Engineering, November 8-12, 2009, Taipei, Taiwan
conditioner prior to data acquisition. The orientation of the inclined square tower model with
respect to the mean wind direction was represented by an inclination angle α in the vertical
plane and a yaw angle β in the horizontal plane, as shown in Figure 2. In this study, the tower
model is defined as backward (forward) inclined when the inclination angle is positive
(negative).
2
Normalized mean wind speed
1.6
Turbulence intensity
1.6
1.2
h
/
z
0.8
Gust wind speed
1.2
0.8
0.4
0.4
0
0
0.0
0.2
0.4
0.6
0.8
Wind characteristics
0.0
1.0
0.2
0.4
(a) uniform smooth flow
(b) turbulent flow
1
lux=200m
2u
/)
n
(u
S
n
0.1
0.01
Mesured spectrum
Harris - von Karman spectrum
0.001
0.01
0.6
0.1
1
0.8
Normalized wind characteristics
σ
h
/
z
2
Turbulence intensity (%)
10
100
nl ux / Um
(c) longitudinal wind spectrum of turbulent flow
Figure 1: Simulated wind characteristics
1.0
The Seventh Asia-Pacific Conference on Wind Engineering, November 8-12, 2009, Taipei, Taiwan
Wind
y
α
β
Figure 2: Orientation of the Square Tower Model
Results and Discussions
Effect of Inclination Angle
For aesthetic reasons, it is inevitable that structures or their slender parts may be
designed to have certain inclination which can affect the wind flow around it. The effect of
inclination angle on the transverse wind response of a slender structure was thus investigated
by a series of wind tunnel tests. The normalized transverse response of the structure is defined
as the ratio of the standard deviation of transverse displacement response of the tower model
to the width of the square tower model. The galloping response of a vertical square cylinder
measured by Kwok and Melbourne (1980) are re-plotted in Figure 3 together with the current
test results. It can be seen that the variation patterns of the galloping response with the wind
incidence angle are remarkably similar. Some discrepancies between the two test results may
be attributed to different surfaces and materials of the models used in the tests as well as wind
tunnel conditions.
0.7
Kw ok &
Melbourne
(1980)
0.6
current test
results
0.5
ξs=0.22%
0.4
ξs=0.33%
0.3
ξs=0.79%
ξs=0.91%
0.2
0.1
0
-20
-15
-10
-5
0
5
10
15
Angle of Wind Incidence β (deg)
20
Figure 3: Comparison to galloping response reported by Kwok & Melbourne (1980)
The measured normalized transverse responses of the square tower at different angles
of incidence of the mean wind with various inclination angles are shown in Figures 4 and 5
The Seventh Asia-Pacific Conference on Wind Engineering, November 8-12, 2009, Taipei, Taiwan
for the smooth and turbulent flow conditions. Similar to the case of a vertical square crosssectioned body reported by Novak and Davenport (1970), the effect of an increase in freestream turbulence decreases the galloping response of an inclined square sectioned structure.
For wind incidence angle within ±7.5o, considerable normalized transverse response can
always be observed for the case where the model is backward inclined to smooth wind
condition, up to the tested maximum angle of +30o. However, when the model is forward
inclined in the smooth wind condition, not only does the normalized transverse response of
the tower decrease with the decreasing inclination angle, so too does the range of wind
incidence angles that can excite the tower to vibrate significantly.
For the model backward inclined in the turbulent wind condition, considerable
normalized transverse responses can be observed at wind incidence angles within ±5o. When
the model is forward inclined in the turbulent wind, the normalized transverse response of the
tower also decreases with the decreasing inclination angle but the range of wind incidence
angles that can excite the tower to vibrate is almost unaffected. For the case where the model
is inclined to the wind at -30o, a notable normalized transverse response of the tower model
can only be observed in the smooth flow condition at a wind incidence angle of 0o. The effect
of inclination is thus considered to be an influencing factor affecting the transverse response
of square-sectioned tower structures. The effect of turbulence will be further studied in
another series of wind tunnel tests at higher reduced velocities.
It is also evident that the maximum normalized transverse response of the tower model
increases when the inclination angle of the model is increased from -30o to +10o in both
smooth and turbulent flow conditions, as shown in Figure 6 for an angle of incidence of 0o.
When the model is inclined at an inclination angle of +30o, the maximum normalized
transverse response is smaller than that at an inclination angle of 0o.
0.7
σy
b
-20
-15
-10
-5
α=0
σy
0.6
α=5
b
0.5
α = 10
0.7
α = 30
0.6
α = −5
0.5
α = −10
α = −15
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
0
0
5
10
15
Angle of Wind Incidence β (deg)
α=0
20
-20
-15
-10
-5
α = −30
0
5
10
15
Angle of Wind Incidence β (deg)
20
Figure 4: Normalized transverse response of the square tower model as a function of angle of
wind incidence for various angles of inclination in uniform smooth flow
The Seventh Asia-Pacific Conference on Wind Engineering, November 8-12, 2009, Taipei, Taiwan
σy
b
0.5
α=0
σy
0.4
α=5
b
0.35
α = 10
0.3
α = 20
0.25
α = 30
0.45
0.5
-15
-10
α = −10
0.35
α = −15
0.3
α = −30
0.25
0.2
0.2
0.15
0.15
0.1
0.1
0.05
0.05
-5
α = −5
0.4
0
-20
α=0
0.45
0
0
5
10
15
20
-20
-15
Angle of Wind Incidence β (deg)
-10
-5
0
5
10
15
20
Angle of Wind Incidence β (deg)
Figure 5: Normalized transverse response of the square tower model as a function of angle of
wind incidence for various angles of inclination in turbulent flow
0.7
0.6
0.5
0.4
0.3
0.2
turbulent flow
0.1
uniform smooth flow
0
-30
-20
-10
0
I ncl ination Angle
10
α
20
30
( deg)
Figure 6: Normalized transverse response of the square tower model for 0o angle of wind
incidence at various angles of inclination in smooth and turbulent flows
Effect of Structural Damping
Galloping usually occurs when the negative aerodynamic damping due to structural
motion is larger than the structural damping. The effect of structural damping is thus an
important factor affecting the onset velocity of galloping. The effect of structural damping on
the transverse response of the tower model was investigated in this study. The normalized
transverse responses of the square tower at different angles of incidence and various levels of
structural damping are shown in Figures 7 and 8 for the smooth and turbulent flow conditions.
It can be seen from Figures 7 and 8 that the transverse response of the tower model
decreases as the structural damping is increased, as expected. Large galloping responses of the
tower model with different inclination angles can be observed at zero angle of incidence,
which normally suggests that the structure starts to gallop when the structural damping is
The Seventh Asia-Pacific Conference on Wind Engineering, November 8-12, 2009, Taipei, Taiwan
below a certain value. A larger damping value is required to prevent the occurrence of
galloping at zero angle of incidence when the tower model has a larger positive inclination
angle. Based on a similar observation made by Kwok and Melbourne (1981), it is believed
that the large transverse responses are due to lock-in effect triggered by wake excitation. The
presence of a negative aerodynamic damping reduces significantly the total damping of the
tower model and consequently the response due to the wake excitation is increased to a larger
magnitude. This suggests that the negative aerodynamic damping is quite significant for an
inclined square tower model.
σy
b
0.7
0.34%
0.6
0.46%
σy
b
0.7
0.33%
0.43%
0.63%
0.91%
0.6
0.62%
0.5
0.5
0.85%
1.15%
σy
b
0.7
0.31%
0.6
0.56%
0.5
0.4
0.4
0.3
0.3
0.3
0.2
0.2
0.2
0.1
0.1
0.1
0.4
0
0
-20 -15 -10 -5
0
5
10 15 20
Angle of Wind Incidence (deg)
-20 -15 -10 -5
0
5
10 15 20
Angle of Wind Incidence (deg)
0.44%
0
-20 -15 -10 -5
0
5
10
15 20
Angle of Wind Incidence (deg)
(a) α = +10o
(b) α = 0o
(c) α = -10o
Figure 7: Normalized transverse response of the square tower model as a function of angle of
wind incidence for various levels of structural damping in smooth flow
σy
b
0.5
0.45
0.4
0.35
0.28%
0.39%
0.57%
0.84%
σy
b
0.5
0.31%
0.45
0.39%
0.60%
0.4
0.97%
0.35
σy
b
0.5
0.3
0.25
0.25
0.25
0.2
0.2
0.2
0.15
0.15
0.15
0.1
0.1
0.1
0.05
0.05
0.05
0
0
5 10 15 20
Angle of Wind Incidence β (deg)
0.60%
0.35
0.3
-20 -15 -10 -5
0.42%
0.4
0.3
0
-20 -15 -10 -5 0 5 10 15 20
Angle of Wind Incidence β (deg)
0.31%
0.45
0
-20 -15 -10 -5 0
5
10 15 20
Angle of Wind Incidence β (deg)
(a) α = +10o
(b) α = 0o
(c) α = -10o
Figure 8: Normalized transverse response of the square tower model as a function of angle of
wind incidence for various levels of structural damping in turbulent flow
The Seventh Asia-Pacific Conference on Wind Engineering, November 8-12, 2009, Taipei, Taiwan
Conclusions
A wind tunnel investigation on the transverse response of a slender square tower
model in a uniform smooth flow and turbulent flow conditions has been carried out. The test
results indicate that the maximum normalized transverse response of the tower model that is
backward inclined to the approaching wind is much larger than that for a forward inclined
model with the same magnitude of inclination. This is mainly attributed to the presence of
negative aerodynamic damping for a backward inclined model. For the smooth flow condition,
considerable galloping responses were always observed for wind incidences angles within
±7.5o for the case where the model is backward inclined. When the model was forward
inclined to smooth flow condition, not only did the galloping response of the tower decrease
with the decreasing inclination angle, so too did the range of wind incidence angles at which
the tower galloped. The effect of increasing in free-stream turbulence decreased the galloping
response of the inclined square sectioned structure. However, for the model backward
inclined to turbulent wind condition, considerable normalized transverse responses were
observed at wind incidence angles within ±5o. When the model was forward inclined to the
turbulent wind, the normalized transverse response of the tower also decreased with the
decreasing inclination angle, but the range of wind incidence angles at which the tower
experienced significant excitation was almost unaffected. It was also found that the transverse
response of the tower model decreased as the structural damping value was increased. A
larger damping value is generally required for the structure with larger inclination angle to
prevent galloping at zero angle of incidence. This suggests that the negative aerodynamic
damping is quite significant for an inclined square tower model.
Acknowledgement
The financial support from The Hong Kong University of Science and Technology (HKUST)
and CLP Power Wind/Wave Tunnel Facility of HKUST through a Postdoctoral Fellowship to
the first author is gratefully acknowledged.
References
Australian/New Zealand Standard, Structural Design Actions Part 2: Wind Actions, AS/NZS 1170.2: 2002.
Kawai H. (1995). “Effects of angle of attack on vortex induced vibration and galloping of tall buildings in
smooth and turbulent boundary layer flows”, Journal of Wind Engineering and Industrial Aerodynamics, 5455, 125-132.
Kwok K.C.S. and Melbourne W.H. (1980). “Freestream turbulence effects on galloping”, Journal of Engineering
Mechanics, ASCE, vol. 106(2), 273-288.
Kwok K.C.S. and Melbourne W.H. (1981). “Wind-induced lock-in excitation of tall building”, Journal of the
Structural Division-ASCE, vol. 107(1), 57-72.
Novak M and Davenport A.G. (1970). “Aeroelastic instability of prisms in turbulent flow”, Proc. ASCE Journal
of Engineering Mechanics, No. EM1, 27-47.
Parkinson G.V. and Smith J.D. (1964). “The square prism as as aeroelastic non-linear oscillator”, Quarterly
Journal of Mechanics and Applied Mathematics, 17(2), 225-239.
Ziller C. and Ruscheweyh H. (1997). “A new approach for determining the onset velocity of galloping instability
taking into account the nonlinearity of the aerodynamic damping characteristic”, Journal of Wind Engineering
and Industrial Aerodynamics, 69-71, 303-314.