The Seventh Asia-Pacific Conference on
Wind Engineering, November 8-12, 2009,
Taipei, Taiwan
EFFECTS OF SECTION SIZE ON AERODYNAMIC FORCES ON
AN ELLIPTIC CYLINDER UNDER SHORT-RISE-TIME GUSTS
Takashi Takeuchi1, Junji Maeda2, Tomohiko Hayata3 and Hiromasa Kawashita4
JSPS Research Fellow (Graduate), 3,4 Graduate, Graduate School of Human-Environment
Studies, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka 812-8581, Japan,
[email protected], [email protected],
[email protected]
2
Professor, Faculty of Human-Environment Studies, Kyushu University, 6-10-1 Hakozaki,
Higashi-ku, Fukuoka 812-8581, Japan, [email protected]
1
ABSTRACT
The characteristics of aerodynamic forces acting on an elliptic cylinder with an angle of attack subjected to
short-rise-time gusts were investigated using a specially-equipped gust wind tunnel. Remarkable overshoot
phenomena of aerodynamic forces were indicated, and we analyzed their patterns as they changed with the
section-size of the cylinder. The overshoot coefficients tended to increase with a decrease in the non-dimensional
rise time regardless of the section-size of cylinder. The overshoot coefficients were explainable as one pattern by
the non-dimensional rise time regardless of the section-size of cylinder. Finally, we showed that a computational
fluid-dynamics-analyzed relationship between the overshoot coefficient and the non-dimensional rise time
agreed well with the experimental results.
KEYWORDS: AERODYNAMIC FORCE, SHORT-RISE-TIME GUST, OVERSHOOT OF WIND FORCE,
SECTION-SIZE
Introduction
Many reports have clarified detailed characteristics of flow over a bluff body and wind
force on such a body under a stationary or a quasi-steady turbulent flow that has an intensity
of turbulence of about 10%. However, there is a possibility that wind gusts with a very short
rise time occur in tornadoes or high winds that are associated with typhoons or frontal
passages. There have been several reports on the characteristics of unsteady aerodynamic
forces on structures under such gusts. [Taneda (1972)] investigated the unsteady lift acting on
an elliptic cylinder rapidly started at an angle of attack using a water tank test and reported
that a remarkably big lift appeared just after starting. [Sarpkaya (1966)] showed that the drag
of a body grew up to about 25 percent higher during the growth of the first pair of vortices
than in a steady flow, using an impulsive flow test over circular cylinders in a vertical water
tunnel, adding some results of potential flow analyses around the circular cylinders. [Morison
and O’Brien et al. (1950) and Keulegan and Carpenter (1958)] evaluated the unsteady
aerodynamic characteristics using a semi-empirical equation added to an inertia term
proportional to flow acceleration. [Nomura and Kitamura et al. (2008)] computed the
unsteady drag acting on a square cylinder under a sudden change of flow speed and reported
that the drag component proportional to flow acceleration played quite an important role in
the total unsteady drag when the flow speed was relatively low. [Shiraishi and Matsumoto et
al. (1982)] evaluated unsteady aerodynamic characteristics using aerodynamic indicial
functions. [Matsumoto and Shimamura et al. (2007)] measured a transient drag on a twodimensional cylindrical model under a suddenly-changing wind speed using a wind tunnel test
The Seventh Asia-Pacific Conference on Wind Engineering, November 8-12, 2009, Taipei, Taiwan
with a working section of 200mm by 200mm square and reported an overshoot phenomenon
in which the drag increased by about 20 % compared to the force in a steady flow.
[Yamaguchi and Kashiwagi et al. (2008)] investigated unsteady aerodynamic characteristics
of rectangular prisms and a truck model subjected to quickly-accelerated flow using a multifan type blow-down wind tunnel with a working section of 2540mm by 1800mm which was
composed of 99 small fans, each of which was independently controlled by a computer.
[Takeuchi and Maeda et al. (2008)] investigated the effects of the rise time of a step-functionlike gust on the overshoot phenomenon of wind forces acting on a railcar-like body using a
specially-equipped wind tunnel, which could generate gusts with a rise time of 0.2 to 5
seconds from a flat calm by controlling the rotation speed of the blade rows, and reported that
the overshoot phenomenon was more remarkable in the case of gusts with a shorter rise time.
[Nakamura and Maeda et al. (2008)] investigated effects of a step-function-like gust on local
wind pressures of a gable-roof body using the same specially-equipped wind tunnel and
reported that the step-function-like gust produced an overshoot phenomenon of wind pressure
bringing much larger local wind pressures than a steady flow on the surface of the body, and
that the overshoots of the surface pressure related to those of the drag acting on the body.
[Kawashita and Maeda et al. (2008)] confirmed some overshoot phenomena of wind forces
acting on an elliptic cylinder with some angles of attack using the same specially-equipped
wind tunnel, and reported that a non-dimensional parameter of a rise time of step-functionlike gust considerably influenced the occurrence of the overshoot phenomenon.
As mentioned, it was apparent that an overshoot phenomenon bringing a much bigger
wind force than in a steady flow occurs in the case of a structure subjected to a short-rise-time
gust. To apply the phenomenon to a gust resistant measure for full-scale structures, it is
necessary to clarify the effects of the scale of a structure on the overshoot phenomenon. In
this paper, with the purpose of verifying the accuracy of the evaluation of the overshoot
phenomenon by the non-dimensional parameter of rise time of a gust, as an example, we
investigated and here discuss the effects of elliptic cylinder section-size on overshoot
phenomena of wind forces under short-time-rise gusts using a specially equipped wind tunnel.
And we weigh the results of our experiment against the results from simulation using CFD
software.
General Specifications of the Wind Tunnel Test
We used a wind tunnel of the Eiffel type at Kyushu University. The site plan of our
testing system is illustrated in Figure 1. The section area of the working space was 1.5m by
1.5m and the available length was 3m. A step-function-like gust was generated by pulsating
rapid rotation of flat blade-rows. The drag and lateral force acting on the specimen were
measured using an aerodynamic balance, and the wind speed in the working space was
confirmed by a hot-wire anemometer and an ultrasonic anemometer. An example of the time
200
1,300
1,500
Dummy model
Hot-wire anemometer
Supersonic anemometer
Wind
Specimen
Aerodynamic
balance
700
900
400
a) Site plan
Plane
board
Blade row
(top)
Blade row
(front)
Blade row
(bottom)
Dummy
Specimen
(mm)
b) Installation of specimen and dummy
Figure 1: Site plan of wind tunnel
The Seventh Asia-Pacific Conference on Wind Engineering, November 8-12, 2009, Taipei, Taiwan
U
Target wind
velocity, Ut
(mm)
0.5D
D
Wind
Small-cylinder D = 70 mm
Rise time, tr
t
Specimen
α
Large-cylinder D = 140 mm
Wind
Aerodynamic
balance
Figure 2: Example of time evolution of
b) Bird’s-eye view
wind velocity measured under step- a) Section view of specimen
Figure 3: Specimens
function-like gust
evolution of the wind velocity generated by control of the blade rows is shown in Figure 2.
The rise time of gust, tr, is defined as the time required for an approaching wind to reach a
target wind, and the target wind velocity, Ut, is referred as the reached wind. The measured
data was scanned at a frequency of 1000Hz. The specimens were two elliptic cylinders of
axial ratio 2:1, 500mm high, and 70mm and 140mm in major axis, as shown in Figure 3, and
referred to as “Small-cylinder” and “Large-cylinder”, respectively. They were fixed to the
aerodynamic balance with an angle of attack, α, from 0 degrees to 90 degrees and the drag
and lateral forces acting on them were measured. The angle of attack was defined as 0 degrees
when the elliptic cylinder was fixed to the aerodynamic balance in such a way that its major
axis was parallel to the wind direction. Additionally, a dummy 350mm in height was set to
realize a two-dimensional flow around the specimens, as shown in Figure 1. The dummy was
placed at a distance of several millimeters from the specimens so as not to measure the wind
force on the dummy. They were subjected to step-function-like gusts with a target wind
velocity, Ut, between 2.0m/s and 7.0m/s and rise time, tr, between 0.2sec and 1.4sec.
Experimental Results and Discussions
Overshoot of wind forces
Figures 4 and 5 show the time evolutions of the wind velocity, drag and lateral force
on Small-cylinder and Large-cylinder at a 45-degree angle of attack respectively, when the
wind velocity reached 2.0m/s in the rise times of 0.2sec and 1.4sec. In the case of the rise time
of 0.2sec, we confirmed the overshoot phenomena of aerodynamic forces, which reached
much larger values than the steady values of the drag and lateral forces. The overshoot
phenomena achieved peaks when wind velocity reached the target wind velocity, and they
decreased immediately and approached a steady state gradually.
The time evolution of the wind velocity for Large-cylinder was almost the same as
that for Small-cylinder but the time evolutions of the wind forces on Large-cylinder were
different from those on Small-cylinder in that the drag on Large-cylinder had two peaks in 0.3
seconds from starting, and the time the lateral force on Large-cylinder achieved a peak was
later than that on Small-cylinder.
Figure 6 shows effects of the dummy on the overshoot of wind force acting on Largecylinder at a 45-degree angle of attack in the case of a target wind velocity of 2.0m/s and a
rising time of 0.2sec. The time evolution of the drag was not affected by the installation of the
dummy. However, the peak value of the lateral force with the dummy was larger than that
without the dummy. And after the peak, the lateral force which vibrated in around 3.5Hz with
the dummy was bigger than that without the dummy. The lateral force acting on the specimen
vibrated under steady flow too, and the frequency of the vibration was proportional to the gust
speed and inversely proportional to the section-size of specimen. Thus, it would appear that
The Seventh Asia-Pacific Conference on Wind Engineering, November 8-12, 2009, Taipei, Taiwan
the vibration was caused by vortex shedding. In this case, the Strouhal number of Largecylinder at a 45-degree angle of attack under steady flow was estimated to be about 0.2. The
reference length for the Strouhal number was defined as the length of the flow direction of the
elliptic cylinder.
Effects of the angle of attack of elliptic cylinder on the overshoot phenomenon
Figure 7 shows the angle of attack plotted against the wind force coefficient of Largecylinder, when the target wind velocity reached 5.0m/s in a rising time of 0.2sec. The wind
force coefficient is defined by the reference area of the model and the steady velocity pressure,
as shown in the following equations:
Steady wind force
(1)
0.5ρU 2 A
Peak wind force
Peak wind force coefficient =
(2)
0.5 ρU 2 A
where ρ is air density, U is the steady wind velocity and A is the projection area of the
Steady wind force coefficient =
elliptic cylinder. The steady drag coefficient increased with an increase in the angle of attack.
The peak drag coefficient was the same as the steady drag coefficient at angles of attack less
than 30 degrees, and was larger at angles of attack from 50 degrees to 80 degrees. The steady
lateral force coefficient was largest at a 10-degree angle of attack. The peak lateral force
coefficient was larger at angles of attack from 25 degrees to 50 degrees. Figure 8 shows the
-0.4
0.0
0.4 0.8 1.2
Time (sec)
tr = 0.2 sec
tr = 1.4 sec
1.6
-0.4
0.0
a) Wind velocity
0.4 0.8 1.2
Time (sec)
0.5
0.4
0.3
0.2
0.1
0.0
-0.1
tr = 0.2 sec
tr = 1.4 sec
Lateral force (N)
tr = 0.2 sec
tr = 1.4 sec
0.5
0.4
0.3
0.2
0.1
0.0
-0.1
Drag (N)
Wind velocity (m/s)
2.5
2.0
1.5
1.0
0.5
0.0
-0.5
-0.4 0.0
1.6
b) Drag
0.4 0.8 1.2
Time (sec)
1.6
c) Lateral force
Figure 4: Time history data of Small-cylinder
(D =70mm, α =45deg., Ut =2.0m/s, tr =0.2sec, 1.4sec, with dummy)
-0.4
0.0
0.4 0.8 1.2
Time (sec)
tr = 0.2 sec
tr = 1.4 sec
1.6
-0.4
0.0
a) Wind velocity
0.4 0.8 1.2
Time (sec)
1.6
0.5
0.4
0.3
0.2
0.1
0.0
-0.1
Lateral force (N)
tr = 0.2 sec
tr = 1.4 sec
0.5
0.4
0.3
0.2
0.1
0.0
-0.1
Drag (N)
Wind velocity (m/s)
2.5
2.0
1.5
1.0
0.5
0.0
-0.5
tr = 0.2 sec
tr = 1.4 sec
-0.4
b) Drag
0.0
0.4 0.8 1.2
Time (sec)
c) Lateral force
Figure 5: Time history data of Large-cylinder
(D =140mm, α =45deg., Ut =2.0m/s, tr =0.2sec, 1.4sec, with dummy)
Drag (N)
With dummy model
Without dummy model
-0.4
0.0
0.4 0.8 1.2
Time (sec)
a) Drag
1.6
0.5
0.4
0.3
0.2
0.1
0.0
-0.1
With dummy model
Without dummy model
Lateral force (N)
0.5
0.4
0.3
0.2
0.1
0.0
-0.1
-0.4
0.0
0.4 0.8 1.2
Time (sec)
1.6
b) Lateral force
Figure 6: Comparison between time history of wind forces with dummy and without
(D =140mm, α =45deg., Ut =2.0m/s, tr =0.2sec)
1.6
The Seventh Asia-Pacific Conference on Wind Engineering, November 8-12, 2009, Taipei, Taiwan
relationship between the overshoot coefficient and the angle of attack and clarifies the effect
of the angle of attack on the overshoot phenomenon. The overshoot coefficient is defined as
the ratio of the peak value to the steady value, as shown in the following equation:
Overshoot coefficient =
Peak wind force
Steady wind force
(3)
where the peak wind force is defined as the actual maximum force, and the steady wind force
is defined as a mean of 20 seconds in a steady flow. The overshoot of drag was remarkable at
angles of attack larger than 50 degrees. The overshoot of lateral force was remarkable at
angles of attack from 30 degrees to 80 degrees.
Effects of the section-size of elliptic cylinder on the overshoot phenomenon
Figure 9 shows the relationship between the target wind velocity and the overshoot
coefficients of wind force on Small-cylinder and Large-cylinder at a 45-degree angle of attack
in the case of the rise time of 0.2sec. The overshoot coefficients of Small-cylinder and Largecylinder increased with a decrease in the target wind velocity. The overshoot coefficient of
Large-cylinder was larger than that of Small-cylinder for all target wind velocities. We
reported that the overshoot phenomenon depended on the non-dimensional rise time, tr',
defined by Eq. (4) in [Kawashita and Maeda et al. (2008) and Takeuchi and Maeda et al.
(2008)]:
t r′ = U t ⋅ t r / d
(4)
in which Ut is the target wind velocity, tr is the rise time and d is a reference length (here, the
length of the flow direction of the elliptic cylinder). Figure 10 shows the relationship between
the non-dimensional rise time and the overshoot coefficient. The overshoot coefficients
ordered according to the non-dimensional rise time are plotted on one line regardless of the
Steady drag coefficient
Peak drag coefficient
2.5
2.0
Peak not
found
1.5
Steady lateral force coefficient
Peak lateral force coefficient
3.0
Wind force coefficient
Wind force coefficient
3.0
1.0
0.5
0.0
-0.5
2.5
Peak not
found
2.0
1.5
1.0
0.5
0.0
-0.5
0
10
20 30 40 50 60 70
Angle of attack, α (degree)
80
90
0
10
20 30 40 50 60 70
Angle of attack, α (degree)
80
90
80
90
b) Lateral force
a) Drag
Figure 7: Wind force coefficient with angle of attack
(D =140mm, Ut =5.0m/s, tr =0.2sec, with dummy)
5
Overshoot coefficient
Overshoot coefficient
5
4
3
Peak not
found
2
1
0
4
3
2
1
Peak not
found
0
0
10
20 30 40 50 60 70
Angle of attack, α (degree)
a) Drag
80
90
0
10
20 30 40 50 60 70
Angle of attack, α (degree)
b) Lateral force
Figure 8: Overshoot coefficient with angle of attack
(D =140mm, α =45deg., Ut =5.0m/s, tr =0.2sec, with dummy)
The Seventh Asia-Pacific Conference on Wind Engineering, November 8-12, 2009, Taipei, Taiwan
target wind velocity. The figure indicates a strong relationship between the overshoot
phenomenon and the non-dimensional rise time. The overshoot coefficient tended to increase
with a decrease in the non-dimensional rise time regardless of the section-size of cylinder.
The overshoot coefficients are plotted on one line regardless of the section-size of cylinder
and are explained by the non-dimensional rise time. The overshoot phenomenon may be
strongly affected by the non-dimensional rise time.
Numerical Investigation
The flow around Small-cylinder subjected to step-function-like gusts was simulated
using CFD software (CDAJ products) using a k-ε model, as shown in Figure 11a. A twodimensional incompressible flow was assumed and the differential equations were discretized
by the finite volume method. The MARS scheme was applied to the convective term. The
8
Small-cylinder
Large-cylinder
6
Overshoot coefficient
Overshoot coefficient
8
4
2
Small-cylinder
Large-cylinder
6
4
2
0
0
2.0
3.5
5.0
Target wind velocity (m/s)
2.0
7.0
3.5
5.0
Target wind velocity (m/s)
7.0
b) Lateral force
a) Drag
Figure 9: Overshoot coefficient with target wind velocity
(D =140mm, α =45deg., tr =0.2sec, with dummy)
10
U t = 2.0m/s
Overshoot coefficient
Overshoot coefficient
10
1
Small-cylinder
experiment
(D = 70 mm)
Large-cylinder
experiment
(D = 140 mm)
1
1
10
100
Non-dimensional rise time
U t = 5.0m/s
U t = 7.0m/s
U t = 2.0m/s
U t = 3.5m/s
U t = 5.0m/s
U t = 7.0m/s
1
10
100
Non-dimensional rise time
b) Lateral force
a) Drag
U t = 3.5m/s
c) Graph legend
Figure 10: Relationships between overshoot coefficient and non-dimensional rise time
(α =45deg., with dummy)
y (mm)
1500
U (m/s)
Nesting1
Nesting3
Ut
Nesting2
Nesting4
1050
U = −2
Ut 3
U
t + 3 2t t 2
t r3
tr
450
0
Inflow boundary
x (mm)
0
700
13000
2000
a) Analytic region
tr
b) Inflow wind velocity
Figure 11: Analytic region and inflow wind velocity
t (sec)
The Seventh Asia-Pacific Conference on Wind Engineering, November 8-12, 2009, Taipei, Taiwan
-0.4
0.0
0.4 0.8 1.2
Time (sec)
Experimental
Calculated
1.6
-0.4
a) Wind velocity
0.0
0.4 0.8 1.2
Time (sec)
0.5
0.4
0.3
0.2
0.1
0.0
-0.1
Lateral force (N)
Experimental
Calculated
0.5
0.4
0.3
0.2
0.1
0.0
-0.1
Drag (N)
Wind velocity (m/s)
2.5
2.0
1.5
1.0
0.5
0.0
-0.5
1.6
b) Drag
Experimental
Calculated
-0.4
0.0
0.4 0.8 1.2
Time (sec)
1.6
c) Lateral force
Figure 12: Comparisons between calculated and experimental results with dummy
(D =70mm, α =45deg. , Ut =2.0m/s, tr =0.2sec)
10
Small-cylinder
with dummy
experiment
(D = 70 mm)
Large-cylinder
with dummy
experiment
(D = 140 mm)
Overshoot coefficient
Overshoot coefficient
10
1
1
1
10
100
Non-dimensional rise time
a) Drag
1
10
100
Non-dimensional rise time
b) Lateral force
CFD
Simulation
(D = 70 mm)
c) Graph legend
Figure 13: Relationships between overshoot coefficient and non-dimensional rise time
(α =45deg.)
pressure and velocities were coupled by means of the PISO method. The standard k-ε model
was used for the turbulence model. The short-rise-time wind velocity measured in the wind
tunnel test was modeled on an approaching flow in the CFD simulation, as shown in Figure
11b. Figure 12 shows the comparisons between the CFD calculation and experimental results
in the case of a target wind velocity of 2.0m/s and a rising time of 0.2 seconds, as an example.
In this case, we confirmed the overshoot phenomenon in the simulation as well as in the
experimental results, but in some cases, we were not able to simulate the overshoot
phenomenon in the experimental results. The steady wind forces of the simulation
corresponded to those of the experimental results in every case. The simulated relationship
between the non-dimensional rise time and the overshoot coefficient in Figure 13 agreed well
with the experimental relationship in that the overshoot phenomenon of lateral force was
more remarkable than of drag.
Conclusions
The characteristics of aerodynamic force on an elliptic cylinder subjected to short-risetime gusts were investigated by using a specially equipped wind gust tunnel. We investigated
mainly the effects of section-size of an elliptic cylinder on overshoot phenomena of wind
forces using two elliptic cylinders of axial ratio 2:1, 70mm and 140mm in major axis. This
revealed the features of the transient wind forces acting on an elliptic cylinder subjected to a
short-time-rising gust as follows:
•
We confirmed a remarkable overshoot phenomenon generating a much larger wind
force than in a steady flow.
•
The overshoot of drag was little affected by the installation of a dummy to realize a
two-dimensional flow around the specimens. On the other hand, the overshoot of lateral
force with the dummy was larger than that without the dummy.
•
For the elliptic cylinder subjected to the gust of the target wind velocity of 5.0m/s and
the rise time of 0.2sec, the overshoot of drag was remarkable at angles of attack larger
The Seventh Asia-Pacific Conference on Wind Engineering, November 8-12, 2009, Taipei, Taiwan
•
•
•
than 50 degrees, and the overshoot of lateral force was remarkable at angles of attack
from 30 degrees to 80 degrees.
The overshoot coefficient, which is defined as the ratio of the maximum to the steadystate value of wind force, was determined by a non-dimensional rise time, which is
defined by rise time, gust speed and section-size, regardless of the rise time and speed
of gust.
The overshoot coefficient increased with a decrease in the non-dimensional rise time
regardless of section-size of cylinder. And the overshoot coefficients followed one
pattern regardless of the section-size of cylinder and were explained by the nondimensional rise time.
Using CFD we estimated the flow around the cylinder subjected to step-function-like
gusts and confirmed that the overshoot phenomenon was the same as in the
experimental results. Finally, it was indicated that the CFD-analyzed relationship
between the overshoot coefficient and the non-dimensional rise time agreed well with
the experimental results.
Acknowledgment
This study was supported by Grant-in-Aid for JSPS Fellows 21-4043, Japan Society
for the Promotion of Science.
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