Suppression of Vortex Shedding from a Circular Cylinder by using

a Traveling Wave Wall

Wenli Chen1, Yang Liu

2 and Hui Hu

3 (�)

Iowa State University, Ames, Iowa, 50011, USA

Feng Xu4

Harbin Institute of Technology Shenzhen Graduate School, Shenzhen 518055, China

and

Hui Li5

School of Civil Engineering, Harbin Institute of Technology, Harbin, Heilongjiang, 150090, China

An experimental study was conducted to suppress the unsteady vortex shedding from a

circular cylinder by using a traveling wave wall (TWW). The leeward surfaces of the

circular cylinder model were replaced by wave surfaces, which can move to form

symmetrical TWW when driven by a motor system. The propagation speed of the wave was

adjustable by controlling the rotational speed of the motor. During the experiments, while

the oncoming wind speed was fixed at U∞∞∞∞=9.1 m/s, the propagation speed of the TWW was

adjusted to have the ratio between of the wave propagation speed and the oncoming wind

speed varied from 0 (i.e., stationary case) to 0.167. It was found that, with the TWW control,

the wake region behind the cylinder model was found to be shortened and the vortex

shedding from the cylinder model was weakened greatly. The average drag force acting on

the test model was also found to be reduced significantly. Two different mechanisms, i.e.,

“forced perturbation mechanism” and “resonant perturbation mechanism”, were found to

play important roles for the TWW flow control.

I. Introduction

hen the flow passes a bluff body, such as a circular cylinder, the vortex shedding can induce the fluctuations

of wall pressure on the cylinder surface, which will result in dynamical loads or vibration of the cylinder. The

vortex-induced vibration (VIV) is often reported in the actual engineering and become a main factor of the problems

of structural instability and fatigue failure. As we all know that the potential VIVs can be prevented when the vortex

shedding is suppressed or controlled. Therefore, it is necessary to eliminate or suppress the alternating wake pattern

in order to control the VIV of the circular cylinder. At present, there are mainly two types of methods to control the

alternating wake patterns of the cylinders: passive and active flow control methods.

The passive method achieves the purpose of the flow control through changing the flow conditions, e.g., the

boundary conditions. This method does not consume external energy and the most popular application is changing,

adjusting and optimizing the geometrical shapes of the structures. Choi (1989), Bechert (1997) and Lee and Jang

(2005) placed the riblets on the surface of the bluff bodies to reduce the drag. For reducing the cylinder VIVs,

Bearman and Owen (1998), Bearman and Brankovic (2004) attached the wavy separation lines on a square cylinder

and the hemispherical bumps on a circular cylinder to control the vibrations of the cylinders. The surface bumps can

destroy or suppress the regular vortex shedding near the wake of the circular cylinder (Owen and Bearman, 2001).

When the flow conditions change, the passive flow control can only achieve certain control effectiveness not the

optimal status because it was determined in advance.

An alternative approach is the active flow control, this method achieves the control purpose by inputting the

1 Postdoctoral Associate, Department of Aerospace Engineering; Associate Professor of Civil Engr. of HIT. 2 Graduate Student, Department of Aerospace Engineering.

3 Professor, Department of Aerospace Engineering. AIAA Associate Fellow. Email: huhui@iastate.edu

4 Assistant Professor, School of Civil Engineering.

5 Professor, School of Civil Engineering.

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52nd Aerospace Sciences Meeting

13-17 January 2014, National Harbor, Maryland

AIAA 2014-0399

Copyright © 2014 by Wenli Chen, Yang Liu, Feng Xu, Hui Li and Hui Hu. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

AIAA SciTech

external energy into the flow field and injecting the proper perturbation interacted with the flow inner mode. At

present, several active flow control approaches were developed to achieve drag reduction, high lift, and vibration

suppression, including: the wall vibration, the bubble method, the synthetic jet, the steady suction, the momentum

injection, the traveling wave wall (TWW) method and so on.

Arturo and Maurizio (1996) and Choi et al. (2002) employed a flow control approach of the wall vibration to

decrease the friction drag in the turbulence boundary layer and channel flows by conducting numerical simulations.

Feng et al. (2010, 2011) and Feng and Wang (2010) performed experimental studies to study the effect of a synthetic

jet to control the unsteady vortex shedding from a circular cylinder. The results indicated that the generated a vortex

pair by the synthetic jet had a significant influence on the wake of the circular cylinder. The suction flow control

method was widely used to suppress the flow separation of circular cylinders and found to lead to drag reduction,

suppress the spanwise vortices formation, reduce the velocity fluctuation level and eliminate the oscillation of the

lift (Delaunay and Kaiktsis, 2001; Li et al., 2003; Fransson et al., 2004; Patil and Ng, 2010). The momentum

injection is also a common method to control to the flow field around airfoils, flat plates, rectangular prisms and D-

section prisms (Modi, 1997; Modi et al., 2001; Munshi et al., 1997, 1999; Patnaik and Wei, 2002). The results

indicated that the injected momentum can delay the flow separation and suppress the vortex shedding generation.

The boundary layer cannot be eliminated when the fluid flows through a rigid wall, however, it may be

weakened or controlled through a flexible or movable wall to obtain a smaller surface friction or a drag reduction

(Choi, 1996). Wu et al. (2003) employed a traveling wave to form a “fluid roller bearing” (FRB) effect to suppress

the large separation and the vortex shedding from the airfoils at large angles of attack by using numerical

simulations. The “FRB” effect of the traveling wave can establish a series of small-scale vortices which can separate

the main stream from the near-wall shear flow and result in a drag reduction (Yang and Wu, 2005). Wu et al. (2007)

conducted a numerical simulation to investigate a TWW approach to control the unsteady flow separated from a

circular cylinder at Re=500. This method can produce a fluid FRB, allow the main stream to keep attached and

completely eliminate the vortex shedding. The previous investigations of the TWW control method were mainly

conducted by numerical simulations and it is necessary to validate this method by using an experimental approach.

In the present paper, an experimental study on the TWW method to suppress the vortex shedding from a circular

cylinder was conducted. As the previous studies on the TWW method are numerical simulations, therefore, the main

purpose is to validate this method in a real wind tunnel test. Further details and comprehensive study on this method

to control the vortex shedding of a circular cylinder will be submitted as a journal paper in the near future.

II. Experimental Setup and PIV System

The experimental study was conducted in the Bill James Wind Tunnel which is an open-return low-speed wind

tunnel located in the Aerospace Engineering Department of Iowa State University. The tunnel has a test section with

a 30 × 36 inch (762 × 915 mm) cross section and the walls of the test section are optically transparent. Figure 1

shows the schematic of the experimental setup used in the present study for the two-dimensional PIV measurements.

The flow was seeded with 1~5 µm oil droplets. Illumination was provided by a double-pulsed Nd: YAG laser (Ever

Green 200) adjusted on the second harmonic and emitting two pulses of 200 mJ at the wavelength of 532 nm with a

maximum repetition rate of 15 Hz. The thickness of the laser sheet in the measurement region is about 1.0 mm. The

high-resolution 12-bit (1376×1040 pixels) CCD camera (SensiCam, CookeCorp) was used to perform two-

dimensional PIV image recording. In the present study, the distance between the laser sheet and image recording

plane of the CCD camera is about 900 mm. The CCD camera and double-pulsed Nd: YAG lasers were connected to

a workstation (host computer) via a Digital Delay Generator (Berkeley Nucleonics, Model 575), which controlled

the timing of the laser illumination and the image acquisition.

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Fig. 1 Schematic of the experimental setup for PIV measurement

Figure 2 shows the assemblage of the test model used in the present study. The circular cylinder was vertically

mounted on the bottom of the wind tunnel as shown in figure 2(c). The diameter and height of the circular cylinder

are 100 mm and 200 mm, respectively. Limited to the machining conditions, two axisymmetric TWWs were

designed to only install in the regions of [90-165°] and [225-270°] of the rear parts of the circular cylinder,

respectively, as shown in figure 2 (b). It is different with the case where two TWWs completely covered the rear

part in the regions of [90-180°] and [180-270°] (Wu, et al., 2007). In the present experiment, two TWWs were

entirely synchronous because they were driven by one motor and a gear system; therefore, two TWWs have same

propagation speed. The direction of traveling wave propagation is along the main flow, e.g., the upper one is

clockwise and the lower one is anticlockwise. The maximum rotational speed of the motor is 960 rpm and the

corresponding propagation speed is 1.52 m/s. The amplitude, wavelength and number of the TWWs are 2.03 mm,

16.38 mm and 4, respectively. In the present wind tunnel, the test oncoming wind speed U∞

was chosen as 9.1 m/s.

The propagation speed c was set from 0 to 1.52 m/s with an interval of 0.304 m/s, therefore, the corresponding

speed ratios c U∞

were listed in table 1 according to different oncoming wind speeds and propagation speeds.

Table 1 Speed ratios of TWW control system

c (m/s)

U∞

(m/s) 0 0.304 0.608 0.912 1.216 1.52

9.1 0 0.033 0.067 0.1 0.134 0.167

As the maximum PIV frequency can only reach to 15 Hz, a Cobra Probe (Turbulent Flow Instrumentation Pty Ltd)

was employed to measure the wake velocity as shown in figure 2(b); and then the frequency characteristics of the

wake velocity can be calculated by a Fast Fourier Transform (FFT). The measurement range of the Cobra Probe is

2-100 m/s and the accuracy is 0.5%. The sampling rate and sampling time for the velocity measurements were set to

be 1250 Hz and 60 s, respectively.

(a) Design of cylinder with TWW (c) Positions of TWWs (d) Snapshot of test cylinder model

Fig. 2 Setup of test cylinder model

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III. Experimental results and discussions

Figure 3 illustrates the mean flow field around the circular cylinder by using the TWW control at different speed

ratios when the oncoming wind speed is 9.1 m/s. As limited by the manufacture and installation precision, two

eddies in the wake are not completely symmetrical by the horizontal central axis even if without a TWW control.

Also, the mean flow field will be not axisymmetrical under a TWW control. The results indicate that the TWW

method has no control effect to the flow structure with the speed ratio less than 0.067, however behaves a better

control effect with the speed ratio larger than 0.1. Under the TWW control, the vortex shedding is dramatically

suppressed: the wake width becomes narrower and the symmetrical vortices are greatly weakened. However, the

T.K.E. in the near wake increases under a TWW control comparing to the no control cases, i.e., the TWW control

will increase the fluctuations of the wake velocities. The reason will be explained combined the wake velocity

measurement results.

(a) c U∞

=0 (b) c U∞

=0.033 (c) c U∞

=0.067

(d) c U∞

=0.1 (e) c U∞

=0.134 (f) c U∞

=0.167

Fig. 3 Mean flow field around a cylinder at different speed ratios with 9.1m sU∞

=

According to the measurement of the Cobra Probe of single point in the near wake as shown in figure 2(b), three

components of the wake velocity can be obtained. For comparing with two-dimensional PIV results (figure 3), the

present study mainly focuses on u and v which are the streamwise and transverse velocity fluctuations,

respectively. According to the time histories of u and v at different speed ratios (0-0.167), the control effectiveness

of the velocity fluctuations were statistically obtained as shown in figure 4. The results given in the figure can

explain why the T.K.E. increases in the near wake when the TWW behaves a better control effect. The TWW

propagation will induce velocity perturbations into the near wake and increase the velocity fluctuations not only in

the streamwise direction but also in the transverse direction. The augmentation of the velocity fluctuation in the

streamwise direction will increase the drag fluctuation of the test cylinder model. This conclusion was also given in

Wu, et al. (2007). But, the velocity fluctuation augmentation in the transverse direction may not increase the lift

fluctuation. The reason should be that the augmentation of the velocity fluctuation is not alternating but synchronous

in two sides of the horizontal centerline of the wake along the transverse direction because two TWWs

synchronously propagate along the main flow. Therefore, the synchronous velocity perturbations in two sides of the

horizontal centerline along the transverse direction will not increase the wall pressure fluctuations on the cylinder

surface and the lift fluctuations of the test cylinder model.

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0 0.03 0.06 0.09 0.12 0.15

1

1.5

2

2.5

3

Speed ratio

Co

ntr

ol

effe

ctiv

enes

s of

vel

oci

ty f

luct

uat

ions

u

v

Fig. 4 Wake velocity fluctuations at different speed ratios

Under the TWW control, the negative velocity region becomes narrower resulting in an extension of the positive

velocity region. It means that the TWW method may achieve a reduction of the mean drag force. The measured PIV

velocity fields were employed to obtain the drag coefficients of the test cylinder model and analyze the control

effect of the TWW method on the mean drag force. According to the information given in Bohl and Koochesfahani

(2009) based on a control volume analysis, the mean drag coefficient of the circular cylinder was estimated by using

the following expression:

( ) ( ) ( ) ( )2 2 2rms rms free-stream

2 2

2 11 d

2

H

DH

U y U y u y v y UC y

D U U U U

+

−∞ ∞ ∞ ∞

− ≈ − − +

∫ (1)

where ( )U y is the mean streamwise velocity profile in the wake, ( )rmsu y and ( )rmsv y are the root mean square

(r.m.s) profiles of the streamwise and transverse velocity fluctuations, respectively, free-stream

U is the free-stream

velocity outside the wake region which is higher than U∞

due to the finite width of the test section, and the last tern

on the right-hand side accounts for the pressure change in the free stream. The integration domain corresponds to

H=1.0D and the force calculation was carried out based on the measured profiles at X=2.0D.

Figure 5 shows the estimated drag coefficient D

C of the circular cylinder with TWWs at different speed ratios.

For the cylinder without a TWW control, D

C was found to be 1.482 ±0.013 corresponding to the oncoming wind

speed of 9.1 m/s, respectively, which are consistent with the data given in Munson (2002). When the speed ratio

increases to 9.1 m/s, figure 5 reveals that the TWW method exhibits no control effect when the speed ratio less than

0.067 and behaves a better control effect with the speed ratio larger than 0.1. When the speed ratio is 0.134, the

mean drag coefficient is found to be 1.333±0.029 and the TWW method can obtain a maximum mean drag reduction

of 10.05%. The critical speed ratio exists between 0.067-0.1. This region is smaller than the value predicted by Wu

et al. (1990).

100

102

104

106

10-1

100

101

102

Re

CD

Munson(2002)

Present experiment

0 0.05 0.1 0.15 0.20.8

0.9

1

1.1

Speed ratio

Contr

ol

effe

cti

ven

ess

of

CD

Fig. 5 Estimated mean drag coefficient at different speed ratios

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For further investigating the detail characteristics in the wake near the TWW, the local region was enlarged and

only the flow field near the lower TWW was shown in figure 6. The streamlines and mean velocities show that the

lower vortex center has an offset to the horizontal centerline, and the negative velocity region and the wake width

are gradually shrunk as the speed ratio increases resulting in an extension of the positive velocity region and the

free-stream range. This conclusion is same with figure 3. The details in figure 6(f) indicate that there is a small-scale

vortex near the TWW troughs which may be produced by the TWW propagation. The wake and the free-stream

region are divided by this small-scale vortex, e.g., the upper region is the wake and the lower side is free-stream

region.

Combining the results in figures 3 and 6, this paper presents a “force perturbation mechanism” for the TWW flow

control. The TWW forcedly induces a perturbation into the flow field and behaves a better control effect when the

speed ratio exceeds a critical value. This mechanism explanation is similar with the “FRB” interpretation in Wu, et

al. (2003, 2007). The “forced perturbation mechanism” will be further studied in the following part combining the

frequency analysis of the wake analysis.

(a) c U∞

=0 (b) c U∞

=0.033 (c) c U∞

=0.067

(d) c U∞

=0.1 (e) c U∞

=0.134 (f) c U∞

=0.167

Fig. 6 Enlarged mean flow field around a circular cylinder at different speed ratios

The mean flow fields from the PIV data, e.g., figures 3 and 6, were difficult to interpret what changes were

happening in the flow when the TWWs propagate. For example, it cannot be determined how does the small-scale

vortex propagate from an ensemble-averaged velocity contour obtained from a non-phase locked case. Therefore,

for a better understanding of the flow differences between each phase and investigating the mechanism of the TWW

control method, the velocity contours were obtained from the phase-locked cases. Within a TWW period T, eight

phases were chosen from T/8 to T with an interval of T/8. Locked to each phase, the velocity contour was averaged

from the PIV data and the streamlines in the flow field of each phase were illustrated in figure 7. The CFD

numerical simulations given in Wu, et al. (2007) showed that the troughs of the TWWs can produce a series of

stable small-scale vortices moving with the TWW propagation. The stable small-scale vortices can separate the main

stream from the near-wall shear flow, effectively suppressing the occurrence of the detached vortices from the

cylinder surface. However, the present experimental results indicate that the troughs can only produce one small-

scale vortex and the control effectiveness is not so good as the CFD results. The reasons may include the following

points: (1) Two-dimensional CFD numerical simulations were conducted by Wu, et al. (2007) and a three-

dimensional experiment was performed in the present test; (2) The TWWs did not completely cover the rear surface

of the test cylinder model and the rear half surface of the simulated cylinder was entirely covered by the TWWs. (3)

Limited to the machining, the start regions of the TWWs of the test cylinder model cannot reach a smooth level

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which can be easily realized in a CFD numerical simulation. (4) The speed ratios (maximum of 0.167) in the present

tests are less than those of CFD cases (>2.0).

Fig. 7 Phase averages of flow field around a circular cylinder under a TWW control

The wake frequency is one of the main characteristics of the vortex shedding from a bluff body. A Cobra Probe

was utilized to measure the wake velocity in the present experiment. By using a FFT approach, the vortex shedding

frequency calculated from the wake velocity of the test cylinder without a TWW control was illustrated in figure 8.

The data given in figure 8 shows a better linear relationship between the vortex shedding frequency and the

oncoming wind speed. For further validating the test data, the Strouhal numbers corresponding to the Reynolds

numbers were calculated and compared with the previous studies as shown in figure 9. The results indicate that the

calculated Reynolds numbers are consistent with the previous test cases and lower than those of numerical

simulation cases. The average of St for all test cases was calculated as 0.187 which will be used to predict the vortex

shedding frequency for a different oncoming wind speed.

T/4 3T/8

T/2 5T/8 3T/4

7T/8 T

T/8

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0 3 6 9 12 15 180

10

20

30

Wind speed (m/s)

Vort

ex s

hed

din

g f

requ

ency

(H

z)Re=2.0*10

4-1.0*10

5

102

103

104

105

0.14

0.16

0.18

0.20

0.22

0.24

0.26

Experiment, Kondo(1993)

Simulation, Cao(2001)

Simualtion, Franke(1990)

Present experiment

St

Re

Experiment, Franke(1990)

Fig. 8 Vortex shedding frequency versus oncoming wind speed

for a test cylinder without a TWW control

Fig. 9 Comparison of Reynolds numbers

between present experiment and previous

studies

The Cobra Probe was then employed to measure the wake velocity of the test cylinder model with the TWWs.

The wake velocity frequencies were calculated and the corresponding frequency spectra were shown in figure 10.

When the TWW propagates in the flow, it will induce a velocity fluctuation with a fixed frequency according to the

propagation speed. According to the speed ratios (0-0.167), the oncoming wind speed of 9.1 m/s and the TWW

wavelength of 16.38 mm, the traveling wave frequencies were determined to be 0, 18.56, 37.12, 55.68, 74.24 and

92.80 Hz corresponding to the speed ratios of 0, 0.033, 0.067, 0.1, 0.134 and 0.167. The vortex shedding frequency

was calculated to be 17.02 Hz by using an oncoming wind speed of 9.1 m/s, an average St of 0.187 and a cylinder

diameter of 0.1 m.

For smaller speed ratios less than 0.067, the wake velocity only has a frequency component of 17.09 Hz which

can be determined as the vortex shedding frequency (17.02 Hz). For larger speed ratio cases of 0.1-0.167, the wake

velocity not only has the vortex shedding frequency, but also has the components of 56.15, 75.68 and 92.77 Hz

which are corresponding to the traveling wave frequencies of 55.68, 74.24 and 92.79 Hz. It means that a better

control effect of the TWW will induced a traveling wave frequency component in the wake velocity.

When the speed ratio continuously increases, e.g., larger than 2.0 (Wu, et al., 2007), the traveling wave frequency

(>1113.6 Hz) will has a greatly offset from the vortex shedding frequency. The vortex shedding frequency will be

entirely locked to the traveling wave frequency when the vortex shedding is completely suppressed (Wu, et al., 2007;

Wu, 2013). Therefore, the frequency analysis of the wake velocity further validates the “forced perturbation

mechanism”.

0 25 50 75 100 125 150 175 2000

0.3

0.6

0.9

1.2

Frequency (Hz)

Am

pli

tude

Speed ratio=0.0

Speed ratio=0.033

Speed ratio=0.06717.09 Hz

0 25 50 75 100 125 150 175 2000

0.3

0.6

0.9

1.2

Frequency (Hz)

Am

pli

tude

Speed ratio=0.1

Speed ratio=0.134

Speed ratio=0.16717.09 Hz

92.77 Hz75.68 Hz56.15 Hz

Fig. 10 Wake frequencies of test cylinder model at different speed ratios

As mentioned above, when the speed ratio is 0.033, the traveling wave frequency is 18.56 Hz which is larger than

the vortex shedding frequency of 17.09 Hz at an oncoming wind speed of 9.1 m/s. If the traveling wave frequency is

equal or close to the vortex shedding frequency, what control effect the TWW will behave? Based on this question,

the oncoming velocity was increased to 9.6 m/s resulting in a corresponding vortex shedding frequency of 17.95 Hz

which is very close to the traveling wave frequency of 18.56 Hz at a speed ratio of 0.0313. The mean flow fields at

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different speed ratios were illustrated in figure 11. The results show that the TWW not only has a better control

effect at larger speed ratios (0.094-0.157), but also behaves a great control effect at a very small speed ratio of

0.0313. The reason is that the upper and lower TWWs synchronously induce velocity perturbations into the flow and

the synchronous velocity perturbations interfere or disturb the alternating vortex shedding from the test model when

the perturbation frequency (traveling wave frequency) is close to the vortex shedding frequency.

As we all know that when the vortex shedding frequency is close to the natural frequency of a vibrating structure

with a low damping ratio, the VIV of the structure is prone to occur. The VIV is a type of resonant vibration for a

dynamic system. It is similar that the synchronous velocity perturbations induced by the TWWs with a frequency

close to the vortex shedding frequency can weaken or suppress the vortex shedding from the test model only at a

very small speed ratio (0.0313). Therefore, this paper presented this new mechanism named as a “resonant

perturbation mechanism” for the TWW flow control. This new mechanism was not predicted or studied by the

precious numerical simulations. According to this mechanism, smaller energy can be consumed to control the vortex

shedding from a flow induced vibration structure only by adjusting the traveling wave frequency close to the vortex

shedding frequency compared with the case by using a larger speed ratio.

(a) c U∞

=0 (b) c U∞

=0.0313 (c) c U∞

=0.0627

(d) c U∞

=0.094 (e) c U∞

=0.125 (f) c U∞

=0.157

Fig. 11 Mean flow field around a circular cylinder at different speed ratios

According to Eq. (1), the mean drag coefficients of the test model with the TWWs were estimated as shown in

figure 12. Different with figure 7, the mean drag coefficient at a small speed ratio of 0.0313 (“resonant perturbation

control”) can reach a drag reduction of 24.25% which is larger than a 9.54 % drag reduction at a speed ratio of 0.125

(“forced perturbation control”).

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0 0.03 0.06 0.09 0.12 0.150.7

0.8

0.9

1

1.1

Speed ratio

Contr

ol

effe

ctiv

enes

s of

CD

Fig. 12 Estimate mean drag coefficient at different speed ratios

IV. Conclusions In this study, the TWW control for suppressing the vortex shedding from a circular cylinder was investigated

combining a PIV measurement and a Cobra Probe measurement through a wind tunnel test. The following

conclusions were obtained from this study:

(1) The present paper firstly validates the control effectiveness and mechanism of the TWW by using an

experimental approach. This method can suppress the vortex shedding, narrow the wake width and decrease the

mean drag coefficient. The present paper also validates the existence of the critical speed ratio; however the critical

speed ratio is different with the predicted value (Wu et al., 1990).

(2) The “forced perturbation mechanism” of the TWW flow control method which is the similar explanation of

Wu, et al. (2007) was validated. This mechanism can be explained not only by the speed ratio but also by the

propagation wave frequency. When the speed ratio is larger than the critical value, the traveling wave method can

suppress the vortex shedding from the cylinder, but it cannot completely eliminate the vortex shedding like the

results of Wu, et al. (2007). The explanation in the frequency domain is that the propagation wave frequency has a

greatly offset with the vortex shedding. The vortex shedding frequency can be entirely locked to the propagation

wave frequency (Wu, et al., 2007; Wu, 2013), or greatly disturbed by the propagation wave frequency.

(3) The “resonant perturbation mechanism” of the TWW flow control method was firstly presented based on the

wake frequency analysis. When the traveling wave frequency is close the vortex shedding frequency, the traveling

wave method can also achieve a same/higher level of control effectiveness with a smaller traveling wave speed

which means smaller energy consumption. This point did not be predicted or studied by the previous numerical

simulations. According to this conclusion, smaller energy will be consumed to control the vortex shedding from a

flow induced vibration structure only by adjusting the traveling wave frequency close to the vortex shedding

frequency rather than using a larger speed ratio.

Acknowledgements

This research was funded by the National Natural Sciences Foundation of China (NSFC) (51008093,

51161120359, 91215302 and 51378153). The authors also want to thank Mr. Bill Richard of Iowa State University

for his help in setting up the experiments.

References

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