12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022

EXPERIMENTAL INVESTIGATION OF VORTEX-INDUCED VIBRATIONS
OF A CIRCULAR CYLINDER

Agathe Schmider1 , F. Kerhervé2 , L. Cordier3 , A. Spohn4 , N. Dellinger5
Institut Pprime1,2,3,4 /ICube5
Université de Poitiers1,2 /ENSMA4 /CNRS3 /Université de Strasbourg5
agathe.schmider@univ-poitiers.fr

ABSTRACTA new device to study flow-induced vibrations (FIV) under adjustable structural damping ratio is presented. In the presented work, an elastically-mounted cylinder is considered forvalidation in the context of vortex-induced vibrations (VIV).
A DC motor is coupled to the oscillating mass and allows
to simulate for positive or negative damping through forcing.
When the forcing is appropriately settled to simulate a low
structural damping ratio, the standard three-branch response
for such system is well recovered and compare well with theliterature. Inversely, when the forcing is settled to simulate
high damping ratio, the two-branch response is also well reproduced. Flow velocity surveys obtained with Particle Image Velocimetry (PIV) are reported and show that the different
VIV wake modes described in the literature are also well recovered by this new experimental device.

Figure 1. Simplified diagram of the water channel and position of the experimental arrangement

EXPERIMENTAL SET-UP
In preamble, the experimental set-up including thewater channel, the VIV device and the instrumentation arepresented.
Water channel
The experiments presented are conducted in the homemade circulating water channel Hydra III at Institut Pprime(Poitiers, France).
The overall set-up is schematically
represented in Figure 1. The flow is entreined by an axial
pump located in the return flow of the closed circuit water
channel. The test section is 2.1 m long, 0.51 m wide and 0.51
m height and is made of glass windows to allow optical accessfrom both sides, as well from below. The water depth in thetest section is fixed to 0.33 m. The freestream velocity ranges
from 5 to 45 cm s−1 . The flow uniformity all along the test
section was checked in different planes by two-dimensional
two-component (2D-2C) Particle Image Velocimetry (PIV).
The measured deviation from flow uniformity of the velocity
profiles is less than 1%. The measured flow unsteadiness isless than 5% in the whole range of velocities.

INTRODUCTION
Flow-induced vibrations (FIV) over elastically mounted
bluff-bodies occur whenever a bluff body structure is immersed in a fluid stream. When vortex shedding frequency isclose to the natural frequency of the bluff structure, large oscillations can occur and may result in potential damages. Suchcoupling is referred to as vortex-induced vibrations (VIVs).
Most of the early research on FIVs and VIVs was mainly
guided towards their suppression (Zdravkovich, 1981) in thecontext of avoiding engineering failures. Only recently, theselarge-scale oscillations were considered an opportunity for energy harvesting in rivers. The VIVACE converter designed by
Bernitsas et al. (2008) is a typical arrangement with a circularcylinder mounted on linear springs and connected to a power
generator. It demonstrated an efficiency comparable to otherwind or marine energy devices.
The goal of the on-going work presented here is to improve the efficiency of a similar system thanks to controllable mechanical characteristics among which damping andstiffness. While former studies focus on arrangements withconstant viscous damping, the present study takes advantage
of an oscillator with adjustable characteristics. At this end,
the present experimental set-up allows to change damping asa function of oscillation amplitude. In addition, the system
stiffness can also be adapted to match the system resonancefrequency to the vortex shedding frequency. The paper is organised as follows. The overall device is first described. Itsvalidation in terms of vibration response is then discussed.

Experimental VIV device
The oscillating device is shown in Figure 2. A circularhollow cylinder made in aluminum of diameter D = 50 mm,
length L = 0.4 m and thickness e = 1.8 mm is vertically
immersed in the water channel. The blockage ratio due tothe presence of the cylinder in the test section is 10%. A gap
between the cylinder end and the channel floor is set to 2 mm.
The cylinder is mounted on a platform made in aluminum
which supports three OAV air bearings which are supplied
by pressurized air at 4 bars. These air bearings guide themobile platform with negligible mechanical friction in the
crossflow direction along two shafts made in high precision
stainless steel of 20 ± 0.02 mm diameter. A pair of linear
springs (LeeSpings LE014B13S) mounted in parallel on eachside furnish the restoring force. The resulting total stiffness
coefficient is k = 0.022 N mm−1 . A low inertia 24V DC servo
motor with a dual track encoder is coupled to the oscillating1

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
50% overlapping is used, leading to a final vector spacing of
0.09D in both directions. A bad-vector-replacement step isprovided using a 5 × 5 median interpolation method. Finally,
for a given PIV run, 3000 snapshots sampled at fPIV = 15 Hz,
covering approximately 50 oscillations of the cylinder, areacquired.

DAMPING SIMULATION

Figure 2.

The elastically-mounted cylinder behaves similarly to a
one-degree of freedom damped oscillator under unsteady external forces, here hydrodynamic forces exerted by the vorticalstructures shed in the wake of the cylinder. The fluid-dynamic
forces can be reduced to the lift force which may be represented by the unsteady lift coefficient CL (t). In addition, dry
friction is also exerted on the oscillating mass due to the coupling of the oscillating platform with the DC motor. This additional force can be modelled as a Coulomb term of the form
Ff sign(ẏ) (Meirovitch, 1986) where Ff has to be evaluated. In
the meantime, the DC motor can be driven such that an additional forcing is applied to the motion of the cylinder to compensate, for example, for dry friction or damping. This may beseen as a forcing of the cylinder displacement. The later canthus be modelled as,

Experimental VIV device.

platform with a rack and pinion mechanism. Such arrangement results in additional dry friction due to the mechanicalcoupling. The motivations for such arrangement is threefold.
First, it allows to measure in real-time accurately and robustly
the position y and velocity ẏ of the cylinder. Second, it
allows to quantify the energy that can be harvested from theoscillating system by measuring on-line the generated current.
Last, the motor can be used to move arbitrarily the cylinderor to simulate positive or negative damping effect, such as tocompensate for the additional source of friction (see below),
for instance.
With this arrangement, the cylinder can operate displacement over ±2D in the cross-flow direction with minimal
damping. The overall oscillating mass is m = 2.486 kg
which results in a mass ratio m∗ = m/mA = 3.8 with mA thedisplaced mass of water.

mÿ + (c − ∆c )ẏ + (k − ∆k )y + (Ff − ∆ f )sign(ẏ)
1= ρU∞2 DLCL (t)2(1)

where the term FDC (γ,t) = ∆c ẏ + ∆k y + ∆ f sign(y), with γ =[∆c , ∆k , ∆ f ]T , accounts for the force exerted by the DC motor. The coefficient ∆c can be fixed to positive or negativevalue when accounting for, respectively, reduction or additionof damping. Similarly, ∆k accounts for simulating additional
stiffness without modifying the linear springs. Note that in thepresent study this coefficient is set to zero. Finally, the valueof ∆ f is here selected such that the dry friction is optimallycompensated as it will be discussed in the following part. For
a given triplet vector γ, the forcing law FDC (γ,t) is applied
to the oscillating platform through the command in current of
the DC motor in a closed-loop manner which gives in returna corresponding torque Γ(t). At this end, a NI PXI-RT board(PXIe-1071) is connected to two NI PXIe-6356 I/O cards, one
being used for the acquisition of signals only (among which y
and ẏ) and one for the command of the DC motor.

Instrumentation
The 24V DC motor is directly used to measure both thedisplacement y and velocity ẏ of the cylinder. The in-built
encoder provides TTL output signals with 500 pulses per
revolution and enables to measure position and speed with
a ±0.15 mm accuracy. Both signals are sampled at 500
Hz with a NI PXIe-6356 I/O acquisition card. A planar
two-component particle image velocimetry (PIV) system isused for velocity surveys in the near-wake of the cylinder. The
PIV system includes a Nano L 50 − 50 PIV laser from Litron
Ltd (wavelength 532 nm) of 50 mJ per pulse and a Dantec
SpeedSence 1040 camera with a resolution of 2320 × 1726
pixels. This camera is oriented towards the wake region,
through a mirror inclined at 45◦ installed underneath the water
channel. The measurement plane is located at mid-height of
the water channel and covers a region of 8D × 9D including
the cylinder. The laser sheet is 1 mm thick. Polyamide
particles of 50 µm diameter are used for flow seeding. The
instantaneous vector fields are obtained using the acquisition
software Davis 10 from Lavision. A dynamic mask following
the cylinder displacement is used to avoid spurious correlations. The location of the mask for a given pair of images
is set by the simultaneous measurements of the cylinder
location. A conventional direct cross-correlation processincluding multipass windows (from 64 × 64 to 32 × 32) with

FREE-DECAY TESTS FOR DRY FRICTION COMPENSATIONFree decay tests were first conducted in air and quiescentwater to evaluate the structural damping natural frequenciesof the VIV device. As a reference, the DC motor is first uncoupled from the oscillating platform so that no dry friction isexerted, i.e. that the plateform oscillates freely with negligible
damping. This configuration is further referred as R0 and issimilar to that investigated by few authors among which Zhao
et al. (2014); Khalak & Williamson (1997). As mentioned previously, while dry friction is added when the DC motor is coupled with the oscillating platform, this arrangement also allows
different configuration to be tested depending on the value ofthe parameter vector γ. These configurations are further referred as C∆ f ,∆c (∆k is here omitted as it is kept fixed to zeroin the presented work). The case C0,0 therefore denotes null2

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022

Air

Water

Case

k (N m−1 )c (N s m−1 )fna (Hz)fnw (Hz)

ζ

m∗ ζ

R0

0.022

0.071

0.04850.433

0.00424

0.016

C0,0

0.022

1.19

0.463

0.419

0.06940.305

C∆∗f ,0

0.022

0.328

0.459

0.0414

0.019

0.079

Table 1. Natural frequencies fna (respectively fnw ) in air (respectively in water), structural damping ratio and structural mass-damping
ratio for the three different arrangements.

recovered. While not reported here for conciseness, similar
trends are observed when the free decay tests are conducted inwater. Values of the natural frequencies fna and fnw for thethree arrangements found in air and still water respectively aresummarised in Table 1. That of the structural damping ratio(defined only in still water) with considerationof the added√
mass and defined as ζ = c fna / fnw 2 km are also reported. As
a key parameter, the structural mass-damping ratio m∗ ζ is also
evaluated for the three arrangements. The C0,0 case exhibitsa high structural mass-damping ratio (an order of magnitudelarger than that of the R0 arrangement) due to the additional
friction. In contrast, the free-damping R0 and compensateddry-friction C∆∗f ,0 cases are characterised by a low ratio. Thissuggests that the presented device can allow to simulate twoand three-branches VIV system’s responses in a straightforward manner. At this stage, arrangements R0 and C∆∗ ,0 exhibit similar free-decay responses in air and still water and are
therefore expected to provide similar vibration responses withregards to freestream velocity.

Figure 3. Time histories of the displacement of the cylinder
for free-decay tests in air for the different arrangements.

compensation for dry friction and damping. The subscript ∆∗f
is further used as the value of ∆ f which allows for full compensation of the dry friction. When this parameter is properly
set, the C∆∗f ,0 arrangement is expected to behave similarly tothe reference arrangement R0 .
Note that for the reference case, since the DC motor is uncoupled, measurement of the displacement of the cylinder can
not be effected thanks to the encoder. Images sampled at a frequency of 20 Hz were therefore recorded thanks to the FLIR
Grasshopper3 camera to track the cylinder and to extract its
displacement over time. While not reported here, specific validation tests have been effected to compare the displacement
obtained from optical tracking with the one obtained from theencoder.
Results obtained for the free-decay tests conducted in air
for the R0 , C0,0 and C∆∗f ,0 arrangements are presented in Figure
3. The free-response of the different arrangements is that of adamped oscillator. When coupling the DC motor to the oscillating platform (C0,0 configuration), the system response is, as
expected, found to experience significant damping comparedto the reference arrangement R0 . This is representative of
higher structural damping for this arrangement. A first guessof the value of ∆∗f which fully compensates for the dry friction
is obtained following the work of Feeny & Liang (1996). Trialand error tests in air are then conducted to adjust ∆∗f such thatthe free-decay responses of the R0 and C∆∗f ,0 properly matches.
As shown in Figure 3, the selected value allows to recover almost perfectly the free-response of the free-friction referencecase. The small discrepancies observed in the free-response
as the time increases are believed to be due to small change
in the mass of the mobile system due to the inertia of the DC
motor itself. This results in a slight decrease of the natural frequency of the system while the structural damping is properly

VIBRATING RESPONSES OF THE DIFFERENTARRANGEMENTS
In this section, the amplitude and frequency responses ofthe different arrangements are investigated. The amplitude of
the cylinder, hereafter A∗10 , is defined as the mean of the highest 10% of peak amplitude response normalised by the cylinder’s diameter.

Reference arrangement & Model response
The amplitude response of the R0 arrangement is illustrated in Figure 4(top) as a function of the reduced velocity
U ∗ = U∞ / fnw D and is compared against the results of Soti
et al. (2018). Note that both arrangement have the same structural damping ratio ζ of approximatively 0.020. The reference
arrangement R0 exhibits a typical VIV amplitude response inthree branches: (i) an initial branch for U ∗ ≤ 4.8 with low
oscillation amplitude, (ii) an upper branch lying in the range
4.8 ≤ U ∗ ≤ 6.6 where the cylinder experiences largest amplitudes of oscillations of ≈ 0.8D and (iii) a lower branchwithin the range 6.6 ≤ U ∗ ≤ 9.5 where A10 limits to ≈ 0.55D.
The region above U ∗ = 9.5 is generally referred as the desyncrhonised region and is characterised by very negligible oscillations. The normalised frequency response is shown in Figure4(bottom) as black square symbols. The power spectral density (PSD) of the displacement for a given value of the reduced
frequency has been evaluated and the frequency of the larger
energy peak is extracted. Along the initial branch, the cylinder’s frequency response equals the shedding frequency fsh
measured to be equal to 0.21U∞ /D. When moving towards
the lower branch, the cylinder’s frequency slightly increases

312th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
open circles symbols. The difference in the structural damping ratio and in the mass of the moving system is believed tobe responsible for the small discrepancies observed. A correction for the virtually added stiffness should also be addressedto perfectly recover the amplitude response of the reference
arrangement. The three branches are however well properly
recovered. Similar conclusion can be made with regards to thefrequency response reported in Figure 4(bottom). The dominant frequency of the oscillating cylinder fully matches thatobserved for the reference arrangement. Even the modulated
oscillations in the desyncrhonisation region (U ∗ > 9.5) observed for the RO arrangement are recovered. The correction
implemented for the added dry friction can therefore be considered as satisfactory.
It is noteworthy that when varying the coefficient ∆c , different response regimes can be examined. This is illustrated
again in Figure 4 where the results for the case Cxx,0 is reported as an illustration. Here, the value of ∆c has been chosen to simulate energy extraction from the system. Adding
some damping to the moving system results in a drop of theamplitude response while the frequency response remains almost unchanged as reported in Figure 4 by the green open symbols. The presented device therefore allows to simulate different VIV regimes between the typical low- and high- mass ratio
typical responses.

Figure 4. (a) Amplitude response A∗ as function of the relative velocity U ∗ for the different arrangements compared by
the results of Soti et al. (2018). (b) Frequency response as afunction of the relative velocity U ∗ of the C∆∗f configuration.

VIV REGIMES

to lock approximatively in the natural system frequency fnw .
This is shown by the horizontal dashed line at f ∗ = 1. The
frequency response along the upper and lower branches is said
to be synchronised until it reaches the desynchronised region.
For the later, the frequency response is found to reach again
the shedding frequency while the vibration response may also
experiences a low amplitude modulation at the natural frequency. In this region, the PSDs effectively exhibit two frequency peaks. These results are well consistent with that reported in the literature for low structural damping ratio m∗ ζ
(Khalak & Williamson, 1999; Zhao et al., 2014) and suggestthat the R0 arrangement is properly designed and can be here
considered as a reference case for what follows.

Since the frequency response of the oscillating cylinder
is quasi-periodic (see Section ??), the formation of the vortices in the cylinder wake is analyzed with a phase-averaged
approach. In what follows, the phase-averaged velocity is defined according to the phase φi ∈ [0, 360◦ ] (i = 0. . . . , Nφ ) of
the dominant oscillation period, where Nφ denotes the total
number of phases considered. Due to a slight variation in timeof the period of the dominant oscillation (±6%), the temporal
position of a given phase changes slightly between two consecutive maxima. Therefore, the instants corresponding to agiven phase φi are first evaluated independently for each oscillation period. For a given value φi , the PIV fields corresponding to the range [φi ± ∆φ ] are then collected and averaged toform the phase-averaged velocity fields u i . The latter thus describes, on average, the velocity field obtained in the wake ofthe cylinder at a given phase instant of the VIV process. In
the following, we consider Nφ = 12 and ∆φ = 10◦ . The lattervalue has been found to present a good compromise between
the phase localization and the number of PIV snapshots necessary to get a satisfactory statistical convergence. The obtained two-dimensional phase-averaged velocity field is thenused to compute a phase-averaged vorticity field from which
wake regimes can be identified.

Effect of dry friction compensation
The C0,0 arrangement is now examined. This arrangement has a high m∗ ζ ratio and is consequently expected toexperience a distinctly different response. The amplitude andfrequency responses as a function of the reduced velocity arereported in Figure 4 as open squares. In contrast to the reference arrangement R0 , the range of reduced velocity where
oscillations are observed for the C0,0 case is limited only to
5 ≤ U ∗ ≤ 8. The synchronisation regime is therefore foundto be narrower. The upper limit of the oscillation amplitude
is also lower with a peak value of about 0.55D comparablewith the amplitude value obtained for the R0 arrangement in
the lower branch regime. The amplitude response is typicalof a Feng-type response (Khalak & Williamson, 1999) where
only the initial and lower branches exist. While not put clearly
here in evidence for conciseness, an hysteretic transition also
occurs between the two branches. The cylinder’s frequency response equals the shedding frequency fsh measured to be equal
to 0.26U∞ /D almost overall the two branches.
When introducing a correction for the dry friction in theform of a time-dependent torque, resulting in the C∆∗f ,0 arrangement, the amplitude response now tends to match thatof the reference arrangement as shown in Figure 4(top) by the

Sequences of phase-averaged vorticity fields are reported
in Figure 5 for four different regimes. The later are highlighted
in Figure 4(top) by the full star symbols. In the sequences reported in Figure 5, the cylinder going from one of its extreme
position to the other. Figure 5(a) refers to a VIV regime at
the end of the initial branch (U ∗ = 4.7). Two streets of vortices of opposite sign are identified. A double-row pattern ofvortices with a streamwise spacing of approximately 2D and across-flow spacing of approximatively 1.5D is observed. The
initial branch is normally known to be associated with a 2Smode (two single vortex structures of opposite sign alternatively shed per oscillation cycle and concentrated along thewake center-line). The regime shown in Figure 5(a) exhibits

4

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022

(a)

(b)

(c)

(d)

Figure 5. Sequences of phase-averaged vorticity snapshots for (a) U ∗ = 4.5, (b) U ∗ = 5.6, (c) U ∗ = 8.0 and (d) U ∗ = 9.5. Dry-friction
compensated arrangement C∆∗f ,0 . The red dashed lines show the extremum location of the cylinder.

thy that the first vortex shed in the oscillation cycle is pushed
further from the center-line due to the equivalent strength of
the second vortex. In Figure 5(d), corresponding to the desynchronisation regime, the phase-averaged wake do not exhibit
clear shedding vortical structures. It is noteworthy here that
this regime is characterised by the coexistence of two dominant frequencies as discussed previously and as highlighted
in Figure 6 where the power-spectral density of the cylinder’s
displacement is shown. The vorticity fields are here phaseaveraged along the dominant frequency corresponding to thelock-in mechanism (first frequency peak) so that comparisons
can be made with the other regimes. However, the vortex shedding occurs at the highest dominant frequency (second frequency peak). Phase-averaging along this second frequency
peak would be required to better visualise the vortex shedding.
Figure 6. Power-spectral density (normalised by the maximum) of the cylinder’s displacement for arrangement C∆∗f ,0 atdifferent reduced velocity U ∗ . The different regimes correspond to that shown in Figure 5

CONCLUSION
A new device for an elastically mounted cylinder experiencing vortex-induced vibrations (VIV) with adjustable damping and stiffness coefficients is presented. The change of thesecoefficients is simulated thanks to the coupling of a DC motor whose action on the oscillating mass can be modelled as a
Coulomb term. Tests conducted show that the oscillating device allows to reproduce vibration regimes ranging from lowto high-mass ratio device configurations with vibrating responses similar to that typically reported in the literature. One
main advantage of the proposed solution is that is is mechanically non-intrusive. Particle Image Velocimetry surveys performed in the wake of the cylinder for different VIV regimes
are reported and shows that the different vortex modes welldocumented in the literature are properly recovered.

a transition from a 2S to a 2P mode observed along the upperand lower branches as shown in Figure 5(b)&(c) respectively.
The 2P mode consists of two vortices of opposite sign shed
per half oscillation cycle. The main difference observed in thewake pattern between the two latter figures, while associatedto a similar 2P mode, is due to the rapid dissipation of the second vortex in the upper branch. Along the lower branch, thetwo vortices shed per oscillation cycle exhibit similar strengthand therefore persists downstream as manifest in Figure 5(c).
While in the lower branch the cylinder experience oscillation
with amplitude lower than in the upper branch, it is notewor-

512th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
ACKNOWLEDGMENTS

and mode transitions in vortex-induced vibrations at low
mass-damping. Journal of fluids and Structures 13 (7-8),
813–851.
Meirovitch, Leornard 1986 Elements of Vibration Analysis,
2nd edn. McGraw-Hill.
Soti, Atul Kumar, Zhao, Jisheng, Thompson, Mark C, Sheridan, John & Bhardwaj, Rajneesh 2018 Damping effects on
vortex-induced vibration of a circular cylinder and implications for power extraction. Journal of Fluids and Structures
81, 289–308.
Zdravkovich, MM 1981 Review and classification of various
aerodynamic and hydrodynamic means for suppressing vortex shedding. Journal of Wind Engineering and Industrial
Aerodynamics 7 (2), 145–189.
Zhao, J., Leontini, J. S., Lo Jacono, D. & Sheridan, J.
2014 Chaotic vortex induced vibrations. Physics of Fluids
26 (12).

The current project was funded by Région NouvelleAquitaine under the project NAQ Maggie 2018-1R10223.

REFERENCES
Bernitsas, MM, Raghavan, K, Ben-Simon, Y & Garcia, EMH
2008 Vivace (vortex induced vibration aquatic clean energy): A new concept in generation of clean and renewableenergy from fluid flow. Journal of offshore mechanics andArctic engineering 130 (4).
Feeny, BF & Liang, JW 1996 A decrement method for thesimultaneous estimation of coulomb and viscous friction.
Khalak, Asif & Williamson, Charles HK 1997 Investigation ofrelative effects of mass and damping in vortex-induced vibration of a circular cylinder. Journal of Wind Engineering
and Industrial Aerodynamics 69, 341–350.
Khalak, Asif & Williamson, Charles HK 1999 Motions, forces6