Research Article Vortex-Induced Vibration Suppression of a

Research ArticleVortex-Induced Vibration Suppression of a Circular Cylinderwith Vortex Generators

Shi-bo Tao12 Ai-ping Tang12 Da-bo Xin12 Ke-tong Liu3 and Hong-fu Zhang12

1Key Lab of Structures Dynamic Behavior and Control Harbin Institute of Technology Ministry of Education HeilongjiangHarbin 150090 China2School of Civil Engineering Harbin Institute of Technology Harbin 150090 China3College of Architecture and Civil Engineering Xirsquoan University of Science and Technology Xirsquoan 710054 China

Correspondence should be addressed to Ai-ping Tang 972870139qqcom

Received 30 November 2015 Revised 24 May 2016 Accepted 9 June 2016

Academic Editor Carlo Trigona

Copyright copy 2016 Shi-bo Tao et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The vortex-induced vibration is one of the most important factors to make the engineering failure in wind engineering This paperfocuses on the suppression method of vortex-induced vibration that occurs on a circular cylinder fitted with vortex generatorsbased on the wind tunnel experimentThe effect of the vortex generators is presented with comparisons including the bare cylinderThe experimental results reveal that the vortex generators can efficiently suppress vortex-induced vibration of the circular cylinderVortex generator control can make the boundary layer profile fuller and hence more resistant to separation The selections of skewangles and the angular position have a significant influence on the vortex generator control effect By correlation analysis it can beconcluded that the vortex generators can inhibit the communication between the two shear layers and produce streamwise vorticesto generate a disturbance in the spanwise direction

1 Introduction

The stay-cables and hangers are the key components of long-span bridges They are prone to vortex-induced vibration(VIV) due to their high flexibility and low damping ratioAlthough the VIV is self-limiting it may induce violentstructural vibrations and stresses that eventually lead toconsiderable fatigue damage and reduction in the structurallifetime of stay-cables and hangers [1] Therefore strategiesaiming at reducing vibration amplitudes for stay-cables andhangers are of great concern for industry and academia [2 3]Most of the algorithms of fatigue analysis of stay-cables andhangers subjected to VIV consider that the flow around aninclined circular cylinder can be considered equivalent to theone in which the free stream velocity is projected onto thedirection orthogonal to the circular cylinder axis [4] In thepresent work we referred this simplification

Flow control involves active and passive devices [5]Active devices require energy expenditure Kim and Choi[6] studied a forcing scheme for cylinder drag reduction byblowing and suction of fluid through two slits located on the

surface of the cylinder Muralidharan et al [7] designed asuction control strategy for a circular cylinder and imple-mented it to assess its efficacy Bigger et al [8] applied open-loop control in the near wake of a disk in subsonic air andwater flows Passive devices require no auxiliary power andno control loop [9 10] Adachi [11] considered the influenceof different surface roughness values for a circular cylinderwake Chen et al [12] investigated passive jet flow controltechnique to manipulate the vortex shedding process froma circular cylinder Oruc [13] studied flow control around acircular cylinder with a screen that had a streamlined shapeBao and Tao [14] used dual plates to control the wake of acircular cylinder

Vortex generators (VGs) are effective at controllingboundary layer This control method can stimulate verticalmotions confined in the boundary layer and its close sur-roundings hence providingmomentum enhancement in thevicinity of a wall [15] The simple geometrical properties ofpassive VGs can provide relatively practical and low costeffective solutions to complex flow separation phenomenaTherefore VGs are commonly used as flow control devices

Hindawi Publishing CorporationShock and VibrationVolume 2016 Article ID 5298687 10 pageshttpdxdoiorg10115520165298687

2 Shock and Vibration

especially in aerodynamic applications Many results of usingVGs to control stationary cylinders were available at presentUnal and Atlar [16] used VGs to control the wake flow of acylinder Their study shows that vortex generators enforcedthe shear layers to bend towards the centreline and decreasethe width of the wake Shur et al [17] show that VGs canproduce a significant delay of separation and drag reductionin flows past smooth bluff bodies in the transcritical flowregime with turbulent boundary layers ahead of separation

In the present investigation a vortex generator controlmethod was adopted to mitigate the VIV of a circularcylinder The Reynolds numbers in the present work were inthe range of 104 sim105 which is within the subcritical regime

2 Vortex Generator Design

Based on the literature survey review the triangular VGsare adopted in this paper This is a thin plastic plate vortexgenerator with a 02 mm thickness as suggested by Godardand Stanislas [18] Figure 1 shows the geometrical parameters119871 is the distance between the trailing edges of two triangularplates of one pair ℎ is the height of the triangular plates119897 is the length of the triangular plates 120582 is the distancebetween two passive devices and 120573 is the skew angle Beforethe experiment we conducted computational simulations todetermine the boundary layer thickness (120575) of the circularcylinder The boundary layer thickness was approximately15mmndash19mm near the separation line (Re = 10000) Theheight of the VGs can be greater than that of the boundarylayer thickness Therefore the VGs used in this experimentwere 120575-scale with ℎ120575 sim 2 In the experiment the heightsof the VGs were set at ℎ = 4mm The sizes of the VGs weredetermined according to the suggestion given in [18] In thisway 119897ℎ = 15 120582ℎ = 4 and 119871ℎ = 15 Configurations ofthe VGs are shown in Figure 2 where 119880 is the free streamand the positive and negative skew angle are shown in Figures2(a) and 2(b)

3 Experimental Setup

31 Experimental Facility This experiment was performed inthe wind tunnel at the Harbin Institute of Technology (HIT)in China The wind tunnel is a closed-circuit tunnel witha rectangular test section that is 4m wide 3m high and25m long The wind speed (119880) is continuously variable andthe flow has a longitudinal turbulence intensity of less than046

32 Cylinder Model The cylinder model used in these exper-iments was made of an acrylic resin pipe with a length(119871119888) of 12m a diameter of 03m and a wall thickness of

6mm The model was approximately 12 kg This cylinderwas instrumented with 120 surface pressure taps arrangedin four rows along the span of the cylinder as shown inFigure 3(a) Each row contained 30 pressure taps distributedazimuthally about the circumference of the cylinder Theywere distributed at an equal spacing (Δ120572 = 12∘) as shownin Figure 3(b) The 119909-coordinate is along the oncoming flow

Flow directi

on

L

h

120582

120573

l

Figure 1 Vortex generator geometry [18]

120573

U

30∘

(a) 120573 = 30∘

120573

U

minus30∘

(b) 120573 = minus30∘

Figure 2 Vortex generator configuration (top view)

direction and the 119910-coordinate is perpendicular to the flowdirection

The cylinder was hung on a free vibration device (Fig-ure 4) Two end-plates were used to foster a bidimensionalflow [19] The stiffness of the coil spring was 860Nm Thecoil springs were attached symmetrically on the lever armswith a lateral spacing of 450mm The vertical damping ratiowas 2permil and the natural vertical frequency (119891

119899) was 38Hz

The blockage ratio of the experiment facility was 45 andit was unnecessary to correct the data for the blockage effectaccording to [20]

In Figure 5(a) the vortex generators were longitudinallyfitted on a circular cylinder In Figure 5(b) the angularposition (0∘ lt 120579 lt 180∘) of the row was from the frontstagnation line

Two Type 4507B accelerometers were fixed on both endsof the circular cylinder The acceleration measurements wereobtained at a sampling frequency of 1000Hz for a period of20 s The DSM 3400 system (Scanivalve Corporation) wasused to measure the pressure The sampling rate was 300HzThe sampling duration was 40 s

Shock and Vibration 3

Pressure taps

20 cm 40 cm 30 cm 15 cm 15 cm

(a) Surface pressure taps

y

x

U 120572 Δ120572

120572p1 = 72∘

120572p2 = 288∘

(b) Arrangement of the pressure taps

Figure 3 Pressure tap arrangements

FrameSpring

Figure 4 Experiment facility

(a) The circular cylinder with VGs

y

x

U 120579

(b) Side view of the circular cylinder with VGs

Figure 5 The angular position

The aerodynamic coefficients were obtained by integrat-ing the wind pressures over all of the taps the drag andlift coefficients 119862

119909and 119862

119910 were then calculated with the

following expression

119862

119901119894=

119901

119894minus 119901

infin

12 sdot 120588119880

2

0

(1a)

119862

1015840

119901119894=

119901

119894rms

12 sdot 120588119880

2

0

(1b)

119862

119909=

119865

119909

12120588119880

2

0119863

=

12 sdot 120588119880

2

0sum

119894119862

119901119894sdot 12 sdot 119863Δ120579

119894sdot cos 120579

119894

12 sdot 120588119880

2

0119863

=

1

2

sum

119894

119862

119901119894Δ120579

119894cos 120579119894

(1c)

119862

119910=

119865

119910

12120588119880

2

0119863


=

12 sdot 120588119880

2

0sum

119894119862

119901119894sdot 12 sdot 119863Δ120579

119894sdot cos 120579

119894

12 sdot 120588119880

2

0119863

=

1

2

sum

119894

119862

119901119894Δ120579

119894sin 120579

119894

(1d)

where 119862

119901119894is the pressure coefficient 119901

119894is the pressure on the

model 119901infinis the static pressure of the free stream 120588 is the air

density 120588 = 1225 kgm31198621015840119901is the pressure fluctuation 119901

119894rmsis the root-mean-square of the pressure fluctuations and 119865

119909

and 119865

119910are the aerodynamic drag and lift forces acting on

the cylinder model in the 119909- and 119910-directions respectivelyEquations (1a) (1b) (1c) and (1d) were used for the spanwisecorrelation coefficients of the lift force

33 Measurement Uncertainty The uncertainty of the Renumber can be written as [21]

119906

2

Re = (

119880

Re120597Re120597119880

119906

119880)

2

+ (

]Re

120597Re120597]

119906])

2

+ (

119867

Re120597Re120597119863

119906

119889)

2

(2)

where ] is the kinematic viscosity m2s and 119906 is theuncertainty Using the values of the partial derivatives

120597Re120597119880

=

119863

]

120597Re120597119863

=

119880

119863

120597Re120597]

= (minus1)

119880119863

]2

(3)

Equation (2) can be rewritten as

119906

2

Re = (

119880

119880119867]119867

]119906

119880)

2

+ (

119880

119880119867]119880

]119906

119867)

2

+ (

119880

119880119867](minus1)

119880119867

]2119906])

2

997904rArr

119906

2

Re = (119906

119880)

2

+ (119906

119867)

2

+ (119906])2

(4)

The uncertainty of the free stream velocity 119906

119880was 15

Theuncertainty of the diameter of the circular cylindermodel119906

119867was 7permil The uncertainty of the kinematic viscosity of

air was approximately 4permil The total uncertainty of the Renumber given by (2) has been determined as 1199062Re = (15)2 +(7permil)2 + (4permil)2 = 29

The surface pressure coefficient uncertainty can be writ-ten as

119906

119862119901= [(

Δ119901

119862

119901

120597119862

119901

120597Δ119901

119906

Δ119901)

2

+ (

120588

119862

119901

120597119862

119901

120597Δ119901

119906

120588)

2

+ (

119880

119862

119901

120597119862

119901

120597119880

119906

119880)

2

]

12

(5)

The partial derivatives in (5) can be written as

120597119862

119901

120597Δ119901

=

2

120588119880

2

120597119862

119901

120597120588

=

minus2Δ119901

120588

2119880

2

120597119862

119901

120597119880

=

minus4Δ119901

120588119880

3

(6)

The uncertainty of the pressure coefficient is obtained as

119906

119862119901= [(

Δ119901

2Δ119901120588119880

2

2

120588119880

2)

2

+ (

120588

2Δ119901120588119880

2

minus2Δ119901

120588

2119880

2119906

120588)

2

+ (

119880

2Δ119901120588119880

2

minus2Δ119901

120588119880

3)

2

]

12

997904rArr

119906

2

119862119901= 119906

2

Δ119901+ 119906

2

120588+ 4119906

2

119880

(7)

where 119906

Δ119901= 25 and 119906

120588= 2 Finally 119906

119862119901= 39

The uncertainty of the accelerometer was obtained fromthe calibration chart for the Type 4507B accelerometer Theexpanded uncertainly was 10 as determined in accordancewith EAL-R2 [22] A coverage factor of 119896 = 2 was used

4 Experiment Results and Analysis

In the experiment the wind speeds ranged from 5ms to13ms The corresponding reduced wind speed (119880119903) was119880119891

119899119863The amplitude of the bare circular cylinder versus the

reduced wind speed is produced in Figure 7 The amplitudeof the model was calculated by

119860 =

radic

2 sdot 120590

2

(8)

where 119860 is the amplitude and 120590

2 is the variance of the dis-placement Equation (8) is likely to give an underestimationof the maximum response but was judged to be perfectlyacceptable for assessing the effectiveness of VIV suppressiondevices The comparison of the ratio of the vortex sheddingfrequency and the vertical natural vibration frequency of thecircular cylinder is shown in Figure 7 as a function of thereduced wind speed

In Figure 6 when the reduced wind speed range is 44ndash107 the vibration amplitude of the circular cylinder increasesfirst peaks at 119880119903 = 7 and then decreases Also as shown inFigure 7 a lock-in phenomenon is observed in the reduced


4 5 6 7 8 9 10 11

Ur

005

004

003

002

001

000

AD

Figure 6 Amplitude of the bare cylinder versus the reduced wind speed

4 5 6 7 8 9 10 11

Ur

22

20

18

16

14

12

10

08

06

04

fL

fn

FreeFixed

Figure 7 Variation of the frequency ratios versus the reduced wind speed

wind velocity region from 50 to 92 For this region in thetest system the circular cylinder motion controls the vortexshedding frequency Therefore according to Figures 7 and 8the synchronization region is from 50 to 92

41 Displacement Amplitude The displacement amplitudesof the circular cylinder with and without vortex generatorsare shown in Figure 8The bare cylinder case was denoted byldquoBCCrdquo throughout this study

The VGs control has the positive effects on shorteningthe lock-in region and reducing the displacement amplitudeof the circular cylinder The results (in Figure 8) show thatthe control effect is excellent when 120579 is 70∘ For 120579 = 70∘a significant displacement amplitude reduction is achieved

from 119880119903 = 5 to 119880119903 = 10 On the other side for 120579 = 90∘ or 120579 =105∘ the VGs are less effective on reducing the displacementamplitude than that of 120579 = 45∘ or 120579 = 70∘ For 120579 = 45∘ there isearly synchronization as that found for the circular cylindersubjected to VIV

42 Surface Pressure Distribution Themean surface pressuredistribution on the circular cylinder is shown in Figure 9By analysing the change of the surface pressure distributionssome conclusions can be drawn First one can observe how119862

119901min is reduced to a value close to minus25 for 120579 = 70

∘

and is reduced to minus2 for 120579 = 45

∘ Second the separationpoint moves towards the higher angles Vortex generatorsmake the boundary layer profile fuller and hence more


4 5 6 7 8 9 10 11

Ur

005

004

003

002

001

000

AD

120579 = 45∘

120579 = 70∘

120579 = 90∘

120579 = 105∘

BCC

120573

minus30∘

(a) 120573 = minus30∘

4 5 6 7 8 9 10 11

Ur

005

004

003

002

001

000

AD

120579 = 45∘

120579 = 70∘

120579 = 90∘

120579 = 105∘

BCC

(b) 120573 = 0∘

4 5 6 7 8 9 10 11

Ur

005

004

003

002

001

000

AD

120579 = 45∘

120579 = 70∘

120579 = 90∘

120579 = 105∘

BCC

120573

30∘

(c) 120573 = 30∘

Figure 8 Displacement amplitude

resistant to separation Third the surface pressure distri-bution for 120579 = 90

∘ is similar to that of the bare circularcylinder

The fluctuating pressure coefficients (1198621015840119901) distribution on

the circular cylinder is plotted in Figure 10The fluctuating pressure distribution of the bare circular

cylinder is roughly symmetrical Every fluctuating pressurecoefficient curve has two peaks For the bare cylinder thetwo peak points of the fluctuating pressure are 120572

1199011= 72

∘

and 120572

1199012= 288

∘ For 120579 = 45

∘ and 120579 = 70

∘ the maximumfluctuating pressure moves towards higher angles (120572 = 108

∘)and then rapidly decreases to approximately 005 For 120579 = 90

∘

the curve is almost the same as the bare cylinder case For120579 = 45

∘ the fluctuating pressure increases to approximately035

43 Correlation Analysis Assuming that 120577 and 120578 are twovariables the correlation coefficient (119903

120577120578) is

119903

120577120578=

sum

119899

119894=1(120577

119894minus 120577) (120578

119894minus 120578)

radicsum

119899

119894=1(120577

119894minus 120577)

2

radicsum

119899

119894=1(120578

119894minus 120578)

2

(9)


120573

minus30∘

15

10

05

00

minus05

minus10

minus15

minus20

minus25

minus30

Cp

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

(a) 120573 = minus30∘

15

10

05

00

minus05

minus10

minus15

minus20

minus25

minus30

Cp

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

(b) 120573 = 0∘

120573

30∘

15

10

05

00

minus05

minus10

minus15

minus20

minus25

minus30

Cp

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

(c) 120573 = 30∘

Figure 9 Distribution of the mean pressure coefficients (119880119903 = 7)

where 119903 is the correlation coefficient 120577 is the mean of all120577

119894-data 120578 is the mean of all 120578

119894-data and 119899 is the sampling

lengthCorrelation analysis can reveal the implicit periodicity

of signals and detect the degree of correlation betweentwo variables The aerodynamic lift forces (119865

119910) are obtained

by integrating the surface pressure around the circularcylinder The spanwise correlation coefficients between theaerodynamic lift forces on the middle section of the cir-cular cylinder and the other three sections are shown inFigure 11

For 120579 = 45∘ or 70∘ the spanwise correlation coefficientsof the aerodynamic lift forces are less than those of a

bare circular cylinder The VGs produce strong streamwisevortices to generate a disturbance in the spanwise directionFor 120579 = 90∘ however the spanwise correlation coefficients arenearly the same as those without control

In Figures 9ndash11 the VGs can influence the bound-ary layer flow even if they are far from the separationline (120579 = 45∘) When the VGs are set after the sepa-ration line (120579 = 90∘) however the control effect is notsignificant

The correlation coefficients between the two peak pointsof the fluctuating pressure for the bare cylinder (120572

1199011= 72

∘

and 120572

1199012= 288

∘) are shown in Figure 12 For the bare cylinderthere is a significant negative correlation coefficient between


120573

minus30∘

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

040

035

030

025

020

015

010

005

000

C998400 p

(a) 120573 = minus30∘

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

040

035

030

025

020

015

010

005

000

C998400 p

(b) 120573 = 0∘

120573

30∘

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

040

035

030

025

020

015

010

005

000

C998400 p

(c) 120573 = 30∘

Figure 10 Distribution of the fluctuating pressure coefficients (119880119903 = 7)

the two peak points indicating that there are two sets ofalternating vortices on two sides For 120579 = 45

∘ or 120579 = 70

∘the correlation coefficients of the two peak points are closerto zero This suggests that communication between the twoshear layers is inhibited For 120579 = 90

∘ the negative coefficientsare larger than that of 120579 = 45

∘ and 120579 = 70

∘

5 Conclusion

Based on the wind tunnel experiment a vibration controlmethod using the vortex generator was studied herein The

vortex-induced vibration of the circular cylinder with andwithout vortex generators is quantified in terms of the dis-placement amplitude pressure distributions and correlationcoefficients The main results show the following

(1) The vortex generators effectively suppress vortex-induced vibration They shorten the lock-in regionand reduce the amplitude of vortex-induced vibra-tion The vortex generators have the best resultfor 120579 = 70∘ which significantly reduces the ampli-tude For 120579 = 45∘ there is early synchronization


120573

minus30∘10

08

06

04

02

00

Cor

relat

ion

coeffi

cien

t

Position of section0 Lc

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

16 Lc 13 Lc 12 Lc 23 Lc 56 Lc

(a) 120573 = minus30∘

10

08

06

04

02

00

Cor

relat

ion

coeffi

cien

t


120579 = 45∘120579 = 70∘

120579 = 90∘BCC

16 Lc 13 Lc 12 Lc 23 Lc 56 Lc

(b) 120573 = 0∘

120573

30∘10

08

06

04

02

00

Cor

relat

ion

coeffi

cien

t


120579 = 45∘120579 = 70∘

120579 = 90∘BCC

16 Lc 13 Lc 12 Lc 23 Lc 56 Lc

(c) 120573 = 30∘

Figure 11 Correlation coefficients of lift (119880119903 = 7)

for a circular cylinder subjected to vortex-inducedvibration

(2) The vortex generators make the boundary layer pro-file fuller and hencemore resistant to separationTheycan influence the boundary layer flow even if they arefar from the separation line

(3) Correlation analysis shows that the vortex generatorscan inhibit communication between the two shearlayers and the vortex generators had a stronger effecton the spanwise correlation coefficientsThe spanwisecorrelation coefficients of the cylinder with vortex

generators are less than those of the bare circularcylinder

We believe that the present study offers some informationto understand the physics of the vortex-induced vibrationof cylinders with and without vortex generators Futuretest should focus on the enhanced physical understand-ing and continued application of vortex generators to realsystems

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper


45∘ 70∘ 90∘

120579

BCC

00

minus01

minus02

minus03

minus04

minus05

minus06

minus07

Cor

relat

ion

coeffi

cien

t

120573 = minus30∘

120573 = 0∘120573 = 30∘

Figure 12 Correlation coefficients of the two peak points (119880119903 = 7)

Acknowledgments

The authors extend their deepest gratitude to Ms Cho MyaDarli for her comments on this paper This research wasfunded by theNational Basic ResearchProgramofChina (973Program 2011CB013705)

References

[1] W-L Chen H Li J-P Ou and F-C Li ldquoNumerical simulationof vortex-induced vibrations of inclined cables under differentwind profilesrdquo Journal of Bridge Engineering vol 18 no 1 pp42ndash53 2013

[2] F C L Borges N Roitman C Magluta D A Castello and RFranciss ldquoA concept to reduce vibrations in steel catenary risersby the use of viscoelastic materialsrdquo Ocean Engineering vol 77no 2 pp 1ndash11 2014

[3] H L Dai A Abdelkefi L Wang and W B Liu ldquoTime-delayfeedback controller for amplitude reduction in vortex-inducedvibrationsrdquoNonlinearDynamics vol 80 no 1-2 pp 59ndash70 2015

[4] G R Franzini A L C Fujarra J R Meneghini I Korkischkoand R Franciss ldquoExperimental investigation of vortex-inducedvibration on rigid smooth and inclined cylindersrdquo Journal ofFluids and Structures vol 25 no 4 pp 742ndash750 2009

[5] F Landolsi S Choura andAHNayfeh ldquoControl of 2D flexiblestructures by confinement of vibrations and regulation of theirenergy flowrdquo Shock and Vibration vol 16 no 2 pp 213ndash2282009

[6] J Kim and H Choi ldquoDistributed forcing of flow over a circularcylinderrdquo Physics of Fluids vol 17 no 3 Article ID 33103 2005

[7] K Muralidharan S Muddada and B S V Patnaik ldquoNumericalsimulation of vortex induced vibrations and its control bysuction and blowingrdquo Applied Mathematical Modelling vol 37no 1-2 pp 284ndash307 2013

[8] R P Bigger H Higuchi and J W Hall ldquoOpen-loop control ofdisk wakesrdquo AIAA Journal vol 47 no 5 pp 1186ndash1194 2009

[9] V J Modi ldquoMoving surface boundary-layer control a reviewrdquoJournal of Fluids and Structures vol 11 no 6 pp 627ndash663 1997

[10] L A R Quadrante and Y Nishi ldquoAmplificationsuppressionof flow-induced motions of an elastically mounted circularcylinder by attaching tripping wiresrdquo Journal of Fluids andStructures vol 48 pp 93ndash102 2014

[11] T Adachi ldquoEffects of surface roughness on the universalStrouhal number over the wide Reynolds number rangerdquoJournal of Wind Engineering and Industrial Aerodynamics vol69ndash71 pp 399ndash412 1997

[12] W-L Chen D-L Gao W-Y Yuan H Li and H Hu ldquoPassivejet control of flow around a circular cylinderrdquo Experiments inFluids vol 56 article 201 2015

[13] V Oruc ldquoPassive control of flow structures around a circularcylinder by using screenrdquo Journal of Fluids and Structures vol33 pp 229ndash242 2012

[14] Y Bao and J Tao ldquoThe passive control of wake flow behind acircular cylinder by parallel dual platesrdquo Journal of Fluids andStructures vol 37 pp 201ndash219 2013

[15] U O Unal and O Goren ldquoEffect of vortex generators on theflow around a circular cylinder computational investigationwith two-equation turbulence modelsrdquo Engineering Applica-tions of Computational Fluid Mechanics vol 5 no 1 pp 99ndash1162011

[16] UO Unal andMAtlar ldquoAn experimental investigation into theeffect of vortex generators on the near-wake flow of a circularcylinderrdquo Experiments in Fluids vol 48 no 6 pp 1059ndash10792010

[17] M L Shur M K Strelets A K Travin and P R SpalartldquoEvaluation of vortex generators for separation control in atranscritical cylinder flowrdquo AIAA Journal vol 53 no 10 pp2967ndash2977 2015

[18] G Godard and M Stanislas ldquoControl of a decelerating bound-ary layer Part 1 optimization of passive vortex generatorsrdquoAerospace Science amp Technology vol 10 no 3 pp 181ndash191 2006

[19] H F Wang Y Zhou and J Mi ldquoEffects of aspect ratio on thedrag of a wall-mounted finite-length cylinder in subcritical andcritical regimesrdquo Experiments in Fluids vol 53 no 2 pp 423ndash436 2012

[20] F Gu J S Wang X Q Qiao and Z Huang ldquoPressuredistribution fluctuating forces and vortex shedding behavior ofcircular cylinder with rotatable splitter platesrdquo Journal of Fluidsand Structures vol 28 pp 263ndash278 2012

[21] B Cuhadaroglu Y E Akansu and A O Turhal ldquoAn experi-mental study on the effects of uniform injection through oneperforated surface of a square cylinder on some aerodynamicparametersrdquo Experimental Thermal amp Fluid Science vol 31 no8 pp 909ndash915 2007

[22] W Kessel ldquoEuropean and international standards for state-ments of uncertaintyrdquo Engineering Science and Education Jour-nal vol 7 no 5 pp 201ndash207 1998

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



especially in aerodynamic applications Many results of usingVGs to control stationary cylinders were available at presentUnal and Atlar [16] used VGs to control the wake flow of acylinder Their study shows that vortex generators enforcedthe shear layers to bend towards the centreline and decreasethe width of the wake Shur et al [17] show that VGs canproduce a significant delay of separation and drag reductionin flows past smooth bluff bodies in the transcritical flowregime with turbulent boundary layers ahead of separation

In the present investigation a vortex generator controlmethod was adopted to mitigate the VIV of a circularcylinder The Reynolds numbers in the present work were inthe range of 104 sim105 which is within the subcritical regime

2 Vortex Generator Design

Based on the literature survey review the triangular VGsare adopted in this paper This is a thin plastic plate vortexgenerator with a 02 mm thickness as suggested by Godardand Stanislas [18] Figure 1 shows the geometrical parameters119871 is the distance between the trailing edges of two triangularplates of one pair ℎ is the height of the triangular plates119897 is the length of the triangular plates 120582 is the distancebetween two passive devices and 120573 is the skew angle Beforethe experiment we conducted computational simulations todetermine the boundary layer thickness (120575) of the circularcylinder The boundary layer thickness was approximately15mmndash19mm near the separation line (Re = 10000) Theheight of the VGs can be greater than that of the boundarylayer thickness Therefore the VGs used in this experimentwere 120575-scale with ℎ120575 sim 2 In the experiment the heightsof the VGs were set at ℎ = 4mm The sizes of the VGs weredetermined according to the suggestion given in [18] In thisway 119897ℎ = 15 120582ℎ = 4 and 119871ℎ = 15 Configurations ofthe VGs are shown in Figure 2 where 119880 is the free streamand the positive and negative skew angle are shown in Figures2(a) and 2(b)

3 Experimental Setup

31 Experimental Facility This experiment was performed inthe wind tunnel at the Harbin Institute of Technology (HIT)in China The wind tunnel is a closed-circuit tunnel witha rectangular test section that is 4m wide 3m high and25m long The wind speed (119880) is continuously variable andthe flow has a longitudinal turbulence intensity of less than046

32 Cylinder Model The cylinder model used in these exper-iments was made of an acrylic resin pipe with a length(119871119888) of 12m a diameter of 03m and a wall thickness of

6mm The model was approximately 12 kg This cylinderwas instrumented with 120 surface pressure taps arrangedin four rows along the span of the cylinder as shown inFigure 3(a) Each row contained 30 pressure taps distributedazimuthally about the circumference of the cylinder Theywere distributed at an equal spacing (Δ120572 = 12∘) as shownin Figure 3(b) The 119909-coordinate is along the oncoming flow

Flow directi

on

L

h

120582

120573

l

Figure 1 Vortex generator geometry [18]

120573

U

30∘

(a) 120573 = 30∘

120573

U

minus30∘

(b) 120573 = minus30∘

Figure 2 Vortex generator configuration (top view)

direction and the 119910-coordinate is perpendicular to the flowdirection

The cylinder was hung on a free vibration device (Fig-ure 4) Two end-plates were used to foster a bidimensionalflow [19] The stiffness of the coil spring was 860Nm Thecoil springs were attached symmetrically on the lever armswith a lateral spacing of 450mm The vertical damping ratiowas 2permil and the natural vertical frequency (119891

119899) was 38Hz

The blockage ratio of the experiment facility was 45 andit was unnecessary to correct the data for the blockage effectaccording to [20]

In Figure 5(a) the vortex generators were longitudinallyfitted on a circular cylinder In Figure 5(b) the angularposition (0∘ lt 120579 lt 180∘) of the row was from the frontstagnation line

Two Type 4507B accelerometers were fixed on both endsof the circular cylinder The acceleration measurements wereobtained at a sampling frequency of 1000Hz for a period of20 s The DSM 3400 system (Scanivalve Corporation) wasused to measure the pressure The sampling rate was 300HzThe sampling duration was 40 s


Pressure taps

20 cm 40 cm 30 cm 15 cm 15 cm


y

x

U 120572 Δ120572

120572p1 = 72∘

120572p2 = 288∘



FrameSpring



y

x

U 120579




119909and 119862



119862

119901119894=

119901

119894minus 119901

infin

12 sdot 120588119880

2

0

(1a)

119862

1015840

119901119894=

119901

119894rms

12 sdot 120588119880

2

0

(1b)

119862

119909=

119865

119909

12120588119880

2

0119863

=

12 sdot 120588119880

2

0sum

119894119862

119901119894sdot 12 sdot 119863Δ120579

119894sdot cos 120579

119894

12 sdot 120588119880

2

0119863

=

1

2

sum

119894

119862

119901119894Δ120579

119894cos 120579119894

(1c)

119862

119910=

119865

119910

12120588119880

2

0119863


=

12 sdot 120588119880

2

0sum

119894119862

119901119894sdot 12 sdot 119863Δ120579

119894sdot cos 120579

119894

12 sdot 120588119880

2

0119863

=

1

2

sum

119894

119862

119901119894Δ120579

119894sin 120579

119894

(1d)

where 119862






119909

and 119865




119906

2

Re = (

119880

Re120597Re120597119880

119906

119880)

2

+ (

]Re

120597Re120597]

119906])

2

+ (

119867

Re120597Re120597119863

119906

119889)

2

(2)


120597Re120597119880

=

119863

]

120597Re120597119863

=

119880

119863

120597Re120597]

= (minus1)

119880119863

]2

(3)


119906

2

Re = (

119880

119880119867]119867

]119906

119880)

2

+ (

119880

119880119867]119880

]119906

119867)

2

+ (

119880

119880119867](minus1)

119880119867

]2119906])

2

997904rArr

119906

2

Re = (119906

119880)

2

+ (119906

119867)

2

+ (119906])2

(4)


119880was 15





119906

119862119901= [(

Δ119901

119862

119901

120597119862

119901

120597Δ119901

119906

Δ119901)

2

+ (

120588

119862

119901

120597119862

119901

120597Δ119901

119906

120588)

2

+ (

119880

119862

119901

120597119862

119901

120597119880

119906

119880)

2

]

12

(5)


120597119862

119901

120597Δ119901

=

2

120588119880

2

120597119862

119901

120597120588

=

minus2Δ119901

120588

2119880

2

120597119862

119901

120597119880

=

minus4Δ119901

120588119880

3

(6)


119906

119862119901= [(

Δ119901

2Δ119901120588119880

2

2

120588119880

2)

2

+ (

120588

2Δ119901120588119880

2

minus2Δ119901

120588

2119880

2119906

120588)

2

+ (

119880

2Δ119901120588119880

2

minus2Δ119901

120588119880

3)

2

]

12

997904rArr

119906

2

119862119901= 119906

2

Δ119901+ 119906

2

120588+ 4119906

2

119880

(7)

where 119906

Δ119901= 25 and 119906

120588= 2 Finally 119906

119862119901= 39






119860 =

radic

2 sdot 120590

2

(8)





4 5 6 7 8 9 10 11

Ur

005

004

003

002

001

000

AD


4 5 6 7 8 9 10 11

Ur

22

20

18

16

14

12

10

08

06

04

fL

fn

FreeFixed








∘




4 5 6 7 8 9 10 11

Ur

005

004

003

002

001

000

AD

120579 = 45∘

120579 = 70∘

120579 = 90∘

120579 = 105∘

BCC

120573

minus30∘

(a) 120573 = minus30∘

4 5 6 7 8 9 10 11

Ur

005

004

003

002

001

000

AD

120579 = 45∘

120579 = 70∘

120579 = 90∘

120579 = 105∘

BCC

(b) 120573 = 0∘

4 5 6 7 8 9 10 11

Ur

005

004

003

002

001

000

AD

120579 = 45∘

120579 = 70∘

120579 = 90∘

120579 = 105∘

BCC

120573

30∘

(c) 120573 = 30∘







1199011= 72

∘

and 120572

1199012= 288

∘ For 120579 = 45

∘ and 120579 = 70



∘




120577120578) is

119903

120577120578=

sum

119899

119894=1(120577

119894minus 120577) (120578

119894minus 120578)

radicsum

119899

119894=1(120577

119894minus 120577)

2

radicsum

119899

119894=1(120578

119894minus 120578)

2

(9)


120573

minus30∘

15

10

05

00

minus05

minus10

minus15

minus20

minus25

minus30

Cp

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

(a) 120573 = minus30∘

15

10

05

00

minus05

minus10

minus15

minus20

minus25

minus30

Cp

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

(b) 120573 = 0∘

120573

30∘

15

10

05

00

minus05

minus10

minus15

minus20

minus25

minus30

Cp

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

(c) 120573 = 30∘













1199011= 72

∘

and 120572

1199012= 288



120573

minus30∘

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

040

035

030

025

020

015

010

005

000

C998400 p

(a) 120573 = minus30∘

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

040

035

030

025

020

015

010

005

000

C998400 p

(b) 120573 = 0∘

120573

30∘

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

040

035

030

025

020

015

010

005

000

C998400 p

(c) 120573 = 30∘



∘ or 120579 = 70



∘ and 120579 = 70

∘

5 Conclusion





120573

minus30∘10

08

06

04

02

00

Cor

relat

ion

coeffi

cien

t


120579 = 45∘120579 = 70∘

120579 = 90∘BCC

16 Lc 13 Lc 12 Lc 23 Lc 56 Lc

(a) 120573 = minus30∘

10

08

06

04

02

00

Cor

relat

ion

coeffi

cien

t


120579 = 45∘120579 = 70∘

120579 = 90∘BCC

16 Lc 13 Lc 12 Lc 23 Lc 56 Lc

(b) 120573 = 0∘

120573

30∘10

08

06

04

02

00

Cor

relat

ion

coeffi

cien

t


120579 = 45∘120579 = 70∘

120579 = 90∘BCC

16 Lc 13 Lc 12 Lc 23 Lc 56 Lc

(c) 120573 = 30∘







Competing Interests



45∘ 70∘ 90∘

120579

BCC

00

minus01

minus02

minus03

minus04

minus05

minus06

minus07

Cor

relat

ion

coeffi

cien

t

120573 = minus30∘

120573 = 0∘120573 = 30∘


Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Pressure taps

20 cm 40 cm 30 cm 15 cm 15 cm


y

x

U 120572 Δ120572

120572p1 = 72∘

120572p2 = 288∘



FrameSpring



y

x

U 120579




119909and 119862



119862

119901119894=

119901

119894minus 119901

infin

12 sdot 120588119880

2

0

(1a)

119862

1015840

119901119894=

119901

119894rms

12 sdot 120588119880

2

0

(1b)

119862

119909=

119865

119909

12120588119880

2

0119863

=

12 sdot 120588119880

2

0sum

119894119862

119901119894sdot 12 sdot 119863Δ120579

119894sdot cos 120579

119894

12 sdot 120588119880

2

0119863

=

1

2

sum

119894

119862

119901119894Δ120579

119894cos 120579119894

(1c)

119862

119910=

119865

119910

12120588119880

2

0119863


=

12 sdot 120588119880

2

0sum

119894119862

119901119894sdot 12 sdot 119863Δ120579

119894sdot cos 120579

119894

12 sdot 120588119880

2

0119863

=

1

2

sum

119894

119862

119901119894Δ120579

119894sin 120579

119894

(1d)

where 119862






119909

and 119865




119906

2

Re = (

119880

Re120597Re120597119880

119906

119880)

2

+ (

]Re

120597Re120597]

119906])

2

+ (

119867

Re120597Re120597119863

119906

119889)

2

(2)


120597Re120597119880

=

119863

]

120597Re120597119863

=

119880

119863

120597Re120597]

= (minus1)

119880119863

]2

(3)


119906

2

Re = (

119880

119880119867]119867

]119906

119880)

2

+ (

119880

119880119867]119880

]119906

119867)

2

+ (

119880

119880119867](minus1)

119880119867

]2119906])

2

997904rArr

119906

2

Re = (119906

119880)

2

+ (119906

119867)

2

+ (119906])2

(4)


119880was 15





119906

119862119901= [(

Δ119901

119862

119901

120597119862

119901

120597Δ119901

119906

Δ119901)

2

+ (

120588

119862

119901

120597119862

119901

120597Δ119901

119906

120588)

2

+ (

119880

119862

119901

120597119862

119901

120597119880

119906

119880)

2

]

12

(5)


120597119862

119901

120597Δ119901

=

2

120588119880

2

120597119862

119901

120597120588

=

minus2Δ119901

120588

2119880

2

120597119862

119901

120597119880

=

minus4Δ119901

120588119880

3

(6)


119906

119862119901= [(

Δ119901

2Δ119901120588119880

2

2

120588119880

2)

2

+ (

120588

2Δ119901120588119880

2

minus2Δ119901

120588

2119880

2119906

120588)

2

+ (

119880

2Δ119901120588119880

2

minus2Δ119901

120588119880

3)

2

]

12

997904rArr

119906

2

119862119901= 119906

2

Δ119901+ 119906

2

120588+ 4119906

2

119880

(7)

where 119906

Δ119901= 25 and 119906

120588= 2 Finally 119906

119862119901= 39






119860 =

radic

2 sdot 120590

2

(8)





4 5 6 7 8 9 10 11

Ur

005

004

003

002

001

000

AD


4 5 6 7 8 9 10 11

Ur

22

20

18

16

14

12

10

08

06

04

fL

fn

FreeFixed








∘




4 5 6 7 8 9 10 11

Ur

005

004

003

002

001

000

AD

120579 = 45∘

120579 = 70∘

120579 = 90∘

120579 = 105∘

BCC

120573

minus30∘

(a) 120573 = minus30∘

4 5 6 7 8 9 10 11

Ur

005

004

003

002

001

000

AD

120579 = 45∘

120579 = 70∘

120579 = 90∘

120579 = 105∘

BCC

(b) 120573 = 0∘

4 5 6 7 8 9 10 11

Ur

005

004

003

002

001

000

AD

120579 = 45∘

120579 = 70∘

120579 = 90∘

120579 = 105∘

BCC

120573

30∘

(c) 120573 = 30∘







1199011= 72

∘

and 120572

1199012= 288

∘ For 120579 = 45

∘ and 120579 = 70



∘




120577120578) is

119903

120577120578=

sum

119899

119894=1(120577

119894minus 120577) (120578

119894minus 120578)

radicsum

119899

119894=1(120577

119894minus 120577)

2

radicsum

119899

119894=1(120578

119894minus 120578)

2

(9)


120573

minus30∘

15

10

05

00

minus05

minus10

minus15

minus20

minus25

minus30

Cp

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

(a) 120573 = minus30∘

15

10

05

00

minus05

minus10

minus15

minus20

minus25

minus30

Cp

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

(b) 120573 = 0∘

120573

30∘

15

10

05

00

minus05

minus10

minus15

minus20

minus25

minus30

Cp

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

(c) 120573 = 30∘













1199011= 72

∘

and 120572

1199012= 288



120573

minus30∘

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

040

035

030

025

020

015

010

005

000

C998400 p

(a) 120573 = minus30∘

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

040

035

030

025

020

015

010

005

000

C998400 p

(b) 120573 = 0∘

120573

30∘

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

040

035

030

025

020

015

010

005

000

C998400 p

(c) 120573 = 30∘



∘ or 120579 = 70



∘ and 120579 = 70

∘

5 Conclusion





120573

minus30∘10

08

06

04

02

00

Cor

relat

ion

coeffi

cien

t


120579 = 45∘120579 = 70∘

120579 = 90∘BCC

16 Lc 13 Lc 12 Lc 23 Lc 56 Lc

(a) 120573 = minus30∘

10

08

06

04

02

00

Cor

relat

ion

coeffi

cien

t


120579 = 45∘120579 = 70∘

120579 = 90∘BCC

16 Lc 13 Lc 12 Lc 23 Lc 56 Lc

(b) 120573 = 0∘

120573

30∘10

08

06

04

02

00

Cor

relat

ion

coeffi

cien

t


120579 = 45∘120579 = 70∘

120579 = 90∘BCC

16 Lc 13 Lc 12 Lc 23 Lc 56 Lc

(c) 120573 = 30∘







Competing Interests



45∘ 70∘ 90∘

120579

BCC

00

minus01

minus02

minus03

minus04

minus05

minus06

minus07

Cor

relat

ion

coeffi

cien

t

120573 = minus30∘

120573 = 0∘120573 = 30∘


Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










=

12 sdot 120588119880

2

0sum

119894119862

119901119894sdot 12 sdot 119863Δ120579

119894sdot cos 120579

119894

12 sdot 120588119880

2

0119863

=

1

2

sum

119894

119862

119901119894Δ120579

119894sin 120579

119894

(1d)

where 119862






119909

and 119865




119906

2

Re = (

119880

Re120597Re120597119880

119906

119880)

2

+ (

]Re

120597Re120597]

119906])

2

+ (

119867

Re120597Re120597119863

119906

119889)

2

(2)


120597Re120597119880

=

119863

]

120597Re120597119863

=

119880

119863

120597Re120597]

= (minus1)

119880119863

]2

(3)


119906

2

Re = (

119880

119880119867]119867

]119906

119880)

2

+ (

119880

119880119867]119880

]119906

119867)

2

+ (

119880

119880119867](minus1)

119880119867

]2119906])

2

997904rArr

119906

2

Re = (119906

119880)

2

+ (119906

119867)

2

+ (119906])2

(4)


119880was 15





119906

119862119901= [(

Δ119901

119862

119901

120597119862

119901

120597Δ119901

119906

Δ119901)

2

+ (

120588

119862

119901

120597119862

119901

120597Δ119901

119906

120588)

2

+ (

119880

119862

119901

120597119862

119901

120597119880

119906

119880)

2

]

12

(5)


120597119862

119901

120597Δ119901

=

2

120588119880

2

120597119862

119901

120597120588

=

minus2Δ119901

120588

2119880

2

120597119862

119901

120597119880

=

minus4Δ119901

120588119880

3

(6)


119906

119862119901= [(

Δ119901

2Δ119901120588119880

2

2

120588119880

2)

2

+ (

120588

2Δ119901120588119880

2

minus2Δ119901

120588

2119880

2119906

120588)

2

+ (

119880

2Δ119901120588119880

2

minus2Δ119901

120588119880

3)

2

]

12

997904rArr

119906

2

119862119901= 119906

2

Δ119901+ 119906

2

120588+ 4119906

2

119880

(7)

where 119906

Δ119901= 25 and 119906

120588= 2 Finally 119906

119862119901= 39






119860 =

radic

2 sdot 120590

2

(8)





4 5 6 7 8 9 10 11

Ur

005

004

003

002

001

000

AD


4 5 6 7 8 9 10 11

Ur

22

20

18

16

14

12

10

08

06

04

fL

fn

FreeFixed








∘




4 5 6 7 8 9 10 11

Ur

005

004

003

002

001

000

AD

120579 = 45∘

120579 = 70∘

120579 = 90∘

120579 = 105∘

BCC

120573

minus30∘

(a) 120573 = minus30∘

4 5 6 7 8 9 10 11

Ur

005

004

003

002

001

000

AD

120579 = 45∘

120579 = 70∘

120579 = 90∘

120579 = 105∘

BCC

(b) 120573 = 0∘

4 5 6 7 8 9 10 11

Ur

005

004

003

002

001

000

AD

120579 = 45∘

120579 = 70∘

120579 = 90∘

120579 = 105∘

BCC

120573

30∘

(c) 120573 = 30∘







1199011= 72

∘

and 120572

1199012= 288

∘ For 120579 = 45

∘ and 120579 = 70



∘




120577120578) is

119903

120577120578=

sum

119899

119894=1(120577

119894minus 120577) (120578

119894minus 120578)

radicsum

119899

119894=1(120577

119894minus 120577)

2

radicsum

119899

119894=1(120578

119894minus 120578)

2

(9)


120573

minus30∘

15

10

05

00

minus05

minus10

minus15

minus20

minus25

minus30

Cp

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

(a) 120573 = minus30∘

15

10

05

00

minus05

minus10

minus15

minus20

minus25

minus30

Cp

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

(b) 120573 = 0∘

120573

30∘

15

10

05

00

minus05

minus10

minus15

minus20

minus25

minus30

Cp

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

(c) 120573 = 30∘













1199011= 72

∘

and 120572

1199012= 288



120573

minus30∘

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

040

035

030

025

020

015

010

005

000

C998400 p

(a) 120573 = minus30∘

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

040

035

030

025

020

015

010

005

000

C998400 p

(b) 120573 = 0∘

120573

30∘

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

040

035

030

025

020

015

010

005

000

C998400 p

(c) 120573 = 30∘



∘ or 120579 = 70



∘ and 120579 = 70

∘

5 Conclusion





120573

minus30∘10

08

06

04

02

00

Cor

relat

ion

coeffi

cien

t


120579 = 45∘120579 = 70∘

120579 = 90∘BCC

16 Lc 13 Lc 12 Lc 23 Lc 56 Lc

(a) 120573 = minus30∘

10

08

06

04

02

00

Cor

relat

ion

coeffi

cien

t


120579 = 45∘120579 = 70∘

120579 = 90∘BCC

16 Lc 13 Lc 12 Lc 23 Lc 56 Lc

(b) 120573 = 0∘

120573

30∘10

08

06

04

02

00

Cor

relat

ion

coeffi

cien

t


120579 = 45∘120579 = 70∘

120579 = 90∘BCC

16 Lc 13 Lc 12 Lc 23 Lc 56 Lc

(c) 120573 = 30∘







Competing Interests



45∘ 70∘ 90∘

120579

BCC

00

minus01

minus02

minus03

minus04

minus05

minus06

minus07

Cor

relat

ion

coeffi

cien

t

120573 = minus30∘

120573 = 0∘120573 = 30∘


Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










4 5 6 7 8 9 10 11

Ur

005

004

003

002

001

000

AD


4 5 6 7 8 9 10 11

Ur

22

20

18

16

14

12

10

08

06

04

fL

fn

FreeFixed








∘




4 5 6 7 8 9 10 11

Ur

005

004

003

002

001

000

AD

120579 = 45∘

120579 = 70∘

120579 = 90∘

120579 = 105∘

BCC

120573

minus30∘

(a) 120573 = minus30∘

4 5 6 7 8 9 10 11

Ur

005

004

003

002

001

000

AD

120579 = 45∘

120579 = 70∘

120579 = 90∘

120579 = 105∘

BCC

(b) 120573 = 0∘

4 5 6 7 8 9 10 11

Ur

005

004

003

002

001

000

AD

120579 = 45∘

120579 = 70∘

120579 = 90∘

120579 = 105∘

BCC

120573

30∘

(c) 120573 = 30∘







1199011= 72

∘

and 120572

1199012= 288

∘ For 120579 = 45

∘ and 120579 = 70



∘




120577120578) is

119903

120577120578=

sum

119899

119894=1(120577

119894minus 120577) (120578

119894minus 120578)

radicsum

119899

119894=1(120577

119894minus 120577)

2

radicsum

119899

119894=1(120578

119894minus 120578)

2

(9)


120573

minus30∘

15

10

05

00

minus05

minus10

minus15

minus20

minus25

minus30

Cp

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

(a) 120573 = minus30∘

15

10

05

00

minus05

minus10

minus15

minus20

minus25

minus30

Cp

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

(b) 120573 = 0∘

120573

30∘

15

10

05

00

minus05

minus10

minus15

minus20

minus25

minus30

Cp

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

(c) 120573 = 30∘













1199011= 72

∘

and 120572

1199012= 288



120573

minus30∘

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

040

035

030

025

020

015

010

005

000

C998400 p

(a) 120573 = minus30∘

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

040

035

030

025

020

015

010

005

000

C998400 p

(b) 120573 = 0∘

120573

30∘

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

040

035

030

025

020

015

010

005

000

C998400 p

(c) 120573 = 30∘



∘ or 120579 = 70



∘ and 120579 = 70

∘

5 Conclusion





120573

minus30∘10

08

06

04

02

00

Cor

relat

ion

coeffi

cien

t


120579 = 45∘120579 = 70∘

120579 = 90∘BCC

16 Lc 13 Lc 12 Lc 23 Lc 56 Lc

(a) 120573 = minus30∘

10

08

06

04

02

00

Cor

relat

ion

coeffi

cien

t


120579 = 45∘120579 = 70∘

120579 = 90∘BCC

16 Lc 13 Lc 12 Lc 23 Lc 56 Lc

(b) 120573 = 0∘

120573

30∘10

08

06

04

02

00

Cor

relat

ion

coeffi

cien

t


120579 = 45∘120579 = 70∘

120579 = 90∘BCC

16 Lc 13 Lc 12 Lc 23 Lc 56 Lc

(c) 120573 = 30∘







Competing Interests



45∘ 70∘ 90∘

120579

BCC

00

minus01

minus02

minus03

minus04

minus05

minus06

minus07

Cor

relat

ion

coeffi

cien

t

120573 = minus30∘

120573 = 0∘120573 = 30∘


Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










4 5 6 7 8 9 10 11

Ur

005

004

003

002

001

000

AD

120579 = 45∘

120579 = 70∘

120579 = 90∘

120579 = 105∘

BCC

120573

minus30∘

(a) 120573 = minus30∘

4 5 6 7 8 9 10 11

Ur

005

004

003

002

001

000

AD

120579 = 45∘

120579 = 70∘

120579 = 90∘

120579 = 105∘

BCC

(b) 120573 = 0∘

4 5 6 7 8 9 10 11

Ur

005

004

003

002

001

000

AD

120579 = 45∘

120579 = 70∘

120579 = 90∘

120579 = 105∘

BCC

120573

30∘

(c) 120573 = 30∘







1199011= 72

∘

and 120572

1199012= 288

∘ For 120579 = 45

∘ and 120579 = 70



∘




120577120578) is

119903

120577120578=

sum

119899

119894=1(120577

119894minus 120577) (120578

119894minus 120578)

radicsum

119899

119894=1(120577

119894minus 120577)

2

radicsum

119899

119894=1(120578

119894minus 120578)

2

(9)


120573

minus30∘

15

10

05

00

minus05

minus10

minus15

minus20

minus25

minus30

Cp

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

(a) 120573 = minus30∘

15

10

05

00

minus05

minus10

minus15

minus20

minus25

minus30

Cp

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

(b) 120573 = 0∘

120573

30∘

15

10

05

00

minus05

minus10

minus15

minus20

minus25

minus30

Cp

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

(c) 120573 = 30∘













1199011= 72

∘

and 120572

1199012= 288



120573

minus30∘

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

040

035

030

025

020

015

010

005

000

C998400 p

(a) 120573 = minus30∘

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

040

035

030

025

020

015

010

005

000

C998400 p

(b) 120573 = 0∘

120573

30∘

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

040

035

030

025

020

015

010

005

000

C998400 p

(c) 120573 = 30∘



∘ or 120579 = 70



∘ and 120579 = 70

∘

5 Conclusion





120573

minus30∘10

08

06

04

02

00

Cor

relat

ion

coeffi

cien

t


120579 = 45∘120579 = 70∘

120579 = 90∘BCC

16 Lc 13 Lc 12 Lc 23 Lc 56 Lc

(a) 120573 = minus30∘

10

08

06

04

02

00

Cor

relat

ion

coeffi

cien

t


120579 = 45∘120579 = 70∘

120579 = 90∘BCC

16 Lc 13 Lc 12 Lc 23 Lc 56 Lc

(b) 120573 = 0∘

120573

30∘10

08

06

04

02

00

Cor

relat

ion

coeffi

cien

t


120579 = 45∘120579 = 70∘

120579 = 90∘BCC

16 Lc 13 Lc 12 Lc 23 Lc 56 Lc

(c) 120573 = 30∘







Competing Interests



45∘ 70∘ 90∘

120579

BCC

00

minus01

minus02

minus03

minus04

minus05

minus06

minus07

Cor

relat

ion

coeffi

cien

t

120573 = minus30∘

120573 = 0∘120573 = 30∘


Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










120573

minus30∘

15

10

05

00

minus05

minus10

minus15

minus20

minus25

minus30

Cp

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

(a) 120573 = minus30∘

15

10

05

00

minus05

minus10

minus15

minus20

minus25

minus30

Cp

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

(b) 120573 = 0∘

120573

30∘

15

10

05

00

minus05

minus10

minus15

minus20

minus25

minus30

Cp

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

(c) 120573 = 30∘













1199011= 72

∘

and 120572

1199012= 288



120573

minus30∘

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

040

035

030

025

020

015

010

005

000

C998400 p

(a) 120573 = minus30∘

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

040

035

030

025

020

015

010

005

000

C998400 p

(b) 120573 = 0∘

120573

30∘

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

040

035

030

025

020

015

010

005

000

C998400 p

(c) 120573 = 30∘



∘ or 120579 = 70



∘ and 120579 = 70

∘

5 Conclusion





120573

minus30∘10

08

06

04

02

00

Cor

relat

ion

coeffi

cien

t


120579 = 45∘120579 = 70∘

120579 = 90∘BCC

16 Lc 13 Lc 12 Lc 23 Lc 56 Lc

(a) 120573 = minus30∘

10

08

06

04

02

00

Cor

relat

ion

coeffi

cien

t


120579 = 45∘120579 = 70∘

120579 = 90∘BCC

16 Lc 13 Lc 12 Lc 23 Lc 56 Lc

(b) 120573 = 0∘

120573

30∘10

08

06

04

02

00

Cor

relat

ion

coeffi

cien

t


120579 = 45∘120579 = 70∘

120579 = 90∘BCC

16 Lc 13 Lc 12 Lc 23 Lc 56 Lc

(c) 120573 = 30∘







Competing Interests



45∘ 70∘ 90∘

120579

BCC

00

minus01

minus02

minus03

minus04

minus05

minus06

minus07

Cor

relat

ion

coeffi

cien

t

120573 = minus30∘

120573 = 0∘120573 = 30∘


Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










120573

minus30∘

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

040

035

030

025

020

015

010

005

000

C998400 p

(a) 120573 = minus30∘

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

040

035

030

025

020

015

010

005

000

C998400 p

(b) 120573 = 0∘

120573

30∘

0 60 120 180 240 360300

120572 (∘)

120579 = 45∘120579 = 70∘

120579 = 90∘BCC

040

035

030

025

020

015

010

005

000

C998400 p

(c) 120573 = 30∘



∘ or 120579 = 70



∘ and 120579 = 70

∘

5 Conclusion





120573

minus30∘10

08

06

04

02

00

Cor

relat

ion

coeffi

cien

t


120579 = 45∘120579 = 70∘

120579 = 90∘BCC

16 Lc 13 Lc 12 Lc 23 Lc 56 Lc

(a) 120573 = minus30∘

10

08

06

04

02

00

Cor

relat

ion

coeffi

cien

t


120579 = 45∘120579 = 70∘

120579 = 90∘BCC

16 Lc 13 Lc 12 Lc 23 Lc 56 Lc

(b) 120573 = 0∘

120573

30∘10

08

06

04

02

00

Cor

relat

ion

coeffi

cien

t


120579 = 45∘120579 = 70∘

120579 = 90∘BCC

16 Lc 13 Lc 12 Lc 23 Lc 56 Lc

(c) 120573 = 30∘







Competing Interests



45∘ 70∘ 90∘

120579

BCC

00

minus01

minus02

minus03

minus04

minus05

minus06

minus07

Cor

relat

ion

coeffi

cien

t

120573 = minus30∘

120573 = 0∘120573 = 30∘


Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










120573

minus30∘10

08

06

04

02

00

Cor

relat

ion

coeffi

cien

t


120579 = 45∘120579 = 70∘

120579 = 90∘BCC

16 Lc 13 Lc 12 Lc 23 Lc 56 Lc

(a) 120573 = minus30∘

10

08

06

04

02

00

Cor

relat

ion

coeffi

cien

t


120579 = 45∘120579 = 70∘

120579 = 90∘BCC

16 Lc 13 Lc 12 Lc 23 Lc 56 Lc

(b) 120573 = 0∘

120573

30∘10

08

06

04

02

00

Cor

relat

ion

coeffi

cien

t


120579 = 45∘120579 = 70∘

120579 = 90∘BCC

16 Lc 13 Lc 12 Lc 23 Lc 56 Lc

(c) 120573 = 30∘







Competing Interests



45∘ 70∘ 90∘

120579

BCC

00

minus01

minus02

minus03

minus04

minus05

minus06

minus07

Cor

relat

ion

coeffi

cien

t

120573 = minus30∘

120573 = 0∘120573 = 30∘


Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










45∘ 70∘ 90∘

120579

BCC

00

minus01

minus02

minus03

minus04

minus05

minus06

minus07

Cor

relat

ion

coeffi

cien

t

120573 = minus30∘

120573 = 0∘120573 = 30∘


Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Documents

Research Article Vortex-Induced Vibration Suppression of a